TPTP Problem File: SEV679+1.p

View Solutions - Solve Problem

%------------------------------------------------------------------------------
% File     : SEV679+1 : TPTP v9.3.1. Released v9.3.0.
% Domain   : Set theory
% Problem  : CoqHammer - UseAuto PreservationProgressReferences.preservation 
% 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    : UseAuto.PreservationProgressReferences.preservation'.p [Kal26]

% Status   : Theorem
% Rating   : 0.61 v9.3.0
% Syntax   : Number of formulae    : 3357 (1408 unt;   0 def)
%            Number of atoms       : 12536 (3828 equ)
%            Maximal formula atoms :  257 (   3 avg)
%            Number of connectives : 9298 ( 119   ~;1054   |;2988   &)
%                                         (1199 <=>;3938  =>;   0  <=;   0 <~>)
%            Maximal formula depth :  258 (   6 avg)
%            Maximal term depth    :   23 (   1 avg)
%            Number of predicates  :  657 ( 656 usr;   0 prp; 1-23 aty)
%            Number of functors    : 2094 (2094 usr;1344 con; 0-22 aty)
%            Number of variables   : 11790 (10347   !;1443   ?)
% SPC      : FOF_THM_RFO_SEQ

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

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

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

fof('$_case_Coq.Init.Datatypes.bool$108704',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
     => ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
       => ( ( cCoq_2eZArith_2eBinIntDef_2eZ_2egtb___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eInit_2eDatatypes_2etrue
            & ( c_24__case__Coq_2eInit_2eDatatypes_2ebool_24108704___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
            <=> cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) ) )
          | ( cCoq_2eZArith_2eBinIntDef_2eZ_2egtb___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eInit_2eDatatypes_2efalse
            & ( c_24__case__Coq_2eInit_2eDatatypes_2ebool_24108704___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
            <=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)) ) ) ) ) ) ).

fof('$_case_Coq.Init.Datatypes.bool$109396',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
      ( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__0)
     => ( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__2)
       => ( ( cPLF_2eMaps_2eeqb__string___24a2(Vv__CANONICAL__0,Vv__CANONICAL__2) = cCoq_2eInit_2eDatatypes_2etrue
            & c_24__case__Coq_2eInit_2eDatatypes_2ebool_24109396___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vv__CANONICAL__3 )
          | ( cPLF_2eMaps_2eeqb__string___24a2(Vv__CANONICAL__0,Vv__CANONICAL__2) = cCoq_2eInit_2eDatatypes_2efalse
            & c_24__case__Coq_2eInit_2eDatatypes_2ebool_24109396___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cPLF_2eStlc_2eSTLC_2esubst___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3) ) ) ) ) ).

fof('$_case_Coq.Init.Datatypes.bool$111211',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
      ( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__0)
     => ( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__2)
       => ( ( cPLF_2eMaps_2eeqb__string___24a2(Vv__CANONICAL__0,Vv__CANONICAL__2) = cCoq_2eInit_2eDatatypes_2etrue
            & c_24__case__Coq_2eInit_2eDatatypes_2ebool_24111211___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vv__CANONICAL__3 )
          | ( cPLF_2eMaps_2eeqb__string___24a2(Vv__CANONICAL__0,Vv__CANONICAL__2) = cCoq_2eInit_2eDatatypes_2efalse
            & c_24__case__Coq_2eInit_2eDatatypes_2ebool_24111211___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = c_24__fix__111186__v__CANONICAL__0___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3) ) ) ) ) ).

fof('$_case_Coq.Init.Datatypes.bool$111428',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
      ( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__0)
     => ( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__2)
       => ( ( cPLF_2eMaps_2eeqb__string___24a2(Vv__CANONICAL__0,Vv__CANONICAL__2) = cCoq_2eInit_2eDatatypes_2etrue
            & c_24__case__Coq_2eInit_2eDatatypes_2ebool_24111428___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vv__CANONICAL__3 )
          | ( cPLF_2eMaps_2eeqb__string___24a2(Vv__CANONICAL__0,Vv__CANONICAL__2) = cCoq_2eInit_2eDatatypes_2efalse
            & c_24__case__Coq_2eInit_2eDatatypes_2ebool_24111428___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = c_24__fix__111186__v__CANONICAL__0___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3) ) ) ) ) ).

fof('$_case_Coq.Init.Datatypes.bool$77532',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
     => ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__4)
       => ( ( c_24__case__Coq_2eInit_2eDatatypes_2enat_2477615___24a2(Vv__CANONICAL__3,Vv__CANONICAL__4) = cCoq_2eInit_2eDatatypes_2etrue
            & c_24__case__Coq_2eInit_2eDatatypes_2ebool_2477532___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cPLF_2eImp_2eBTrue )
          | ( c_24__case__Coq_2eInit_2eDatatypes_2enat_2477615___24a2(Vv__CANONICAL__3,Vv__CANONICAL__4) = cCoq_2eInit_2eDatatypes_2efalse
            & c_24__case__Coq_2eInit_2eDatatypes_2ebool_2477532___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cPLF_2eImp_2eBFalse ) ) ) ) ).

fof('$_case_Coq.Init.Datatypes.bool$77863',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
     => ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__4)
       => ( ( c_24__case__Coq_2eInit_2eDatatypes_2enat_2477928___24a2(Vv__CANONICAL__3,Vv__CANONICAL__4) = cCoq_2eInit_2eDatatypes_2etrue
            & c_24__case__Coq_2eInit_2eDatatypes_2ebool_2477863___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cPLF_2eImp_2eBTrue )
          | ( c_24__case__Coq_2eInit_2eDatatypes_2enat_2477928___24a2(Vv__CANONICAL__3,Vv__CANONICAL__4) = cCoq_2eInit_2eDatatypes_2efalse
            & c_24__case__Coq_2eInit_2eDatatypes_2ebool_2477863___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cPLF_2eImp_2eBFalse ) ) ) ) ).

fof('$_case_Coq.Init.Datatypes.list$115259',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_24115346___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_24115259___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__115263] :
                ( t(Vvar__1___24Anonymous__115263,Vv__CANONICAL__0)
                & ? [Vvar__2___24Anonymous__115264] :
                    ( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vvar__2___24Anonymous__115264)
                    & c_24__case__Coq_2eInit_2eDatatypes_2elist_24115346___24a3(Vv__CANONICAL__0,Vv__CANONICAL__4,Vv__CANONICAL__5) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__115263,Vvar__2___24Anonymous__115264)
                    & c_24__case__Coq_2eInit_2eDatatypes_2elist_24115259___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__115263,c_24__fix__115391__v__CANONICAL__1___24a3(Vv__CANONICAL__0,Vvar__2___24Anonymous__115264,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$115346',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_24115346___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__115350] :
              ( t(Vvar__1___24Anonymous__115350,Vv__CANONICAL__0)
              & ? [Vvar__2___24Anonymous__115351] :
                  ( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vvar__2___24Anonymous__115351)
                  & Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__115350,Vvar__2___24Anonymous__115351)
                  & c_24__case__Coq_2eInit_2eDatatypes_2elist_24115346___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__115350,c_24__fix__115391__v__CANONICAL__1___24a3(Vv__CANONICAL__0,Vvar__2___24Anonymous__115351,cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)))) ) ) ) ) ) ).

fof('$_case_Coq.Init.Datatypes.list$210988',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] :
      ( cPLF_2eReferences_2eSTLCRef_2estore___24t(Vv__CANONICAL__2)
     => ( ( Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2enil___24a1(cPLF_2eReferences_2eSTLCRef_2etm)
          & c_24__case__Coq_2eInit_2eDatatypes_2elist_24210988___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eDatatypes_2eO )
        | ? [Vvar__1___24Anonymous__210992] :
            ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__1___24Anonymous__210992)
            & ? [Vvar__2___24Anonymous__210993] :
                ( cCoq_2eInit_2eDatatypes_2elist___24t(cPLF_2eReferences_2eSTLCRef_2etm,Vvar__2___24Anonymous__210993)
                & Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2econs___24a3(cPLF_2eReferences_2eSTLCRef_2etm,Vvar__1___24Anonymous__210992,Vvar__2___24Anonymous__210993)
                & c_24__case__Coq_2eInit_2eDatatypes_2elist_24210988___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eDatatypes_2eS___24a1(c_24__fix__211015__v__CANONICAL__0___24a1(Vvar__2___24Anonymous__210993)) ) ) ) ) ).

fof('$_case_Coq.Init.Datatypes.list$211097',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
      ( cPLF_2eReferences_2eSTLCRef_2estore___24t(Vv__CANONICAL__3)
     => ( ( Vv__CANONICAL__3 = cCoq_2eInit_2eDatatypes_2enil___24a1(cPLF_2eReferences_2eSTLCRef_2etm)
          & c_24__case__Coq_2eInit_2eDatatypes_2elist_24211097___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2econs___24a3(cPLF_2eReferences_2eSTLCRef_2etm,Vv__CANONICAL__2,cCoq_2eInit_2eDatatypes_2enil___24a1(cPLF_2eReferences_2eSTLCRef_2etm)) )
        | ? [Vvar__1___24Anonymous__211101] :
            ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__1___24Anonymous__211101)
            & ? [Vvar__2___24Anonymous__211102] :
                ( cCoq_2eInit_2eDatatypes_2elist___24t(cPLF_2eReferences_2eSTLCRef_2etm,Vvar__2___24Anonymous__211102)
                & Vv__CANONICAL__3 = cCoq_2eInit_2eDatatypes_2econs___24a3(cPLF_2eReferences_2eSTLCRef_2etm,Vvar__1___24Anonymous__211101,Vvar__2___24Anonymous__211102)
                & c_24__case__Coq_2eInit_2eDatatypes_2elist_24211097___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2econs___24a3(cPLF_2eReferences_2eSTLCRef_2etm,Vvar__1___24Anonymous__211101,c_24__fix__211134__v__CANONICAL__0___24a2(Vvar__2___24Anonymous__211102,cCoq_2eInit_2eDatatypes_2econs___24a3(cPLF_2eReferences_2eSTLCRef_2etm,Vv__CANONICAL__2,cCoq_2eInit_2eDatatypes_2enil___24a1(cPLF_2eReferences_2eSTLCRef_2etm)))) ) ) ) ) ).

fof('$_case_Coq.Init.Datatypes.list$211642',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
      ( cCoq_2eInit_2eDatatypes_2elist___24t(cPLF_2eReferences_2eSTLCRef_2etm,Vv__CANONICAL__4)
     => ( ( Vv__CANONICAL__4 = cCoq_2eInit_2eDatatypes_2enil___24a1(cPLF_2eReferences_2eSTLCRef_2etm)
          & c_24__case__Coq_2eInit_2eDatatypes_2elist_24211642___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cCoq_2eInit_2eDatatypes_2enil___24a1(cPLF_2eReferences_2eSTLCRef_2etm) )
        | ? [Vvar__1___24Anonymous__211646] :
            ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__1___24Anonymous__211646)
            & ? [Vvar__2___24Anonymous__211647] :
                ( cCoq_2eInit_2eDatatypes_2elist___24t(cPLF_2eReferences_2eSTLCRef_2etm,Vvar__2___24Anonymous__211647)
                & ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
                 => ( Vv__CANONICAL__4 = cCoq_2eInit_2eDatatypes_2econs___24a3(cPLF_2eReferences_2eSTLCRef_2etm,Vvar__1___24Anonymous__211646,Vvar__2___24Anonymous__211647)
                    & ( ( Vv__CANONICAL__3 = cCoq_2eInit_2eDatatypes_2eO
                        & c_24__case__Coq_2eInit_2eDatatypes_2elist_24211642___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cCoq_2eInit_2eDatatypes_2econs___24a3(cPLF_2eReferences_2eSTLCRef_2etm,Vv__CANONICAL__2,Vvar__2___24Anonymous__211647) )
                      | ? [Vvar__0___24Anonymous__211681] :
                          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__211681)
                          & Vv__CANONICAL__3 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__211681)
                          & c_24__case__Coq_2eInit_2eDatatypes_2elist_24211642___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cCoq_2eInit_2eDatatypes_2econs___24a3(cPLF_2eReferences_2eSTLCRef_2etm,Vvar__1___24Anonymous__211646,c_24__fix__211742__v__CANONICAL__0___24a4(cPLF_2eReferences_2eSTLCRef_2etm,Vvar__0___24Anonymous__211681,Vv__CANONICAL__2,Vvar__2___24Anonymous__211647)) ) ) ) ) ) ) ) ) ).

fof('$_case_Coq.Init.Datatypes.nat$1023',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_241023___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vv__CANONICAL__3 )
        | ? [Vvar__0___24Anonymous__1024] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__1024)
            & Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__1024)
            & c_24__case__Coq_2eInit_2eDatatypes_2enat_241023___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2eS___24a1(c_24__fix__1042__v__CANONICAL__0___24a2(Vvar__0___24Anonymous__1024,Vv__CANONICAL__3)) ) ) ) ).

fof('$_case_Coq.Init.Datatypes.nat$113313',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_24113313___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZ0 )
        | ? [Vvar__0___24Anonymous__113314] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__113314)
            & Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__113314)
            & c_24__case__Coq_2eInit_2eDatatypes_2enat_24113313___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__113314)) ) ) ) ).

fof('$_case_Coq.Init.Datatypes.nat$113335',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_24113335___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZ0 )
        | ? [Vvar__0___24Anonymous__113336] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__113336)
            & Vv__CANONICAL__0 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__113336)
            & c_24__case__Coq_2eInit_2eDatatypes_2enat_24113335___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(Vvar__0___24Anonymous__113336)) ) ) ) ).

fof('$_case_Coq.Init.Datatypes.nat$162913',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__4)
     => ( ( Vv__CANONICAL__4 = cCoq_2eInit_2eDatatypes_2eO
          & c_24__case__Coq_2eInit_2eDatatypes_2enat_24162913___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = Vv__CANONICAL__3 )
        | ? [Vvar__0___24Anonymous__162914] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__162914)
            & Vv__CANONICAL__4 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__162914)
            & c_24__case__Coq_2eInit_2eDatatypes_2enat_24162913___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cCoq_2eInit_2eDatatypes_2eS___24a1(c_24__fix__1042__v__CANONICAL__0___24a2(Vvar__0___24Anonymous__162914,Vv__CANONICAL__3)) ) ) ) ).

fof('$_case_Coq.Init.Datatypes.nat$163035',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__4)
     => ( ( Vv__CANONICAL__4 = cCoq_2eInit_2eDatatypes_2eO
          & c_24__case__Coq_2eInit_2eDatatypes_2enat_24163035___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = Vv__CANONICAL__4 )
        | ? [Vvar__0___24Anonymous__163036] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__163036)
            & ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
             => ( Vv__CANONICAL__4 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__163036)
                & ( ( Vv__CANONICAL__3 = cCoq_2eInit_2eDatatypes_2eO
                    & c_24__case__Coq_2eInit_2eDatatypes_2enat_24163035___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = Vv__CANONICAL__4 )
                  | ? [Vvar__0___24Anonymous__163048] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__163048)
                      & Vv__CANONICAL__3 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__163048)
                      & c_24__case__Coq_2eInit_2eDatatypes_2enat_24163035___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = c_24__fix__77213__v__CANONICAL__0___24a2(Vvar__0___24Anonymous__163036,Vvar__0___24Anonymous__163048) ) ) ) ) ) ) ) ).

fof('$_case_Coq.Init.Datatypes.nat$163138',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__4)
     => ( ( Vv__CANONICAL__4 = cCoq_2eInit_2eDatatypes_2eO
          & c_24__case__Coq_2eInit_2eDatatypes_2enat_24163138___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cCoq_2eInit_2eDatatypes_2eO )
        | ? [Vvar__0___24Anonymous__163139] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__163139)
            & Vv__CANONICAL__4 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__163139)
            & c_24__case__Coq_2eInit_2eDatatypes_2enat_24163138___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cCoq_2eInit_2eNat_2eadd___24a2(Vv__CANONICAL__3,c_24__fix__77299__v__CANONICAL__0___24a2(Vvar__0___24Anonymous__163139,Vv__CANONICAL__3)) ) ) ) ).

fof('$_case_Coq.Init.Datatypes.nat$210866',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_24210866___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = Vv__CANONICAL__2 )
        | ? [Vvar__0___24Anonymous__210867] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__210867)
            & Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__210867)
            & c_24__case__Coq_2eInit_2eDatatypes_2enat_24210866___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = Vvar__0___24Anonymous__210867 ) ) ) ).

fof('$_case_Coq.Init.Datatypes.nat$210921',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_24210921___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2eO )
        | ? [Vvar__0___24Anonymous__210922] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__210922)
            & Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__210922)
            & c_24__case__Coq_2eInit_2eDatatypes_2enat_24210921___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eNat_2eadd___24a2(Vv__CANONICAL__3,c_24__fix__77299__v__CANONICAL__0___24a2(Vvar__0___24Anonymous__210922,Vv__CANONICAL__3)) ) ) ) ).

fof('$_case_Coq.Init.Datatypes.nat$211329',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
     => ( ( cCoq_2eInit_2eDatatypes_2elist___24t(cPLF_2eReferences_2eSTLCRef_2etm,Vv__CANONICAL__2)
         => ( Vv__CANONICAL__3 = cCoq_2eInit_2eDatatypes_2eO
            & ( ( Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2enil___24a1(cPLF_2eReferences_2eSTLCRef_2etm)
                & c_24__case__Coq_2eInit_2eDatatypes_2enat_24211329___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cPLF_2eReferences_2eSTLCRef_2eunit )
              | ? [Vvar__1___24Anonymous__211333] :
                  ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__1___24Anonymous__211333)
                  & ? [Vvar__2___24Anonymous__211334] :
                      ( cCoq_2eInit_2eDatatypes_2elist___24t(cPLF_2eReferences_2eSTLCRef_2etm,Vvar__2___24Anonymous__211334)
                      & Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2econs___24a3(cPLF_2eReferences_2eSTLCRef_2etm,Vvar__1___24Anonymous__211333,Vvar__2___24Anonymous__211334)
                      & c_24__case__Coq_2eInit_2eDatatypes_2enat_24211329___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vvar__1___24Anonymous__211333 ) ) ) ) )
        | ? [Vvar__0___24Anonymous__211336] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__211336)
            & ( cCoq_2eInit_2eDatatypes_2elist___24t(cPLF_2eReferences_2eSTLCRef_2etm,Vv__CANONICAL__2)
             => ( Vv__CANONICAL__3 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__211336)
                & ( ( Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2enil___24a1(cPLF_2eReferences_2eSTLCRef_2etm)
                    & c_24__case__Coq_2eInit_2eDatatypes_2enat_24211329___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cPLF_2eReferences_2eSTLCRef_2eunit )
                  | ? [Vvar__1___24Anonymous__211358] :
                      ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__1___24Anonymous__211358)
                      & ? [Vvar__2___24Anonymous__211359] :
                          ( cCoq_2eInit_2eDatatypes_2elist___24t(cPLF_2eReferences_2eSTLCRef_2etm,Vvar__2___24Anonymous__211359)
                          & Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2econs___24a3(cPLF_2eReferences_2eSTLCRef_2etm,Vvar__1___24Anonymous__211358,Vvar__2___24Anonymous__211359)
                          & c_24__case__Coq_2eInit_2eDatatypes_2enat_24211329___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = c_24__fix__211437__v__CANONICAL__0___24a3(Vvar__0___24Anonymous__211336,Vvar__2___24Anonymous__211359,cPLF_2eReferences_2eSTLCRef_2eunit) ) ) ) ) ) ) ) ) ).

fof('$_case_Coq.Init.Datatypes.nat$212097',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__5)
     => ( ( cCoq_2eInit_2eDatatypes_2elist___24t(cPLF_2eReferences_2eSTLCRef_2ety,Vv__CANONICAL__4)
         => ( Vv__CANONICAL__5 = cCoq_2eInit_2eDatatypes_2eO
            & ( ( Vv__CANONICAL__4 = cCoq_2eInit_2eDatatypes_2enil___24a1(cPLF_2eReferences_2eSTLCRef_2ety)
                & c_24__case__Coq_2eInit_2eDatatypes_2enat_24212097___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = cPLF_2eReferences_2eSTLCRef_2eUnit )
              | ? [Vvar__1___24Anonymous__212101] :
                  ( cPLF_2eReferences_2eSTLCRef_2ety___24t(Vvar__1___24Anonymous__212101)
                  & ? [Vvar__2___24Anonymous__212102] :
                      ( cCoq_2eInit_2eDatatypes_2elist___24t(cPLF_2eReferences_2eSTLCRef_2ety,Vvar__2___24Anonymous__212102)
                      & Vv__CANONICAL__4 = cCoq_2eInit_2eDatatypes_2econs___24a3(cPLF_2eReferences_2eSTLCRef_2ety,Vvar__1___24Anonymous__212101,Vvar__2___24Anonymous__212102)
                      & c_24__case__Coq_2eInit_2eDatatypes_2enat_24212097___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = Vvar__1___24Anonymous__212101 ) ) ) ) )
        | ? [Vvar__0___24Anonymous__212104] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__212104)
            & ( cCoq_2eInit_2eDatatypes_2elist___24t(cPLF_2eReferences_2eSTLCRef_2ety,Vv__CANONICAL__4)
             => ( Vv__CANONICAL__5 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__212104)
                & ( ( Vv__CANONICAL__4 = cCoq_2eInit_2eDatatypes_2enil___24a1(cPLF_2eReferences_2eSTLCRef_2ety)
                    & c_24__case__Coq_2eInit_2eDatatypes_2enat_24212097___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = cPLF_2eReferences_2eSTLCRef_2eUnit )
                  | ? [Vvar__1___24Anonymous__212126] :
                      ( cPLF_2eReferences_2eSTLCRef_2ety___24t(Vvar__1___24Anonymous__212126)
                      & ? [Vvar__2___24Anonymous__212127] :
                          ( cCoq_2eInit_2eDatatypes_2elist___24t(cPLF_2eReferences_2eSTLCRef_2ety,Vvar__2___24Anonymous__212127)
                          & Vv__CANONICAL__4 = cCoq_2eInit_2eDatatypes_2econs___24a3(cPLF_2eReferences_2eSTLCRef_2ety,Vvar__1___24Anonymous__212126,Vvar__2___24Anonymous__212127)
                          & c_24__case__Coq_2eInit_2eDatatypes_2enat_24212097___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = c_24__fix__212205__v__CANONICAL__0___24a3(Vvar__0___24Anonymous__212104,Vvar__2___24Anonymous__212127,cPLF_2eReferences_2eSTLCRef_2eUnit) ) ) ) ) ) ) ) ) ).

fof('$_case_Coq.Init.Datatypes.nat$77050',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
     => ( ( Vv__CANONICAL__3 = cCoq_2eInit_2eDatatypes_2eO
          & c_24__case__Coq_2eInit_2eDatatypes_2enat_2477050___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = Vv__CANONICAL__4 )
        | ? [Vvar__0___24Anonymous__77051] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__77051)
            & Vv__CANONICAL__3 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__77051)
            & c_24__case__Coq_2eInit_2eDatatypes_2enat_2477050___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cCoq_2eInit_2eDatatypes_2eS___24a1(c_24__fix__1042__v__CANONICAL__0___24a2(Vvar__0___24Anonymous__77051,Vv__CANONICAL__4)) ) ) ) ).

fof('$_case_Coq.Init.Datatypes.nat$77172',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
     => ( ( Vv__CANONICAL__3 = cCoq_2eInit_2eDatatypes_2eO
          & c_24__case__Coq_2eInit_2eDatatypes_2enat_2477172___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = Vv__CANONICAL__3 )
        | ? [Vvar__0___24Anonymous__77173] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__77173)
            & ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__4)
             => ( Vv__CANONICAL__3 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__77173)
                & ( ( Vv__CANONICAL__4 = cCoq_2eInit_2eDatatypes_2eO
                    & c_24__case__Coq_2eInit_2eDatatypes_2enat_2477172___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = Vv__CANONICAL__3 )
                  | ? [Vvar__0___24Anonymous__77185] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__77185)
                      & Vv__CANONICAL__4 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__77185)
                      & c_24__case__Coq_2eInit_2eDatatypes_2enat_2477172___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = c_24__fix__77213__v__CANONICAL__0___24a2(Vvar__0___24Anonymous__77173,Vvar__0___24Anonymous__77185) ) ) ) ) ) ) ) ).

fof('$_case_Coq.Init.Datatypes.nat$77280',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
     => ( ( Vv__CANONICAL__3 = cCoq_2eInit_2eDatatypes_2eO
          & c_24__case__Coq_2eInit_2eDatatypes_2enat_2477280___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cCoq_2eInit_2eDatatypes_2eO )
        | ? [Vvar__0___24Anonymous__77281] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__77281)
            & Vv__CANONICAL__3 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__77281)
            & c_24__case__Coq_2eInit_2eDatatypes_2enat_2477280___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cCoq_2eInit_2eNat_2eadd___24a2(Vv__CANONICAL__4,c_24__fix__77299__v__CANONICAL__0___24a2(Vvar__0___24Anonymous__77281,Vv__CANONICAL__4)) ) ) ) ).

fof('$_case_Coq.Init.Datatypes.nat$77615',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
     => ( ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
         => ( Vv__CANONICAL__0 = cCoq_2eInit_2eDatatypes_2eO
            & ( ( Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2eO
                & c_24__case__Coq_2eInit_2eDatatypes_2enat_2477615___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eInit_2eDatatypes_2etrue )
              | ? [Vvar__0___24Anonymous__77616] :
                  ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__77616)
                  & Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__77616)
                  & c_24__case__Coq_2eInit_2eDatatypes_2enat_2477615___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) )
        | ? [Vvar__0___24Anonymous__77617] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__77617)
            & ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
             => ( Vv__CANONICAL__0 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__77617)
                & ( ( Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2eO
                    & c_24__case__Coq_2eInit_2eDatatypes_2enat_2477615___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eInit_2eDatatypes_2efalse )
                  | ? [Vvar__0___24Anonymous__77631] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__77631)
                      & Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__77631)
                      & c_24__case__Coq_2eInit_2eDatatypes_2enat_2477615___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = c_24__fix__77667__v__CANONICAL__0___24a2(Vvar__0___24Anonymous__77617,Vvar__0___24Anonymous__77631) ) ) ) ) ) ) ) ).

fof('$_case_Coq.Init.Datatypes.nat$77928',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
     => ( ( Vv__CANONICAL__0 = cCoq_2eInit_2eDatatypes_2eO
          & c_24__case__Coq_2eInit_2eDatatypes_2enat_2477928___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eInit_2eDatatypes_2etrue )
        | ? [Vvar__0___24Anonymous__77929] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__77929)
            & ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
             => ( Vv__CANONICAL__0 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__77929)
                & ( ( Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2eO
                    & c_24__case__Coq_2eInit_2eDatatypes_2enat_2477928___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eInit_2eDatatypes_2efalse )
                  | ? [Vvar__0___24Anonymous__77941] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__77941)
                      & Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__77941)
                      & c_24__case__Coq_2eInit_2eDatatypes_2enat_2477928___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = c_24__fix__77969__v__CANONICAL__0___24a2(Vvar__0___24Anonymous__77929,Vvar__0___24Anonymous__77941) ) ) ) ) ) ) ) ).

fof('$_case_Coq.Init.Specif.sumor$168291',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
     => ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
       => ( ? [Vvar__2___24Anonymous__168296] :
              ( cCoq_2eInit_2eSpecif_2esumbool___24t(cCoq_2eInit_2ePeano_2elt___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),c_24__prop__168300___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),Vvar__2___24Anonymous__168296)
              & c_24__let__3__s__168284___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eInit_2eSpecif_2einleft___24a3(cCoq_2eInit_2eSpecif_2esumbool___24a2(cCoq_2eInit_2ePeano_2elt___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),c_24__prop__168301___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)),cCoq_2eInit_2ePeano_2elt___24a2(Vv__CANONICAL__1,Vv__CANONICAL__0),Vvar__2___24Anonymous__168296)
              & c_24__case__Coq_2eInit_2eSpecif_2esumor_24168291___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = Vvar__2___24Anonymous__168296 )
          | ( p(cCoq_2eInit_2ePeano_2elt___24a2(Vv__CANONICAL__1,Vv__CANONICAL__0))
            & c_24__let__3__s__168284___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eInit_2eSpecif_2einright___24a2(cCoq_2eInit_2eSpecif_2esumbool___24a2(cCoq_2eInit_2ePeano_2elt___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),c_24__prop__168302___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)),cCoq_2eInit_2ePeano_2elt___24a2(Vv__CANONICAL__1,Vv__CANONICAL__0))
            & c_24__case__Coq_2eInit_2eSpecif_2esumor_24168291___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eInit_2eLogic_2eFalse__rec___24a2(cCoq_2eInit_2eSpecif_2esumbool___24a2(cCoq_2eInit_2ePeano_2elt___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),c_24__prop__168303___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)),cCoq_2eArith_2eLt_2ele__not__lt___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)) ) ) ) ) ).

fof('$_case_Coq.Numbers.BinNums.Z$113330',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_24113335___24a1(Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZ0
          & c_24__case__Coq_2eNumbers_2eBinNums_2eZ_24113330___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZ0 )
        | ? [Vvar__0___24Anonymous__113331] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__113331)
            & c_24__case__Coq_2eInit_2eDatatypes_2enat_24113335___24a1(Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__113331)
            & c_24__case__Coq_2eNumbers_2eBinNums_2eZ_24113330___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__113331) )
        | ? [Vvar__0___24Anonymous__113332] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__113332)
            & c_24__case__Coq_2eInit_2eDatatypes_2enat_24113335___24a1(Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__113332)
            & c_24__case__Coq_2eNumbers_2eBinNums_2eZ_24113330___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__113332) ) ) ) ).

fof('$_case_Coq.Numbers.BinNums.positive$109181',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
     => ( ? [Vvar__0___24Anonymous__109182] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__109182)
            & Vv__CANONICAL__1 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__109182)
            & c_24__case__Coq_2eNumbers_2eBinNums_2epositive_24109181___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2exO___24a1(c_24__fix__109197__v__CANONICAL__0___24a1(Vvar__0___24Anonymous__109182)) )
        | ? [Vvar__0___24Anonymous__109189] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__109189)
            & Vv__CANONICAL__1 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__109189)
            & c_24__case__Coq_2eNumbers_2eBinNums_2epositive_24109181___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__109189) )
        | ( Vv__CANONICAL__1 = cCoq_2eNumbers_2eBinNums_2exH
          & c_24__case__Coq_2eNumbers_2eBinNums_2epositive_24109181___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ) ) ).

fof('$_case_PLF.References.STLCRef.tm$208442',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
      ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vv__CANONICAL__3)
     => ( ? [Vvar__0___24Anonymous__208443] :
            ( cCoq_2eStrings_2eString_2estring___24t(Vvar__0___24Anonymous__208443)
            & ( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__2)
             => ( cCoq_2eStrings_2eString_2estring___24t(Vvar__0___24Anonymous__208443)
               => ( Vv__CANONICAL__3 = cPLF_2eReferences_2eSTLCRef_2evar___24a1(Vvar__0___24Anonymous__208443)
                  & ( ( cPLF_2eMaps_2eeqb__string___24a2(Vv__CANONICAL__2,Vvar__0___24Anonymous__208443) = cCoq_2eInit_2eDatatypes_2etrue
                      & c_24__case__PLF_2eReferences_2eSTLCRef_2etm_24208442___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = Vv__CANONICAL__4 )
                    | ( cPLF_2eMaps_2eeqb__string___24a2(Vv__CANONICAL__2,Vvar__0___24Anonymous__208443) = cCoq_2eInit_2eDatatypes_2efalse
                      & c_24__case__PLF_2eReferences_2eSTLCRef_2etm_24208442___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = Vv__CANONICAL__3 ) ) ) ) ) )
        | ? [Vvar__0___24Anonymous__208445] :
            ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__0___24Anonymous__208445)
            & ? [Vvar__1___24Anonymous__208446] :
                ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__1___24Anonymous__208446)
                & Vv__CANONICAL__3 = cPLF_2eReferences_2eSTLCRef_2eapp___24a2(Vvar__0___24Anonymous__208445,Vvar__1___24Anonymous__208446)
                & c_24__case__PLF_2eReferences_2eSTLCRef_2etm_24208442___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cPLF_2eReferences_2eSTLCRef_2eapp___24a2(c_24__fix__209397__v__CANONICAL__0___24a3(Vv__CANONICAL__2,Vv__CANONICAL__4,Vvar__0___24Anonymous__208445),c_24__fix__209397__v__CANONICAL__0___24a3(Vv__CANONICAL__2,Vv__CANONICAL__4,Vvar__1___24Anonymous__208446)) ) )
        | ? [Vvar__0___24Anonymous__208564] :
            ( cCoq_2eStrings_2eString_2estring___24t(Vvar__0___24Anonymous__208564)
            & ? [Vvar__1___24Anonymous__208565] :
                ( cPLF_2eReferences_2eSTLCRef_2ety___24t(Vvar__1___24Anonymous__208565)
                & ? [Vvar__2___24Anonymous__208566] :
                    ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__2___24Anonymous__208566)
                    & ( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__2)
                     => ( cCoq_2eStrings_2eString_2estring___24t(Vvar__0___24Anonymous__208564)
                       => ( Vv__CANONICAL__3 = cPLF_2eReferences_2eSTLCRef_2eabs___24a3(Vvar__0___24Anonymous__208564,Vvar__1___24Anonymous__208565,Vvar__2___24Anonymous__208566)
                          & ( ( cPLF_2eMaps_2eeqb__string___24a2(Vv__CANONICAL__2,Vvar__0___24Anonymous__208564) = cCoq_2eInit_2eDatatypes_2etrue
                              & c_24__case__PLF_2eReferences_2eSTLCRef_2etm_24208442___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = Vv__CANONICAL__3 )
                            | ( cPLF_2eMaps_2eeqb__string___24a2(Vv__CANONICAL__2,Vvar__0___24Anonymous__208564) = cCoq_2eInit_2eDatatypes_2efalse
                              & c_24__case__PLF_2eReferences_2eSTLCRef_2etm_24208442___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cPLF_2eReferences_2eSTLCRef_2eabs___24a3(Vvar__0___24Anonymous__208564,Vvar__1___24Anonymous__208565,c_24__fix__209397__v__CANONICAL__0___24a3(Vv__CANONICAL__2,Vv__CANONICAL__4,Vvar__2___24Anonymous__208566)) ) ) ) ) ) ) ) )
        | ? [Vvar__0___24Anonymous__208660] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__208660)
            & Vv__CANONICAL__3 = cPLF_2eReferences_2eSTLCRef_2econst___24a1(Vvar__0___24Anonymous__208660)
            & c_24__case__PLF_2eReferences_2eSTLCRef_2etm_24208442___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = Vv__CANONICAL__3 )
        | ? [Vvar__0___24Anonymous__208661] :
            ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__0___24Anonymous__208661)
            & Vv__CANONICAL__3 = cPLF_2eReferences_2eSTLCRef_2escc___24a1(Vvar__0___24Anonymous__208661)
            & c_24__case__PLF_2eReferences_2eSTLCRef_2etm_24208442___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cPLF_2eReferences_2eSTLCRef_2escc___24a1(c_24__fix__209397__v__CANONICAL__0___24a3(Vv__CANONICAL__2,Vv__CANONICAL__4,Vvar__0___24Anonymous__208661)) )
        | ? [Vvar__0___24Anonymous__208691] :
            ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__0___24Anonymous__208691)
            & Vv__CANONICAL__3 = cPLF_2eReferences_2eSTLCRef_2eprd___24a1(Vvar__0___24Anonymous__208691)
            & c_24__case__PLF_2eReferences_2eSTLCRef_2etm_24208442___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cPLF_2eReferences_2eSTLCRef_2eprd___24a1(c_24__fix__209397__v__CANONICAL__0___24a3(Vv__CANONICAL__2,Vv__CANONICAL__4,Vvar__0___24Anonymous__208691)) )
        | ? [Vvar__0___24Anonymous__208721] :
            ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__0___24Anonymous__208721)
            & ? [Vvar__1___24Anonymous__208722] :
                ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__1___24Anonymous__208722)
                & Vv__CANONICAL__3 = cPLF_2eReferences_2eSTLCRef_2emlt___24a2(Vvar__0___24Anonymous__208721,Vvar__1___24Anonymous__208722)
                & c_24__case__PLF_2eReferences_2eSTLCRef_2etm_24208442___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cPLF_2eReferences_2eSTLCRef_2emlt___24a2(c_24__fix__209397__v__CANONICAL__0___24a3(Vv__CANONICAL__2,Vv__CANONICAL__4,Vvar__0___24Anonymous__208721),c_24__fix__209397__v__CANONICAL__0___24a3(Vv__CANONICAL__2,Vv__CANONICAL__4,Vvar__1___24Anonymous__208722)) ) )
        | ? [Vvar__0___24Anonymous__208840] :
            ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__0___24Anonymous__208840)
            & ? [Vvar__1___24Anonymous__208841] :
                ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__1___24Anonymous__208841)
                & ? [Vvar__2___24Anonymous__208842] :
                    ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__2___24Anonymous__208842)
                    & Vv__CANONICAL__3 = cPLF_2eReferences_2eSTLCRef_2etest0___24a3(Vvar__0___24Anonymous__208840,Vvar__1___24Anonymous__208841,Vvar__2___24Anonymous__208842)
                    & c_24__case__PLF_2eReferences_2eSTLCRef_2etm_24208442___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cPLF_2eReferences_2eSTLCRef_2etest0___24a3(c_24__fix__209397__v__CANONICAL__0___24a3(Vv__CANONICAL__2,Vv__CANONICAL__4,Vvar__0___24Anonymous__208840),c_24__fix__209397__v__CANONICAL__0___24a3(Vv__CANONICAL__2,Vv__CANONICAL__4,Vvar__1___24Anonymous__208841),c_24__fix__209397__v__CANONICAL__0___24a3(Vv__CANONICAL__2,Vv__CANONICAL__4,Vvar__2___24Anonymous__208842)) ) ) )
        | ( Vv__CANONICAL__3 = cPLF_2eReferences_2eSTLCRef_2eunit
          & c_24__case__PLF_2eReferences_2eSTLCRef_2etm_24208442___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = Vv__CANONICAL__3 )
        | ? [Vvar__0___24Anonymous__209107] :
            ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__0___24Anonymous__209107)
            & Vv__CANONICAL__3 = cPLF_2eReferences_2eSTLCRef_2eref___24a1(Vvar__0___24Anonymous__209107)
            & c_24__case__PLF_2eReferences_2eSTLCRef_2etm_24208442___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cPLF_2eReferences_2eSTLCRef_2eref___24a1(c_24__fix__209397__v__CANONICAL__0___24a3(Vv__CANONICAL__2,Vv__CANONICAL__4,Vvar__0___24Anonymous__209107)) )
        | ? [Vvar__0___24Anonymous__209137] :
            ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__0___24Anonymous__209137)
            & Vv__CANONICAL__3 = cPLF_2eReferences_2eSTLCRef_2ederef___24a1(Vvar__0___24Anonymous__209137)
            & c_24__case__PLF_2eReferences_2eSTLCRef_2etm_24208442___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cPLF_2eReferences_2eSTLCRef_2ederef___24a1(c_24__fix__209397__v__CANONICAL__0___24a3(Vv__CANONICAL__2,Vv__CANONICAL__4,Vvar__0___24Anonymous__209137)) )
        | ? [Vvar__0___24Anonymous__209167] :
            ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__0___24Anonymous__209167)
            & ? [Vvar__1___24Anonymous__209168] :
                ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__1___24Anonymous__209168)
                & Vv__CANONICAL__3 = cPLF_2eReferences_2eSTLCRef_2eassign___24a2(Vvar__0___24Anonymous__209167,Vvar__1___24Anonymous__209168)
                & c_24__case__PLF_2eReferences_2eSTLCRef_2etm_24208442___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cPLF_2eReferences_2eSTLCRef_2eassign___24a2(c_24__fix__209397__v__CANONICAL__0___24a3(Vv__CANONICAL__2,Vv__CANONICAL__4,Vvar__0___24Anonymous__209167),c_24__fix__209397__v__CANONICAL__0___24a3(Vv__CANONICAL__2,Vv__CANONICAL__4,Vvar__1___24Anonymous__209168)) ) )
        | ? [Vvar__0___24Anonymous__209286] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__209286)
            & Vv__CANONICAL__3 = cPLF_2eReferences_2eSTLCRef_2eloc___24a1(Vvar__0___24Anonymous__209286)
            & c_24__case__PLF_2eReferences_2eSTLCRef_2etm_24208442___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = Vv__CANONICAL__3 ) ) ) ).

fof('$_case_PLF.Stlc.STLC.tm$110793',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
      ( cPLF_2eStlc_2eSTLC_2etm___24t(Vv__CANONICAL__3)
     => ( ? [Vvar__0___24Anonymous__110794] :
            ( cCoq_2eStrings_2eString_2estring___24t(Vvar__0___24Anonymous__110794)
            & ( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__2)
             => ( cCoq_2eStrings_2eString_2estring___24t(Vvar__0___24Anonymous__110794)
               => ( Vv__CANONICAL__3 = cPLF_2eStlc_2eSTLC_2evar___24a1(Vvar__0___24Anonymous__110794)
                  & ( ( cPLF_2eMaps_2eeqb__string___24a2(Vv__CANONICAL__2,Vvar__0___24Anonymous__110794) = cCoq_2eInit_2eDatatypes_2etrue
                      & c_24__case__PLF_2eStlc_2eSTLC_2etm_24110793___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = Vv__CANONICAL__4 )
                    | ( cPLF_2eMaps_2eeqb__string___24a2(Vv__CANONICAL__2,Vvar__0___24Anonymous__110794) = cCoq_2eInit_2eDatatypes_2efalse
                      & c_24__case__PLF_2eStlc_2eSTLC_2etm_24110793___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = Vv__CANONICAL__3 ) ) ) ) ) )
        | ? [Vvar__0___24Anonymous__110796] :
            ( cPLF_2eStlc_2eSTLC_2etm___24t(Vvar__0___24Anonymous__110796)
            & ? [Vvar__1___24Anonymous__110797] :
                ( cPLF_2eStlc_2eSTLC_2etm___24t(Vvar__1___24Anonymous__110797)
                & Vv__CANONICAL__3 = cPLF_2eStlc_2eSTLC_2eapp___24a2(Vvar__0___24Anonymous__110796,Vvar__1___24Anonymous__110797)
                & c_24__case__PLF_2eStlc_2eSTLC_2etm_24110793___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cPLF_2eStlc_2eSTLC_2eapp___24a2(c_24__fix__111186__v__CANONICAL__0___24a3(Vv__CANONICAL__2,Vv__CANONICAL__4,Vvar__0___24Anonymous__110796),c_24__fix__111186__v__CANONICAL__0___24a3(Vv__CANONICAL__2,Vv__CANONICAL__4,Vvar__1___24Anonymous__110797)) ) )
        | ? [Vvar__0___24Anonymous__110875] :
            ( cCoq_2eStrings_2eString_2estring___24t(Vvar__0___24Anonymous__110875)
            & ? [Vvar__1___24Anonymous__110876] :
                ( cPLF_2eStlc_2eSTLC_2ety___24t(Vvar__1___24Anonymous__110876)
                & ? [Vvar__2___24Anonymous__110877] :
                    ( cPLF_2eStlc_2eSTLC_2etm___24t(Vvar__2___24Anonymous__110877)
                    & Vv__CANONICAL__3 = cPLF_2eStlc_2eSTLC_2eabs___24a3(Vvar__0___24Anonymous__110875,Vvar__1___24Anonymous__110876,Vvar__2___24Anonymous__110877)
                    & c_24__case__PLF_2eStlc_2eSTLC_2etm_24110793___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cPLF_2eStlc_2eSTLC_2eabs___24a3(Vvar__0___24Anonymous__110875,Vvar__1___24Anonymous__110876,c_24__case__Coq_2eInit_2eDatatypes_2ebool_24111428___24a4(Vv__CANONICAL__2,Vv__CANONICAL__4,Vvar__0___24Anonymous__110875,Vvar__2___24Anonymous__110877)) ) ) )
        | ( Vv__CANONICAL__3 = cPLF_2eStlc_2eSTLC_2etru
          & c_24__case__PLF_2eStlc_2eSTLC_2etm_24110793___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cPLF_2eStlc_2eSTLC_2etru )
        | ( Vv__CANONICAL__3 = cPLF_2eStlc_2eSTLC_2efls
          & c_24__case__PLF_2eStlc_2eSTLC_2etm_24110793___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cPLF_2eStlc_2eSTLC_2efls )
        | ? [Vvar__0___24Anonymous__110941] :
            ( cPLF_2eStlc_2eSTLC_2etm___24t(Vvar__0___24Anonymous__110941)
            & ? [Vvar__1___24Anonymous__110942] :
                ( cPLF_2eStlc_2eSTLC_2etm___24t(Vvar__1___24Anonymous__110942)
                & ? [Vvar__2___24Anonymous__110943] :
                    ( cPLF_2eStlc_2eSTLC_2etm___24t(Vvar__2___24Anonymous__110943)
                    & Vv__CANONICAL__3 = cPLF_2eStlc_2eSTLC_2etest___24a3(Vvar__0___24Anonymous__110941,Vvar__1___24Anonymous__110942,Vvar__2___24Anonymous__110943)
                    & c_24__case__PLF_2eStlc_2eSTLC_2etm_24110793___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cPLF_2eStlc_2eSTLC_2etest___24a3(c_24__fix__111186__v__CANONICAL__0___24a3(Vv__CANONICAL__2,Vv__CANONICAL__4,Vvar__0___24Anonymous__110941),c_24__fix__111186__v__CANONICAL__0___24a3(Vv__CANONICAL__2,Vv__CANONICAL__4,Vvar__1___24Anonymous__110942),c_24__fix__111186__v__CANONICAL__0___24a3(Vv__CANONICAL__2,Vv__CANONICAL__4,Vvar__2___24Anonymous__110943)) ) ) ) ) ) ).

fof('$_def_$_let_11_subst_l_1650',axiom,
    ! [V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V7__ceqb,V8__cdiv,V9__n,V10__lmp,V11__P] : c_24__let__11__subst__l__1650___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V7__ceqb,V8__cdiv,V9__n,V10__lmp,V11__P) = cCoq_2esetoid__ring_2eRing__polynom_2ePNSubstL___24a11(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V7__ceqb,V8__cdiv,V11__P,V10__lmp,V9__n,V9__n) ).

fof('$_def_$_let_3_s_168284',axiom,
    ! [V0__n,V1__m] : c_24__let__3__s__168284___24a2(V0__n,V1__m) = cCoq_2eArith_2eCompare__dec_2elt__eq__lt__dec___24a2(V0__n,V1__m) ).

fof('$_def_$_let_var_6_p_113399_113402',axiom,
    ! [V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__113398] : c_24__let__var__6__p__113399__113402___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__113398) = cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__113398) ).

fof('$_def_$_let_var_6_p_113401_113403',axiom,
    ! [V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__113400] : c_24__let__var__6__p__113401__113403___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__113400) = cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__113400) ).

fof('$_def_Coq.Arith.Compare_dec.le_lt_eq_dec',axiom,
    ! [V0__n,V1__m] : cCoq_2eArith_2eCompare__dec_2ele__lt__eq__dec___24a2(V0__n,V1__m) = c_24__case__Coq_2eInit_2eSpecif_2esumor_24168291___24a2(V0__n,V1__m) ).

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__82730] :
                  ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__82730)
                  & V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__82730)
                  & ( cCoq_2eArith_2eEqNat_2eeq__nat___24a2(V1__n,V2__m)
                  <=> p(c_24False) ) ) ) ) )
        | ? [Vvar__0___24Anonymous__82731] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__82731)
            & ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
             => ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__82731)
                & ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
                    & ( cCoq_2eArith_2eEqNat_2eeq__nat___24a2(V1__n,V2__m)
                    <=> p(c_24False) ) )
                  | ? [Vvar__0___24Anonymous__82734] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__82734)
                      & V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__82734)
                      & ( cCoq_2eArith_2eEqNat_2eeq__nat___24a2(V1__n,V2__m)
                      <=> cCoq_2eArith_2eEqNat_2eeq__nat___24a2(Vvar__0___24Anonymous__82731,Vvar__0___24Anonymous__82734) ) ) ) ) ) ) ) ) ).

fof('$_def_Coq.Arith.PeanoNat.Nat.divmod',axiom,
    ! [V1__x,V2__y,V3__q,V4__u] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__x)
     => ( ( V1__x = cCoq_2eInit_2eDatatypes_2eO
          & cCoq_2eArith_2ePeanoNat_2eNat_2edivmod___24a4(V1__x,V2__y,V3__q,V4__u) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eInit_2eDatatypes_2enat,cCoq_2eInit_2eDatatypes_2enat,V3__q,V4__u) )
        | ? [Vvar__0___24Anonymous__218736] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__218736)
            & ( cCoq_2eInit_2eDatatypes_2enat___24t(V4__u)
             => ( V1__x = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__218736)
                & ( ( V4__u = cCoq_2eInit_2eDatatypes_2eO
                    & cCoq_2eArith_2ePeanoNat_2eNat_2edivmod___24a4(V1__x,V2__y,V3__q,V4__u) = cCoq_2eArith_2ePeanoNat_2eNat_2edivmod___24a4(Vvar__0___24Anonymous__218736,V2__y,cCoq_2eInit_2eDatatypes_2eS___24a1(V3__q),V2__y) )
                  | ? [Vvar__0___24Anonymous__218739] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__218739)
                      & V4__u = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__218739)
                      & cCoq_2eArith_2ePeanoNat_2eNat_2edivmod___24a4(V1__x,V2__y,V3__q,V4__u) = cCoq_2eArith_2ePeanoNat_2eNat_2edivmod___24a4(Vvar__0___24Anonymous__218736,V2__y,V3__q,Vvar__0___24Anonymous__218739) ) ) ) ) ) ) ) ).

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.pred',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => ( ( V0__n = cCoq_2eInit_2eDatatypes_2eO
          & cCoq_2eArith_2ePeanoNat_2eNat_2epred___24a1(V0__n) = V0__n )
        | ? [Vvar__0___24Anonymous__200892] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__200892)
            & V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__200892)
            & cCoq_2eArith_2ePeanoNat_2eNat_2epred___24a1(V0__n) = Vvar__0___24Anonymous__200892 ) ) ) ).

fof('$_def_Coq.Arith.PeanoNat.Nat.sub',axiom,
    ! [V1__n,V2__m] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
     => ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
          & cCoq_2eArith_2ePeanoNat_2eNat_2esub___24a2(V1__n,V2__m) = V1__n )
        | ? [Vvar__0___24Anonymous__200897] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__200897)
            & ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
             => ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__200897)
                & ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
                    & cCoq_2eArith_2ePeanoNat_2eNat_2esub___24a2(V1__n,V2__m) = V1__n )
                  | ? [Vvar__0___24Anonymous__200900] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__200900)
                      & V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__200900)
                      & cCoq_2eArith_2ePeanoNat_2eNat_2esub___24a2(V1__n,V2__m) = cCoq_2eArith_2ePeanoNat_2eNat_2esub___24a2(Vvar__0___24Anonymous__200897,Vvar__0___24Anonymous__200900) ) ) ) ) ) ) ) ).

fof('$_def_Coq.Arith.PeanoNat.Nat.succ',axiom,
    cCoq_2eArith_2ePeanoNat_2eNat_2esucc = cCoq_2eInit_2eDatatypes_2eS ).

fof('$_def_Coq.Arith.PeanoNat.Nat.t',axiom,
    ! [Vvar__200660] :
      ( cCoq_2eArith_2ePeanoNat_2eNat_2et___24t(Vvar__200660)
    <=> cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__200660) ) ).

fof('$_def_Coq.Arith.PeanoNat.Nat.zero',axiom,
    cCoq_2eArith_2ePeanoNat_2eNat_2ezero = cCoq_2eInit_2eDatatypes_2eO ).

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.FSets.FSetPositive.PositiveSet.E.bits_lt',axiom,
    ! [V1__p,V2__q] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p)
     => ( ? [Vvar__0___24Anonymous__200855] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__200855)
            & ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__q)
             => ( V1__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__200855)
                & ( ? [Vvar__0___24Anonymous__200859] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__200859)
                      & V2__q = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__200859)
                      & ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eE_2ebits__lt___24a2(V1__p,V2__q)
                      <=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eE_2ebits__lt___24a2(Vvar__0___24Anonymous__200855,Vvar__0___24Anonymous__200859) ) )
                  | ? [Vvar__0___24Anonymous__200860] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__200860)
                      & V2__q = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__200860)
                      & ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eE_2ebits__lt___24a2(V1__p,V2__q)
                      <=> p(c_24False) ) )
                  | ( V2__q = cCoq_2eNumbers_2eBinNums_2exH
                    & ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eE_2ebits__lt___24a2(V1__p,V2__q)
                    <=> p(c_24False) ) ) ) ) ) )
        | ? [Vvar__0___24Anonymous__200861] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__200861)
            & ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__q)
             => ( V1__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__200861)
                & ( ? [Vvar__0___24Anonymous__200865] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__200865)
                      & V2__q = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__200865)
                      & ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eE_2ebits__lt___24a2(V1__p,V2__q)
                      <=> p(c_24True) ) )
                  | ? [Vvar__0___24Anonymous__200866] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__200866)
                      & V2__q = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__200866)
                      & ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eE_2ebits__lt___24a2(V1__p,V2__q)
                      <=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eE_2ebits__lt___24a2(Vvar__0___24Anonymous__200861,Vvar__0___24Anonymous__200866) ) )
                  | ( V2__q = cCoq_2eNumbers_2eBinNums_2exH
                    & ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eE_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__200867] :
                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__200867)
                  & V2__q = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__200867)
                  & ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eE_2ebits__lt___24a2(V1__p,V2__q)
                  <=> p(c_24True) ) )
              | ? [Vvar__0___24Anonymous__200868] :
                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__200868)
                  & V2__q = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__200868)
                  & ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eE_2ebits__lt___24a2(V1__p,V2__q)
                  <=> p(c_24False) ) )
              | ( V2__q = cCoq_2eNumbers_2eBinNums_2exH
                & ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eE_2ebits__lt___24a2(V1__p,V2__q)
                <=> p(c_24False) ) ) ) ) ) ) ) ).

fof('$_def_Coq.FSets.FSetPositive.PositiveSet.E.t',axiom,
    ! [Vvar__200852] :
      ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eE_2et___24t(Vvar__200852)
    <=> cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__200852) ) ).

fof('$_def_Coq.FSets.FSetPositive.PositiveSet.elt',axiom,
    ! [Vvar__80364] :
      ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vvar__80364)
    <=> cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__80364) ) ).

fof('$_def_Coq.FSets.FSetPositive.PositiveSet.filter',axiom,
    ! [V0__f,V1__m] : cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2efilter___24a2(V0__f,V1__m) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2exfilter___24a3(V0__f,V1__m,cCoq_2eNumbers_2eBinNums_2exH) ).

fof('$_def_Coq.FSets.FSetPositive.PositiveSet.rev',axiom,
    ! [V0__x] : cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2erev___24a1(V0__x) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2erev__append___24a2(V0__x,cCoq_2eNumbers_2eBinNums_2exH) ).

fof('$_def_Coq.FSets.FSetPositive.PositiveSet.t',axiom,
    ! [Vvar__80365] :
      ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__80365)
    <=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__80365) ) ).

fof('$_def_Coq.Init.Datatypes.ID',axiom,
    ! [Vvar__88857] :
      ( cCoq_2eInit_2eDatatypes_2eID___24t(Vvar__88857)
    <=> ! [V0__A] :
          ( cType___24t(V0__A)
         => ! [V1___24Anonymous] :
              ( t(V1___24Anonymous,V0__A)
             => t(happ(happ(Vvar__88857,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__75712] :
              ( t(Vvar__1___24Anonymous__75712,V0__A)
              & ? [Vvar__2___24Anonymous__75713] :
                  ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__75713)
                  & V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__75712,Vvar__2___24Anonymous__75713)
                  & cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__l,V3__m) = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__75712,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,Vvar__2___24Anonymous__75713,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__75672] :
              ( t(Vvar__2___24Anonymous__75672,V0__A)
              & ? [Vvar__3___24Anonymous__75673] :
                  ( t(Vvar__3___24Anonymous__75673,V1__B)
                  & V2__p = cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V1__B,Vvar__2___24Anonymous__75672,Vvar__3___24Anonymous__75673)
                  & cCoq_2eInit_2eDatatypes_2efst___24a3(V0__A,V1__B,V2__p) = Vvar__2___24Anonymous__75672 ) ) ) ) ) ).

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__75702] :
              ( t(Vvar__1___24Anonymous__75702,V0__A)
              & ? [Vvar__2___24Anonymous__75703] :
                  ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__75703)
                  & V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__75702,Vvar__2___24Anonymous__75703)
                  & cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__l) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,Vvar__2___24Anonymous__75703)) ) ) ) ) ) ).

fof('$_def_Coq.Init.Datatypes.nat_rect',axiom,
    ! [V0__P,V1__f,V2__f,V4__n] :
      ( c_24__type__80621___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__80619] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__80619)
              & V4__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__80619)
              & cCoq_2eInit_2eDatatypes_2enat__rect___24a4(V0__P,V1__f,V2__f,V4__n) = happ(happ(V2__f,Vvar__0___24Anonymous__80619),cCoq_2eInit_2eDatatypes_2enat__rect___24a4(V0__P,V1__f,V2__f,Vvar__0___24Anonymous__80619)) ) ) ) ) ).

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

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

fof('$_def_Coq.Init.Datatypes.prod_rec',axiom,
    ! [V0__A,V1__B,V2__P] : cCoq_2eInit_2eDatatypes_2eprod__rec___24a3(V0__A,V1__B,V2__P) = cCoq_2eInit_2eDatatypes_2eprod__rect___24a3(V0__A,V1__B,V2__P) ).

fof('$_def_Coq.Init.Datatypes.prod_rect',axiom,
    ! [V0__A,V1__B,V2__P,V3__f,V4__p] :
      ( cType___24t(V0__A)
     => ( cType___24t(V1__B)
       => ( c_24__type__212688___24t(V0__A,V1__B,V2__P,V2__P)
         => ( cCoq_2eInit_2eDatatypes_2eprod___24t(V0__A,V1__B,V4__p)
           => ? [Vvar__2___24Anonymous__212681] :
                ( t(Vvar__2___24Anonymous__212681,V0__A)
                & ? [Vvar__3___24Anonymous__212682] :
                    ( t(Vvar__3___24Anonymous__212682,V1__B)
                    & V4__p = cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V1__B,Vvar__2___24Anonymous__212681,Vvar__3___24Anonymous__212682)
                    & cCoq_2eInit_2eDatatypes_2eprod__rect___24a5(V0__A,V1__B,V2__P,V3__f,V4__p) = happ(happ(V3__f,Vvar__2___24Anonymous__212681),Vvar__3___24Anonymous__212682) ) ) ) ) ) ) ).

fof('$_def_Coq.Init.Datatypes.prod_uncurry',axiom,
    ! [V0__A,V1__B,V2__C,V3__f,V4__x,V5__y] : cCoq_2eInit_2eDatatypes_2eprod__uncurry___24a6(V0__A,V1__B,V2__C,V3__f,V4__x,V5__y) = happ(V3__f,cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V1__B,V4__x,V5__y)) ).

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__75684] :
              ( t(Vvar__2___24Anonymous__75684,V0__A)
              & ? [Vvar__3___24Anonymous__75685] :
                  ( t(Vvar__3___24Anonymous__75685,V1__B)
                  & V2__p = cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V1__B,Vvar__2___24Anonymous__75684,Vvar__3___24Anonymous__75685)
                  & cCoq_2eInit_2eDatatypes_2esnd___24a3(V0__A,V1__B,V2__p) = Vvar__3___24Anonymous__75685 ) ) ) ) ) ).

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.nb_digits',axiom,
    ! [V1__d] :
      ( cCoq_2eInit_2eDecimal_2euint___24t(V1__d)
     => ( ( V1__d = cCoq_2eInit_2eDecimal_2eNil
          & cCoq_2eInit_2eDecimal_2enb__digits___24a1(V1__d) = cCoq_2eInit_2eDatatypes_2eO )
        | ? [Vvar__0___24Anonymous__82715] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__82715)
            & V1__d = cCoq_2eInit_2eDecimal_2eD0___24a1(Vvar__0___24Anonymous__82715)
            & cCoq_2eInit_2eDecimal_2enb__digits___24a1(V1__d) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDecimal_2enb__digits___24a1(Vvar__0___24Anonymous__82715)) )
        | ? [Vvar__0___24Anonymous__82716] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__82716)
            & V1__d = cCoq_2eInit_2eDecimal_2eD1___24a1(Vvar__0___24Anonymous__82716)
            & cCoq_2eInit_2eDecimal_2enb__digits___24a1(V1__d) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDecimal_2enb__digits___24a1(Vvar__0___24Anonymous__82716)) )
        | ? [Vvar__0___24Anonymous__82717] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__82717)
            & V1__d = cCoq_2eInit_2eDecimal_2eD2___24a1(Vvar__0___24Anonymous__82717)
            & cCoq_2eInit_2eDecimal_2enb__digits___24a1(V1__d) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDecimal_2enb__digits___24a1(Vvar__0___24Anonymous__82717)) )
        | ? [Vvar__0___24Anonymous__82718] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__82718)
            & V1__d = cCoq_2eInit_2eDecimal_2eD3___24a1(Vvar__0___24Anonymous__82718)
            & cCoq_2eInit_2eDecimal_2enb__digits___24a1(V1__d) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDecimal_2enb__digits___24a1(Vvar__0___24Anonymous__82718)) )
        | ? [Vvar__0___24Anonymous__82719] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__82719)
            & V1__d = cCoq_2eInit_2eDecimal_2eD4___24a1(Vvar__0___24Anonymous__82719)
            & cCoq_2eInit_2eDecimal_2enb__digits___24a1(V1__d) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDecimal_2enb__digits___24a1(Vvar__0___24Anonymous__82719)) )
        | ? [Vvar__0___24Anonymous__82720] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__82720)
            & V1__d = cCoq_2eInit_2eDecimal_2eD5___24a1(Vvar__0___24Anonymous__82720)
            & cCoq_2eInit_2eDecimal_2enb__digits___24a1(V1__d) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDecimal_2enb__digits___24a1(Vvar__0___24Anonymous__82720)) )
        | ? [Vvar__0___24Anonymous__82721] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__82721)
            & V1__d = cCoq_2eInit_2eDecimal_2eD6___24a1(Vvar__0___24Anonymous__82721)
            & cCoq_2eInit_2eDecimal_2enb__digits___24a1(V1__d) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDecimal_2enb__digits___24a1(Vvar__0___24Anonymous__82721)) )
        | ? [Vvar__0___24Anonymous__82722] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__82722)
            & V1__d = cCoq_2eInit_2eDecimal_2eD7___24a1(Vvar__0___24Anonymous__82722)
            & cCoq_2eInit_2eDecimal_2enb__digits___24a1(V1__d) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDecimal_2enb__digits___24a1(Vvar__0___24Anonymous__82722)) )
        | ? [Vvar__0___24Anonymous__82723] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__82723)
            & V1__d = cCoq_2eInit_2eDecimal_2eD8___24a1(Vvar__0___24Anonymous__82723)
            & cCoq_2eInit_2eDecimal_2enb__digits___24a1(V1__d) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDecimal_2enb__digits___24a1(Vvar__0___24Anonymous__82723)) )
        | ? [Vvar__0___24Anonymous__82724] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__82724)
            & V1__d = cCoq_2eInit_2eDecimal_2eD9___24a1(Vvar__0___24Anonymous__82724)
            & cCoq_2eInit_2eDecimal_2enb__digits___24a1(V1__d) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDecimal_2enb__digits___24a1(Vvar__0___24Anonymous__82724)) ) ) ) ).

fof('$_def_Coq.Init.Decimal.rev',axiom,
    ! [V0__d] : cCoq_2eInit_2eDecimal_2erev___24a1(V0__d) = cCoq_2eInit_2eDecimal_2erevapp___24a2(V0__d,cCoq_2eInit_2eDecimal_2eNil) ).

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__180] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__180)
            & V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__180)
            & cCoq_2eInit_2eNat_2eadd___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2eadd___24a2(Vvar__0___24Anonymous__180,V2__m)) ) ) ) ).

fof('$_def_Coq.Init.Nat.divmod',axiom,
    ! [V1__x,V2__y,V3__q,V4__u] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__x)
     => ( ( V1__x = cCoq_2eInit_2eDatatypes_2eO
          & cCoq_2eInit_2eNat_2edivmod___24a4(V1__x,V2__y,V3__q,V4__u) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eInit_2eDatatypes_2enat,cCoq_2eInit_2eDatatypes_2enat,V3__q,V4__u) )
        | ? [Vvar__0___24Anonymous__76731] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__76731)
            & ( cCoq_2eInit_2eDatatypes_2enat___24t(V4__u)
             => ( V1__x = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__76731)
                & ( ( V4__u = cCoq_2eInit_2eDatatypes_2eO
                    & cCoq_2eInit_2eNat_2edivmod___24a4(V1__x,V2__y,V3__q,V4__u) = cCoq_2eInit_2eNat_2edivmod___24a4(Vvar__0___24Anonymous__76731,V2__y,cCoq_2eInit_2eDatatypes_2eS___24a1(V3__q),V2__y) )
                  | ? [Vvar__0___24Anonymous__76734] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__76734)
                      & V4__u = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__76734)
                      & cCoq_2eInit_2eNat_2edivmod___24a4(V1__x,V2__y,V3__q,V4__u) = cCoq_2eInit_2eNat_2edivmod___24a4(Vvar__0___24Anonymous__76731,V2__y,V3__q,Vvar__0___24Anonymous__76734) ) ) ) ) ) ) ) ).

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__76669] :
                  ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__76669)
                  & V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__76669)
                  & cCoq_2eInit_2eNat_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) )
        | ? [Vvar__0___24Anonymous__76670] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__76670)
            & ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
             => ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__76670)
                & ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
                    & cCoq_2eInit_2eNat_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse )
                  | ? [Vvar__0___24Anonymous__76673] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__76673)
                      & V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__76673)
                      & cCoq_2eInit_2eNat_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2eeqb___24a2(Vvar__0___24Anonymous__76670,Vvar__0___24Anonymous__76673) ) ) ) ) ) ) ) ).

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__76703] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__76703)
            & ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__76703)
             => ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__76703)
                & ( ( Vvar__0___24Anonymous__76703 = cCoq_2eInit_2eDatatypes_2eO
                    & cCoq_2eInit_2eNat_2eeven___24a1(V1__n) = cCoq_2eInit_2eDatatypes_2efalse )
                  | ? [Vvar__0___24Anonymous__76706] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__76706)
                      & Vvar__0___24Anonymous__76703 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__76706)
                      & cCoq_2eInit_2eNat_2eeven___24a1(V1__n) = cCoq_2eInit_2eNat_2eeven___24a1(Vvar__0___24Anonymous__76706) ) ) ) ) ) ) ) ).

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__76691] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__76691)
            & ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
             => ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__76691)
                & ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
                    & cCoq_2eInit_2eNat_2emax___24a2(V1__n,V2__m) = V1__n )
                  | ? [Vvar__0___24Anonymous__76694] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__76694)
                      & V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__76694)
                      & cCoq_2eInit_2eNat_2emax___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2emax___24a2(Vvar__0___24Anonymous__76691,Vvar__0___24Anonymous__76694)) ) ) ) ) ) ) ) ).

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__76697] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__76697)
            & ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
             => ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__76697)
                & ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
                    & cCoq_2eInit_2eNat_2emin___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eO )
                  | ? [Vvar__0___24Anonymous__76700] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__76700)
                      & V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__76700)
                      & cCoq_2eInit_2eNat_2emin___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2emin___24a2(Vvar__0___24Anonymous__76697,Vvar__0___24Anonymous__76700)) ) ) ) ) ) ) ) ).

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__570] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__570)
            & V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__570)
            & cCoq_2eInit_2eNat_2emul___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2eadd___24a2(V2__m,cCoq_2eInit_2eNat_2emul___24a2(Vvar__0___24Anonymous__570,V2__m)) ) ) ) ).

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__568] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__568)
            & V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__568)
            & cCoq_2eInit_2eNat_2epred___24a1(V0__n) = Vvar__0___24Anonymous__568 ) ) ) ).

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__76663] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__76663)
            & ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
             => ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__76663)
                & ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
                    & cCoq_2eInit_2eNat_2esub___24a2(V1__n,V2__m) = V1__n )
                  | ? [Vvar__0___24Anonymous__76666] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__76666)
                      & V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__76666)
                      & cCoq_2eInit_2eNat_2esub___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2esub___24a2(Vvar__0___24Anonymous__76663,Vvar__0___24Anonymous__76666) ) ) ) ) ) ) ) ).

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

fof('$_def_Coq.Init.Nat.t',axiom,
    ! [Vvar__113283] :
      ( cCoq_2eInit_2eNat_2et___24t(Vvar__113283)
    <=> cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__113283) ) ).

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__113284] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__113284)
            & V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__113284)
            & ( cCoq_2eInit_2ePeano_2eIsSucc___24a1(V0__n)
            <=> p(c_24True) ) ) ) ) ).

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

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

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

fof('$_def_Coq.Init.Wf.Fix_F_2',axiom,
    ! [V0__A,V1__B,V2__R,V3__P,V4__F,V6__x,V7__x_27] : cCoq_2eInit_2eWf_2eFix__F__2___24a7(V0__A,V1__B,V2__R,V3__P,V4__F,V6__x,V7__x_27) = happ(happ(happ(V4__F,V6__x),V7__x_27),c_24__lam__218144___24a7(V0__A,V1__B,V2__R,V3__P,V4__F,V6__x,V7__x_27)) ).

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

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

fof('$_def_Coq.Lists.List.In',axiom,
    ! [V0__A,V2__a,V3__l] :
      ( cType___24t(V0__A)
     => ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
       => ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
            & ( cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__a,V3__l)
            <=> p(c_24False) ) )
          | ? [Vvar__1___24Anonymous__76459] :
              ( t(Vvar__1___24Anonymous__76459,V0__A)
              & ? [Vvar__2___24Anonymous__76460] :
                  ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__76460)
                  & V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__76459,Vvar__2___24Anonymous__76460)
                  & ( cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__a,V3__l)
                  <=> ( Vvar__1___24Anonymous__76459 = V2__a
                      | cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__a,Vvar__2___24Anonymous__76460) ) ) ) ) ) ) ) ).

fof('$_def_Coq.Lists.List.combine',axiom,
    ! [V0__A,V1__B,V3__l,V4__l_27] :
      ( cType___24t(V0__A)
     => ( cType___24t(V1__B)
       => ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
         => ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
              & cCoq_2eLists_2eList_2ecombine___24a4(V0__A,V1__B,V3__l,V4__l_27) = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__A,V1__B)) )
            | ? [Vvar__1___24Anonymous__214380] :
                ( t(Vvar__1___24Anonymous__214380,V0__A)
                & ? [Vvar__2___24Anonymous__214381] :
                    ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__214381)
                    & ( cType___24t(V0__A)
                     => ( cType___24t(V1__B)
                       => ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,V4__l_27)
                         => ( V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__214380,Vvar__2___24Anonymous__214381)
                            & ( ( V4__l_27 = cCoq_2eInit_2eDatatypes_2enil___24a1(V1__B)
                                & cCoq_2eLists_2eList_2ecombine___24a4(V0__A,V1__B,V3__l,V4__l_27) = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__A,V1__B)) )
                              | ? [Vvar__1___24Anonymous__214392] :
                                  ( t(Vvar__1___24Anonymous__214392,V1__B)
                                  & ? [Vvar__2___24Anonymous__214393] :
                                      ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,Vvar__2___24Anonymous__214393)
                                      & V4__l_27 = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__B,Vvar__1___24Anonymous__214392,Vvar__2___24Anonymous__214393)
                                      & cCoq_2eLists_2eList_2ecombine___24a4(V0__A,V1__B,V3__l,V4__l_27) = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__A,V1__B),cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V1__B,Vvar__1___24Anonymous__214380,Vvar__1___24Anonymous__214392),cCoq_2eLists_2eList_2ecombine___24a4(V0__A,V1__B,Vvar__2___24Anonymous__214381,Vvar__2___24Anonymous__214393)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('$_def_Coq.Lists.List.flat_map',axiom,
    ! [V0__A,V1__B,V2__f,V4__l] :
      ( cType___24t(V0__A)
     => ( cType___24t(V1__B)
       => ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
         => ( ( V4__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
              & cCoq_2eLists_2eList_2eflat__map___24a4(V0__A,V1__B,V2__f,V4__l) = cCoq_2eInit_2eDatatypes_2enil___24a1(V1__B) )
            | ? [Vvar__1___24Anonymous__214277] :
                ( t(Vvar__1___24Anonymous__214277,V0__A)
                & ? [Vvar__2___24Anonymous__214278] :
                    ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__214278)
                    & V4__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__214277,Vvar__2___24Anonymous__214278)
                    & cCoq_2eLists_2eList_2eflat__map___24a4(V0__A,V1__B,V2__f,V4__l) = cCoq_2eInit_2eDatatypes_2eapp___24a3(V1__B,happ(V2__f,Vvar__1___24Anonymous__214277),cCoq_2eLists_2eList_2eflat__map___24a4(V0__A,V1__B,V2__f,Vvar__2___24Anonymous__214278)) ) ) ) ) ) ) ).

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__83630] :
                ( t(Vvar__1___24Anonymous__83630,V1__B)
                & ? [Vvar__2___24Anonymous__83631] :
                    ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,Vvar__2___24Anonymous__83631)
                    & V5__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__B,Vvar__1___24Anonymous__83630,Vvar__2___24Anonymous__83631)
                    & cCoq_2eLists_2eList_2efold__right___24a5(V0__A,V1__B,V2__f,V3__a0,V5__l) = happ(happ(V2__f,Vvar__1___24Anonymous__83630),cCoq_2eLists_2eList_2efold__right___24a5(V0__A,V1__B,V2__f,V3__a0,Vvar__2___24Anonymous__83631)) ) ) ) ) ) ) ).

fof('$_def_Coq.Lists.List.map',axiom,
    ! [V0__A,V1__B,V2__f,V4__l] :
      ( cType___24t(V0__A)
     => ( cType___24t(V1__B)
       => ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
         => ( ( V4__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
              & cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V2__f,V4__l) = cCoq_2eInit_2eDatatypes_2enil___24a1(V1__B) )
            | ? [Vvar__1___24Anonymous__96785] :
                ( t(Vvar__1___24Anonymous__96785,V0__A)
                & ? [Vvar__2___24Anonymous__96786] :
                    ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__96786)
                    & V4__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__96785,Vvar__2___24Anonymous__96786)
                    & cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V2__f,V4__l) = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__B,happ(V2__f,Vvar__1___24Anonymous__96785),cCoq_2eLists_2eList_2emap___24a4(V0__A,V1__B,V2__f,Vvar__2___24Anonymous__96786)) ) ) ) ) ) ) ).

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__76471] :
                      ( t(Vvar__1___24Anonymous__76471,V0__A)
                      & ? [Vvar__2___24Anonymous__76472] :
                          ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__76472)
                          & V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__76471,Vvar__2___24Anonymous__76472)
                          & cCoq_2eLists_2eList_2enth___24a4(V0__A,V2__n,V3__l,V4__default) = Vvar__1___24Anonymous__76471 ) ) ) ) ) )
          | ? [Vvar__0___24Anonymous__76474] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__76474)
              & ( cType___24t(V0__A)
               => ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
                 => ( V2__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__76474)
                    & ( ( 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__76481] :
                          ( t(Vvar__1___24Anonymous__76481,V0__A)
                          & ? [Vvar__2___24Anonymous__76482] :
                              ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__76482)
                              & V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__76481,Vvar__2___24Anonymous__76482)
                              & cCoq_2eLists_2eList_2enth___24a4(V0__A,V2__n,V3__l,V4__default) = cCoq_2eLists_2eList_2enth___24a4(V0__A,Vvar__0___24Anonymous__76474,Vvar__2___24Anonymous__76482,V4__default) ) ) ) ) ) ) ) ) ) ) ).

fof('$_def_Coq.Lists.List.partition',axiom,
    ! [V0__A,V1__f,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_2epartition___24a3(V0__A,V1__f,V3__l) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A),cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)) )
          | ? [Vvar__1___24Anonymous__76575] :
              ( t(Vvar__1___24Anonymous__76575,V0__A)
              & ? [Vvar__2___24Anonymous__76576] :
                  ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__76576)
                  & ( cType___24t(V0__A)
                   => ( c_24__type__76596___24t(V0__A,V1__f)
                     => ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__76576)
                       => ( V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__76575,Vvar__2___24Anonymous__76576)
                          & ? [Vvar__2___24Anonymous__76590] :
                              ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__76590)
                              & ? [Vvar__3___24Anonymous__76591] :
                                  ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__3___24Anonymous__76591)
                                  & ( cType___24t(V0__A)
                                   => ( c_24__type__76596___24t(V0__A,V1__f)
                                     => ( t(Vvar__1___24Anonymous__76575,V0__A)
                                       => ( cCoq_2eLists_2eList_2epartition___24a3(V0__A,V1__f,Vvar__2___24Anonymous__76576) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),Vvar__2___24Anonymous__76590,Vvar__3___24Anonymous__76591)
                                          & ( ( happ(V1__f,Vvar__1___24Anonymous__76575) = cCoq_2eInit_2eDatatypes_2etrue
                                              & cCoq_2eLists_2eList_2epartition___24a3(V0__A,V1__f,V3__l) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__76575,Vvar__2___24Anonymous__76590),Vvar__3___24Anonymous__76591) )
                                            | ( happ(V1__f,Vvar__1___24Anonymous__76575) = cCoq_2eInit_2eDatatypes_2efalse
                                              & cCoq_2eLists_2eList_2epartition___24a3(V0__A,V1__f,V3__l) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),Vvar__2___24Anonymous__76590,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__76575,Vvar__3___24Anonymous__76591)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

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

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

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

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

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

fof('$_def_Coq.NArith.BinNat.N.div_eucl',axiom,
    ! [V0__a,V1__b] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
     => ( ( V0__a = cCoq_2eNumbers_2eBinNums_2eN0
          & cCoq_2eNArith_2eBinNat_2eN_2ediv__eucl___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN0,cCoq_2eNumbers_2eBinNums_2eN0) )
        | ? [Vvar__0___24Anonymous__218636] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__218636)
            & ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__b)
             => ( V0__a = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__218636)
                & ( ( V1__b = cCoq_2eNumbers_2eBinNums_2eN0
                    & cCoq_2eNArith_2eBinNat_2eN_2ediv__eucl___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN0,V0__a) )
                  | ? [Vvar__0___24Anonymous__218639] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__218639)
                      & V1__b = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__218639)
                      & cCoq_2eNArith_2eBinNat_2eN_2ediv__eucl___24a2(V0__a,V1__b) = cCoq_2eNArith_2eBinNatDef_2eN_2epos__div__eucl___24a2(Vvar__0___24Anonymous__218636,V1__b) ) ) ) ) ) ) ) ).

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.t',axiom,
    ! [Vvar__200888] :
      ( cCoq_2eNArith_2eBinNat_2eN_2et___24t(Vvar__200888)
    <=> cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__200888) ) ).

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__2358] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2358)
            & ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
             => ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__2358)
                & ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
                    & cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m) = V0__n )
                  | ? [Vvar__0___24Anonymous__2361] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2361)
                      & V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__2361)
                      & cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__2358,Vvar__0___24Anonymous__2361)) ) ) ) ) ) ) ) ).

fof('$_def_Coq.NArith.BinNatDef.N.div_eucl',axiom,
    ! [V0__a,V1__b] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
     => ( ( V0__a = cCoq_2eNumbers_2eBinNums_2eN0
          & cCoq_2eNArith_2eBinNatDef_2eN_2ediv__eucl___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN0,cCoq_2eNumbers_2eBinNums_2eN0) )
        | ? [Vvar__0___24Anonymous__2379] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2379)
            & ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__b)
             => ( V0__a = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__2379)
                & ( ( V1__b = cCoq_2eNumbers_2eBinNums_2eN0
                    & cCoq_2eNArith_2eBinNatDef_2eN_2ediv__eucl___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN0,V0__a) )
                  | ? [Vvar__0___24Anonymous__2382] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2382)
                      & V1__b = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__2382)
                      & cCoq_2eNArith_2eBinNatDef_2eN_2ediv__eucl___24a2(V0__a,V1__b) = cCoq_2eNArith_2eBinNatDef_2eN_2epos__div__eucl___24a2(Vvar__0___24Anonymous__2379,V1__b) ) ) ) ) ) ) ) ).

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__80054] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__80054)
            & V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__80054)
            & cCoq_2eNArith_2eBinNatDef_2eN_2edouble___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__80054)) ) ) ) ).

fof('$_def_Coq.NArith.BinNatDef.N.leb',axiom,
    ! [V0__x,V1__y] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
     => ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
       => ( ( cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eEq
            & cCoq_2eNArith_2eBinNatDef_2eN_2eleb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2etrue )
          | ( cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt
            & cCoq_2eNArith_2eBinNatDef_2eN_2eleb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2etrue )
          | ( cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt
            & cCoq_2eNArith_2eBinNatDef_2eN_2eleb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ).

fof('$_def_Coq.NArith.BinNatDef.N.sub',axiom,
    ! [V0__n,V1__m] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
     => ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
          & cCoq_2eNArith_2eBinNatDef_2eN_2esub___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eN0 )
        | ? [Vvar__0___24Anonymous__108988] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__108988)
            & ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
             => ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__108988)
                & ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
                    & cCoq_2eNArith_2eBinNatDef_2eN_2esub___24a2(V0__n,V1__m) = V0__n )
                  | ? [Vvar__0___24Anonymous__108993] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__108993)
                      & ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__108988)
                       => ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__108993)
                         => ( V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__108993)
                            & ( ( cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask___24a2(Vvar__0___24Anonymous__108988,Vvar__0___24Anonymous__108993) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNul
                                & cCoq_2eNArith_2eBinNatDef_2eN_2esub___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eN0 )
                              | ? [Vvar__0___24Anonymous__108996] :
                                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__108996)
                                  & cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask___24a2(Vvar__0___24Anonymous__108988,Vvar__0___24Anonymous__108993) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__108996)
                                  & cCoq_2eNArith_2eBinNatDef_2eN_2esub___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__108996) )
                              | ( cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask___24a2(Vvar__0___24Anonymous__108988,Vvar__0___24Anonymous__108993) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNeg
                                & cCoq_2eNArith_2eBinNatDef_2eN_2esub___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eN0 ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('$_def_Coq.NArith.BinNatDef.N.succ_double',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
     => ( ( V0__x = cCoq_2eNumbers_2eBinNums_2eN0
          & cCoq_2eNArith_2eBinNatDef_2eN_2esucc__double___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exH) )
        | ? [Vvar__0___24Anonymous__80051] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__80051)
            & V0__x = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__80051)
            & cCoq_2eNArith_2eBinNatDef_2eN_2esucc__double___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__80051)) ) ) ) ).

fof('$_def_Coq.NArith.BinNatDef.N.t',axiom,
    ! [Vvar__108986] :
      ( cCoq_2eNArith_2eBinNatDef_2eN_2et___24t(Vvar__108986)
    <=> cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__108986) ) ).

fof('$_def_Coq.PArith.BinPos.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__200932] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__200932)
              & V4__n = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__200932)
              & cCoq_2ePArith_2eBinPos_2ePos_2eiter___24a4(V0__A,V1__f,V3__x,V4__n) = happ(V1__f,cCoq_2ePArith_2eBinPos_2ePos_2eiter___24a4(V0__A,V1__f,cCoq_2ePArith_2eBinPos_2ePos_2eiter___24a4(V0__A,V1__f,V3__x,Vvar__0___24Anonymous__200932),Vvar__0___24Anonymous__200932)) )
          | ? [Vvar__0___24Anonymous__200933] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__200933)
              & V4__n = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__200933)
              & cCoq_2ePArith_2eBinPos_2ePos_2eiter___24a4(V0__A,V1__f,V3__x,V4__n) = cCoq_2ePArith_2eBinPos_2ePos_2eiter___24a4(V0__A,V1__f,cCoq_2ePArith_2eBinPos_2ePos_2eiter___24a4(V0__A,V1__f,V3__x,Vvar__0___24Anonymous__200933),Vvar__0___24Anonymous__200933) )
          | ( V4__n = cCoq_2eNumbers_2eBinNums_2exH
            & cCoq_2ePArith_2eBinPos_2ePos_2eiter___24a4(V0__A,V1__f,V3__x,V4__n) = happ(V1__f,V3__x) ) ) ) ) ).

fof('$_def_Coq.PArith.BinPos.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__200944] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__200944)
              & V3__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__200944)
              & cCoq_2ePArith_2eBinPos_2ePos_2eiter__op___24a4(V0__A,V1__op,V3__p,V4__a) = happ(happ(V1__op,V4__a),cCoq_2ePArith_2eBinPos_2ePos_2eiter__op___24a4(V0__A,V1__op,Vvar__0___24Anonymous__200944,happ(happ(V1__op,V4__a),V4__a))) )
          | ? [Vvar__0___24Anonymous__200945] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__200945)
              & V3__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__200945)
              & cCoq_2ePArith_2eBinPos_2ePos_2eiter__op___24a4(V0__A,V1__op,V3__p,V4__a) = cCoq_2ePArith_2eBinPos_2ePos_2eiter__op___24a4(V0__A,V1__op,Vvar__0___24Anonymous__200945,happ(happ(V1__op,V4__a),V4__a)) )
          | ( V3__p = cCoq_2eNumbers_2eBinNums_2exH
            & cCoq_2ePArith_2eBinPos_2ePos_2eiter__op___24a4(V0__A,V1__op,V3__p,V4__a) = V4__a ) ) ) ) ).

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

fof('$_def_Coq.PArith.BinPos.Pos.t',axiom,
    ! [Vvar__200924] :
      ( cCoq_2ePArith_2eBinPos_2ePos_2et___24t(Vvar__200924)
    <=> cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__200924) ) ).

fof('$_def_Coq.PArith.BinPosDef.Pos.add',axiom,
    ! [V2__x,V3__y] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__x)
     => ( ? [Vvar__0___24Anonymous__80267] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__80267)
            & ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
             => ( V2__x = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__80267)
                & ( ? [Vvar__0___24Anonymous__80271] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__80271)
                      & V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__80271)
                      & cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(c_24__fix__80266__1__add__carry___24a2(Vvar__0___24Anonymous__80267,Vvar__0___24Anonymous__80271)) )
                  | ? [Vvar__0___24Anonymous__80272] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__80272)
                      & V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__80272)
                      & cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__80267,Vvar__0___24Anonymous__80272)) )
                  | ( V3__y = cCoq_2eNumbers_2eBinNums_2exH
                    & cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__80267)) ) ) ) ) )
        | ? [Vvar__0___24Anonymous__80273] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__80273)
            & ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
             => ( V2__x = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__80273)
                & ( ? [Vvar__0___24Anonymous__80277] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__80277)
                      & V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__80277)
                      & cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__80273,Vvar__0___24Anonymous__80277)) )
                  | ? [Vvar__0___24Anonymous__80278] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__80278)
                      & V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__80278)
                      & cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__80273,Vvar__0___24Anonymous__80278)) )
                  | ( V3__y = cCoq_2eNumbers_2eBinNums_2exH
                    & cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__80273) ) ) ) ) )
        | ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
         => ( V2__x = cCoq_2eNumbers_2eBinNums_2exH
            & ( ? [Vvar__0___24Anonymous__80279] :
                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__80279)
                  & V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__80279)
                  & cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__80279)) )
              | ? [Vvar__0___24Anonymous__80280] :
                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__80280)
                  & V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__80280)
                  & cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__80280) )
              | ( V3__y = cCoq_2eNumbers_2eBinNums_2exH
                & cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ) ) ) ) ) ).

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

fof('$_def_Coq.PArith.BinPosDef.Pos.div2',axiom,
    ! [V0__p] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
     => ( ? [Vvar__0___24Anonymous__116343] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__116343)
            & V0__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__116343)
            & cCoq_2ePArith_2eBinPosDef_2ePos_2ediv2___24a1(V0__p) = Vvar__0___24Anonymous__116343 )
        | ? [Vvar__0___24Anonymous__116344] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__116344)
            & V0__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__116344)
            & cCoq_2ePArith_2eBinPosDef_2ePos_2ediv2___24a1(V0__p) = Vvar__0___24Anonymous__116344 )
        | ( V0__p = cCoq_2eNumbers_2eBinNums_2exH
          & cCoq_2ePArith_2eBinPosDef_2ePos_2ediv2___24a1(V0__p) = cCoq_2eNumbers_2eBinNums_2exH ) ) ) ).

fof('$_def_Coq.PArith.BinPosDef.Pos.ggcd',axiom,
    ! [V0__a,V1__b] : cCoq_2ePArith_2eBinPosDef_2ePos_2eggcd___24a2(V0__a,V1__b) = cCoq_2ePArith_2eBinPosDef_2ePos_2eggcdn___24a3(cCoq_2eInit_2eNat_2eadd___24a2(cCoq_2ePArith_2eBinPosDef_2ePos_2esize__nat___24a1(V0__a),cCoq_2ePArith_2eBinPosDef_2ePos_2esize__nat___24a1(V1__b)),V0__a,V1__b) ).

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__93885] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__93885)
              & V4__n = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__93885)
              & 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__93885),Vvar__0___24Anonymous__93885)) )
          | ? [Vvar__0___24Anonymous__93886] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__93886)
              & V4__n = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__93886)
              & 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__93886),Vvar__0___24Anonymous__93886) )
          | ( 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__80329] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__80329)
              & V3__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__80329)
              & 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__80329,happ(happ(V1__op,V4__a),V4__a))) )
          | ? [Vvar__0___24Anonymous__80330] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__80330)
              & V3__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__80330)
              & 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__80330,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.leb',axiom,
    ! [V0__x,V1__y] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
     => ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__y)
       => ( ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eEq
            & cCoq_2ePArith_2eBinPosDef_2ePos_2eleb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2etrue )
          | ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt
            & cCoq_2ePArith_2eBinPosDef_2ePos_2eleb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2etrue )
          | ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt
            & cCoq_2ePArith_2eBinPosDef_2ePos_2eleb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ).

fof('$_def_Coq.PArith.BinPosDef.Pos.mul',axiom,
    ! [V1__x,V2__y] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__x)
     => ( ? [Vvar__0___24Anonymous__93881] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__93881)
            & V1__x = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__93881)
            & 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__93881,V2__y))) )
        | ? [Vvar__0___24Anonymous__93882] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__93882)
            & V1__x = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__93882)
            & cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(V1__x,V2__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__93882,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.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__82615] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__82615)
              & cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask___24a2(V0__x,V1__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__82615)
              & cCoq_2ePArith_2eBinPosDef_2ePos_2esub___24a2(V0__x,V1__y) = Vvar__0___24Anonymous__82615 )
          | ( 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.t',axiom,
    ! [Vvar__113595] :
      ( cCoq_2ePArith_2eBinPosDef_2ePos_2et___24t(Vvar__113595)
    <=> cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__113595) ) ).

fof('$_def_Coq.PArith.BinPosDef.Pos.to_nat',axiom,
    ! [V0__x] : cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(V0__x) = cCoq_2ePArith_2eBinPosDef_2ePos_2eiter__op___24a4(cCoq_2eInit_2eDatatypes_2enat,cCoq_2eInit_2eNat_2eadd,V0__x,cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)) ).

fof('$_def_Coq.QArith.QArith_base.Qden',axiom,
    ! [V0__q] :
      ( cCoq_2eQArith_2eQArith__base_2eQ___24t(V0__q)
     => ? [Vvar__0__Qnum__96927] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__Qnum__96927)
          & ? [Vvar__1__Qden__96928] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__Qden__96928)
              & V0__q = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__96927,Vvar__1__Qden__96928)
              & cCoq_2eQArith_2eQArith__base_2eQden___24a1(V0__q) = Vvar__1__Qden__96928 ) ) ) ).

fof('$_def_Coq.QArith.QArith_base.Qnum',axiom,
    ! [V0__q] :
      ( cCoq_2eQArith_2eQArith__base_2eQ___24t(V0__q)
     => ? [Vvar__0__Qnum__96922] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__Qnum__96922)
          & ? [Vvar__1__Qden__96923] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__Qden__96923)
              & V0__q = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__96922,Vvar__1__Qden__96923)
              & cCoq_2eQArith_2eQArith__base_2eQnum___24a1(V0__q) = Vvar__0__Qnum__96922 ) ) ) ).

fof('$_def_Coq.Relations.Relation_Definitions.relation',axiom,
    ! [V0__A] : cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A) = c_24__type__76843___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__76843___24a1(V0__U) ).

fof('$_def_Coq.Strings.Ascii.byte_of_ascii',axiom,
    ! [V0__a] :
      ( cCoq_2eStrings_2eAscii_2eascii___24t(V0__a)
     => ? [Vvar__0___24Anonymous__212639] :
          ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__0___24Anonymous__212639)
          & ? [Vvar__1___24Anonymous__212640] :
              ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__212640)
              & ? [Vvar__2___24Anonymous__212641] :
                  ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__2___24Anonymous__212641)
                  & ? [Vvar__3___24Anonymous__212642] :
                      ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__3___24Anonymous__212642)
                      & ? [Vvar__4___24Anonymous__212643] :
                          ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__4___24Anonymous__212643)
                          & ? [Vvar__5___24Anonymous__212644] :
                              ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__5___24Anonymous__212644)
                              & ? [Vvar__6___24Anonymous__212645] :
                                  ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__6___24Anonymous__212645)
                                  & ? [Vvar__7___24Anonymous__212646] :
                                      ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__7___24Anonymous__212646)
                                      & V0__a = cCoq_2eStrings_2eAscii_2eAscii___24a8(Vvar__0___24Anonymous__212639,Vvar__1___24Anonymous__212640,Vvar__2___24Anonymous__212641,Vvar__3___24Anonymous__212642,Vvar__4___24Anonymous__212643,Vvar__5___24Anonymous__212644,Vvar__6___24Anonymous__212645,Vvar__7___24Anonymous__212646)
                                      & cCoq_2eStrings_2eAscii_2ebyte__of__ascii___24a1(V0__a) = cCoq_2eInit_2eByte_2eof__bits___24a1(cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2ebool)))))),Vvar__0___24Anonymous__212639,cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2ebool))))),Vvar__1___24Anonymous__212640,cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2ebool)))),Vvar__2___24Anonymous__212641,cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2ebool))),Vvar__3___24Anonymous__212642,cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2ebool)),Vvar__4___24Anonymous__212643,cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2ebool),Vvar__5___24Anonymous__212644,cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eInit_2eDatatypes_2ebool,cCoq_2eInit_2eDatatypes_2ebool,Vvar__6___24Anonymous__212645,Vvar__7___24Anonymous__212646)))))))) ) ) ) ) ) ) ) ) ) ).

fof('$_def_Coq.Structures.DecidableTypeEx.N_as_DT.t',axiom,
    ! [Vvar__200889] :
      ( cCoq_2eStructures_2eDecidableTypeEx_2eN__as__DT_2et___24t(Vvar__200889)
    <=> cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__200889) ) ).

fof('$_def_Coq.Structures.DecidableTypeEx.Nat_as_DT.lt',axiom,
    cCoq_2eStructures_2eDecidableTypeEx_2eNat__as__DT_2elt = cCoq_2eInit_2ePeano_2elt ).

fof('$_def_Coq.Structures.DecidableTypeEx.Nat_as_DT.t',axiom,
    ! [Vvar__200661] :
      ( cCoq_2eStructures_2eDecidableTypeEx_2eNat__as__DT_2et___24t(Vvar__200661)
    <=> cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__200661) ) ).

fof('$_def_Coq.Structures.DecidableTypeEx.Positive_as_DT.t',axiom,
    ! [Vvar__200955] :
      ( cCoq_2eStructures_2eDecidableTypeEx_2ePositive__as__DT_2et___24t(Vvar__200955)
    <=> cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__200955) ) ).

fof('$_def_Coq.Structures.DecidableTypeEx.Z_as_DT.t',axiom,
    ! [Vvar__200813] :
      ( cCoq_2eStructures_2eDecidableTypeEx_2eZ__as__DT_2et___24t(Vvar__200813)
    <=> cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__200813) ) ).

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__113592] :
      ( cCoq_2eStructures_2eOrderedTypeEx_2eN__as__OT_2et___24t(Vvar__113592)
    <=> cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__113592) ) ).

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__113593] :
      ( cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2et___24t(Vvar__113593)
    <=> cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__113593) ) ).

fof('$_def_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.bits_lt',axiom,
    ! [V1__p,V2__q] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p)
     => ( ? [Vvar__0___24Anonymous__113577] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__113577)
            & ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__q)
             => ( V1__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__113577)
                & ( ? [Vvar__0___24Anonymous__113581] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__113581)
                      & V2__q = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__113581)
                      & ( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(V1__p,V2__q)
                      <=> cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(Vvar__0___24Anonymous__113577,Vvar__0___24Anonymous__113581) ) )
                  | ? [Vvar__0___24Anonymous__113582] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__113582)
                      & V2__q = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__113582)
                      & ( 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__113583] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__113583)
            & ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__q)
             => ( V1__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__113583)
                & ( ? [Vvar__0___24Anonymous__113587] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__113587)
                      & V2__q = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__113587)
                      & ( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(V1__p,V2__q)
                      <=> p(c_24True) ) )
                  | ? [Vvar__0___24Anonymous__113588] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__113588)
                      & V2__q = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__113588)
                      & ( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(V1__p,V2__q)
                      <=> cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(Vvar__0___24Anonymous__113583,Vvar__0___24Anonymous__113588) ) )
                  | ( 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__113589] :
                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__113589)
                  & V2__q = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__113589)
                  & ( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(V1__p,V2__q)
                  <=> p(c_24True) ) )
              | ? [Vvar__0___24Anonymous__113590] :
                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__113590)
                  & V2__q = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__113590)
                  & ( 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__108939] :
      ( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2et___24t(Vvar__108939)
    <=> cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__108939) ) ).

fof('$_def_Coq.Structures.OrderedTypeEx.Positive_as_OT.t',axiom,
    ! [Vvar__94089] :
      ( cCoq_2eStructures_2eOrderedTypeEx_2ePositive__as__OT_2et___24t(Vvar__94089)
    <=> cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__94089) ) ).

fof('$_def_Coq.Structures.OrderedTypeEx.String_as_OT.t',axiom,
    ! [Vvar__113596] :
      ( cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2et___24t(Vvar__113596)
    <=> cCoq_2eStrings_2eString_2estring___24t(Vvar__113596) ) ).

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

fof('$_def_Coq.Structures.OrderedTypeEx.Z_as_OT.t',axiom,
    ! [Vvar__113616] :
      ( cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2et___24t(Vvar__113616)
    <=> cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__113616) ) ).

fof('$_def_Coq.Vectors.VectorDef.append',axiom,
    ! [V1__A,V2__n,V3__p,V4__v,V5__w] :
      ( cType___24t(V1__A)
     => ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
       => ( cCoq_2eInit_2eDatatypes_2enat___24t(V3__p)
         => ( cCoq_2eVectors_2eVectorDef_2et___24t(V1__A,V2__n,V4__v)
           => ( ( V4__v = cCoq_2eVectors_2eVectorDef_2enil___24a1(V1__A)
                & cCoq_2eVectors_2eVectorDef_2eappend___24a5(V1__A,V2__n,V3__p,V4__v,V5__w) = V5__w )
              | ? [Vvar__1__h__168170] :
                  ( t(Vvar__1__h__168170,V1__A)
                  & ? [Vvar__2__n__168171] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__168171)
                      & ? [Vvar__3___24Anonymous__168172] :
                          ( cCoq_2eVectors_2eVectorDef_2et___24t(V1__A,Vvar__2__n__168171,Vvar__3___24Anonymous__168172)
                          & V4__v = cCoq_2eVectors_2eVectorDef_2econs___24a4(V1__A,Vvar__1__h__168170,Vvar__2__n__168171,Vvar__3___24Anonymous__168172)
                          & cCoq_2eVectors_2eVectorDef_2eappend___24a5(V1__A,V2__n,V3__p,V4__v,V5__w) = cCoq_2eVectors_2eVectorDef_2econs___24a4(V1__A,Vvar__1__h__168170,cCoq_2eInit_2eNat_2eadd___24a2(Vvar__2__n__168171,V3__p),cCoq_2eVectors_2eVectorDef_2eappend___24a5(V1__A,Vvar__2__n__168171,V3__p,Vvar__3___24Anonymous__168172,V5__w)) ) ) ) ) ) ) ) ) ).

fof('$_def_Coq.Vectors.VectorDef.hd',axiom,
    ! [V0__A] : cCoq_2eVectors_2eVectorDef_2ehd___24a1(V0__A) = cCoq_2eVectors_2eVectorDef_2ecaseS___24a3(V0__A,c_24__lam__2102___24a1(V0__A),c_24__lam__2109___24a1(V0__A)) ).

fof('$_def_Coq.Vectors.VectorDef.tl',axiom,
    ! [V0__A] : cCoq_2eVectors_2eVectorDef_2etl___24a1(V0__A) = cCoq_2eVectors_2eVectorDef_2ecaseS___24a3(V0__A,c_24__lam__2119___24a1(V0__A),c_24__lam__2126___24a1(V0__A)) ).

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.ge',axiom,
    ! [V0__x,V1__y] :
      ( p(cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(V0__x,V1__y))
    <=> cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) != cCoq_2eInit_2eDatatypes_2eLt ) ).

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

fof('$_def_Coq.ZArith.BinInt.Z.le',axiom,
    ! [V0__x,V1__y] :
      ( 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.Z.t',axiom,
    ! [Vvar__200812] :
      ( cCoq_2eZArith_2eBinInt_2eZ_2et___24t(Vvar__200812)
    <=> cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__200812) ) ).

fof('$_def_Coq.ZArith.BinInt.Z.zero',axiom,
    cCoq_2eZArith_2eBinInt_2eZ_2ezero = cCoq_2eNumbers_2eBinNums_2eZ0 ).

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__80588] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__80588)
            & V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__80588)
            & cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__80588) )
        | ? [Vvar__0___24Anonymous__80589] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__80589)
            & V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__80589)
            & cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__80589) ) ) ) ).

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__2458] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2458)
            & ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
             => ( V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__2458)
                & ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
                    & cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = V0__x )
                  | ? [Vvar__0___24Anonymous__2462] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2462)
                      & V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__2462)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__2458,Vvar__0___24Anonymous__2462)) )
                  | ? [Vvar__0___24Anonymous__2463] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2463)
                      & V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__2463)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(Vvar__0___24Anonymous__2458,Vvar__0___24Anonymous__2463) ) ) ) ) )
        | ? [Vvar__0___24Anonymous__2464] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2464)
            & ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
             => ( V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__2464)
                & ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
                    & cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = V0__x )
                  | ? [Vvar__0___24Anonymous__2468] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2468)
                      & V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__2468)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(Vvar__0___24Anonymous__2468,Vvar__0___24Anonymous__2464) )
                  | ? [Vvar__0___24Anonymous__2469] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2469)
                      & V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__2469)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__2464,Vvar__0___24Anonymous__2469)) ) ) ) ) ) ) ) ).

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__80571] :
                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__80571)
                  & V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__80571)
                  & cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt )
              | ? [Vvar__0___24Anonymous__80572] :
                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__80572)
                  & V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__80572)
                  & cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt ) ) ) )
        | ? [Vvar__0___24Anonymous__80573] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__80573)
            & ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
             => ( V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__80573)
                & ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
                    & cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt )
                  | ? [Vvar__0___24Anonymous__80577] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__80577)
                      & V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__80577)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__0___24Anonymous__80573,Vvar__0___24Anonymous__80577) )
                  | ? [Vvar__0___24Anonymous__80578] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__80578)
                      & V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__80578)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt ) ) ) ) )
        | ? [Vvar__0___24Anonymous__80579] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__80579)
            & ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
             => ( V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__80579)
                & ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
                    & cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt )
                  | ? [Vvar__0___24Anonymous__80583] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__80583)
                      & V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__80583)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt )
                  | ? [Vvar__0___24Anonymous__80584] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__80584)
                      & V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__80584)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eCompOpp___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__0___24Anonymous__80579,Vvar__0___24Anonymous__80584)) ) ) ) ) ) ) ) ).

fof('$_def_Coq.ZArith.BinIntDef.Z.gcd',axiom,
    ! [V0__a,V1__b] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
     => ( ( V0__a = cCoq_2eNumbers_2eBinNums_2eZ0
          & cCoq_2eZArith_2eBinIntDef_2eZ_2egcd___24a2(V0__a,V1__b) = cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V1__b) )
        | ? [Vvar__0___24Anonymous__111845] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__111845)
            & ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
             => ( V0__a = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__111845)
                & ( ( V1__b = cCoq_2eNumbers_2eBinNums_2eZ0
                    & cCoq_2eZArith_2eBinIntDef_2eZ_2egcd___24a2(V0__a,V1__b) = cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V0__a) )
                  | ? [Vvar__0___24Anonymous__111849] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__111849)
                      & V1__b = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__111849)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2egcd___24a2(V0__a,V1__b) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2egcd___24a2(Vvar__0___24Anonymous__111845,Vvar__0___24Anonymous__111849)) )
                  | ? [Vvar__0___24Anonymous__111850] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__111850)
                      & V1__b = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__111850)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2egcd___24a2(V0__a,V1__b) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2egcd___24a2(Vvar__0___24Anonymous__111845,Vvar__0___24Anonymous__111850)) ) ) ) ) )
        | ? [Vvar__0___24Anonymous__111851] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__111851)
            & ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
             => ( V0__a = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__111851)
                & ( ( V1__b = cCoq_2eNumbers_2eBinNums_2eZ0
                    & cCoq_2eZArith_2eBinIntDef_2eZ_2egcd___24a2(V0__a,V1__b) = cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V0__a) )
                  | ? [Vvar__0___24Anonymous__111855] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__111855)
                      & V1__b = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__111855)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2egcd___24a2(V0__a,V1__b) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2egcd___24a2(Vvar__0___24Anonymous__111851,Vvar__0___24Anonymous__111855)) )
                  | ? [Vvar__0___24Anonymous__111856] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__111856)
                      & V1__b = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__111856)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2egcd___24a2(V0__a,V1__b) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2egcd___24a2(Vvar__0___24Anonymous__111851,Vvar__0___24Anonymous__111856)) ) ) ) ) ) ) ) ).

fof('$_def_Coq.ZArith.BinIntDef.Z.gtb',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_2egtb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efalse )
          | ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt
            & cCoq_2eZArith_2eBinIntDef_2eZ_2egtb___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_2eBinIntDef_2eZ_2egtb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) ).

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.ltb',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_2eltb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efalse )
          | ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt
            & cCoq_2eZArith_2eBinIntDef_2eZ_2eltb___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_2eltb___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.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__2478] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2478)
            & ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
             => ( V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__2478)
                & ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
                    & cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZ0 )
                  | ? [Vvar__0___24Anonymous__2482] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2482)
                      & V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__2482)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__2478,Vvar__0___24Anonymous__2482)) )
                  | ? [Vvar__0___24Anonymous__2483] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2483)
                      & V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__2483)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__2478,Vvar__0___24Anonymous__2483)) ) ) ) ) )
        | ? [Vvar__0___24Anonymous__2484] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2484)
            & ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
             => ( V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__2484)
                & ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
                    & cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZ0 )
                  | ? [Vvar__0___24Anonymous__2488] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2488)
                      & V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__2488)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__2484,Vvar__0___24Anonymous__2488)) )
                  | ? [Vvar__0___24Anonymous__2489] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2489)
                      & V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__2489)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__2484,Vvar__0___24Anonymous__2489)) ) ) ) ) ) ) ) ).

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__116809] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__116809)
            & V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__116809)
            & cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__116809) ) ) ) ).

fof('$_def_Coq.ZArith.BinIntDef.Z.of_int',axiom,
    ! [V0__d] :
      ( cCoq_2eInit_2eDecimal_2eint___24t(V0__d)
     => ( ? [Vvar__0__d__220583] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0__d__220583)
            & V0__d = cCoq_2eInit_2eDecimal_2ePos___24a1(Vvar__0__d__220583)
            & cCoq_2eZArith_2eBinIntDef_2eZ_2eof__int___24a1(V0__d) = cCoq_2eZArith_2eBinIntDef_2eZ_2eof__uint___24a1(Vvar__0__d__220583) )
        | ? [Vvar__0__d__220584] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0__d__220584)
            & V0__d = cCoq_2eInit_2eDecimal_2eNeg___24a1(Vvar__0__d__220584)
            & cCoq_2eZArith_2eBinIntDef_2eZ_2eof__int___24a1(V0__d) = cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__uint___24a1(Vvar__0__d__220584)) ) ) ) ).

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__2491] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__2491)
            & V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__2491)
            & 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__2491)) ) ) ) ).

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__2473] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2473)
            & V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__2473)
            & cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__2473) )
        | ? [Vvar__0___24Anonymous__2474] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2474)
            & V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__2474)
            & cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__2474) ) ) ) ).

fof('$_def_Coq.ZArith.BinIntDef.Z.quotrem',axiom,
    ! [V0__a,V1__b] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
     => ( ( V0__a = cCoq_2eNumbers_2eBinNums_2eZ0
          & cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eNumbers_2eBinNums_2eZ0) )
        | ? [Vvar__0___24Anonymous__2494] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2494)
            & ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
             => ( V0__a = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__2494)
                & ( ( V1__b = cCoq_2eNumbers_2eBinNums_2eZ0
                    & cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ0,V0__a) )
                  | ? [Vvar__0___24Anonymous__2504] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2504)
                      & ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2494)
                       => ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2504)
                         => ( V1__b = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__2504)
                            & ? [Vvar__2___24Anonymous__2512] :
                                ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__2512)
                                & ? [Vvar__3___24Anonymous__2513] :
                                    ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__3___24Anonymous__2513)
                                    & cCoq_2eNArith_2eBinNatDef_2eN_2epos__div__eucl___24a2(Vvar__0___24Anonymous__2494,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__2504)) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN,Vvar__2___24Anonymous__2512,Vvar__3___24Anonymous__2513)
                                    & cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(Vvar__2___24Anonymous__2512),cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(Vvar__3___24Anonymous__2513)) ) ) ) ) ) )
                  | ? [Vvar__0___24Anonymous__2515] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2515)
                      & ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2494)
                       => ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2515)
                         => ( V1__b = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__2515)
                            & ? [Vvar__2___24Anonymous__2523] :
                                ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__2523)
                                & ? [Vvar__3___24Anonymous__2524] :
                                    ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__3___24Anonymous__2524)
                                    & cCoq_2eNArith_2eBinNatDef_2eN_2epos__div__eucl___24a2(Vvar__0___24Anonymous__2494,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__2515)) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN,Vvar__2___24Anonymous__2523,Vvar__3___24Anonymous__2524)
                                    & cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(Vvar__2___24Anonymous__2523)),cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(Vvar__3___24Anonymous__2524)) ) ) ) ) ) ) ) ) ) )
        | ? [Vvar__0___24Anonymous__2526] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2526)
            & ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
             => ( V0__a = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__2526)
                & ( ( V1__b = cCoq_2eNumbers_2eBinNums_2eZ0
                    & cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ0,V0__a) )
                  | ? [Vvar__0___24Anonymous__2536] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2536)
                      & ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2526)
                       => ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2536)
                         => ( V1__b = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__2536)
                            & ? [Vvar__2___24Anonymous__2544] :
                                ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__2544)
                                & ? [Vvar__3___24Anonymous__2545] :
                                    ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__3___24Anonymous__2545)
                                    & cCoq_2eNArith_2eBinNatDef_2eN_2epos__div__eucl___24a2(Vvar__0___24Anonymous__2526,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__2536)) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN,Vvar__2___24Anonymous__2544,Vvar__3___24Anonymous__2545)
                                    & cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(Vvar__2___24Anonymous__2544)),cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(Vvar__3___24Anonymous__2545))) ) ) ) ) ) )
                  | ? [Vvar__0___24Anonymous__2547] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2547)
                      & ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2526)
                       => ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__2547)
                         => ( V1__b = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__2547)
                            & ? [Vvar__2___24Anonymous__2555] :
                                ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__2555)
                                & ? [Vvar__3___24Anonymous__2556] :
                                    ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__3___24Anonymous__2556)
                                    & cCoq_2eNArith_2eBinNatDef_2eN_2epos__div__eucl___24a2(Vvar__0___24Anonymous__2526,cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__2547)) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN,Vvar__2___24Anonymous__2555,Vvar__3___24Anonymous__2556)
                                    & cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem___24a2(V0__a,V1__b) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(Vvar__2___24Anonymous__2555),cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(Vvar__3___24Anonymous__2556))) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('$_def_Coq.ZArith.BinIntDef.Z.sgn',axiom,
    ! [V0__z] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
     => ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
          & cCoq_2eZArith_2eBinIntDef_2eZ_2esgn___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZ0 )
        | ? [Vvar__0___24Anonymous__161929] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__161929)
            & V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__161929)
            & cCoq_2eZArith_2eBinIntDef_2eZ_2esgn___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH) )
        | ? [Vvar__0___24Anonymous__161930] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__161930)
            & V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__161930)
            & cCoq_2eZArith_2eBinIntDef_2eZ_2esgn___24a1(V0__z) = 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__113611] :
      ( cCoq_2eZArith_2eBinIntDef_2eZ_2et___24t(Vvar__113611)
    <=> cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__113611) ) ).

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__113612] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__113612)
            & V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__113612)
            & cCoq_2eZArith_2eBinIntDef_2eZ_2eto__pos___24a1(V0__z) = Vvar__0___24Anonymous__113612 )
        | ? [Vvar__0___24Anonymous__113613] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__113613)
            & V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__113613)
            & 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__108705] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__108705)
            & ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__108705)
             => ( V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__108705)
                & ( ? [Vvar__0___24Anonymous__108709] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__108709)
                      & Vvar__0___24Anonymous__108705 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__108709)
                      & ( cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)
                      <=> p(c_24False) ) )
                  | ? [Vvar__0___24Anonymous__108710] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__108710)
                      & Vvar__0___24Anonymous__108705 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__108710)
                      & ( cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)
                      <=> p(c_24True) ) )
                  | ( Vvar__0___24Anonymous__108705 = cCoq_2eNumbers_2eBinNums_2exH
                    & ( cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)
                    <=> p(c_24False) ) ) ) ) ) )
        | ? [Vvar__0___24Anonymous__108711] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__108711)
            & ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__108711)
             => ( V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__108711)
                & ( ? [Vvar__0___24Anonymous__108715] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__108715)
                      & Vvar__0___24Anonymous__108711 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__108715)
                      & ( cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)
                      <=> p(c_24False) ) )
                  | ? [Vvar__0___24Anonymous__108716] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__108716)
                      & Vvar__0___24Anonymous__108711 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__108716)
                      & ( cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)
                      <=> p(c_24True) ) )
                  | ( Vvar__0___24Anonymous__108711 = 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__113460] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__113460)
            & ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__113460)
             => ( V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__113460)
                & ( ? [Vvar__0___24Anonymous__113464] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__113464)
                      & Vvar__0___24Anonymous__113460 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__113464)
                      & ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
                      <=> p(c_24True) ) )
                  | ? [Vvar__0___24Anonymous__113465] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__113465)
                      & Vvar__0___24Anonymous__113460 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__113465)
                      & ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
                      <=> p(c_24False) ) )
                  | ( Vvar__0___24Anonymous__113460 = cCoq_2eNumbers_2eBinNums_2exH
                    & ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
                    <=> p(c_24True) ) ) ) ) ) )
        | ? [Vvar__0___24Anonymous__113466] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__113466)
            & ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__113466)
             => ( V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__113466)
                & ( ? [Vvar__0___24Anonymous__113470] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__113470)
                      & Vvar__0___24Anonymous__113466 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__113470)
                      & ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
                      <=> p(c_24True) ) )
                  | ? [Vvar__0___24Anonymous__113471] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__113471)
                      & Vvar__0___24Anonymous__113466 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__113471)
                      & ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
                      <=> p(c_24False) ) )
                  | ( Vvar__0___24Anonymous__113466 = 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__113473] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__113473)
            & V1__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__113473)
            & ( cCoq_2eZArith_2eZlogarithm_2eIs__power___24a1(V1__p)
            <=> p(c_24False) ) )
        | ? [Vvar__0___24Anonymous__113474] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__113474)
            & V1__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__113474)
            & ( cCoq_2eZArith_2eZlogarithm_2eIs__power___24a1(V1__p)
            <=> cCoq_2eZArith_2eZlogarithm_2eIs__power___24a1(Vvar__0___24Anonymous__113474) ) )
        | ( V1__p = cCoq_2eNumbers_2eBinNums_2exH
          & ( cCoq_2eZArith_2eZlogarithm_2eIs__power___24a1(V1__p)
          <=> p(c_24True) ) ) ) ) ).

fof('$_def_Coq.ZArith.Zpower.two_power_nat',axiom,
    ! [V0__n] : cCoq_2eZArith_2eZpower_2etwo__power__nat___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eZArith_2eZpower_2eshift__nat___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2exH)) ).

fof('$_def_Coq.ZArith.Zpower.two_power_pos',axiom,
    ! [V0__x] : cCoq_2eZArith_2eZpower_2etwo__power__pos___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eZArith_2eZpower_2eshift__pos___24a2(V0__x,cCoq_2eNumbers_2eBinNums_2exH)) ).

fof('$_def_Coq.micromega.Env.Env',axiom,
    ! [V0__D] : cCoq_2emicromega_2eEnv_2eEnv___24a1(V0__D) = c_24__type__112884___24a1(V0__D) ).

fof('$_def_Coq.micromega.Env.hd',axiom,
    ! [V0__D,V1__e] : cCoq_2emicromega_2eEnv_2ehd___24a2(V0__D,V1__e) = cCoq_2emicromega_2eEnv_2enth___24a3(V0__D,cCoq_2eNumbers_2eBinNums_2exH,V1__e) ).

fof('$_def_Coq.micromega.Env.jump',axiom,
    ! [V0__D,V1__j,V2__e,V3__x] : cCoq_2emicromega_2eEnv_2ejump___24a4(V0__D,V1__j,V2__e,V3__x) = happ(V2__e,cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V3__x,V1__j)) ).

fof('$_def_Coq.micromega.Env.tail',axiom,
    ! [V0__D,V1__e] : cCoq_2emicromega_2eEnv_2etail___24a2(V0__D,V1__e) = cCoq_2emicromega_2eEnv_2ejump___24a3(V0__D,cCoq_2eNumbers_2eBinNums_2exH,V1__e) ).

fof('$_def_Coq.micromega.EnvRing.PsubC',axiom,
    ! [V0__C,V1__csub,V3__P,V4__c] :
      ( cType___24t(V0__C)
     => ( cCoq_2emicromega_2eEnvRing_2ePol___24t(V0__C,V3__P)
       => ( ? [Vvar__1___24Anonymous__94752] :
              ( t(Vvar__1___24Anonymous__94752,V0__C)
              & V3__P = cCoq_2emicromega_2eEnvRing_2ePc___24a2(V0__C,Vvar__1___24Anonymous__94752)
              & cCoq_2emicromega_2eEnvRing_2ePsubC___24a4(V0__C,V1__csub,V3__P,V4__c) = cCoq_2emicromega_2eEnvRing_2ePc___24a2(V0__C,happ(happ(V1__csub,Vvar__1___24Anonymous__94752),V4__c)) )
          | ? [Vvar__1___24Anonymous__94754] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__94754)
              & ? [Vvar__2___24Anonymous__94755] :
                  ( cCoq_2emicromega_2eEnvRing_2ePol___24t(V0__C,Vvar__2___24Anonymous__94755)
                  & V3__P = cCoq_2emicromega_2eEnvRing_2ePinj___24a3(V0__C,Vvar__1___24Anonymous__94754,Vvar__2___24Anonymous__94755)
                  & cCoq_2emicromega_2eEnvRing_2ePsubC___24a4(V0__C,V1__csub,V3__P,V4__c) = cCoq_2emicromega_2eEnvRing_2ePinj___24a3(V0__C,Vvar__1___24Anonymous__94754,cCoq_2emicromega_2eEnvRing_2ePsubC___24a4(V0__C,V1__csub,Vvar__2___24Anonymous__94755,V4__c)) ) )
          | ? [Vvar__1___24Anonymous__94758] :
              ( cCoq_2emicromega_2eEnvRing_2ePol___24t(V0__C,Vvar__1___24Anonymous__94758)
              & ? [Vvar__2___24Anonymous__94759] :
                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__94759)
                  & ? [Vvar__3___24Anonymous__94760] :
                      ( cCoq_2emicromega_2eEnvRing_2ePol___24t(V0__C,Vvar__3___24Anonymous__94760)
                      & V3__P = cCoq_2emicromega_2eEnvRing_2ePX___24a4(V0__C,Vvar__1___24Anonymous__94758,Vvar__2___24Anonymous__94759,Vvar__3___24Anonymous__94760)
                      & cCoq_2emicromega_2eEnvRing_2ePsubC___24a4(V0__C,V1__csub,V3__P,V4__c) = cCoq_2emicromega_2eEnvRing_2ePX___24a4(V0__C,Vvar__1___24Anonymous__94758,Vvar__2___24Anonymous__94759,cCoq_2emicromega_2eEnvRing_2ePsubC___24a4(V0__C,V1__csub,Vvar__3___24Anonymous__94760,V4__c)) ) ) ) ) ) ) ).

fof('$_def_Coq.micromega.EnvRing.mkPinj',axiom,
    ! [V0__C,V1__j,V2__P] :
      ( cType___24t(V0__C)
     => ( cCoq_2emicromega_2eEnvRing_2ePol___24t(V0__C,V2__P)
       => ( ? [Vvar__1___24Anonymous__212811] :
              ( t(Vvar__1___24Anonymous__212811,V0__C)
              & V2__P = cCoq_2emicromega_2eEnvRing_2ePc___24a2(V0__C,Vvar__1___24Anonymous__212811)
              & cCoq_2emicromega_2eEnvRing_2emkPinj___24a3(V0__C,V1__j,V2__P) = V2__P )
          | ? [Vvar__1___24Anonymous__212813] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__212813)
              & ? [Vvar__2___24Anonymous__212814] :
                  ( cCoq_2emicromega_2eEnvRing_2ePol___24t(V0__C,Vvar__2___24Anonymous__212814)
                  & V2__P = cCoq_2emicromega_2eEnvRing_2ePinj___24a3(V0__C,Vvar__1___24Anonymous__212813,Vvar__2___24Anonymous__212814)
                  & cCoq_2emicromega_2eEnvRing_2emkPinj___24a3(V0__C,V1__j,V2__P) = cCoq_2emicromega_2eEnvRing_2ePinj___24a3(V0__C,cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V1__j,Vvar__1___24Anonymous__212813),Vvar__2___24Anonymous__212814) ) )
          | ? [Vvar__1___24Anonymous__212817] :
              ( cCoq_2emicromega_2eEnvRing_2ePol___24t(V0__C,Vvar__1___24Anonymous__212817)
              & ? [Vvar__2___24Anonymous__212818] :
                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__212818)
                  & ? [Vvar__3___24Anonymous__212819] :
                      ( cCoq_2emicromega_2eEnvRing_2ePol___24t(V0__C,Vvar__3___24Anonymous__212819)
                      & V2__P = cCoq_2emicromega_2eEnvRing_2ePX___24a4(V0__C,Vvar__1___24Anonymous__212817,Vvar__2___24Anonymous__212818,Vvar__3___24Anonymous__212819)
                      & cCoq_2emicromega_2eEnvRing_2emkPinj___24a3(V0__C,V1__j,V2__P) = cCoq_2emicromega_2eEnvRing_2ePinj___24a3(V0__C,V1__j,V2__P) ) ) ) ) ) ) ).

fof('$_def_Coq.micromega.EnvRing.mkZmon',axiom,
    ! [V0__j,V1__M] :
      ( cCoq_2emicromega_2eEnvRing_2eMon___24t(V1__M)
     => ( ( V1__M = cCoq_2emicromega_2eEnvRing_2emon0
          & cCoq_2emicromega_2eEnvRing_2emkZmon___24a2(V0__j,V1__M) = cCoq_2emicromega_2eEnvRing_2emon0 )
        | ? [Vvar__0___24Anonymous__213268] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__213268)
            & ? [Vvar__1___24Anonymous__213269] :
                ( cCoq_2emicromega_2eEnvRing_2eMon___24t(Vvar__1___24Anonymous__213269)
                & V1__M = cCoq_2emicromega_2eEnvRing_2ezmon___24a2(Vvar__0___24Anonymous__213268,Vvar__1___24Anonymous__213269)
                & cCoq_2emicromega_2eEnvRing_2emkZmon___24a2(V0__j,V1__M) = cCoq_2emicromega_2eEnvRing_2ezmon___24a2(V0__j,V1__M) ) )
        | ? [Vvar__0___24Anonymous__213271] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__213271)
            & ? [Vvar__1___24Anonymous__213272] :
                ( cCoq_2emicromega_2eEnvRing_2eMon___24t(Vvar__1___24Anonymous__213272)
                & V1__M = cCoq_2emicromega_2eEnvRing_2evmon___24a2(Vvar__0___24Anonymous__213271,Vvar__1___24Anonymous__213272)
                & cCoq_2emicromega_2eEnvRing_2emkZmon___24a2(V0__j,V1__M) = cCoq_2emicromega_2eEnvRing_2ezmon___24a2(V0__j,V1__M) ) ) ) ) ).

fof('$_def_Coq.micromega.EnvRing.zmon_pred',axiom,
    ! [V0__j,V1__M] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__j)
     => ( ? [Vvar__0___24Anonymous__213275] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__213275)
            & V0__j = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__213275)
            & cCoq_2emicromega_2eEnvRing_2ezmon__pred___24a2(V0__j,V1__M) = cCoq_2emicromega_2eEnvRing_2emkZmon___24a2(cCoq_2ePArith_2eBinPosDef_2ePos_2epred___24a1(V0__j),V1__M) )
        | ? [Vvar__0___24Anonymous__213276] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__213276)
            & V0__j = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__213276)
            & cCoq_2emicromega_2eEnvRing_2ezmon__pred___24a2(V0__j,V1__M) = cCoq_2emicromega_2eEnvRing_2emkZmon___24a2(cCoq_2ePArith_2eBinPosDef_2ePos_2epred___24a1(V0__j),V1__M) )
        | ( V0__j = cCoq_2eNumbers_2eBinNums_2exH
          & cCoq_2emicromega_2eEnvRing_2ezmon__pred___24a2(V0__j,V1__M) = V1__M ) ) ) ).

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

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

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

fof('$_def_Coq.micromega.RingMicromega.check_inconsistent',axiom,
    ! [V0__C,V1__cO,V2__ceqb,V3__cleb,V4__f] :
      ( cType___24t(V0__C)
     => ( cCoq_2emicromega_2eRingMicromega_2eNFormula___24t(V0__C,V4__f)
       => ? [Vvar__2___24Anonymous__102831] :
            ( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(V0__C,Vvar__2___24Anonymous__102831)
            & ? [Vvar__3___24Anonymous__102832] :
                ( cCoq_2emicromega_2eRingMicromega_2eOp1___24t(Vvar__3___24Anonymous__102832)
                & ( cType___24t(V0__C)
                 => ( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(V0__C,Vvar__2___24Anonymous__102831)
                   => ( V4__f = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2emicromega_2eRingMicromega_2ePolC___24a1(V0__C),cCoq_2emicromega_2eRingMicromega_2eOp1,Vvar__2___24Anonymous__102831,Vvar__3___24Anonymous__102832)
                      & ( ? [Vvar__1___24Anonymous__102852] :
                            ( t(Vvar__1___24Anonymous__102852,V0__C)
                            & ( cType___24t(V0__C)
                             => ( cCoq_2emicromega_2eRingMicromega_2eOp1___24t(Vvar__3___24Anonymous__102832)
                               => ( Vvar__2___24Anonymous__102831 = cCoq_2emicromega_2eEnvRing_2ePc___24a2(V0__C,Vvar__1___24Anonymous__102852)
                                  & ( ( Vvar__3___24Anonymous__102832 = cCoq_2emicromega_2eRingMicromega_2eEqual
                                      & cCoq_2emicromega_2eRingMicromega_2echeck__inconsistent___24a5(V0__C,V1__cO,V2__ceqb,V3__cleb,V4__f) = cCoq_2emicromega_2eRingMicromega_2ecneqb___24a4(V0__C,V2__ceqb,Vvar__1___24Anonymous__102852,V1__cO) )
                                    | ( Vvar__3___24Anonymous__102832 = cCoq_2emicromega_2eRingMicromega_2eNonEqual
                                      & cCoq_2emicromega_2eRingMicromega_2echeck__inconsistent___24a5(V0__C,V1__cO,V2__ceqb,V3__cleb,V4__f) = happ(happ(V2__ceqb,Vvar__1___24Anonymous__102852),V1__cO) )
                                    | ( Vvar__3___24Anonymous__102832 = cCoq_2emicromega_2eRingMicromega_2eStrict
                                      & cCoq_2emicromega_2eRingMicromega_2echeck__inconsistent___24a5(V0__C,V1__cO,V2__ceqb,V3__cleb,V4__f) = happ(happ(V3__cleb,Vvar__1___24Anonymous__102852),V1__cO) )
                                    | ( Vvar__3___24Anonymous__102832 = cCoq_2emicromega_2eRingMicromega_2eNonStrict
                                      & cCoq_2emicromega_2eRingMicromega_2echeck__inconsistent___24a5(V0__C,V1__cO,V2__ceqb,V3__cleb,V4__f) = cCoq_2emicromega_2eRingMicromega_2ecltb___24a5(V0__C,V2__ceqb,V3__cleb,Vvar__1___24Anonymous__102852,V1__cO) ) ) ) ) ) )
                        | ? [Vvar__1___24Anonymous__102855] :
                            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__102855)
                            & ? [Vvar__2___24Anonymous__102856] :
                                ( cCoq_2emicromega_2eEnvRing_2ePol___24t(V0__C,Vvar__2___24Anonymous__102856)
                                & Vvar__2___24Anonymous__102831 = cCoq_2emicromega_2eEnvRing_2ePinj___24a3(V0__C,Vvar__1___24Anonymous__102855,Vvar__2___24Anonymous__102856)
                                & cCoq_2emicromega_2eRingMicromega_2echeck__inconsistent___24a5(V0__C,V1__cO,V2__ceqb,V3__cleb,V4__f) = cCoq_2eInit_2eDatatypes_2efalse ) )
                        | ? [Vvar__1___24Anonymous__102859] :
                            ( cCoq_2emicromega_2eEnvRing_2ePol___24t(V0__C,Vvar__1___24Anonymous__102859)
                            & ? [Vvar__2___24Anonymous__102860] :
                                ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__102860)
                                & ? [Vvar__3___24Anonymous__102861] :
                                    ( cCoq_2emicromega_2eEnvRing_2ePol___24t(V0__C,Vvar__3___24Anonymous__102861)
                                    & Vvar__2___24Anonymous__102831 = cCoq_2emicromega_2eEnvRing_2ePX___24a4(V0__C,Vvar__1___24Anonymous__102859,Vvar__2___24Anonymous__102860,Vvar__3___24Anonymous__102861)
                                    & cCoq_2emicromega_2eRingMicromega_2echeck__inconsistent___24a5(V0__C,V1__cO,V2__ceqb,V3__cleb,V4__f) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) ) ) ) ) ).

fof('$_def_Coq.micromega.RingMicromega.cltb',axiom,
    ! [V0__C,V1__ceqb,V2__cleb,V3__x,V4__y] : cCoq_2emicromega_2eRingMicromega_2ecltb___24a5(V0__C,V1__ceqb,V2__cleb,V3__x,V4__y) = cCoq_2eInit_2eDatatypes_2eandb___24a2(happ(happ(V2__cleb,V3__x),V4__y),cCoq_2emicromega_2eRingMicromega_2ecneqb___24a4(V0__C,V1__ceqb,V3__x,V4__y)) ).

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_nformula',axiom,
    ! [V0__R,V1__rO,V2__rplus,V3__rtimes,V4__req,V5__rle,V6__rlt,V7__C,V8__phi,V9__env,V10__f] :
      ( cType___24t(V0__R)
     => ( cType___24t(V7__C)
       => ( cCoq_2emicromega_2eRingMicromega_2eNFormula___24t(V7__C,V10__f)
         => ? [Vvar__2___24Anonymous__102512] :
              ( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(V7__C,Vvar__2___24Anonymous__102512)
              & ? [Vvar__3___24Anonymous__102513] :
                  ( cCoq_2emicromega_2eRingMicromega_2eOp1___24t(Vvar__3___24Anonymous__102513)
                  & V10__f = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2emicromega_2eRingMicromega_2ePolC___24a1(V7__C),cCoq_2emicromega_2eRingMicromega_2eOp1,Vvar__2___24Anonymous__102512,Vvar__3___24Anonymous__102513)
                  & ( cCoq_2emicromega_2eRingMicromega_2eeval__nformula___24a11(V0__R,V1__rO,V2__rplus,V3__rtimes,V4__req,V5__rle,V6__rlt,V7__C,V8__phi,V9__env,V10__f)
                  <=> cCoq_2emicromega_2eRingMicromega_2eeval__op1___24a7(V0__R,V1__rO,V4__req,V5__rle,V6__rlt,Vvar__3___24Anonymous__102513,cCoq_2emicromega_2eRingMicromega_2eeval__pol___24a7(V0__R,V2__rplus,V3__rtimes,V7__C,V8__phi,V9__env,Vvar__2___24Anonymous__102512)) ) ) ) ) ) ) ).

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__102430___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__102438___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__102446___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__102454___24a3(V0__R,V1__rO,V3__rle) ) ) ) ) ).

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

fof('$_def_Coq.micromega.RingMicromega.map_option',axiom,
    ! [V0__A,V1__B,V2__f,V3__o] :
      ( cType___24t(V0__A)
     => ( cType___24t(V1__B)
       => ( cCoq_2eInit_2eDatatypes_2eoption___24t(V0__A,V3__o)
         => ( ? [Vvar__1___24Anonymous__214627] :
                ( t(Vvar__1___24Anonymous__214627,V0__A)
                & V3__o = cCoq_2eInit_2eDatatypes_2eSome___24a2(V0__A,Vvar__1___24Anonymous__214627)
                & cCoq_2emicromega_2eRingMicromega_2emap__option___24a4(V0__A,V1__B,V2__f,V3__o) = happ(V2__f,Vvar__1___24Anonymous__214627) )
            | ( V3__o = cCoq_2eInit_2eDatatypes_2eNone___24a1(V0__A)
              & cCoq_2emicromega_2eRingMicromega_2emap__option___24a4(V0__A,V1__B,V2__f,V3__o) = cCoq_2eInit_2eDatatypes_2eNone___24a1(V1__B) ) ) ) ) ) ).

fof('$_def_Coq.micromega.RingMicromega.map_option2',axiom,
    ! [V0__A,V1__B,V2__C,V3__f,V4__o,V5__o_27] :
      ( cType___24t(V0__A)
     => ( cType___24t(V1__B)
       => ( cType___24t(V2__C)
         => ( cCoq_2eInit_2eDatatypes_2eoption___24t(V0__A,V4__o)
           => ( ? [Vvar__1___24Anonymous__214645] :
                  ( t(Vvar__1___24Anonymous__214645,V0__A)
                  & ( cType___24t(V0__A)
                   => ( cType___24t(V1__B)
                     => ( cType___24t(V2__C)
                       => ( cCoq_2eInit_2eDatatypes_2eoption___24t(V1__B,V5__o_27)
                         => ( V4__o = cCoq_2eInit_2eDatatypes_2eSome___24a2(V0__A,Vvar__1___24Anonymous__214645)
                            & ( ? [Vvar__1___24Anonymous__214650] :
                                  ( t(Vvar__1___24Anonymous__214650,V1__B)
                                  & V5__o_27 = cCoq_2eInit_2eDatatypes_2eSome___24a2(V1__B,Vvar__1___24Anonymous__214650)
                                  & cCoq_2emicromega_2eRingMicromega_2emap__option2___24a6(V0__A,V1__B,V2__C,V3__f,V4__o,V5__o_27) = happ(happ(V3__f,Vvar__1___24Anonymous__214645),Vvar__1___24Anonymous__214650) )
                              | ( V5__o_27 = cCoq_2eInit_2eDatatypes_2eNone___24a1(V1__B)
                                & cCoq_2emicromega_2eRingMicromega_2emap__option2___24a6(V0__A,V1__B,V2__C,V3__f,V4__o,V5__o_27) = cCoq_2eInit_2eDatatypes_2eNone___24a1(V2__C) ) ) ) ) ) ) ) )
              | ( V4__o = cCoq_2eInit_2eDatatypes_2eNone___24a1(V0__A)
                & cCoq_2emicromega_2eRingMicromega_2emap__option2___24a6(V0__A,V1__B,V2__C,V3__f,V4__o,V5__o_27) = cCoq_2eInit_2eDatatypes_2eNone___24a1(V2__C) ) ) ) ) ) ) ).

fof('$_def_Coq.micromega.RingMicromega.padd',axiom,
    ! [V0__C,V1__cO,V2__cplus,V3__ceqb] : cCoq_2emicromega_2eRingMicromega_2epadd___24a4(V0__C,V1__cO,V2__cplus,V3__ceqb) = cCoq_2emicromega_2eEnvRing_2ePadd___24a4(V0__C,V1__cO,V2__cplus,V3__ceqb) ).

fof('$_def_Coq.micromega.RingMicromega.psub',axiom,
    ! [V0__C,V1__cO,V2__cplus,V3__cminus,V4__copp,V5__ceqb] : cCoq_2emicromega_2eRingMicromega_2epsub___24a6(V0__C,V1__cO,V2__cplus,V3__cminus,V4__copp,V5__ceqb) = cCoq_2emicromega_2eEnvRing_2ePsub___24a6(V0__C,V1__cO,V2__cplus,V3__cminus,V4__copp,V5__ceqb) ).

fof('$_def_Coq.micromega.RingMicromega.psubC',axiom,
    ! [V0__C,V1__cminus] : cCoq_2emicromega_2eRingMicromega_2epsubC___24a2(V0__C,V1__cminus) = cCoq_2emicromega_2eEnvRing_2ePsubC___24a2(V0__C,V1__cminus) ).

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

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

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

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

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

fof('$_def_Coq.micromega.ZMicromega.Vars.E.bits_lt',axiom,
    ! [V1__p,V2__q] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p)
     => ( ? [Vvar__0___24Anonymous__200873] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__200873)
            & ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__q)
             => ( V1__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__200873)
                & ( ? [Vvar__0___24Anonymous__200877] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__200877)
                      & V2__q = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__200877)
                      & ( cCoq_2emicromega_2eZMicromega_2eVars_2eE_2ebits__lt___24a2(V1__p,V2__q)
                      <=> cCoq_2emicromega_2eZMicromega_2eVars_2eE_2ebits__lt___24a2(Vvar__0___24Anonymous__200873,Vvar__0___24Anonymous__200877) ) )
                  | ? [Vvar__0___24Anonymous__200878] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__200878)
                      & V2__q = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__200878)
                      & ( cCoq_2emicromega_2eZMicromega_2eVars_2eE_2ebits__lt___24a2(V1__p,V2__q)
                      <=> p(c_24False) ) )
                  | ( V2__q = cCoq_2eNumbers_2eBinNums_2exH
                    & ( cCoq_2emicromega_2eZMicromega_2eVars_2eE_2ebits__lt___24a2(V1__p,V2__q)
                    <=> p(c_24False) ) ) ) ) ) )
        | ? [Vvar__0___24Anonymous__200879] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__200879)
            & ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__q)
             => ( V1__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__200879)
                & ( ? [Vvar__0___24Anonymous__200883] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__200883)
                      & V2__q = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__200883)
                      & ( cCoq_2emicromega_2eZMicromega_2eVars_2eE_2ebits__lt___24a2(V1__p,V2__q)
                      <=> p(c_24True) ) )
                  | ? [Vvar__0___24Anonymous__200884] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__200884)
                      & V2__q = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__200884)
                      & ( cCoq_2emicromega_2eZMicromega_2eVars_2eE_2ebits__lt___24a2(V1__p,V2__q)
                      <=> cCoq_2emicromega_2eZMicromega_2eVars_2eE_2ebits__lt___24a2(Vvar__0___24Anonymous__200879,Vvar__0___24Anonymous__200884) ) )
                  | ( V2__q = cCoq_2eNumbers_2eBinNums_2exH
                    & ( cCoq_2emicromega_2eZMicromega_2eVars_2eE_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__200885] :
                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__200885)
                  & V2__q = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__200885)
                  & ( cCoq_2emicromega_2eZMicromega_2eVars_2eE_2ebits__lt___24a2(V1__p,V2__q)
                  <=> p(c_24True) ) )
              | ? [Vvar__0___24Anonymous__200886] :
                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__200886)
                  & V2__q = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__200886)
                  & ( cCoq_2emicromega_2eZMicromega_2eVars_2eE_2ebits__lt___24a2(V1__p,V2__q)
                  <=> p(c_24False) ) )
              | ( V2__q = cCoq_2eNumbers_2eBinNums_2exH
                & ( cCoq_2emicromega_2eZMicromega_2eVars_2eE_2ebits__lt___24a2(V1__p,V2__q)
                <=> p(c_24False) ) ) ) ) ) ) ) ).

fof('$_def_Coq.micromega.ZMicromega.Vars.E.t',axiom,
    ! [Vvar__200870] :
      ( cCoq_2emicromega_2eZMicromega_2eVars_2eE_2et___24t(Vvar__200870)
    <=> cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__200870) ) ).

fof('$_def_Coq.micromega.ZMicromega.Vars.elt',axiom,
    ! [Vvar__200960] :
      ( cCoq_2emicromega_2eZMicromega_2eVars_2eelt___24t(Vvar__200960)
    <=> cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__200960) ) ).

fof('$_def_Coq.micromega.ZMicromega.ZWitness',axiom,
    ! [Vvar__83794] :
      ( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__83794)
    <=> cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(cCoq_2eNumbers_2eBinNums_2eZ,Vvar__83794) ) ).

fof('$_def_Coq.micromega.ZMicromega.Zdiv_pol',axiom,
    ! [V1__p,V2__x] :
      ( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(cCoq_2eNumbers_2eBinNums_2eZ,V1__p)
     => ( ? [Vvar__1___24Anonymous__218513] :
            ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__1___24Anonymous__218513)
            & V1__p = cCoq_2emicromega_2eEnvRing_2ePc___24a2(cCoq_2eNumbers_2eBinNums_2eZ,Vvar__1___24Anonymous__218513)
            & cCoq_2emicromega_2eZMicromega_2eZdiv__pol___24a2(V1__p,V2__x) = cCoq_2emicromega_2eEnvRing_2ePc___24a2(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(Vvar__1___24Anonymous__218513,V2__x)) )
        | ? [Vvar__1___24Anonymous__218515] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__218515)
            & ? [Vvar__2___24Anonymous__218516] :
                ( cCoq_2emicromega_2eEnvRing_2ePol___24t(cCoq_2eNumbers_2eBinNums_2eZ,Vvar__2___24Anonymous__218516)
                & V1__p = cCoq_2emicromega_2eEnvRing_2ePinj___24a3(cCoq_2eNumbers_2eBinNums_2eZ,Vvar__1___24Anonymous__218515,Vvar__2___24Anonymous__218516)
                & cCoq_2emicromega_2eZMicromega_2eZdiv__pol___24a2(V1__p,V2__x) = cCoq_2emicromega_2eEnvRing_2ePinj___24a3(cCoq_2eNumbers_2eBinNums_2eZ,Vvar__1___24Anonymous__218515,cCoq_2emicromega_2eZMicromega_2eZdiv__pol___24a2(Vvar__2___24Anonymous__218516,V2__x)) ) )
        | ? [Vvar__1___24Anonymous__218519] :
            ( cCoq_2emicromega_2eEnvRing_2ePol___24t(cCoq_2eNumbers_2eBinNums_2eZ,Vvar__1___24Anonymous__218519)
            & ? [Vvar__2___24Anonymous__218520] :
                ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__218520)
                & ? [Vvar__3___24Anonymous__218521] :
                    ( cCoq_2emicromega_2eEnvRing_2ePol___24t(cCoq_2eNumbers_2eBinNums_2eZ,Vvar__3___24Anonymous__218521)
                    & V1__p = cCoq_2emicromega_2eEnvRing_2ePX___24a4(cCoq_2eNumbers_2eBinNums_2eZ,Vvar__1___24Anonymous__218519,Vvar__2___24Anonymous__218520,Vvar__3___24Anonymous__218521)
                    & cCoq_2emicromega_2eZMicromega_2eZdiv__pol___24a2(V1__p,V2__x) = cCoq_2emicromega_2eEnvRing_2ePX___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2emicromega_2eZMicromega_2eZdiv__pol___24a2(Vvar__1___24Anonymous__218519,V2__x),Vvar__2___24Anonymous__218520,cCoq_2emicromega_2eZMicromega_2eZdiv__pol___24a2(Vvar__3___24Anonymous__218521,V2__x)) ) ) ) ) ) ).

fof('$_def_Coq.micromega.ZMicromega.ZgcdM',axiom,
    ! [V0__x,V1__y] : cCoq_2emicromega_2eZMicromega_2eZgcdM___24a2(V0__x,V1__y) = cCoq_2eZArith_2eBinIntDef_2eZ_2emax___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2egcd___24a2(V0__x,V1__y),cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) ).

fof('$_def_Coq.micromega.ZMicromega.Zgcd_pol',axiom,
    ! [V1__p] :
      ( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(cCoq_2eNumbers_2eBinNums_2eZ,V1__p)
     => ( ? [Vvar__1___24Anonymous__199983] :
            ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__1___24Anonymous__199983)
            & V1__p = cCoq_2emicromega_2eEnvRing_2ePc___24a2(cCoq_2eNumbers_2eBinNums_2eZ,Vvar__1___24Anonymous__199983)
            & cCoq_2emicromega_2eZMicromega_2eZgcd__pol___24a1(V1__p) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ0,Vvar__1___24Anonymous__199983) )
        | ? [Vvar__1___24Anonymous__199985] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__199985)
            & ? [Vvar__2___24Anonymous__199986] :
                ( cCoq_2emicromega_2eEnvRing_2ePol___24t(cCoq_2eNumbers_2eBinNums_2eZ,Vvar__2___24Anonymous__199986)
                & V1__p = cCoq_2emicromega_2eEnvRing_2ePinj___24a3(cCoq_2eNumbers_2eBinNums_2eZ,Vvar__1___24Anonymous__199985,Vvar__2___24Anonymous__199986)
                & cCoq_2emicromega_2eZMicromega_2eZgcd__pol___24a1(V1__p) = cCoq_2emicromega_2eZMicromega_2eZgcd__pol___24a1(Vvar__2___24Anonymous__199986) ) )
        | ? [Vvar__1___24Anonymous__199989] :
            ( cCoq_2emicromega_2eEnvRing_2ePol___24t(cCoq_2eNumbers_2eBinNums_2eZ,Vvar__1___24Anonymous__199989)
            & ? [Vvar__2___24Anonymous__199990] :
                ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__199990)
                & ? [Vvar__3___24Anonymous__199991] :
                    ( cCoq_2emicromega_2eEnvRing_2ePol___24t(cCoq_2eNumbers_2eBinNums_2eZ,Vvar__3___24Anonymous__199991)
                    & ( cCoq_2emicromega_2eEnvRing_2ePol___24t(cCoq_2eNumbers_2eBinNums_2eZ,Vvar__1___24Anonymous__199989)
                     => ( V1__p = cCoq_2emicromega_2eEnvRing_2ePX___24a4(cCoq_2eNumbers_2eBinNums_2eZ,Vvar__1___24Anonymous__199989,Vvar__2___24Anonymous__199990,Vvar__3___24Anonymous__199991)
                        & ? [Vvar__2___24Anonymous__200017] :
                            ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2___24Anonymous__200017)
                            & ? [Vvar__3___24Anonymous__200018] :
                                ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3___24Anonymous__200018)
                                & ( cCoq_2emicromega_2eEnvRing_2ePol___24t(cCoq_2eNumbers_2eBinNums_2eZ,Vvar__3___24Anonymous__199991)
                                 => ( cCoq_2emicromega_2eZMicromega_2eZgcd__pol___24a1(Vvar__1___24Anonymous__199989) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,Vvar__2___24Anonymous__200017,Vvar__3___24Anonymous__200018)
                                    & ? [Vvar__2___24Anonymous__200030] :
                                        ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2___24Anonymous__200030)
                                        & ? [Vvar__3___24Anonymous__200031] :
                                            ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3___24Anonymous__200031)
                                            & cCoq_2emicromega_2eZMicromega_2eZgcd__pol___24a1(Vvar__3___24Anonymous__199991) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,Vvar__2___24Anonymous__200030,Vvar__3___24Anonymous__200031)
                                            & cCoq_2emicromega_2eZMicromega_2eZgcd__pol___24a1(V1__p) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2emicromega_2eZMicromega_2eZgcdM___24a2(cCoq_2emicromega_2eZMicromega_2eZgcdM___24a2(Vvar__2___24Anonymous__200017,Vvar__3___24Anonymous__200018),Vvar__2___24Anonymous__200030),Vvar__3___24Anonymous__200031) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('$_def_Coq.micromega.ZMicromega.ceiling',axiom,
    ! [V0__a,V1__b] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
     => ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
       => ? [Vvar__2___24Anonymous__218498] :
            ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2___24Anonymous__218498)
            & ? [Vvar__3___24Anonymous__218499] :
                ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3___24Anonymous__218499)
                & ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3___24Anonymous__218499)
                 => ( 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__218498,Vvar__3___24Anonymous__218499)
                    & ( ( Vvar__3___24Anonymous__218499 = cCoq_2eNumbers_2eBinNums_2eZ0
                        & cCoq_2emicromega_2eZMicromega_2eceiling___24a2(V0__a,V1__b) = Vvar__2___24Anonymous__218498 )
                      | ? [Vvar__0___24Anonymous__218507] :
                          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__218507)
                          & Vvar__3___24Anonymous__218499 = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__218507)
                          & cCoq_2emicromega_2eZMicromega_2eceiling___24a2(V0__a,V1__b) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(Vvar__2___24Anonymous__218498,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) )
                      | ? [Vvar__0___24Anonymous__218508] :
                          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__218508)
                          & Vvar__3___24Anonymous__218499 = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__218508)
                          & cCoq_2emicromega_2eZMicromega_2eceiling___24a2(V0__a,V1__b) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(Vvar__2___24Anonymous__218498,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) ) ) ) ) ) ) ) ) ).

fof('$_def_Coq.micromega.ZMicromega.eval_nformula',axiom,
    cCoq_2emicromega_2eZMicromega_2eeval__nformula = cCoq_2emicromega_2eRingMicromega_2eeval__nformula___24a9(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd,cCoq_2eZArith_2eBinIntDef_2eZ_2emul,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eZ),cCoq_2eZArith_2eBinInt_2eZ_2ele,cCoq_2eZArith_2eBinInt_2eZ_2elt,cCoq_2eNumbers_2eBinNums_2eZ,c_24__lam__108016) ).

fof('$_def_Coq.micromega.ZMicromega.eval_pol',axiom,
    cCoq_2emicromega_2eZMicromega_2eeval__pol = cCoq_2emicromega_2eRingMicromega_2eeval__pol___24a5(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd,cCoq_2eZArith_2eBinIntDef_2eZ_2emul,cCoq_2eNumbers_2eBinNums_2eZ,c_24__lam__108016) ).

fof('$_def_Coq.micromega.ZMicromega.padd',axiom,
    cCoq_2emicromega_2eZMicromega_2epadd = cCoq_2emicromega_2eRingMicromega_2epadd___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd,cCoq_2eZArith_2eZbool_2eZeq__bool) ).

fof('$_def_Coq.micromega.ZMicromega.valid_cut_sign',axiom,
    ! [V0__op] :
      ( cCoq_2emicromega_2eRingMicromega_2eOp1___24t(V0__op)
     => ( ( V0__op = cCoq_2emicromega_2eRingMicromega_2eEqual
          & cCoq_2emicromega_2eZMicromega_2evalid__cut__sign___24a1(V0__op) = cCoq_2eInit_2eDatatypes_2etrue )
        | ( V0__op = cCoq_2emicromega_2eRingMicromega_2eNonEqual
          & cCoq_2emicromega_2eZMicromega_2evalid__cut__sign___24a1(V0__op) = cCoq_2eInit_2eDatatypes_2efalse )
        | ( V0__op = cCoq_2emicromega_2eRingMicromega_2eStrict
          & cCoq_2emicromega_2eZMicromega_2evalid__cut__sign___24a1(V0__op) = cCoq_2eInit_2eDatatypes_2efalse )
        | ( V0__op = cCoq_2emicromega_2eRingMicromega_2eNonStrict
          & cCoq_2emicromega_2eZMicromega_2evalid__cut__sign___24a1(V0__op) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ).

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__112941] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__112941)
              & ( cType___24t(V0__R)
               => ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__112941)
                 => ( V5__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__112941)
                    & ( ? [Vvar__0___24Anonymous__112945] :
                          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__112945)
                          & Vvar__0___24Anonymous__112941 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__112945)
                          & 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__112941))) )
                      | ? [Vvar__0___24Anonymous__112946] :
                          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__112946)
                          & Vvar__0___24Anonymous__112941 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__112946)
                          & 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__112941))) )
                      | ( Vvar__0___24Anonymous__112941 = 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__112947] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__112947)
              & ( cType___24t(V0__R)
               => ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__112947)
                 => ( V5__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__112947)
                    & ( ? [Vvar__0___24Anonymous__112951] :
                          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__112951)
                          & Vvar__0___24Anonymous__112947 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__112951)
                          & 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__112947)) )
                      | ? [Vvar__0___24Anonymous__112952] :
                          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__112952)
                          & Vvar__0___24Anonymous__112947 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__112952)
                          & 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__112947)) )
                      | ( Vvar__0___24Anonymous__112947 = 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__112908] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__112908)
              & V5__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__112908)
              & 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__112908))) )
          | ? [Vvar__0___24Anonymous__112909] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__112909)
              & V5__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__112909)
              & 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__112909)) )
          | ( 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.triv_div',axiom,
    ! [V0__C,V1__cO,V2__cI,V3__ceqb,V4__x,V5__y] :
      ( cType___24t(V0__C)
     => ( c_24__type__1372___24t(V0__C,V3__ceqb)
       => ( t(V4__x,V0__C)
         => ( t(V5__y,V0__C)
           => ( ( happ(happ(V3__ceqb,V4__x),V5__y) = cCoq_2eInit_2eDatatypes_2etrue
                & cCoq_2esetoid__ring_2eInitialRing_2etriv__div___24a6(V0__C,V1__cO,V2__cI,V3__ceqb,V4__x,V5__y) = cCoq_2eInit_2eDatatypes_2epair___24a4(V0__C,V0__C,V2__cI,V1__cO) )
              | ( happ(happ(V3__ceqb,V4__x),V5__y) = cCoq_2eInit_2eDatatypes_2efalse
                & cCoq_2esetoid__ring_2eInitialRing_2etriv__div___24a6(V0__C,V1__cO,V2__cI,V3__ceqb,V4__x,V5__y) = cCoq_2eInit_2eDatatypes_2epair___24a4(V0__C,V0__C,V1__cO,V4__x) ) ) ) ) ) ) ).

fof('$_def_Coq.setoid_ring.Ring_polynom.P0',axiom,
    ! [V0__C,V1__cO] : cCoq_2esetoid__ring_2eRing__polynom_2eP0___24a2(V0__C,V1__cO) = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V0__C,V1__cO) ).

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__1257] :
              ( t(Vvar__1___24Anonymous__1257,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__1257)
                    & ( ? [Vvar__1___24Anonymous__1267] :
                          ( t(Vvar__1___24Anonymous__1267,V0__C)
                          & V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V0__C,Vvar__1___24Anonymous__1267)
                          & cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = happ(happ(V1__ceqb,Vvar__1___24Anonymous__1257),Vvar__1___24Anonymous__1267) )
                      | ? [Vvar__1___24Anonymous__1269] :
                          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__1269)
                          & ? [Vvar__2___24Anonymous__1270] :
                              ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__1270)
                              & V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V0__C,Vvar__1___24Anonymous__1269,Vvar__2___24Anonymous__1270)
                              & cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) )
                      | ? [Vvar__1___24Anonymous__1273] :
                          ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__1273)
                          & ? [Vvar__2___24Anonymous__1274] :
                              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__1274)
                              & ? [Vvar__3___24Anonymous__1275] :
                                  ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__1275)
                                  & V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V0__C,Vvar__1___24Anonymous__1273,Vvar__2___24Anonymous__1274,Vvar__3___24Anonymous__1275)
                                  & cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) )
          | ? [Vvar__1___24Anonymous__1280] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__1280)
              & ? [Vvar__2___24Anonymous__1281] :
                  ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__1281)
                  & ( 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__1280,Vvar__2___24Anonymous__1281)
                        & ( ? [Vvar__1___24Anonymous__1301] :
                              ( t(Vvar__1___24Anonymous__1301,V0__C)
                              & V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V0__C,Vvar__1___24Anonymous__1301)
                              & cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse )
                          | ? [Vvar__1___24Anonymous__1303] :
                              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__1303)
                              & ? [Vvar__2___24Anonymous__1304] :
                                  ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__1304)
                                  & ( cType___24t(V0__C)
                                   => ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__1280)
                                     => ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__1303)
                                       => ( V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V0__C,Vvar__1___24Anonymous__1303,Vvar__2___24Anonymous__1304)
                                          & ( ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__1___24Anonymous__1280,Vvar__1___24Anonymous__1303) = 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__1281,Vvar__2___24Anonymous__1304) )
                                            | ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__1___24Anonymous__1280,Vvar__1___24Anonymous__1303) = 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__1280,Vvar__1___24Anonymous__1303) = 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__1309] :
                              ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__1309)
                              & ? [Vvar__2___24Anonymous__1310] :
                                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__1310)
                                  & ? [Vvar__3___24Anonymous__1311] :
                                      ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__1311)
                                      & V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V0__C,Vvar__1___24Anonymous__1309,Vvar__2___24Anonymous__1310,Vvar__3___24Anonymous__1311)
                                      & cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) ) )
          | ? [Vvar__1___24Anonymous__1316] :
              ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__1316)
              & ? [Vvar__2___24Anonymous__1317] :
                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__1317)
                  & ? [Vvar__3___24Anonymous__1318] :
                      ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__1318)
                      & ( 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__1316,Vvar__2___24Anonymous__1317,Vvar__3___24Anonymous__1318)
                            & ( ? [Vvar__1___24Anonymous__1351] :
                                  ( t(Vvar__1___24Anonymous__1351,V0__C)
                                  & V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V0__C,Vvar__1___24Anonymous__1351)
                                  & cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse )
                              | ? [Vvar__1___24Anonymous__1353] :
                                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__1353)
                                  & ? [Vvar__2___24Anonymous__1354] :
                                      ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__1354)
                                      & V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V0__C,Vvar__1___24Anonymous__1353,Vvar__2___24Anonymous__1354)
                                      & cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) )
                              | ? [Vvar__1___24Anonymous__1357] :
                                  ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__1357)
                                  & ? [Vvar__2___24Anonymous__1358] :
                                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__1358)
                                      & ? [Vvar__3___24Anonymous__1359] :
                                          ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__1359)
                                          & ( cType___24t(V0__C)
                                           => ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__1317)
                                             => ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__1358)
                                               => ( V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V0__C,Vvar__1___24Anonymous__1357,Vvar__2___24Anonymous__1358,Vvar__3___24Anonymous__1359)
                                                  & ( ( cType___24t(V0__C)
                                                     => ( c_24__type__1372___24t(V0__C,V1__ceqb)
                                                       => ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__1316)
                                                         => ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__1357)
                                                           => ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__2___24Anonymous__1317,Vvar__2___24Anonymous__1358) = cCoq_2eInit_2eDatatypes_2eEq
                                                              & ( ( cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,Vvar__1___24Anonymous__1316,Vvar__1___24Anonymous__1357) = 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__1318,Vvar__3___24Anonymous__1359) )
                                                                | ( cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,Vvar__1___24Anonymous__1316,Vvar__1___24Anonymous__1357) = 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__1317,Vvar__2___24Anonymous__1358) = 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__1317,Vvar__2___24Anonymous__1358) = 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.add_pow_list',axiom,
    ! [V0__R,V1__r,V2__n,V3__l] :
      ( cType___24t(V0__R)
     => ( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__n)
       => ( ( V2__n = cCoq_2eNumbers_2eBinNums_2eN0
            & cCoq_2esetoid__ring_2eRing__polynom_2eadd__pow__list___24a4(V0__R,V1__r,V2__n,V3__l) = V3__l )
          | ? [Vvar__0___24Anonymous__216908] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__216908)
              & V2__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__216908)
              & cCoq_2esetoid__ring_2eRing__polynom_2eadd__pow__list___24a4(V0__R,V1__r,V2__n,V3__l) = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__R,cCoq_2eNumbers_2eBinNums_2epositive),cCoq_2eInit_2eDatatypes_2epair___24a4(V0__R,cCoq_2eNumbers_2eBinNums_2epositive,V1__r,Vvar__0___24Anonymous__216908),V3__l) ) ) ) ) ).

fof('$_def_Coq.setoid_ring.Ring_polynom.mkPinj',axiom,
    ! [V0__C,V1__j,V2__P] :
      ( cType___24t(V0__C)
     => ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,V2__P)
       => ( ? [Vvar__1___24Anonymous__216147] :
              ( t(Vvar__1___24Anonymous__216147,V0__C)
              & V2__P = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V0__C,Vvar__1___24Anonymous__216147)
              & cCoq_2esetoid__ring_2eRing__polynom_2emkPinj___24a3(V0__C,V1__j,V2__P) = V2__P )
          | ? [Vvar__1___24Anonymous__216149] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__216149)
              & ? [Vvar__2___24Anonymous__216150] :
                  ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__216150)
                  & V2__P = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V0__C,Vvar__1___24Anonymous__216149,Vvar__2___24Anonymous__216150)
                  & cCoq_2esetoid__ring_2eRing__polynom_2emkPinj___24a3(V0__C,V1__j,V2__P) = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V0__C,cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V1__j,Vvar__1___24Anonymous__216149),Vvar__2___24Anonymous__216150) ) )
          | ? [Vvar__1___24Anonymous__216153] :
              ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__216153)
              & ? [Vvar__2___24Anonymous__216154] :
                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__216154)
                  & ? [Vvar__3___24Anonymous__216155] :
                      ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__216155)
                      & V2__P = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V0__C,Vvar__1___24Anonymous__216153,Vvar__2___24Anonymous__216154,Vvar__3___24Anonymous__216155)
                      & cCoq_2esetoid__ring_2eRing__polynom_2emkPinj___24a3(V0__C,V1__j,V2__P) = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V0__C,V1__j,V2__P) ) ) ) ) ) ) ).

fof('$_def_Coq.setoid_ring.Ring_polynom.mkZmon',axiom,
    ! [V0__j,V1__M] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(V1__M)
     => ( ( V1__M = cCoq_2esetoid__ring_2eRing__polynom_2emon0
          & cCoq_2esetoid__ring_2eRing__polynom_2emkZmon___24a2(V0__j,V1__M) = cCoq_2esetoid__ring_2eRing__polynom_2emon0 )
        | ? [Vvar__0___24Anonymous__216211] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__216211)
            & ? [Vvar__1___24Anonymous__216212] :
                ( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(Vvar__1___24Anonymous__216212)
                & V1__M = cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__216211,Vvar__1___24Anonymous__216212)
                & cCoq_2esetoid__ring_2eRing__polynom_2emkZmon___24a2(V0__j,V1__M) = cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(V0__j,V1__M) ) )
        | ? [Vvar__0___24Anonymous__216214] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__216214)
            & ? [Vvar__1___24Anonymous__216215] :
                ( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(Vvar__1___24Anonymous__216215)
                & V1__M = cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(Vvar__0___24Anonymous__216214,Vvar__1___24Anonymous__216215)
                & cCoq_2esetoid__ring_2eRing__polynom_2emkZmon___24a2(V0__j,V1__M) = cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(V0__j,V1__M) ) ) ) ) ).

fof('$_def_Coq.setoid_ring.Ring_polynom.mk_monpol_list',axiom,
    ! [V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,V10__lpe] :
      ( cType___24t(V0__C)
     => ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C)),V10__lpe)
       => ( ( V10__lpe = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C)))
            & cCoq_2esetoid__ring_2eRing__polynom_2emk__monpol__list___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,V10__lpe) = cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__C,cCoq_2esetoid__ring_2eRing__polynom_2eMon),cCoq_2esetoid__ring_2eRing__polynom_2ePol___24a1(V0__C))) )
          | ? [Vvar__1___24Anonymous__1882] :
              ( cCoq_2eInit_2eDatatypes_2eprod___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),Vvar__1___24Anonymous__1882)
              & ? [Vvar__2___24Anonymous__1883] :
                  ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C)),Vvar__2___24Anonymous__1883)
                  & ( cType___24t(V0__C)
                   => ( cCoq_2eInit_2eDatatypes_2eprod___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),Vvar__1___24Anonymous__1882)
                     => ( V10__lpe = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C)),Vvar__1___24Anonymous__1882,Vvar__2___24Anonymous__1883)
                        & ? [Vvar__2___24Anonymous__1899] :
                            ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__1899)
                            & ? [Vvar__3___24Anonymous__1900] :
                                ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__3___24Anonymous__1900)
                                & ( cType___24t(V0__C)
                                 => ( t(V1__cO,V0__C)
                                   => ( t(V2__cI,V0__C)
                                     => ( c_24__type__1859___24t(V0__C,V3__cadd)
                                       => ( c_24__type__1859___24t(V0__C,V4__cmul)
                                         => ( c_24__type__1859___24t(V0__C,V5__csub)
                                           => ( c_24__type__1868___24t(V0__C,V6__copp)
                                             => ( c_24__type__1372___24t(V0__C,V7__ceqb)
                                               => ( c_24__type__1876___24t(V0__C,V8__cdiv)
                                                 => ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(V0__C,Vvar__2___24Anonymous__1899)
                                                   => ( Vvar__1___24Anonymous__1882 = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V0__C),Vvar__2___24Anonymous__1899,Vvar__3___24Anonymous__1900)
                                                      & ( ? [Vvar__1___24Anonymous__1908] :
                                                            ( cCoq_2eInit_2eDatatypes_2eprod___24t(V0__C,cCoq_2esetoid__ring_2eRing__polynom_2eMon,Vvar__1___24Anonymous__1908)
                                                            & cCoq_2esetoid__ring_2eRing__polynom_2emon__of__pol___24a4(V0__C,V1__cO,V7__ceqb,cCoq_2esetoid__ring_2eRing__polynom_2enorm__subst___24a12(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,cCoq_2eInit_2eDatatypes_2eO,cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__C,cCoq_2esetoid__ring_2eRing__polynom_2eMon),cCoq_2esetoid__ring_2eRing__polynom_2ePol___24a1(V0__C))),Vvar__2___24Anonymous__1899)) = cCoq_2eInit_2eDatatypes_2eSome___24a2(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__C,cCoq_2esetoid__ring_2eRing__polynom_2eMon),Vvar__1___24Anonymous__1908)
                                                            & cCoq_2esetoid__ring_2eRing__polynom_2emk__monpol__list___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,V10__lpe) = cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__C,cCoq_2esetoid__ring_2eRing__polynom_2eMon),cCoq_2esetoid__ring_2eRing__polynom_2ePol___24a1(V0__C)),cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__C,cCoq_2esetoid__ring_2eRing__polynom_2eMon),cCoq_2esetoid__ring_2eRing__polynom_2ePol___24a1(V0__C),Vvar__1___24Anonymous__1908,cCoq_2esetoid__ring_2eRing__polynom_2enorm__subst___24a12(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,cCoq_2eInit_2eDatatypes_2eO,cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__C,cCoq_2esetoid__ring_2eRing__polynom_2eMon),cCoq_2esetoid__ring_2eRing__polynom_2ePol___24a1(V0__C))),Vvar__3___24Anonymous__1900)),cCoq_2esetoid__ring_2eRing__polynom_2emk__monpol__list___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,Vvar__2___24Anonymous__1883)) )
                                                        | ( cCoq_2esetoid__ring_2eRing__polynom_2emon__of__pol___24a4(V0__C,V1__cO,V7__ceqb,cCoq_2esetoid__ring_2eRing__polynom_2enorm__subst___24a12(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,cCoq_2eInit_2eDatatypes_2eO,cCoq_2eInit_2eDatatypes_2enil___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__C,cCoq_2esetoid__ring_2eRing__polynom_2eMon),cCoq_2esetoid__ring_2eRing__polynom_2ePol___24a1(V0__C))),Vvar__2___24Anonymous__1899)) = cCoq_2eInit_2eDatatypes_2eNone___24a1(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__C,cCoq_2esetoid__ring_2eRing__polynom_2eMon))
                                                          & cCoq_2esetoid__ring_2eRing__polynom_2emk__monpol__list___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,V10__lpe) = cCoq_2esetoid__ring_2eRing__polynom_2emk__monpol__list___24a10(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,Vvar__2___24Anonymous__1883) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

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__113377] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__113377)
              & V5__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__113377)
              & 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__113377),V4__x,Vvar__0___24Anonymous__113377) )
          | ? [Vvar__0___24Anonymous__113378] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__113378)
              & V5__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__113378)
              & 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__113378),V4__x,Vvar__0___24Anonymous__113378) )
          | ( 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_polynom.norm_subst',axiom,
    ! [V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,V9__n,V10__lmp] : cCoq_2esetoid__ring_2eRing__polynom_2enorm__subst___24a11(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,V9__n,V10__lmp) = c_24__lam__1722___24a11(V0__C,V1__cO,V2__cI,V3__cadd,V4__cmul,V5__csub,V6__copp,V7__ceqb,V8__cdiv,V9__n,V10__lmp) ).

fof('$_def_Coq.setoid_ring.Ring_polynom.zmon_pred',axiom,
    ! [V0__j,V1__M] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__j)
     => ( ? [Vvar__0___24Anonymous__216218] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__216218)
            & V0__j = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__216218)
            & cCoq_2esetoid__ring_2eRing__polynom_2ezmon__pred___24a2(V0__j,V1__M) = cCoq_2esetoid__ring_2eRing__polynom_2emkZmon___24a2(cCoq_2ePArith_2eBinPosDef_2ePos_2epred___24a1(V0__j),V1__M) )
        | ? [Vvar__0___24Anonymous__216219] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__216219)
            & V0__j = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__216219)
            & cCoq_2esetoid__ring_2eRing__polynom_2ezmon__pred___24a2(V0__j,V1__M) = cCoq_2esetoid__ring_2eRing__polynom_2emkZmon___24a2(cCoq_2ePArith_2eBinPosDef_2ePos_2epred___24a1(V0__j),V1__M) )
        | ( V0__j = cCoq_2eNumbers_2eBinNums_2exH
          & cCoq_2esetoid__ring_2eRing__polynom_2ezmon__pred___24a2(V0__j,V1__M) = V1__M ) ) ) ).

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.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__81181] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__81181)
              & V4__p = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__81181)
              & 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__81181) ) ) ) ) ).

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__113398] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__113398)
              & V4__i = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__113398)
              & 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__113399__113402___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__113398)),c_24__let__var__6__p__113399__113402___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__113398))) )
          | ? [Vvar__0___24Anonymous__113400] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__113400)
              & V4__i = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__113400)
              & 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__113401__113403___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__113400)),c_24__let__var__6__p__113401__113403___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__113400)) )
          | ( 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_PLF.Imp.X',axiom,
    cPLF_2eImp_2eX = cCoq_2eStrings_2eString_2eString___24a2(cCoq_2eStrings_2eAscii_2eAscii___24a8(cCoq_2eInit_2eDatatypes_2efalse,cCoq_2eInit_2eDatatypes_2efalse,cCoq_2eInit_2eDatatypes_2efalse,cCoq_2eInit_2eDatatypes_2etrue,cCoq_2eInit_2eDatatypes_2etrue,cCoq_2eInit_2eDatatypes_2efalse,cCoq_2eInit_2eDatatypes_2etrue,cCoq_2eInit_2eDatatypes_2efalse),cCoq_2eStrings_2eString_2eEmptyString) ).

fof('$_def_PLF.Imp.Y',axiom,
    cPLF_2eImp_2eY = cCoq_2eStrings_2eString_2eString___24a2(cCoq_2eStrings_2eAscii_2eAscii___24a8(cCoq_2eInit_2eDatatypes_2etrue,cCoq_2eInit_2eDatatypes_2efalse,cCoq_2eInit_2eDatatypes_2efalse,cCoq_2eInit_2eDatatypes_2etrue,cCoq_2eInit_2eDatatypes_2etrue,cCoq_2eInit_2eDatatypes_2efalse,cCoq_2eInit_2eDatatypes_2etrue,cCoq_2eInit_2eDatatypes_2efalse),cCoq_2eStrings_2eString_2eEmptyString) ).

fof('$_def_PLF.Imp.empty_st',axiom,
    cPLF_2eImp_2eempty__st = cPLF_2eMaps_2et__empty___24a2(cCoq_2eInit_2eDatatypes_2enat,cCoq_2eInit_2eDatatypes_2eO) ).

fof('$_def_PLF.Imp.state',axiom,
    ! [Vvar__333] :
      ( cPLF_2eImp_2estate___24t(Vvar__333)
    <=> cPLF_2eMaps_2etotal__map___24t(cCoq_2eInit_2eDatatypes_2enat,Vvar__333) ) ).

fof('$_def_PLF.LibTactics.COIND',axiom,
    ! [V0__P] :
      ( cPLF_2eLibTactics_2eCOIND___24a1(V0__P)
    <=> p(V0__P) ) ).

fof('$_def_PLF.LibTactics.eq\'',axiom,
    cPLF_2eLibTactics_2eeq_27 = c_3d ).

fof('$_def_PLF.LibTactics.ltac_something',axiom,
    ! [V0__P,V1__e] : cPLF_2eLibTactics_2eltac__something___24a2(V0__P,V1__e) = V1__e ).

fof('$_def_PLF.LibTactics.ltac_tag_subst',axiom,
    ! [V0__A,V1__x] : cPLF_2eLibTactics_2eltac__tag__subst___24a2(V0__A,V1__x) = V1__x ).

fof('$_def_PLF.LibTactics.ltac_to_generalize',axiom,
    ! [V0__A,V1__x] : cPLF_2eLibTactics_2eltac__to__generalize___24a2(V0__A,V1__x) = V1__x ).

fof('$_def_PLF.LibTactics.rm',axiom,
    ! [V0__A,V1__X] : cPLF_2eLibTactics_2erm___24a2(V0__A,V1__X) = V1__X ).

fof('$_def_PLF.Maps.empty',axiom,
    ! [V0__A] : cPLF_2eMaps_2eempty___24a1(V0__A) = cPLF_2eMaps_2et__empty___24a2(cCoq_2eInit_2eDatatypes_2eoption___24a1(V0__A),cCoq_2eInit_2eDatatypes_2eNone___24a1(V0__A)) ).

fof('$_def_PLF.Maps.eqb_string',axiom,
    ! [V0__x,V1__y] :
      ( cCoq_2eStrings_2eString_2estring___24t(V0__x)
     => ( cCoq_2eStrings_2eString_2estring___24t(V1__y)
       => ( ( V0__x = V1__y
            & cCoq_2eStrings_2eString_2estring__dec___24a2(V0__x,V1__y) = cCoq_2eInit_2eSpecif_2eleft___24a2(c_24__prop__154310___24a2(V0__x,V1__y),c_24__prop__154311___24a2(V0__x,V1__y))
            & cPLF_2eMaps_2eeqb__string___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2etrue )
          | ( V0__x != V1__y
            & cCoq_2eStrings_2eString_2estring__dec___24a2(V0__x,V1__y) = cCoq_2eInit_2eSpecif_2eright___24a2(c_24__prop__154312___24a2(V0__x,V1__y),c_24__prop__154313___24a2(V0__x,V1__y))
            & cPLF_2eMaps_2eeqb__string___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ).

fof('$_def_PLF.Maps.partial_map',axiom,
    ! [V0__A] : cPLF_2eMaps_2epartial__map___24a1(V0__A) = cPLF_2eMaps_2etotal__map___24a1(cCoq_2eInit_2eDatatypes_2eoption___24a1(V0__A)) ).

fof('$_def_PLF.Maps.t_empty',axiom,
    ! [V0__A,V1__v,V2___24Anonymous] : cPLF_2eMaps_2et__empty___24a3(V0__A,V1__v,V2___24Anonymous) = V1__v ).

fof('$_def_PLF.Maps.t_update',axiom,
    ! [V0__A,V1__m,V2__x,V3__v,V4__x_27] :
      ( cType___24t(V0__A)
     => ( cCoq_2eStrings_2eString_2estring___24t(V2__x)
       => ( cCoq_2eStrings_2eString_2estring___24t(V4__x_27)
         => ( ( cPLF_2eMaps_2eeqb__string___24a2(V2__x,V4__x_27) = cCoq_2eInit_2eDatatypes_2etrue
              & cPLF_2eMaps_2et__update___24a5(V0__A,V1__m,V2__x,V3__v,V4__x_27) = V3__v )
            | ( cPLF_2eMaps_2eeqb__string___24a2(V2__x,V4__x_27) = cCoq_2eInit_2eDatatypes_2efalse
              & cPLF_2eMaps_2et__update___24a5(V0__A,V1__m,V2__x,V3__v,V4__x_27) = happ(V1__m,V4__x_27) ) ) ) ) ) ).

fof('$_def_PLF.Maps.total_map',axiom,
    ! [V0__A] : cPLF_2eMaps_2etotal__map___24a1(V0__A) = c_24__type__76653___24a1(V0__A) ).

fof('$_def_PLF.Maps.update',axiom,
    ! [V0__A,V1__m,V2__x,V3__v] : cPLF_2eMaps_2eupdate___24a4(V0__A,V1__m,V2__x,V3__v) = cPLF_2eMaps_2et__update___24a4(cCoq_2eInit_2eDatatypes_2eoption___24a1(V0__A),V1__m,V2__x,cCoq_2eInit_2eDatatypes_2eSome___24a2(V0__A,V3__v)) ).

fof('$_def_PLF.References.STLCRef.ExampleVariables.r',axiom,
    cPLF_2eReferences_2eSTLCRef_2eExampleVariables_2er = cCoq_2eStrings_2eString_2eString___24a2(cCoq_2eStrings_2eAscii_2eAscii___24a8(cCoq_2eInit_2eDatatypes_2efalse,cCoq_2eInit_2eDatatypes_2etrue,cCoq_2eInit_2eDatatypes_2efalse,cCoq_2eInit_2eDatatypes_2efalse,cCoq_2eInit_2eDatatypes_2etrue,cCoq_2eInit_2eDatatypes_2etrue,cCoq_2eInit_2eDatatypes_2etrue,cCoq_2eInit_2eDatatypes_2efalse),cCoq_2eStrings_2eString_2eEmptyString) ).

fof('$_def_PLF.References.STLCRef.ExampleVariables.x',axiom,
    cPLF_2eReferences_2eSTLCRef_2eExampleVariables_2ex = cCoq_2eStrings_2eString_2eString___24a2(cCoq_2eStrings_2eAscii_2eAscii___24a8(cCoq_2eInit_2eDatatypes_2efalse,cCoq_2eInit_2eDatatypes_2efalse,cCoq_2eInit_2eDatatypes_2efalse,cCoq_2eInit_2eDatatypes_2etrue,cCoq_2eInit_2eDatatypes_2etrue,cCoq_2eInit_2eDatatypes_2etrue,cCoq_2eInit_2eDatatypes_2etrue,cCoq_2eInit_2eDatatypes_2efalse),cCoq_2eStrings_2eString_2eEmptyString) ).

fof('$_def_PLF.References.STLCRef.RefsAndNontermination.loop',axiom,
    cPLF_2eReferences_2eSTLCRef_2eRefsAndNontermination_2eloop = cPLF_2eReferences_2eSTLCRef_2eapp___24a2(cPLF_2eReferences_2eSTLCRef_2eabs___24a3(cPLF_2eReferences_2eSTLCRef_2eExampleVariables_2er,cPLF_2eReferences_2eSTLCRef_2eRef___24a1(cPLF_2eReferences_2eSTLCRef_2eArrow___24a2(cPLF_2eReferences_2eSTLCRef_2eUnit,cPLF_2eReferences_2eSTLCRef_2eUnit)),cPLF_2eReferences_2eSTLCRef_2etseq___24a2(cPLF_2eReferences_2eSTLCRef_2eassign___24a2(cPLF_2eReferences_2eSTLCRef_2evar___24a1(cPLF_2eReferences_2eSTLCRef_2eExampleVariables_2er),cPLF_2eReferences_2eSTLCRef_2eRefsAndNontermination_2eloop__fun),cPLF_2eReferences_2eSTLCRef_2eapp___24a2(cPLF_2eReferences_2eSTLCRef_2ederef___24a1(cPLF_2eReferences_2eSTLCRef_2evar___24a1(cPLF_2eReferences_2eSTLCRef_2eExampleVariables_2er)),cPLF_2eReferences_2eSTLCRef_2eunit))),cPLF_2eReferences_2eSTLCRef_2eref___24a1(cPLF_2eReferences_2eSTLCRef_2eabs___24a3(cPLF_2eReferences_2eSTLCRef_2eExampleVariables_2ex,cPLF_2eReferences_2eSTLCRef_2eUnit,cPLF_2eReferences_2eSTLCRef_2eunit))) ).

fof('$_def_PLF.References.STLCRef.RefsAndNontermination.loop_fun',axiom,
    cPLF_2eReferences_2eSTLCRef_2eRefsAndNontermination_2eloop__fun = cPLF_2eReferences_2eSTLCRef_2eabs___24a3(cPLF_2eReferences_2eSTLCRef_2eExampleVariables_2ex,cPLF_2eReferences_2eSTLCRef_2eUnit,cPLF_2eReferences_2eSTLCRef_2eapp___24a2(cPLF_2eReferences_2eSTLCRef_2ederef___24a1(cPLF_2eReferences_2eSTLCRef_2evar___24a1(cPLF_2eReferences_2eSTLCRef_2eExampleVariables_2er)),cPLF_2eReferences_2eSTLCRef_2eunit)) ).

fof('$_def_PLF.References.STLCRef.RefsAndNontermination.multistep1',axiom,
    cPLF_2eReferences_2eSTLCRef_2eRefsAndNontermination_2emultistep1 = cPLF_2eReferences_2eSTLCRef_2eRefsAndNontermination_2estep__closure___24a2(cCoq_2eInit_2eDatatypes_2eprod___24a2(cPLF_2eReferences_2eSTLCRef_2etm,cPLF_2eReferences_2eSTLCRef_2estore),cPLF_2eReferences_2eSTLCRef_2estep) ).

fof('$_def_PLF.References.STLCRef.context',axiom,
    ! [Vvar__211754] :
      ( cPLF_2eReferences_2eSTLCRef_2econtext___24t(Vvar__211754)
    <=> cPLF_2eMaps_2epartial__map___24t(cPLF_2eReferences_2eSTLCRef_2ety,Vvar__211754) ) ).

fof('$_def_PLF.References.STLCRef.multistep',axiom,
    cPLF_2eReferences_2eSTLCRef_2emultistep = cPLF_2eSmallstep_2emulti___24a2(cCoq_2eInit_2eDatatypes_2eprod___24a2(cPLF_2eReferences_2eSTLCRef_2etm,cPLF_2eReferences_2eSTLCRef_2estore),cPLF_2eReferences_2eSTLCRef_2estep) ).

fof('$_def_PLF.References.STLCRef.preservation_theorem',axiom,
    ( p(cPLF_2eReferences_2eSTLCRef_2epreservation__theorem)
  <=> ! [V0__ST] :
        ( cPLF_2eReferences_2eSTLCRef_2estore__ty___24t(V0__ST)
       => ! [V1__t] :
            ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V1__t)
           => ! [V2__t_27] :
                ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V2__t_27)
               => ! [V3__T] :
                    ( cPLF_2eReferences_2eSTLCRef_2ety___24t(V3__T)
                   => ! [V4__st] :
                        ( cPLF_2eReferences_2eSTLCRef_2estore___24t(V4__st)
                       => ! [V5__st_27] :
                            ( cPLF_2eReferences_2eSTLCRef_2estore___24t(V5__st_27)
                           => ( cPLF_2eReferences_2eSTLCRef_2ehas__type___24a4(cPLF_2eMaps_2eempty___24a1(cPLF_2eReferences_2eSTLCRef_2ety),V0__ST,V1__t,V3__T)
                             => ( cPLF_2eReferences_2eSTLCRef_2estore__well__typed___24a2(V0__ST,V4__st)
                               => ( cPLF_2eReferences_2eSTLCRef_2estep___24a2(cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cPLF_2eReferences_2eSTLCRef_2estore,V1__t,V4__st),cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cPLF_2eReferences_2eSTLCRef_2estore,V2__t_27,V5__st_27))
                                 => ? [V9__ST_27] :
                                      ( cPLF_2eReferences_2eSTLCRef_2estore__ty___24t(V9__ST_27)
                                      & cPLF_2eReferences_2eSTLCRef_2eextends___24a2(V9__ST_27,V0__ST)
                                      & cPLF_2eReferences_2eSTLCRef_2ehas__type___24a4(cPLF_2eMaps_2eempty___24a1(cPLF_2eReferences_2eSTLCRef_2ety),V9__ST_27,V2__t_27,V3__T)
                                      & cPLF_2eReferences_2eSTLCRef_2estore__well__typed___24a2(V9__ST_27,V5__st_27) ) ) ) ) ) ) ) ) ) ) ) ).

fof('$_def_PLF.References.STLCRef.replace',axiom,
    ! [V1__A,V2__n,V3__x,V4__l] :
      ( cType___24t(V1__A)
     => ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,V4__l)
       => ( ( V4__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V1__A)
            & cPLF_2eReferences_2eSTLCRef_2ereplace___24a4(V1__A,V2__n,V3__x,V4__l) = cCoq_2eInit_2eDatatypes_2enil___24a1(V1__A) )
          | ? [Vvar__1___24Anonymous__203747] :
              ( t(Vvar__1___24Anonymous__203747,V1__A)
              & ? [Vvar__2___24Anonymous__203748] :
                  ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__203748)
                  & ( cType___24t(V1__A)
                   => ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
                     => ( V4__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__A,Vvar__1___24Anonymous__203747,Vvar__2___24Anonymous__203748)
                        & ( ( V2__n = cCoq_2eInit_2eDatatypes_2eO
                            & cPLF_2eReferences_2eSTLCRef_2ereplace___24a4(V1__A,V2__n,V3__x,V4__l) = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__A,V3__x,Vvar__2___24Anonymous__203748) )
                          | ? [Vvar__0___24Anonymous__203754] :
                              ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__203754)
                              & V2__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__203754)
                              & cPLF_2eReferences_2eSTLCRef_2ereplace___24a4(V1__A,V2__n,V3__x,V4__l) = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__A,Vvar__1___24Anonymous__203747,cPLF_2eReferences_2eSTLCRef_2ereplace___24a4(V1__A,Vvar__0___24Anonymous__203754,V3__x,Vvar__2___24Anonymous__203748)) ) ) ) ) ) ) ) ) ) ) ).

fof('$_def_PLF.References.STLCRef.store',axiom,
    ! [Vvar__203739] :
      ( cPLF_2eReferences_2eSTLCRef_2estore___24t(Vvar__203739)
    <=> cCoq_2eInit_2eDatatypes_2elist___24t(cPLF_2eReferences_2eSTLCRef_2etm,Vvar__203739) ) ).

fof('$_def_PLF.References.STLCRef.store_Tlookup',axiom,
    ! [V0__n,V1__ST] : cPLF_2eReferences_2eSTLCRef_2estore__Tlookup___24a2(V0__n,V1__ST) = cCoq_2eLists_2eList_2enth___24a4(cPLF_2eReferences_2eSTLCRef_2ety,V0__n,V1__ST,cPLF_2eReferences_2eSTLCRef_2eUnit) ).

fof('$_def_PLF.References.STLCRef.store_lookup',axiom,
    ! [V0__n,V1__st] : cPLF_2eReferences_2eSTLCRef_2estore__lookup___24a2(V0__n,V1__st) = cCoq_2eLists_2eList_2enth___24a4(cPLF_2eReferences_2eSTLCRef_2etm,V0__n,V1__st,cPLF_2eReferences_2eSTLCRef_2eunit) ).

fof('$_def_PLF.References.STLCRef.store_ty',axiom,
    ! [Vvar__211755] :
      ( cPLF_2eReferences_2eSTLCRef_2estore__ty___24t(Vvar__211755)
    <=> cCoq_2eInit_2eDatatypes_2elist___24t(cPLF_2eReferences_2eSTLCRef_2ety,Vvar__211755) ) ).

fof('$_def_PLF.References.STLCRef.store_well_typed',axiom,
    ! [V0__ST,V1__st] :
      ( cPLF_2eReferences_2eSTLCRef_2estore__well__typed___24a2(V0__ST,V1__st)
    <=> ( cCoq_2eInit_2eDatatypes_2elength___24a2(cPLF_2eReferences_2eSTLCRef_2ety,V0__ST) = cCoq_2eInit_2eDatatypes_2elength___24a2(cPLF_2eReferences_2eSTLCRef_2etm,V1__st)
        & ! [V2__l] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__l)
           => ( p(cCoq_2eInit_2ePeano_2elt___24a2(V2__l,cCoq_2eInit_2eDatatypes_2elength___24a2(cPLF_2eReferences_2eSTLCRef_2etm,V1__st)))
             => cPLF_2eReferences_2eSTLCRef_2ehas__type___24a4(cPLF_2eMaps_2eempty___24a1(cPLF_2eReferences_2eSTLCRef_2ety),V0__ST,cPLF_2eReferences_2eSTLCRef_2estore__lookup___24a2(V2__l,V1__st),cPLF_2eReferences_2eSTLCRef_2estore__Tlookup___24a2(V2__l,V0__ST)) ) ) ) ) ).

fof('$_def_PLF.References.STLCRef.subst',axiom,
    ! [V1__x,V2__s,V3__t] :
      ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V3__t)
     => ( ? [Vvar__0___24Anonymous__203702] :
            ( cCoq_2eStrings_2eString_2estring___24t(Vvar__0___24Anonymous__203702)
            & ( cCoq_2eStrings_2eString_2estring___24t(V1__x)
             => ( cCoq_2eStrings_2eString_2estring___24t(Vvar__0___24Anonymous__203702)
               => ( V3__t = cPLF_2eReferences_2eSTLCRef_2evar___24a1(Vvar__0___24Anonymous__203702)
                  & ( ( cPLF_2eMaps_2eeqb__string___24a2(V1__x,Vvar__0___24Anonymous__203702) = cCoq_2eInit_2eDatatypes_2etrue
                      & cPLF_2eReferences_2eSTLCRef_2esubst___24a3(V1__x,V2__s,V3__t) = V2__s )
                    | ( cPLF_2eMaps_2eeqb__string___24a2(V1__x,Vvar__0___24Anonymous__203702) = cCoq_2eInit_2eDatatypes_2efalse
                      & cPLF_2eReferences_2eSTLCRef_2esubst___24a3(V1__x,V2__s,V3__t) = V3__t ) ) ) ) ) )
        | ? [Vvar__0___24Anonymous__203704] :
            ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__0___24Anonymous__203704)
            & ? [Vvar__1___24Anonymous__203705] :
                ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__1___24Anonymous__203705)
                & V3__t = cPLF_2eReferences_2eSTLCRef_2eapp___24a2(Vvar__0___24Anonymous__203704,Vvar__1___24Anonymous__203705)
                & cPLF_2eReferences_2eSTLCRef_2esubst___24a3(V1__x,V2__s,V3__t) = cPLF_2eReferences_2eSTLCRef_2eapp___24a2(cPLF_2eReferences_2eSTLCRef_2esubst___24a3(V1__x,V2__s,Vvar__0___24Anonymous__203704),cPLF_2eReferences_2eSTLCRef_2esubst___24a3(V1__x,V2__s,Vvar__1___24Anonymous__203705)) ) )
        | ? [Vvar__0___24Anonymous__203707] :
            ( cCoq_2eStrings_2eString_2estring___24t(Vvar__0___24Anonymous__203707)
            & ? [Vvar__1___24Anonymous__203708] :
                ( cPLF_2eReferences_2eSTLCRef_2ety___24t(Vvar__1___24Anonymous__203708)
                & ? [Vvar__2___24Anonymous__203709] :
                    ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__2___24Anonymous__203709)
                    & ( cCoq_2eStrings_2eString_2estring___24t(V1__x)
                     => ( cCoq_2eStrings_2eString_2estring___24t(Vvar__0___24Anonymous__203707)
                       => ( V3__t = cPLF_2eReferences_2eSTLCRef_2eabs___24a3(Vvar__0___24Anonymous__203707,Vvar__1___24Anonymous__203708,Vvar__2___24Anonymous__203709)
                          & ( ( cPLF_2eMaps_2eeqb__string___24a2(V1__x,Vvar__0___24Anonymous__203707) = cCoq_2eInit_2eDatatypes_2etrue
                              & cPLF_2eReferences_2eSTLCRef_2esubst___24a3(V1__x,V2__s,V3__t) = V3__t )
                            | ( cPLF_2eMaps_2eeqb__string___24a2(V1__x,Vvar__0___24Anonymous__203707) = cCoq_2eInit_2eDatatypes_2efalse
                              & cPLF_2eReferences_2eSTLCRef_2esubst___24a3(V1__x,V2__s,V3__t) = cPLF_2eReferences_2eSTLCRef_2eabs___24a3(Vvar__0___24Anonymous__203707,Vvar__1___24Anonymous__203708,cPLF_2eReferences_2eSTLCRef_2esubst___24a3(V1__x,V2__s,Vvar__2___24Anonymous__203709)) ) ) ) ) ) ) ) )
        | ? [Vvar__0___24Anonymous__203716] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__203716)
            & V3__t = cPLF_2eReferences_2eSTLCRef_2econst___24a1(Vvar__0___24Anonymous__203716)
            & cPLF_2eReferences_2eSTLCRef_2esubst___24a3(V1__x,V2__s,V3__t) = V3__t )
        | ? [Vvar__0___24Anonymous__203717] :
            ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__0___24Anonymous__203717)
            & V3__t = cPLF_2eReferences_2eSTLCRef_2escc___24a1(Vvar__0___24Anonymous__203717)
            & cPLF_2eReferences_2eSTLCRef_2esubst___24a3(V1__x,V2__s,V3__t) = cPLF_2eReferences_2eSTLCRef_2escc___24a1(cPLF_2eReferences_2eSTLCRef_2esubst___24a3(V1__x,V2__s,Vvar__0___24Anonymous__203717)) )
        | ? [Vvar__0___24Anonymous__203718] :
            ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__0___24Anonymous__203718)
            & V3__t = cPLF_2eReferences_2eSTLCRef_2eprd___24a1(Vvar__0___24Anonymous__203718)
            & cPLF_2eReferences_2eSTLCRef_2esubst___24a3(V1__x,V2__s,V3__t) = cPLF_2eReferences_2eSTLCRef_2eprd___24a1(cPLF_2eReferences_2eSTLCRef_2esubst___24a3(V1__x,V2__s,Vvar__0___24Anonymous__203718)) )
        | ? [Vvar__0___24Anonymous__203719] :
            ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__0___24Anonymous__203719)
            & ? [Vvar__1___24Anonymous__203720] :
                ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__1___24Anonymous__203720)
                & V3__t = cPLF_2eReferences_2eSTLCRef_2emlt___24a2(Vvar__0___24Anonymous__203719,Vvar__1___24Anonymous__203720)
                & cPLF_2eReferences_2eSTLCRef_2esubst___24a3(V1__x,V2__s,V3__t) = cPLF_2eReferences_2eSTLCRef_2emlt___24a2(cPLF_2eReferences_2eSTLCRef_2esubst___24a3(V1__x,V2__s,Vvar__0___24Anonymous__203719),cPLF_2eReferences_2eSTLCRef_2esubst___24a3(V1__x,V2__s,Vvar__1___24Anonymous__203720)) ) )
        | ? [Vvar__0___24Anonymous__203722] :
            ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__0___24Anonymous__203722)
            & ? [Vvar__1___24Anonymous__203723] :
                ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__1___24Anonymous__203723)
                & ? [Vvar__2___24Anonymous__203724] :
                    ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__2___24Anonymous__203724)
                    & V3__t = cPLF_2eReferences_2eSTLCRef_2etest0___24a3(Vvar__0___24Anonymous__203722,Vvar__1___24Anonymous__203723,Vvar__2___24Anonymous__203724)
                    & cPLF_2eReferences_2eSTLCRef_2esubst___24a3(V1__x,V2__s,V3__t) = cPLF_2eReferences_2eSTLCRef_2etest0___24a3(cPLF_2eReferences_2eSTLCRef_2esubst___24a3(V1__x,V2__s,Vvar__0___24Anonymous__203722),cPLF_2eReferences_2eSTLCRef_2esubst___24a3(V1__x,V2__s,Vvar__1___24Anonymous__203723),cPLF_2eReferences_2eSTLCRef_2esubst___24a3(V1__x,V2__s,Vvar__2___24Anonymous__203724)) ) ) )
        | ( V3__t = cPLF_2eReferences_2eSTLCRef_2eunit
          & cPLF_2eReferences_2eSTLCRef_2esubst___24a3(V1__x,V2__s,V3__t) = V3__t )
        | ? [Vvar__0___24Anonymous__203728] :
            ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__0___24Anonymous__203728)
            & V3__t = cPLF_2eReferences_2eSTLCRef_2eref___24a1(Vvar__0___24Anonymous__203728)
            & cPLF_2eReferences_2eSTLCRef_2esubst___24a3(V1__x,V2__s,V3__t) = cPLF_2eReferences_2eSTLCRef_2eref___24a1(cPLF_2eReferences_2eSTLCRef_2esubst___24a3(V1__x,V2__s,Vvar__0___24Anonymous__203728)) )
        | ? [Vvar__0___24Anonymous__203729] :
            ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__0___24Anonymous__203729)
            & V3__t = cPLF_2eReferences_2eSTLCRef_2ederef___24a1(Vvar__0___24Anonymous__203729)
            & cPLF_2eReferences_2eSTLCRef_2esubst___24a3(V1__x,V2__s,V3__t) = cPLF_2eReferences_2eSTLCRef_2ederef___24a1(cPLF_2eReferences_2eSTLCRef_2esubst___24a3(V1__x,V2__s,Vvar__0___24Anonymous__203729)) )
        | ? [Vvar__0___24Anonymous__203730] :
            ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__0___24Anonymous__203730)
            & ? [Vvar__1___24Anonymous__203731] :
                ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__1___24Anonymous__203731)
                & V3__t = cPLF_2eReferences_2eSTLCRef_2eassign___24a2(Vvar__0___24Anonymous__203730,Vvar__1___24Anonymous__203731)
                & cPLF_2eReferences_2eSTLCRef_2esubst___24a3(V1__x,V2__s,V3__t) = cPLF_2eReferences_2eSTLCRef_2eassign___24a2(cPLF_2eReferences_2eSTLCRef_2esubst___24a3(V1__x,V2__s,Vvar__0___24Anonymous__203730),cPLF_2eReferences_2eSTLCRef_2esubst___24a3(V1__x,V2__s,Vvar__1___24Anonymous__203731)) ) )
        | ? [Vvar__0___24Anonymous__203733] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__203733)
            & V3__t = cPLF_2eReferences_2eSTLCRef_2eloc___24a1(Vvar__0___24Anonymous__203733)
            & cPLF_2eReferences_2eSTLCRef_2esubst___24a3(V1__x,V2__s,V3__t) = V3__t ) ) ) ).

fof('$_def_PLF.References.STLCRef.tseq',axiom,
    ! [V0__t1,V1__t2] : cPLF_2eReferences_2eSTLCRef_2etseq___24a2(V0__t1,V1__t2) = cPLF_2eReferences_2eSTLCRef_2eapp___24a2(cPLF_2eReferences_2eSTLCRef_2eabs___24a3(cCoq_2eStrings_2eString_2eString___24a2(cCoq_2eStrings_2eAscii_2eAscii___24a8(cCoq_2eInit_2eDatatypes_2efalse,cCoq_2eInit_2eDatatypes_2efalse,cCoq_2eInit_2eDatatypes_2efalse,cCoq_2eInit_2eDatatypes_2etrue,cCoq_2eInit_2eDatatypes_2etrue,cCoq_2eInit_2eDatatypes_2etrue,cCoq_2eInit_2eDatatypes_2etrue,cCoq_2eInit_2eDatatypes_2efalse),cCoq_2eStrings_2eString_2eEmptyString),cPLF_2eReferences_2eSTLCRef_2eUnit,V1__t2),V0__t1) ).

fof('$_def_PLF.References.STLCRef.ty_rec',axiom,
    ! [V0__P] : cPLF_2eReferences_2eSTLCRef_2ety__rec___24a1(V0__P) = cPLF_2eReferences_2eSTLCRef_2ety__rect___24a1(V0__P) ).

fof('$_def_PLF.References.STLCRef.ty_rect',axiom,
    ! [V0__P,V1__f,V2__f,V3__f,V4__f,V6__t] :
      ( c_24__type__219117___24t(V0__P,V0__P)
     => ( cPLF_2eReferences_2eSTLCRef_2ety___24t(V6__t)
       => ( ( V6__t = cPLF_2eReferences_2eSTLCRef_2eNat
            & cPLF_2eReferences_2eSTLCRef_2ety__rect___24a6(V0__P,V1__f,V2__f,V3__f,V4__f,V6__t) = V1__f )
          | ( V6__t = cPLF_2eReferences_2eSTLCRef_2eUnit
            & cPLF_2eReferences_2eSTLCRef_2ety__rect___24a6(V0__P,V1__f,V2__f,V3__f,V4__f,V6__t) = V2__f )
          | ? [Vvar__0___24Anonymous__219112] :
              ( cPLF_2eReferences_2eSTLCRef_2ety___24t(Vvar__0___24Anonymous__219112)
              & ? [Vvar__1___24Anonymous__219113] :
                  ( cPLF_2eReferences_2eSTLCRef_2ety___24t(Vvar__1___24Anonymous__219113)
                  & V6__t = cPLF_2eReferences_2eSTLCRef_2eArrow___24a2(Vvar__0___24Anonymous__219112,Vvar__1___24Anonymous__219113)
                  & cPLF_2eReferences_2eSTLCRef_2ety__rect___24a6(V0__P,V1__f,V2__f,V3__f,V4__f,V6__t) = happ(happ(happ(happ(V3__f,Vvar__0___24Anonymous__219112),cPLF_2eReferences_2eSTLCRef_2ety__rect___24a6(V0__P,V1__f,V2__f,V3__f,V4__f,Vvar__0___24Anonymous__219112)),Vvar__1___24Anonymous__219113),cPLF_2eReferences_2eSTLCRef_2ety__rect___24a6(V0__P,V1__f,V2__f,V3__f,V4__f,Vvar__1___24Anonymous__219113)) ) )
          | ? [Vvar__0___24Anonymous__219115] :
              ( cPLF_2eReferences_2eSTLCRef_2ety___24t(Vvar__0___24Anonymous__219115)
              & V6__t = cPLF_2eReferences_2eSTLCRef_2eRef___24a1(Vvar__0___24Anonymous__219115)
              & cPLF_2eReferences_2eSTLCRef_2ety__rect___24a6(V0__P,V1__f,V2__f,V3__f,V4__f,V6__t) = happ(happ(V4__f,Vvar__0___24Anonymous__219115),cPLF_2eReferences_2eSTLCRef_2ety__rect___24a6(V0__P,V1__f,V2__f,V3__f,V4__f,Vvar__0___24Anonymous__219115)) ) ) ) ) ).

fof('$_def_PLF.Smallstep.prog',axiom,
    ! [Vvar__167694] :
      ( cPLF_2eSmallstep_2eprog___24t(Vvar__167694)
    <=> cCoq_2eInit_2eDatatypes_2elist___24t(cPLF_2eImp_2esinstr,Vvar__167694) ) ).

fof('$_def_PLF.Smallstep.relation',axiom,
    ! [V0__X] : cPLF_2eSmallstep_2erelation___24a1(V0__X) = c_24__type__76843___24a1(V0__X) ).

fof('$_def_PLF.Smallstep.stack',axiom,
    ! [Vvar__115655] :
      ( cPLF_2eSmallstep_2estack___24t(Vvar__115655)
    <=> cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2enat,Vvar__115655) ) ).

fof('$_def_PLF.Stlc.STLC.context',axiom,
    ! [Vvar__162054] :
      ( cPLF_2eStlc_2eSTLC_2econtext___24t(Vvar__162054)
    <=> cPLF_2eMaps_2epartial__map___24t(cPLF_2eStlc_2eSTLC_2ety,Vvar__162054) ) ).

fof('$_def_PLF.Stlc.STLC.subst',axiom,
    ! [V1__x,V2__s,V3__t] :
      ( cPLF_2eStlc_2eSTLC_2etm___24t(V3__t)
     => ( ? [Vvar__0___24Anonymous__109372] :
            ( cCoq_2eStrings_2eString_2estring___24t(Vvar__0___24Anonymous__109372)
            & ( cCoq_2eStrings_2eString_2estring___24t(V1__x)
             => ( cCoq_2eStrings_2eString_2estring___24t(Vvar__0___24Anonymous__109372)
               => ( V3__t = cPLF_2eStlc_2eSTLC_2evar___24a1(Vvar__0___24Anonymous__109372)
                  & ( ( cPLF_2eMaps_2eeqb__string___24a2(V1__x,Vvar__0___24Anonymous__109372) = cCoq_2eInit_2eDatatypes_2etrue
                      & cPLF_2eStlc_2eSTLC_2esubst___24a3(V1__x,V2__s,V3__t) = V2__s )
                    | ( cPLF_2eMaps_2eeqb__string___24a2(V1__x,Vvar__0___24Anonymous__109372) = cCoq_2eInit_2eDatatypes_2efalse
                      & cPLF_2eStlc_2eSTLC_2esubst___24a3(V1__x,V2__s,V3__t) = V3__t ) ) ) ) ) )
        | ? [Vvar__0___24Anonymous__109374] :
            ( cPLF_2eStlc_2eSTLC_2etm___24t(Vvar__0___24Anonymous__109374)
            & ? [Vvar__1___24Anonymous__109375] :
                ( cPLF_2eStlc_2eSTLC_2etm___24t(Vvar__1___24Anonymous__109375)
                & V3__t = cPLF_2eStlc_2eSTLC_2eapp___24a2(Vvar__0___24Anonymous__109374,Vvar__1___24Anonymous__109375)
                & cPLF_2eStlc_2eSTLC_2esubst___24a3(V1__x,V2__s,V3__t) = cPLF_2eStlc_2eSTLC_2eapp___24a2(cPLF_2eStlc_2eSTLC_2esubst___24a3(V1__x,V2__s,Vvar__0___24Anonymous__109374),cPLF_2eStlc_2eSTLC_2esubst___24a3(V1__x,V2__s,Vvar__1___24Anonymous__109375)) ) )
        | ? [Vvar__0___24Anonymous__109377] :
            ( cCoq_2eStrings_2eString_2estring___24t(Vvar__0___24Anonymous__109377)
            & ? [Vvar__1___24Anonymous__109378] :
                ( cPLF_2eStlc_2eSTLC_2ety___24t(Vvar__1___24Anonymous__109378)
                & ? [Vvar__2___24Anonymous__109379] :
                    ( cPLF_2eStlc_2eSTLC_2etm___24t(Vvar__2___24Anonymous__109379)
                    & V3__t = cPLF_2eStlc_2eSTLC_2eabs___24a3(Vvar__0___24Anonymous__109377,Vvar__1___24Anonymous__109378,Vvar__2___24Anonymous__109379)
                    & cPLF_2eStlc_2eSTLC_2esubst___24a3(V1__x,V2__s,V3__t) = cPLF_2eStlc_2eSTLC_2eabs___24a3(Vvar__0___24Anonymous__109377,Vvar__1___24Anonymous__109378,c_24__case__Coq_2eInit_2eDatatypes_2ebool_24109396___24a4(V1__x,V2__s,Vvar__0___24Anonymous__109377,Vvar__2___24Anonymous__109379)) ) ) )
        | ( V3__t = cPLF_2eStlc_2eSTLC_2etru
          & cPLF_2eStlc_2eSTLC_2esubst___24a3(V1__x,V2__s,V3__t) = cPLF_2eStlc_2eSTLC_2etru )
        | ( V3__t = cPLF_2eStlc_2eSTLC_2efls
          & cPLF_2eStlc_2eSTLC_2esubst___24a3(V1__x,V2__s,V3__t) = cPLF_2eStlc_2eSTLC_2efls )
        | ? [Vvar__0___24Anonymous__109386] :
            ( cPLF_2eStlc_2eSTLC_2etm___24t(Vvar__0___24Anonymous__109386)
            & ? [Vvar__1___24Anonymous__109387] :
                ( cPLF_2eStlc_2eSTLC_2etm___24t(Vvar__1___24Anonymous__109387)
                & ? [Vvar__2___24Anonymous__109388] :
                    ( cPLF_2eStlc_2eSTLC_2etm___24t(Vvar__2___24Anonymous__109388)
                    & V3__t = cPLF_2eStlc_2eSTLC_2etest___24a3(Vvar__0___24Anonymous__109386,Vvar__1___24Anonymous__109387,Vvar__2___24Anonymous__109388)
                    & cPLF_2eStlc_2eSTLC_2esubst___24a3(V1__x,V2__s,V3__t) = cPLF_2eStlc_2eSTLC_2etest___24a3(cPLF_2eStlc_2eSTLC_2esubst___24a3(V1__x,V2__s,Vvar__0___24Anonymous__109386),cPLF_2eStlc_2eSTLC_2esubst___24a3(V1__x,V2__s,Vvar__1___24Anonymous__109387),cPLF_2eStlc_2eSTLC_2esubst___24a3(V1__x,V2__s,Vvar__2___24Anonymous__109388)) ) ) ) ) ) ).

fof('$_def_PLF.Stlc.STLC.x',axiom,
    cPLF_2eStlc_2eSTLC_2ex = cCoq_2eStrings_2eString_2eString___24a2(cCoq_2eStrings_2eAscii_2eAscii___24a8(cCoq_2eInit_2eDatatypes_2efalse,cCoq_2eInit_2eDatatypes_2efalse,cCoq_2eInit_2eDatatypes_2efalse,cCoq_2eInit_2eDatatypes_2etrue,cCoq_2eInit_2eDatatypes_2etrue,cCoq_2eInit_2eDatatypes_2etrue,cCoq_2eInit_2eDatatypes_2etrue,cCoq_2eInit_2eDatatypes_2efalse),cCoq_2eStrings_2eString_2eEmptyString) ).

fof('$_def_PLF.Stlc.STLC.y',axiom,
    cPLF_2eStlc_2eSTLC_2ey = cCoq_2eStrings_2eString_2eString___24a2(cCoq_2eStrings_2eAscii_2eAscii___24a8(cCoq_2eInit_2eDatatypes_2etrue,cCoq_2eInit_2eDatatypes_2efalse,cCoq_2eInit_2eDatatypes_2efalse,cCoq_2eInit_2eDatatypes_2etrue,cCoq_2eInit_2eDatatypes_2etrue,cCoq_2eInit_2eDatatypes_2etrue,cCoq_2eInit_2eDatatypes_2etrue,cCoq_2eInit_2eDatatypes_2efalse),cCoq_2eStrings_2eString_2eEmptyString) ).

fof('$_def_PLF.Stlc.STLC.z',axiom,
    cPLF_2eStlc_2eSTLC_2ez = cCoq_2eStrings_2eString_2eString___24a2(cCoq_2eStrings_2eAscii_2eAscii___24a8(cCoq_2eInit_2eDatatypes_2efalse,cCoq_2eInit_2eDatatypes_2etrue,cCoq_2eInit_2eDatatypes_2efalse,cCoq_2eInit_2eDatatypes_2etrue,cCoq_2eInit_2eDatatypes_2etrue,cCoq_2eInit_2eDatatypes_2etrue,cCoq_2eInit_2eDatatypes_2etrue,cCoq_2eInit_2eDatatypes_2efalse),cCoq_2eStrings_2eString_2eEmptyString) ).

fof('$_def_PLF.StlcProp.STLCProp.closed',axiom,
    ! [V0__t] :
      ( cPLF_2eStlcProp_2eSTLCProp_2eclosed___24a1(V0__t)
    <=> ! [V1__x] :
          ( cCoq_2eStrings_2eString_2estring___24t(V1__x)
         => ~ cPLF_2eStlcProp_2eSTLCProp_2eappears__free__in___24a2(V1__x,V0__t) ) ) ).

fof('$_discrim_Coq.Bool.Bool.ReflectT$Coq.Bool.Bool.ReflectF',axiom,
    ! [Vvar__0__P__92263,Vvar__1___24Anonymous__92264,Vvar__0__P__92265,Vvar__1___24Anonymous__92266] : cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__92263) != cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__92265) ).

fof('$_discrim_Coq.FSets.FSetPositive.PositiveSet.Leaf$Coq.FSets.FSetPositive.PositiveSet.Node',axiom,
    ! [Vvar__0___24Anonymous__82631,Vvar__1___24Anonymous__82632,Vvar__2___24Anonymous__82633] : cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf != cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__82631,Vvar__1___24Anonymous__82632,Vvar__2___24Anonymous__82633) ).

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__112851,Vvar__1__Plt__112852,Vvar__2__Pgt__112853,Vvar__3___24Anonymous__112854,Vvar__0__Peq__112855,Vvar__1__Plt__112856,Vvar__2__Pgt__112857,Vvar__3___24Anonymous__112858] : cCoq_2eInit_2eDatatypes_2eCompEqT___24a3(Vvar__0__Peq__112851,Vvar__1__Plt__112852,Vvar__2__Pgt__112853) != cCoq_2eInit_2eDatatypes_2eCompLtT___24a3(Vvar__0__Peq__112855,Vvar__1__Plt__112856,Vvar__2__Pgt__112857) ).

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

fof('$_discrim_Coq.Init.Datatypes.O$Coq.Init.Datatypes.S',axiom,
    ! [Vvar__0___24Anonymous__3] : cCoq_2eInit_2eDatatypes_2eO != cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__3) ).

fof('$_discrim_Coq.Init.Datatypes.Some$Coq.Init.Datatypes.None',axiom,
    ! [Vvar__0__A__75636,Vvar__1___24Anonymous__75637,Vvar__0__A__75638] : cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__75636,Vvar__1___24Anonymous__75637) != cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__75638) ).

fof('$_discrim_Coq.Init.Datatypes.inl$Coq.Init.Datatypes.inr',axiom,
    ! [Vvar__0__A__88839,Vvar__1__B__88840,Vvar__2___24Anonymous__88841,Vvar__0__A__88842,Vvar__1__B__88843,Vvar__2___24Anonymous__88844] : cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__88839,Vvar__1__B__88840,Vvar__2___24Anonymous__88841) != cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__88842,Vvar__1__B__88843,Vvar__2___24Anonymous__88844) ).

fof('$_discrim_Coq.Init.Datatypes.nil$Coq.Init.Datatypes.cons',axiom,
    ! [Vvar__0__A__1143,Vvar__0__A__1144,Vvar__1___24Anonymous__1145,Vvar__2___24Anonymous__1146] : cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__1143) != cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__1144,Vvar__1___24Anonymous__1145,Vvar__2___24Anonymous__1146) ).

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__88873,Vvar__1__f__88874,Vvar__0__i__88875,Vvar__1__f__88876,Vvar__2__e__88877] : cCoq_2eInit_2eDecimal_2eDecimal___24a2(Vvar__0__i__88873,Vvar__1__f__88874) != cCoq_2eInit_2eDecimal_2eDecimalExp___24a3(Vvar__0__i__88875,Vvar__1__f__88876,Vvar__2__e__88877) ).

fof('$_discrim_Coq.Init.Decimal.Nil$Coq.Init.Decimal.D0',axiom,
    ! [Vvar__0___24Anonymous__75850] : cCoq_2eInit_2eDecimal_2eNil != cCoq_2eInit_2eDecimal_2eD0___24a1(Vvar__0___24Anonymous__75850) ).

fof('$_discrim_Coq.Init.Decimal.Pos$Coq.Init.Decimal.Neg',axiom,
    ! [Vvar__0__d__88861,Vvar__0__d__88862] : cCoq_2eInit_2eDecimal_2ePos___24a1(Vvar__0__d__88861) != cCoq_2eInit_2eDecimal_2eNeg___24a1(Vvar__0__d__88862) ).

fof('$_discrim_Coq.Init.Specif.inleft$Coq.Init.Specif.inright',axiom,
    ! [Vvar__0__A__303,Vvar__1__B__304,Vvar__2___24Anonymous__305,Vvar__0__A__306,Vvar__1__B__307,Vvar__2___24Anonymous__308] : cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__303,Vvar__1__B__304,Vvar__2___24Anonymous__305) != cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__306,Vvar__1__B__307) ).

fof('$_discrim_Coq.Init.Specif.left$Coq.Init.Specif.right',axiom,
    ! [Vvar__0__A__263,Vvar__1__B__264,Vvar__2___24Anonymous__265,Vvar__0__A__266,Vvar__1__B__267,Vvar__2___24Anonymous__268] : cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__263,Vvar__1__B__264) != cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__266,Vvar__1__B__267) ).

fof('$_discrim_Coq.Numbers.BinNums.N0$Coq.Numbers.BinNums.Npos',axiom,
    ! [Vvar__0___24Anonymous__1091] : cCoq_2eNumbers_2eBinNums_2eN0 != cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__1091) ).

fof('$_discrim_Coq.Numbers.BinNums.Z0$Coq.Numbers.BinNums.Zpos',axiom,
    ! [Vvar__0___24Anonymous__1102] : cCoq_2eNumbers_2eBinNums_2eZ0 != cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__1102) ).

fof('$_discrim_Coq.Numbers.BinNums.xI$Coq.Numbers.BinNums.xO',axiom,
    ! [Vvar__0___24Anonymous__1081,Vvar__0___24Anonymous__1082] : cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__1081) != cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__1082) ).

fof('$_discrim_Coq.PArith.BinPos.Pos.IsNul$Coq.PArith.BinPos.Pos.IsPos',axiom,
    ! [Vvar__0___24Anonymous__200928] : cCoq_2ePArith_2eBinPos_2ePos_2eIsNul != cCoq_2ePArith_2eBinPos_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__200928) ).

fof('$_discrim_Coq.PArith.BinPos.Pos.PeanoOne$Coq.PArith.BinPos.Pos.PeanoSucc',axiom,
    ! [Vvar__0__p__109202,Vvar__1___24Anonymous__109203] : cCoq_2ePArith_2eBinPos_2ePos_2ePeanoOne != cCoq_2ePArith_2eBinPos_2ePos_2ePeanoSucc___24a2(Vvar__0__p__109202,Vvar__1___24Anonymous__109203) ).

fof('$_discrim_Coq.PArith.BinPosDef.Pos.IsNul$Coq.PArith.BinPosDef.Pos.IsPos',axiom,
    ! [Vvar__0___24Anonymous__88809] : cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNul != cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__88809) ).

fof('$_discrim_Coq.Reals.Rfunctions.ZintNull$Coq.Reals.Rfunctions.ZintPos',axiom,
    ! [Vvar__0__x__113355,Vvar__1___24Anonymous__113356,Vvar__0__x__113357,Vvar__1__n__113358,Vvar__2___24Anonymous__113359] : cCoq_2eReals_2eRfunctions_2eZintNull___24a1(Vvar__0__x__113355) != cCoq_2eReals_2eRfunctions_2eZintPos___24a2(Vvar__0__x__113357,Vvar__1__n__113358) ).

fof('$_discrim_Coq.Strings.String.EmptyString$Coq.Strings.String.String',axiom,
    ! [Vvar__0___24Anonymous__585,Vvar__1___24Anonymous__586] : cCoq_2eStrings_2eString_2eEmptyString != cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__585,Vvar__1___24Anonymous__586) ).

fof('$_discrim_Coq.Structures.OrderedType.LT$Coq.Structures.OrderedType.EQ',axiom,
    ! [Vvar__0__X__90915,Vvar__1__lt__90916,Vvar__2__eq__90917,Vvar__3__x__90918,Vvar__4__y__90919,Vvar__5___24Anonymous__90920,Vvar__0__X__90921,Vvar__1__lt__90922,Vvar__2__eq__90923,Vvar__3__x__90924,Vvar__4__y__90925,Vvar__5___24Anonymous__90926] : cCoq_2eStructures_2eOrderedType_2eLT___24a5(Vvar__0__X__90915,Vvar__1__lt__90916,Vvar__2__eq__90917,Vvar__3__x__90918,Vvar__4__y__90919) != cCoq_2eStructures_2eOrderedType_2eEQ___24a5(Vvar__0__X__90921,Vvar__1__lt__90922,Vvar__2__eq__90923,Vvar__3__x__90924,Vvar__4__y__90925) ).

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__15,Vvar__0__n__16,Vvar__1___24Anonymous__17] : cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__15) != cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__16,Vvar__1___24Anonymous__17) ).

fof('$_discrim_Coq.Vectors.Vector.nil$Coq.Vectors.Vector.cons',axiom,
    ! [Vvar__0__A__200645,Vvar__0__A__200646,Vvar__1__h__200647,Vvar__2__n__200648,Vvar__3___24Anonymous__200649] : cCoq_2eVectors_2eVector_2enil___24a1(Vvar__0__A__200645) != cCoq_2eVectors_2eVector_2econs___24a4(Vvar__0__A__200646,Vvar__1__h__200647,Vvar__2__n__200648,Vvar__3___24Anonymous__200649) ).

fof('$_discrim_Coq.Vectors.VectorDef.nil$Coq.Vectors.VectorDef.cons',axiom,
    ! [Vvar__0__A__2073,Vvar__0__A__2074,Vvar__1__h__2075,Vvar__2__n__2076,Vvar__3___24Anonymous__2077] : cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__2073) != cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__2074,Vvar__1__h__2075,Vvar__2__n__2076,Vvar__3___24Anonymous__2077) ).

fof('$_discrim_Coq.micromega.EnvRing.PEc$Coq.micromega.EnvRing.PEX',axiom,
    ! [Vvar__0__C__86586,Vvar__1___24Anonymous__86587,Vvar__0__C__86588,Vvar__1___24Anonymous__86589] : cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__86586,Vvar__1___24Anonymous__86587) != cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__86588,Vvar__1___24Anonymous__86589) ).

fof('$_discrim_Coq.micromega.EnvRing.Pc$Coq.micromega.EnvRing.Pinj',axiom,
    ! [Vvar__0__C__88912,Vvar__1___24Anonymous__88913,Vvar__0__C__88914,Vvar__1___24Anonymous__88915,Vvar__2___24Anonymous__88916] : cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__88912,Vvar__1___24Anonymous__88913) != cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__88914,Vvar__1___24Anonymous__88915,Vvar__2___24Anonymous__88916) ).

fof('$_discrim_Coq.micromega.EnvRing.mon0$Coq.micromega.EnvRing.zmon',axiom,
    ! [Vvar__0___24Anonymous__85153,Vvar__1___24Anonymous__85154] : cCoq_2emicromega_2eEnvRing_2emon0 != cCoq_2emicromega_2eEnvRing_2ezmon___24a2(Vvar__0___24Anonymous__85153,Vvar__1___24Anonymous__85154) ).

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__85659,Vvar__1___24Anonymous__85660,Vvar__0__C__85661,Vvar__1___24Anonymous__85662] : cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(Vvar__0__C__85659,Vvar__1___24Anonymous__85660) != cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(Vvar__0__C__85661,Vvar__1___24Anonymous__85662) ).

fof('$_discrim_Coq.micromega.Tauto.TT$Coq.micromega.Tauto.FF',axiom,
    ! [Vvar__0__TA__86331,Vvar__1__TX__86332,Vvar__2__AA__86333,Vvar__3__AF__86334,Vvar__0__TA__86335,Vvar__1__TX__86336,Vvar__2__AA__86337,Vvar__3__AF__86338] : cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__86331,Vvar__1__TX__86332,Vvar__2__AA__86333,Vvar__3__AF__86334) != cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__86335,Vvar__1__TX__86336,Vvar__2__AA__86337,Vvar__3__AF__86338) ).

fof('$_discrim_Coq.micromega.VarMap.Empty$Coq.micromega.VarMap.Elt',axiom,
    ! [Vvar__0__A__86445,Vvar__0__A__86446,Vvar__1___24Anonymous__86447] : cCoq_2emicromega_2eVarMap_2eEmpty___24a1(Vvar__0__A__86445) != cCoq_2emicromega_2eVarMap_2eElt___24a2(Vvar__0__A__86446,Vvar__1___24Anonymous__86447) ).

fof('$_discrim_Coq.micromega.ZMicromega.DoneProof$Coq.micromega.ZMicromega.RatProof',axiom,
    ! [Vvar__0___24Anonymous__83822,Vvar__1___24Anonymous__83823] : cCoq_2emicromega_2eZMicromega_2eDoneProof != cCoq_2emicromega_2eZMicromega_2eRatProof___24a2(Vvar__0___24Anonymous__83822,Vvar__1___24Anonymous__83823) ).

fof('$_discrim_Coq.micromega.ZMicromega.Vars.Leaf$Coq.micromega.ZMicromega.Vars.Node',axiom,
    ! [Vvar__0___24Anonymous__200965,Vvar__1___24Anonymous__200966,Vvar__2___24Anonymous__200967] : cCoq_2emicromega_2eZMicromega_2eVars_2eLeaf != cCoq_2emicromega_2eZMicromega_2eVars_2eNode___24a3(Vvar__0___24Anonymous__200965,Vvar__1___24Anonymous__200966,Vvar__2___24Anonymous__200967) ).

fof('$_discrim_Coq.setoid_ring.Field_theory.FEO$Coq.setoid_ring.Field_theory.FEI',axiom,
    ! [Vvar__0__C__85462,Vvar__0__C__85463] : cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__85462) != cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__85463) ).

fof('$_discrim_Coq.setoid_ring.Ring_polynom.PEO$Coq.setoid_ring.Ring_polynom.PEI',axiom,
    ! [Vvar__0__C__1589,Vvar__0__C__1590] : cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__1589) != cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__1590) ).

fof('$_discrim_Coq.setoid_ring.Ring_polynom.Pc$Coq.setoid_ring.Ring_polynom.Pinj',axiom,
    ! [Vvar__0__C__1231,Vvar__1___24Anonymous__1232,Vvar__0__C__1233,Vvar__1___24Anonymous__1234,Vvar__2___24Anonymous__1235] : cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__1231,Vvar__1___24Anonymous__1232) != cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__1233,Vvar__1___24Anonymous__1234,Vvar__2___24Anonymous__1235) ).

fof('$_discrim_Coq.setoid_ring.Ring_polynom.mon0$Coq.setoid_ring.Ring_polynom.zmon',axiom,
    ! [Vvar__0___24Anonymous__1399,Vvar__1___24Anonymous__1400] : cCoq_2esetoid__ring_2eRing__polynom_2emon0 != cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__1399,Vvar__1___24Anonymous__1400) ).

fof('$_discrim_Coq.setoid_ring.Ring_theory.Abstract$Coq.setoid_ring.Ring_theory.Computational',axiom,
    ! [Vvar__0__R__85857,Vvar__1__req__85858,Vvar__2__reqb__85859,Vvar__3___24Anonymous__85860] : cCoq_2esetoid__ring_2eRing__theory_2eAbstract != cCoq_2esetoid__ring_2eRing__theory_2eComputational___24a3(Vvar__0__R__85857,Vvar__1__req__85858,Vvar__2__reqb__85859) ).

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

fof('$_discrim_PLF.Imp.AExp.ANum$PLF.Imp.AExp.APlus',axiom,
    ! [Vvar__0__n__79394,Vvar__0__a1__79395,Vvar__1__a2__79396] : cPLF_2eImp_2eAExp_2eANum___24a1(Vvar__0__n__79394) != cPLF_2eImp_2eAExp_2eAPlus___24a2(Vvar__0__a1__79395,Vvar__1__a2__79396) ).

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__373,Vvar__0__x__374] : cPLF_2eImp_2eANum___24a1(Vvar__0__n__373) != cPLF_2eImp_2eAId___24a1(Vvar__0__x__374) ).

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__528,Vvar__1__a__529] : cPLF_2eImp_2eCSkip != cPLF_2eImp_2eCAss___24a2(Vvar__0__x__528,Vvar__1__a__529) ).

fof('$_discrim_PLF.Imp.SPush$PLF.Imp.SLoad',axiom,
    ! [Vvar__0__n__76438,Vvar__0__x__76439] : cPLF_2eImp_2eSPush___24a1(Vvar__0__n__76438) != cPLF_2eImp_2eSLoad___24a1(Vvar__0__x__76439) ).

fof('$_discrim_PLF.Imp.aevalR_division.ANum$PLF.Imp.aevalR_division.APlus',axiom,
    ! [Vvar__0__n__83930,Vvar__0__a1__83931,Vvar__1__a2__83932] : cPLF_2eImp_2eaevalR__division_2eANum___24a1(Vvar__0__n__83930) != cPLF_2eImp_2eaevalR__division_2eAPlus___24a2(Vvar__0__a1__83931,Vvar__1__a2__83932) ).

fof('$_discrim_PLF.Imp.aevalR_extended.AAny$PLF.Imp.aevalR_extended.ANum',axiom,
    ! [Vvar__0__n__92234] : cPLF_2eImp_2eaevalR__extended_2eAAny != cPLF_2eImp_2eaevalR__extended_2eANum___24a1(Vvar__0__n__92234) ).

fof('$_discrim_PLF.References.STLCRef.Nat$PLF.References.STLCRef.Unit',axiom,
    cPLF_2eReferences_2eSTLCRef_2eNat != cPLF_2eReferences_2eSTLCRef_2eUnit ).

fof('$_discrim_PLF.References.STLCRef.var$PLF.References.STLCRef.app',axiom,
    ! [Vvar__0___24Anonymous__203632,Vvar__0___24Anonymous__203633,Vvar__1___24Anonymous__203634] : cPLF_2eReferences_2eSTLCRef_2evar___24a1(Vvar__0___24Anonymous__203632) != cPLF_2eReferences_2eSTLCRef_2eapp___24a2(Vvar__0___24Anonymous__203633,Vvar__1___24Anonymous__203634) ).

fof('$_discrim_PLF.Smallstep.C$PLF.Smallstep.P',axiom,
    ! [Vvar__0___24Anonymous__940,Vvar__0___24Anonymous__941,Vvar__1___24Anonymous__942] : cPLF_2eSmallstep_2eC___24a1(Vvar__0___24Anonymous__940) != cPLF_2eSmallstep_2eP___24a2(Vvar__0___24Anonymous__941,Vvar__1___24Anonymous__942) ).

fof('$_discrim_PLF.Smallstep.CImp.CSkip$PLF.Smallstep.CImp.CAss',axiom,
    ! [Vvar__0___24Anonymous__79540,Vvar__1___24Anonymous__79541] : cPLF_2eSmallstep_2eCImp_2eCSkip != cPLF_2eSmallstep_2eCImp_2eCAss___24a2(Vvar__0___24Anonymous__79540,Vvar__1___24Anonymous__79541) ).

fof('$_discrim_PLF.Smallstep.Combined.C$PLF.Smallstep.Combined.P',axiom,
    ! [Vvar__0___24Anonymous__92055,Vvar__0___24Anonymous__92056,Vvar__1___24Anonymous__92057] : cPLF_2eSmallstep_2eCombined_2eC___24a1(Vvar__0___24Anonymous__92055) != cPLF_2eSmallstep_2eCombined_2eP___24a2(Vvar__0___24Anonymous__92056,Vvar__1___24Anonymous__92057) ).

fof('$_discrim_PLF.Smallstep.Temp4.tru$PLF.Smallstep.Temp4.fls',axiom,
    cPLF_2eSmallstep_2eTemp4_2etru != cPLF_2eSmallstep_2eTemp4_2efls ).

fof('$_discrim_PLF.Stlc.STLC.Bool$PLF.Stlc.STLC.Arrow',axiom,
    ! [Vvar__0___24Anonymous__92120,Vvar__1___24Anonymous__92121] : cPLF_2eStlc_2eSTLC_2eBool != cPLF_2eStlc_2eSTLC_2eArrow___24a2(Vvar__0___24Anonymous__92120,Vvar__1___24Anonymous__92121) ).

fof('$_discrim_PLF.Stlc.STLC.var$PLF.Stlc.STLC.app',axiom,
    ! [Vvar__0___24Anonymous__92178,Vvar__0___24Anonymous__92179,Vvar__1___24Anonymous__92180] : cPLF_2eStlc_2eSTLC_2evar___24a1(Vvar__0___24Anonymous__92178) != cPLF_2eStlc_2eSTLC_2eapp___24a2(Vvar__0___24Anonymous__92179,Vvar__1___24Anonymous__92180) ).

fof('$_discrim_PLF.StlcProp.STLCArith.Arrow$PLF.StlcProp.STLCArith.Nat',axiom,
    ! [Vvar__0___24Anonymous__200665,Vvar__1___24Anonymous__200666] : cPLF_2eStlcProp_2eSTLCArith_2eArrow___24a2(Vvar__0___24Anonymous__200665,Vvar__1___24Anonymous__200666) != cPLF_2eStlcProp_2eSTLCArith_2eNat ).

fof('$_discrim_PLF.StlcProp.STLCArith.var$PLF.StlcProp.STLCArith.app',axiom,
    ! [Vvar__0___24Anonymous__200781,Vvar__0___24Anonymous__200782,Vvar__1___24Anonymous__200783] : cPLF_2eStlcProp_2eSTLCArith_2evar___24a1(Vvar__0___24Anonymous__200781) != cPLF_2eStlcProp_2eSTLCArith_2eapp___24a2(Vvar__0___24Anonymous__200782,Vvar__1___24Anonymous__200783) ).

fof('$_discrim_PLF.Types.Bool$PLF.Types.Nat',axiom,
    cPLF_2eTypes_2eBool != cPLF_2eTypes_2eNat ).

fof('$_discrim_PLF.Types.tru$PLF.Types.fls',axiom,
    cPLF_2eTypes_2etru != cPLF_2eTypes_2efls ).

fof('$_fix_1042_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__1042__v__CANONICAL__0___24a2(Vv__CANONICAL__1,Vv__CANONICAL__2) = Vv__CANONICAL__2 )
        | ? [Vvar__0___24Anonymous__1043] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__1043)
            & Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__1043)
            & c_24__fix__1042__v__CANONICAL__0___24a2(Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eDatatypes_2eS___24a1(c_24__fix__1042__v__CANONICAL__0___24a2(Vvar__0___24Anonymous__1043,Vv__CANONICAL__2)) ) ) ) ).

fof('$_fix_109197_v_CANONICAL_0',axiom,
    ! [Vv__CANONICAL__1] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
     => ( ? [Vvar__0___24Anonymous__109198] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__109198)
            & Vv__CANONICAL__1 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__109198)
            & c_24__fix__109197__v__CANONICAL__0___24a1(Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2exO___24a1(c_24__fix__109197__v__CANONICAL__0___24a1(Vvar__0___24Anonymous__109198)) )
        | ? [Vvar__0___24Anonymous__109199] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__109199)
            & Vv__CANONICAL__1 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__109199)
            & c_24__fix__109197__v__CANONICAL__0___24a1(Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__109199) )
        | ( Vv__CANONICAL__1 = cCoq_2eNumbers_2eBinNums_2exH
          & c_24__fix__109197__v__CANONICAL__0___24a1(Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ) ) ).

fof('$_fix_111186_v_CANONICAL_0',axiom,
    ! [Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
      ( cPLF_2eStlc_2eSTLC_2etm___24t(Vv__CANONICAL__3)
     => ( ? [Vvar__0___24Anonymous__111187] :
            ( cCoq_2eStrings_2eString_2estring___24t(Vvar__0___24Anonymous__111187)
            & ( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__1)
             => ( cCoq_2eStrings_2eString_2estring___24t(Vvar__0___24Anonymous__111187)
               => ( Vv__CANONICAL__3 = cPLF_2eStlc_2eSTLC_2evar___24a1(Vvar__0___24Anonymous__111187)
                  & ( ( cPLF_2eMaps_2eeqb__string___24a2(Vv__CANONICAL__1,Vvar__0___24Anonymous__111187) = cCoq_2eInit_2eDatatypes_2etrue
                      & c_24__fix__111186__v__CANONICAL__0___24a3(Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vv__CANONICAL__2 )
                    | ( cPLF_2eMaps_2eeqb__string___24a2(Vv__CANONICAL__1,Vvar__0___24Anonymous__111187) = cCoq_2eInit_2eDatatypes_2efalse
                      & c_24__fix__111186__v__CANONICAL__0___24a3(Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vv__CANONICAL__3 ) ) ) ) ) )
        | ? [Vvar__0___24Anonymous__111189] :
            ( cPLF_2eStlc_2eSTLC_2etm___24t(Vvar__0___24Anonymous__111189)
            & ? [Vvar__1___24Anonymous__111190] :
                ( cPLF_2eStlc_2eSTLC_2etm___24t(Vvar__1___24Anonymous__111190)
                & Vv__CANONICAL__3 = cPLF_2eStlc_2eSTLC_2eapp___24a2(Vvar__0___24Anonymous__111189,Vvar__1___24Anonymous__111190)
                & c_24__fix__111186__v__CANONICAL__0___24a3(Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cPLF_2eStlc_2eSTLC_2eapp___24a2(c_24__fix__111186__v__CANONICAL__0___24a3(Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__0___24Anonymous__111189),c_24__fix__111186__v__CANONICAL__0___24a3(Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__1___24Anonymous__111190)) ) )
        | ? [Vvar__0___24Anonymous__111192] :
            ( cCoq_2eStrings_2eString_2estring___24t(Vvar__0___24Anonymous__111192)
            & ? [Vvar__1___24Anonymous__111193] :
                ( cPLF_2eStlc_2eSTLC_2ety___24t(Vvar__1___24Anonymous__111193)
                & ? [Vvar__2___24Anonymous__111194] :
                    ( cPLF_2eStlc_2eSTLC_2etm___24t(Vvar__2___24Anonymous__111194)
                    & Vv__CANONICAL__3 = cPLF_2eStlc_2eSTLC_2eabs___24a3(Vvar__0___24Anonymous__111192,Vvar__1___24Anonymous__111193,Vvar__2___24Anonymous__111194)
                    & c_24__fix__111186__v__CANONICAL__0___24a3(Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cPLF_2eStlc_2eSTLC_2eabs___24a3(Vvar__0___24Anonymous__111192,Vvar__1___24Anonymous__111193,c_24__case__Coq_2eInit_2eDatatypes_2ebool_24111211___24a4(Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__0___24Anonymous__111192,Vvar__2___24Anonymous__111194)) ) ) )
        | ( Vv__CANONICAL__3 = cPLF_2eStlc_2eSTLC_2etru
          & c_24__fix__111186__v__CANONICAL__0___24a3(Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cPLF_2eStlc_2eSTLC_2etru )
        | ( Vv__CANONICAL__3 = cPLF_2eStlc_2eSTLC_2efls
          & c_24__fix__111186__v__CANONICAL__0___24a3(Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cPLF_2eStlc_2eSTLC_2efls )
        | ? [Vvar__0___24Anonymous__111201] :
            ( cPLF_2eStlc_2eSTLC_2etm___24t(Vvar__0___24Anonymous__111201)
            & ? [Vvar__1___24Anonymous__111202] :
                ( cPLF_2eStlc_2eSTLC_2etm___24t(Vvar__1___24Anonymous__111202)
                & ? [Vvar__2___24Anonymous__111203] :
                    ( cPLF_2eStlc_2eSTLC_2etm___24t(Vvar__2___24Anonymous__111203)
                    & Vv__CANONICAL__3 = cPLF_2eStlc_2eSTLC_2etest___24a3(Vvar__0___24Anonymous__111201,Vvar__1___24Anonymous__111202,Vvar__2___24Anonymous__111203)
                    & c_24__fix__111186__v__CANONICAL__0___24a3(Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cPLF_2eStlc_2eSTLC_2etest___24a3(c_24__fix__111186__v__CANONICAL__0___24a3(Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__0___24Anonymous__111201),c_24__fix__111186__v__CANONICAL__0___24a3(Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__1___24Anonymous__111202),c_24__fix__111186__v__CANONICAL__0___24a3(Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__2___24Anonymous__111203)) ) ) ) ) ) ).

fof('$_fix_115391_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__115391__v__CANONICAL__1___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vv__CANONICAL__3 )
          | ? [Vvar__1___24Anonymous__115395] :
              ( t(Vvar__1___24Anonymous__115395,Vv__CANONICAL__0)
              & ? [Vvar__2___24Anonymous__115396] :
                  ( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vvar__2___24Anonymous__115396)
                  & Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__115395,Vvar__2___24Anonymous__115396)
                  & c_24__fix__115391__v__CANONICAL__1___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__115395,c_24__fix__115391__v__CANONICAL__1___24a3(Vv__CANONICAL__0,Vvar__2___24Anonymous__115396,Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_fix_209397_v_CANONICAL_0',axiom,
    ! [Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
      ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vv__CANONICAL__3)
     => ( ? [Vvar__0___24Anonymous__209398] :
            ( cCoq_2eStrings_2eString_2estring___24t(Vvar__0___24Anonymous__209398)
            & ( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__1)
             => ( cCoq_2eStrings_2eString_2estring___24t(Vvar__0___24Anonymous__209398)
               => ( Vv__CANONICAL__3 = cPLF_2eReferences_2eSTLCRef_2evar___24a1(Vvar__0___24Anonymous__209398)
                  & ( ( cPLF_2eMaps_2eeqb__string___24a2(Vv__CANONICAL__1,Vvar__0___24Anonymous__209398) = cCoq_2eInit_2eDatatypes_2etrue
                      & c_24__fix__209397__v__CANONICAL__0___24a3(Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vv__CANONICAL__2 )
                    | ( cPLF_2eMaps_2eeqb__string___24a2(Vv__CANONICAL__1,Vvar__0___24Anonymous__209398) = cCoq_2eInit_2eDatatypes_2efalse
                      & c_24__fix__209397__v__CANONICAL__0___24a3(Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vv__CANONICAL__3 ) ) ) ) ) )
        | ? [Vvar__0___24Anonymous__209400] :
            ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__0___24Anonymous__209400)
            & ? [Vvar__1___24Anonymous__209401] :
                ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__1___24Anonymous__209401)
                & Vv__CANONICAL__3 = cPLF_2eReferences_2eSTLCRef_2eapp___24a2(Vvar__0___24Anonymous__209400,Vvar__1___24Anonymous__209401)
                & c_24__fix__209397__v__CANONICAL__0___24a3(Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cPLF_2eReferences_2eSTLCRef_2eapp___24a2(c_24__fix__209397__v__CANONICAL__0___24a3(Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__0___24Anonymous__209400),c_24__fix__209397__v__CANONICAL__0___24a3(Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__1___24Anonymous__209401)) ) )
        | ? [Vvar__0___24Anonymous__209403] :
            ( cCoq_2eStrings_2eString_2estring___24t(Vvar__0___24Anonymous__209403)
            & ? [Vvar__1___24Anonymous__209404] :
                ( cPLF_2eReferences_2eSTLCRef_2ety___24t(Vvar__1___24Anonymous__209404)
                & ? [Vvar__2___24Anonymous__209405] :
                    ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__2___24Anonymous__209405)
                    & ( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__1)
                     => ( cCoq_2eStrings_2eString_2estring___24t(Vvar__0___24Anonymous__209403)
                       => ( Vv__CANONICAL__3 = cPLF_2eReferences_2eSTLCRef_2eabs___24a3(Vvar__0___24Anonymous__209403,Vvar__1___24Anonymous__209404,Vvar__2___24Anonymous__209405)
                          & ( ( cPLF_2eMaps_2eeqb__string___24a2(Vv__CANONICAL__1,Vvar__0___24Anonymous__209403) = cCoq_2eInit_2eDatatypes_2etrue
                              & c_24__fix__209397__v__CANONICAL__0___24a3(Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vv__CANONICAL__3 )
                            | ( cPLF_2eMaps_2eeqb__string___24a2(Vv__CANONICAL__1,Vvar__0___24Anonymous__209403) = cCoq_2eInit_2eDatatypes_2efalse
                              & c_24__fix__209397__v__CANONICAL__0___24a3(Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cPLF_2eReferences_2eSTLCRef_2eabs___24a3(Vvar__0___24Anonymous__209403,Vvar__1___24Anonymous__209404,c_24__fix__209397__v__CANONICAL__0___24a3(Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__2___24Anonymous__209405)) ) ) ) ) ) ) ) )
        | ? [Vvar__0___24Anonymous__209412] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__209412)
            & Vv__CANONICAL__3 = cPLF_2eReferences_2eSTLCRef_2econst___24a1(Vvar__0___24Anonymous__209412)
            & c_24__fix__209397__v__CANONICAL__0___24a3(Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vv__CANONICAL__3 )
        | ? [Vvar__0___24Anonymous__209413] :
            ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__0___24Anonymous__209413)
            & Vv__CANONICAL__3 = cPLF_2eReferences_2eSTLCRef_2escc___24a1(Vvar__0___24Anonymous__209413)
            & c_24__fix__209397__v__CANONICAL__0___24a3(Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cPLF_2eReferences_2eSTLCRef_2escc___24a1(c_24__fix__209397__v__CANONICAL__0___24a3(Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__0___24Anonymous__209413)) )
        | ? [Vvar__0___24Anonymous__209414] :
            ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__0___24Anonymous__209414)
            & Vv__CANONICAL__3 = cPLF_2eReferences_2eSTLCRef_2eprd___24a1(Vvar__0___24Anonymous__209414)
            & c_24__fix__209397__v__CANONICAL__0___24a3(Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cPLF_2eReferences_2eSTLCRef_2eprd___24a1(c_24__fix__209397__v__CANONICAL__0___24a3(Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__0___24Anonymous__209414)) )
        | ? [Vvar__0___24Anonymous__209415] :
            ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__0___24Anonymous__209415)
            & ? [Vvar__1___24Anonymous__209416] :
                ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__1___24Anonymous__209416)
                & Vv__CANONICAL__3 = cPLF_2eReferences_2eSTLCRef_2emlt___24a2(Vvar__0___24Anonymous__209415,Vvar__1___24Anonymous__209416)
                & c_24__fix__209397__v__CANONICAL__0___24a3(Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cPLF_2eReferences_2eSTLCRef_2emlt___24a2(c_24__fix__209397__v__CANONICAL__0___24a3(Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__0___24Anonymous__209415),c_24__fix__209397__v__CANONICAL__0___24a3(Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__1___24Anonymous__209416)) ) )
        | ? [Vvar__0___24Anonymous__209418] :
            ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__0___24Anonymous__209418)
            & ? [Vvar__1___24Anonymous__209419] :
                ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__1___24Anonymous__209419)
                & ? [Vvar__2___24Anonymous__209420] :
                    ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__2___24Anonymous__209420)
                    & Vv__CANONICAL__3 = cPLF_2eReferences_2eSTLCRef_2etest0___24a3(Vvar__0___24Anonymous__209418,Vvar__1___24Anonymous__209419,Vvar__2___24Anonymous__209420)
                    & c_24__fix__209397__v__CANONICAL__0___24a3(Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cPLF_2eReferences_2eSTLCRef_2etest0___24a3(c_24__fix__209397__v__CANONICAL__0___24a3(Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__0___24Anonymous__209418),c_24__fix__209397__v__CANONICAL__0___24a3(Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__1___24Anonymous__209419),c_24__fix__209397__v__CANONICAL__0___24a3(Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__2___24Anonymous__209420)) ) ) )
        | ( Vv__CANONICAL__3 = cPLF_2eReferences_2eSTLCRef_2eunit
          & c_24__fix__209397__v__CANONICAL__0___24a3(Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vv__CANONICAL__3 )
        | ? [Vvar__0___24Anonymous__209424] :
            ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__0___24Anonymous__209424)
            & Vv__CANONICAL__3 = cPLF_2eReferences_2eSTLCRef_2eref___24a1(Vvar__0___24Anonymous__209424)
            & c_24__fix__209397__v__CANONICAL__0___24a3(Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cPLF_2eReferences_2eSTLCRef_2eref___24a1(c_24__fix__209397__v__CANONICAL__0___24a3(Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__0___24Anonymous__209424)) )
        | ? [Vvar__0___24Anonymous__209425] :
            ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__0___24Anonymous__209425)
            & Vv__CANONICAL__3 = cPLF_2eReferences_2eSTLCRef_2ederef___24a1(Vvar__0___24Anonymous__209425)
            & c_24__fix__209397__v__CANONICAL__0___24a3(Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cPLF_2eReferences_2eSTLCRef_2ederef___24a1(c_24__fix__209397__v__CANONICAL__0___24a3(Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__0___24Anonymous__209425)) )
        | ? [Vvar__0___24Anonymous__209426] :
            ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__0___24Anonymous__209426)
            & ? [Vvar__1___24Anonymous__209427] :
                ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__1___24Anonymous__209427)
                & Vv__CANONICAL__3 = cPLF_2eReferences_2eSTLCRef_2eassign___24a2(Vvar__0___24Anonymous__209426,Vvar__1___24Anonymous__209427)
                & c_24__fix__209397__v__CANONICAL__0___24a3(Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cPLF_2eReferences_2eSTLCRef_2eassign___24a2(c_24__fix__209397__v__CANONICAL__0___24a3(Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__0___24Anonymous__209426),c_24__fix__209397__v__CANONICAL__0___24a3(Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__1___24Anonymous__209427)) ) )
        | ? [Vvar__0___24Anonymous__209429] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__209429)
            & Vv__CANONICAL__3 = cPLF_2eReferences_2eSTLCRef_2eloc___24a1(Vvar__0___24Anonymous__209429)
            & c_24__fix__209397__v__CANONICAL__0___24a3(Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vv__CANONICAL__3 ) ) ) ).

fof('$_fix_211015_v_CANONICAL_0',axiom,
    ! [Vv__CANONICAL__1] :
      ( cCoq_2eInit_2eDatatypes_2elist___24t(cPLF_2eReferences_2eSTLCRef_2etm,Vv__CANONICAL__1)
     => ( ( Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2enil___24a1(cPLF_2eReferences_2eSTLCRef_2etm)
          & c_24__fix__211015__v__CANONICAL__0___24a1(Vv__CANONICAL__1) = cCoq_2eInit_2eDatatypes_2eO )
        | ? [Vvar__1___24Anonymous__211019] :
            ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__1___24Anonymous__211019)
            & ? [Vvar__2___24Anonymous__211020] :
                ( cCoq_2eInit_2eDatatypes_2elist___24t(cPLF_2eReferences_2eSTLCRef_2etm,Vvar__2___24Anonymous__211020)
                & Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2econs___24a3(cPLF_2eReferences_2eSTLCRef_2etm,Vvar__1___24Anonymous__211019,Vvar__2___24Anonymous__211020)
                & c_24__fix__211015__v__CANONICAL__0___24a1(Vv__CANONICAL__1) = cCoq_2eInit_2eDatatypes_2eS___24a1(c_24__fix__211015__v__CANONICAL__0___24a1(Vvar__2___24Anonymous__211020)) ) ) ) ) ).

fof('$_fix_211134_v_CANONICAL_0',axiom,
    ! [Vv__CANONICAL__1,Vv__CANONICAL__2] :
      ( cCoq_2eInit_2eDatatypes_2elist___24t(cPLF_2eReferences_2eSTLCRef_2etm,Vv__CANONICAL__1)
     => ( ( Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2enil___24a1(cPLF_2eReferences_2eSTLCRef_2etm)
          & c_24__fix__211134__v__CANONICAL__0___24a2(Vv__CANONICAL__1,Vv__CANONICAL__2) = Vv__CANONICAL__2 )
        | ? [Vvar__1___24Anonymous__211138] :
            ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__1___24Anonymous__211138)
            & ? [Vvar__2___24Anonymous__211139] :
                ( cCoq_2eInit_2eDatatypes_2elist___24t(cPLF_2eReferences_2eSTLCRef_2etm,Vvar__2___24Anonymous__211139)
                & Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2econs___24a3(cPLF_2eReferences_2eSTLCRef_2etm,Vvar__1___24Anonymous__211138,Vvar__2___24Anonymous__211139)
                & c_24__fix__211134__v__CANONICAL__0___24a2(Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eDatatypes_2econs___24a3(cPLF_2eReferences_2eSTLCRef_2etm,Vvar__1___24Anonymous__211138,c_24__fix__211134__v__CANONICAL__0___24a2(Vvar__2___24Anonymous__211139,Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_fix_211437_v_CANONICAL_0',axiom,
    ! [Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
     => ( ( cCoq_2eInit_2eDatatypes_2elist___24t(cPLF_2eReferences_2eSTLCRef_2etm,Vv__CANONICAL__2)
         => ( Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2eO
            & ( ( Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2enil___24a1(cPLF_2eReferences_2eSTLCRef_2etm)
                & c_24__fix__211437__v__CANONICAL__0___24a3(Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vv__CANONICAL__3 )
              | ? [Vvar__1___24Anonymous__211441] :
                  ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__1___24Anonymous__211441)
                  & ? [Vvar__2___24Anonymous__211442] :
                      ( cCoq_2eInit_2eDatatypes_2elist___24t(cPLF_2eReferences_2eSTLCRef_2etm,Vvar__2___24Anonymous__211442)
                      & Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2econs___24a3(cPLF_2eReferences_2eSTLCRef_2etm,Vvar__1___24Anonymous__211441,Vvar__2___24Anonymous__211442)
                      & c_24__fix__211437__v__CANONICAL__0___24a3(Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vvar__1___24Anonymous__211441 ) ) ) ) )
        | ? [Vvar__0___24Anonymous__211444] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__211444)
            & ( cCoq_2eInit_2eDatatypes_2elist___24t(cPLF_2eReferences_2eSTLCRef_2etm,Vv__CANONICAL__2)
             => ( Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__211444)
                & ( ( Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2enil___24a1(cPLF_2eReferences_2eSTLCRef_2etm)
                    & c_24__fix__211437__v__CANONICAL__0___24a3(Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vv__CANONICAL__3 )
                  | ? [Vvar__1___24Anonymous__211451] :
                      ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__1___24Anonymous__211451)
                      & ? [Vvar__2___24Anonymous__211452] :
                          ( cCoq_2eInit_2eDatatypes_2elist___24t(cPLF_2eReferences_2eSTLCRef_2etm,Vvar__2___24Anonymous__211452)
                          & Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2econs___24a3(cPLF_2eReferences_2eSTLCRef_2etm,Vvar__1___24Anonymous__211451,Vvar__2___24Anonymous__211452)
                          & c_24__fix__211437__v__CANONICAL__0___24a3(Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = c_24__fix__211437__v__CANONICAL__0___24a3(Vvar__0___24Anonymous__211444,Vvar__2___24Anonymous__211452,Vv__CANONICAL__3) ) ) ) ) ) ) ) ) ).

fof('$_fix_211742_v_CANONICAL_0',axiom,
    ! [Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
      ( cType___24t(Vv__CANONICAL__1)
     => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__1,Vv__CANONICAL__4)
       => ( ( Vv__CANONICAL__4 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__1)
            & c_24__fix__211742__v__CANONICAL__0___24a4(Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__1) )
          | ? [Vvar__1___24Anonymous__211746] :
              ( t(Vvar__1___24Anonymous__211746,Vv__CANONICAL__1)
              & ? [Vvar__2___24Anonymous__211747] :
                  ( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__1,Vvar__2___24Anonymous__211747)
                  & ( cType___24t(Vv__CANONICAL__1)
                   => ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
                     => ( Vv__CANONICAL__4 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__1,Vvar__1___24Anonymous__211746,Vvar__2___24Anonymous__211747)
                        & ( ( Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2eO
                            & c_24__fix__211742__v__CANONICAL__0___24a4(Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__1,Vv__CANONICAL__3,Vvar__2___24Anonymous__211747) )
                          | ? [Vvar__0___24Anonymous__211753] :
                              ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__211753)
                              & Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__211753)
                              & c_24__fix__211742__v__CANONICAL__0___24a4(Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__1,Vvar__1___24Anonymous__211746,c_24__fix__211742__v__CANONICAL__0___24a4(Vv__CANONICAL__1,Vvar__0___24Anonymous__211753,Vv__CANONICAL__3,Vvar__2___24Anonymous__211747)) ) ) ) ) ) ) ) ) ) ) ).

fof('$_fix_212205_v_CANONICAL_0',axiom,
    ! [Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
     => ( ( cCoq_2eInit_2eDatatypes_2elist___24t(cPLF_2eReferences_2eSTLCRef_2ety,Vv__CANONICAL__2)
         => ( Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2eO
            & ( ( Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2enil___24a1(cPLF_2eReferences_2eSTLCRef_2ety)
                & c_24__fix__212205__v__CANONICAL__0___24a3(Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vv__CANONICAL__3 )
              | ? [Vvar__1___24Anonymous__212209] :
                  ( cPLF_2eReferences_2eSTLCRef_2ety___24t(Vvar__1___24Anonymous__212209)
                  & ? [Vvar__2___24Anonymous__212210] :
                      ( cCoq_2eInit_2eDatatypes_2elist___24t(cPLF_2eReferences_2eSTLCRef_2ety,Vvar__2___24Anonymous__212210)
                      & Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2econs___24a3(cPLF_2eReferences_2eSTLCRef_2ety,Vvar__1___24Anonymous__212209,Vvar__2___24Anonymous__212210)
                      & c_24__fix__212205__v__CANONICAL__0___24a3(Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vvar__1___24Anonymous__212209 ) ) ) ) )
        | ? [Vvar__0___24Anonymous__212212] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__212212)
            & ( cCoq_2eInit_2eDatatypes_2elist___24t(cPLF_2eReferences_2eSTLCRef_2ety,Vv__CANONICAL__2)
             => ( Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__212212)
                & ( ( Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2enil___24a1(cPLF_2eReferences_2eSTLCRef_2ety)
                    & c_24__fix__212205__v__CANONICAL__0___24a3(Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vv__CANONICAL__3 )
                  | ? [Vvar__1___24Anonymous__212219] :
                      ( cPLF_2eReferences_2eSTLCRef_2ety___24t(Vvar__1___24Anonymous__212219)
                      & ? [Vvar__2___24Anonymous__212220] :
                          ( cCoq_2eInit_2eDatatypes_2elist___24t(cPLF_2eReferences_2eSTLCRef_2ety,Vvar__2___24Anonymous__212220)
                          & Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2econs___24a3(cPLF_2eReferences_2eSTLCRef_2ety,Vvar__1___24Anonymous__212219,Vvar__2___24Anonymous__212220)
                          & c_24__fix__212205__v__CANONICAL__0___24a3(Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = c_24__fix__212205__v__CANONICAL__0___24a3(Vvar__0___24Anonymous__212212,Vvar__2___24Anonymous__212220,Vv__CANONICAL__3) ) ) ) ) ) ) ) ) ).

fof('$_fix_77213_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__77213__v__CANONICAL__0___24a2(Vv__CANONICAL__1,Vv__CANONICAL__2) = Vv__CANONICAL__1 )
        | ? [Vvar__0___24Anonymous__77214] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__77214)
            & ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
             => ( Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__77214)
                & ( ( Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2eO
                    & c_24__fix__77213__v__CANONICAL__0___24a2(Vv__CANONICAL__1,Vv__CANONICAL__2) = Vv__CANONICAL__1 )
                  | ? [Vvar__0___24Anonymous__77217] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__77217)
                      & Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__77217)
                      & c_24__fix__77213__v__CANONICAL__0___24a2(Vv__CANONICAL__1,Vv__CANONICAL__2) = c_24__fix__77213__v__CANONICAL__0___24a2(Vvar__0___24Anonymous__77214,Vvar__0___24Anonymous__77217) ) ) ) ) ) ) ) ).

fof('$_fix_77299_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__77299__v__CANONICAL__0___24a2(Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eDatatypes_2eO )
        | ? [Vvar__0___24Anonymous__77300] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__77300)
            & Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__77300)
            & c_24__fix__77299__v__CANONICAL__0___24a2(Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eNat_2eadd___24a2(Vv__CANONICAL__2,c_24__fix__77299__v__CANONICAL__0___24a2(Vvar__0___24Anonymous__77300,Vv__CANONICAL__2)) ) ) ) ).

fof('$_fix_77667_v_CANONICAL_0',axiom,
    ! [Vv__CANONICAL__1,Vv__CANONICAL__2] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
     => ( ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
         => ( Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2eO
            & ( ( Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2eO
                & c_24__fix__77667__v__CANONICAL__0___24a2(Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eDatatypes_2etrue )
              | ? [Vvar__0___24Anonymous__77668] :
                  ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__77668)
                  & Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__77668)
                  & c_24__fix__77667__v__CANONICAL__0___24a2(Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) )
        | ? [Vvar__0___24Anonymous__77669] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__77669)
            & ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
             => ( Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__77669)
                & ( ( Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2eO
                    & c_24__fix__77667__v__CANONICAL__0___24a2(Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eDatatypes_2efalse )
                  | ? [Vvar__0___24Anonymous__77672] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__77672)
                      & Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__77672)
                      & c_24__fix__77667__v__CANONICAL__0___24a2(Vv__CANONICAL__1,Vv__CANONICAL__2) = c_24__fix__77667__v__CANONICAL__0___24a2(Vvar__0___24Anonymous__77669,Vvar__0___24Anonymous__77672) ) ) ) ) ) ) ) ).

fof('$_fix_77969_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__77969__v__CANONICAL__0___24a2(Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eDatatypes_2etrue )
        | ? [Vvar__0___24Anonymous__77970] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__77970)
            & ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
             => ( Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__77970)
                & ( ( Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2eO
                    & c_24__fix__77969__v__CANONICAL__0___24a2(Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eDatatypes_2efalse )
                  | ? [Vvar__0___24Anonymous__77973] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__77973)
                      & Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__77973)
                      & c_24__fix__77969__v__CANONICAL__0___24a2(Vv__CANONICAL__1,Vv__CANONICAL__2) = c_24__fix__77969__v__CANONICAL__0___24a2(Vvar__0___24Anonymous__77970,Vvar__0___24Anonymous__77973) ) ) ) ) ) ) ) ).

fof('$_fix_80266_1_add_carry',axiom,
    ! [V2__x,V3__y] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__x)
     => ( ? [Vvar__0___24Anonymous__80281] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__80281)
            & ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
             => ( V2__x = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__80281)
                & ( ? [Vvar__0___24Anonymous__80285] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__80285)
                      & V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__80285)
                      & c_24__fix__80266__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(c_24__fix__80266__1__add__carry___24a2(Vvar__0___24Anonymous__80281,Vvar__0___24Anonymous__80285)) )
                  | ? [Vvar__0___24Anonymous__80286] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__80286)
                      & V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__80286)
                      & c_24__fix__80266__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(c_24__fix__80266__1__add__carry___24a2(Vvar__0___24Anonymous__80281,Vvar__0___24Anonymous__80286)) )
                  | ( V3__y = cCoq_2eNumbers_2eBinNums_2exH
                    & c_24__fix__80266__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__80281)) ) ) ) ) )
        | ? [Vvar__0___24Anonymous__80287] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__80287)
            & ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
             => ( V2__x = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__80287)
                & ( ? [Vvar__0___24Anonymous__80291] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__80291)
                      & V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__80291)
                      & c_24__fix__80266__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(c_24__fix__80266__1__add__carry___24a2(Vvar__0___24Anonymous__80287,Vvar__0___24Anonymous__80291)) )
                  | ? [Vvar__0___24Anonymous__80292] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__80292)
                      & V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__80292)
                      & c_24__fix__80266__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__80287,Vvar__0___24Anonymous__80292)) )
                  | ( V3__y = cCoq_2eNumbers_2eBinNums_2exH
                    & c_24__fix__80266__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__80287)) ) ) ) ) )
        | ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__y)
         => ( V2__x = cCoq_2eNumbers_2eBinNums_2exH
            & ( ? [Vvar__0___24Anonymous__80293] :
                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__80293)
                  & V3__y = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__80293)
                  & c_24__fix__80266__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__80293)) )
              | ? [Vvar__0___24Anonymous__80294] :
                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__80294)
                  & V3__y = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__80294)
                  & c_24__fix__80266__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__80294)) )
              | ( V3__y = cCoq_2eNumbers_2eBinNums_2exH
                & c_24__fix__80266__1__add__carry___24a2(V2__x,V3__y) = cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ) ) ) ) ) ).

fof('$_inj_Coq.Bool.Bool.ReflectF',axiom,
    ! [Vvar__0__P__92271,Vvar__0__P__92272,Vvar__1___24Anonymous__92273,Vvar__1___24Anonymous__92274] :
      ( cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__92271) = cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__92272)
     => ( c_24Proof = c_24Proof
        & Vvar__0__P__92271 = Vvar__0__P__92272 ) ) ).

fof('$_inj_Coq.Bool.Bool.ReflectT',axiom,
    ! [Vvar__0__P__92267,Vvar__0__P__92268,Vvar__1___24Anonymous__92269,Vvar__1___24Anonymous__92270] :
      ( cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__92267) = cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__92268)
     => ( c_24Proof = c_24Proof
        & Vvar__0__P__92267 = Vvar__0__P__92268 ) ) ).

fof('$_inj_Coq.FSets.FSetPositive.PositiveSet.Node',axiom,
    ! [Vvar__0___24Anonymous__82634,Vvar__0___24Anonymous__82635,Vvar__1___24Anonymous__82636,Vvar__1___24Anonymous__82637,Vvar__2___24Anonymous__82638,Vvar__2___24Anonymous__82639] :
      ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__82634,Vvar__1___24Anonymous__82636,Vvar__2___24Anonymous__82638) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__82635,Vvar__1___24Anonymous__82637,Vvar__2___24Anonymous__82639)
     => ( Vvar__2___24Anonymous__82638 = Vvar__2___24Anonymous__82639
        & Vvar__1___24Anonymous__82636 = Vvar__1___24Anonymous__82637
        & Vvar__0___24Anonymous__82634 = Vvar__0___24Anonymous__82635 ) ) ).

fof('$_inj_Coq.Init.Datatypes.CompEqT',axiom,
    ! [Vvar__0__Peq__112859,Vvar__0__Peq__112860,Vvar__1__Plt__112861,Vvar__1__Plt__112862,Vvar__2__Pgt__112863,Vvar__2__Pgt__112864,Vvar__3___24Anonymous__112865,Vvar__3___24Anonymous__112866] :
      ( cCoq_2eInit_2eDatatypes_2eCompEqT___24a3(Vvar__0__Peq__112859,Vvar__1__Plt__112861,Vvar__2__Pgt__112863) = cCoq_2eInit_2eDatatypes_2eCompEqT___24a3(Vvar__0__Peq__112860,Vvar__1__Plt__112862,Vvar__2__Pgt__112864)
     => ( c_24Proof = c_24Proof
        & Vvar__2__Pgt__112863 = Vvar__2__Pgt__112864
        & Vvar__1__Plt__112861 = Vvar__1__Plt__112862
        & Vvar__0__Peq__112859 = Vvar__0__Peq__112860 ) ) ).

fof('$_inj_Coq.Init.Datatypes.CompGtT',axiom,
    ! [Vvar__0__Peq__112875,Vvar__0__Peq__112876,Vvar__1__Plt__112877,Vvar__1__Plt__112878,Vvar__2__Pgt__112879,Vvar__2__Pgt__112880,Vvar__3___24Anonymous__112881,Vvar__3___24Anonymous__112882] :
      ( cCoq_2eInit_2eDatatypes_2eCompGtT___24a3(Vvar__0__Peq__112875,Vvar__1__Plt__112877,Vvar__2__Pgt__112879) = cCoq_2eInit_2eDatatypes_2eCompGtT___24a3(Vvar__0__Peq__112876,Vvar__1__Plt__112878,Vvar__2__Pgt__112880)
     => ( c_24Proof = c_24Proof
        & Vvar__2__Pgt__112879 = Vvar__2__Pgt__112880
        & Vvar__1__Plt__112877 = Vvar__1__Plt__112878
        & Vvar__0__Peq__112875 = Vvar__0__Peq__112876 ) ) ).

fof('$_inj_Coq.Init.Datatypes.CompLtT',axiom,
    ! [Vvar__0__Peq__112867,Vvar__0__Peq__112868,Vvar__1__Plt__112869,Vvar__1__Plt__112870,Vvar__2__Pgt__112871,Vvar__2__Pgt__112872,Vvar__3___24Anonymous__112873,Vvar__3___24Anonymous__112874] :
      ( cCoq_2eInit_2eDatatypes_2eCompLtT___24a3(Vvar__0__Peq__112867,Vvar__1__Plt__112869,Vvar__2__Pgt__112871) = cCoq_2eInit_2eDatatypes_2eCompLtT___24a3(Vvar__0__Peq__112868,Vvar__1__Plt__112870,Vvar__2__Pgt__112872)
     => ( c_24Proof = c_24Proof
        & Vvar__2__Pgt__112871 = Vvar__2__Pgt__112872
        & Vvar__1__Plt__112869 = Vvar__1__Plt__112870
        & Vvar__0__Peq__112867 = Vvar__0__Peq__112868 ) ) ).

fof('$_inj_Coq.Init.Datatypes.None',axiom,
    ! [Vvar__0__A__75643,Vvar__0__A__75644] :
      ( cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__75643) = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__75644)
     => Vvar__0__A__75643 = Vvar__0__A__75644 ) ).

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

fof('$_inj_Coq.Init.Datatypes.Some',axiom,
    ! [Vvar__0__A__75639,Vvar__0__A__75640,Vvar__1___24Anonymous__75641,Vvar__1___24Anonymous__75642] :
      ( cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__75639,Vvar__1___24Anonymous__75641) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__75640,Vvar__1___24Anonymous__75642)
     => ( Vvar__1___24Anonymous__75641 = Vvar__1___24Anonymous__75642
        & Vvar__0__A__75639 = Vvar__0__A__75640 ) ) ).

fof('$_inj_Coq.Init.Datatypes.cons',axiom,
    ! [Vvar__0__A__1149,Vvar__0__A__1150,Vvar__1___24Anonymous__1151,Vvar__1___24Anonymous__1152,Vvar__2___24Anonymous__1153,Vvar__2___24Anonymous__1154] :
      ( cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__1149,Vvar__1___24Anonymous__1151,Vvar__2___24Anonymous__1153) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__1150,Vvar__1___24Anonymous__1152,Vvar__2___24Anonymous__1154)
     => ( Vvar__2___24Anonymous__1153 = Vvar__2___24Anonymous__1154
        & Vvar__1___24Anonymous__1151 = Vvar__1___24Anonymous__1152
        & Vvar__0__A__1149 = Vvar__0__A__1150 ) ) ).

fof('$_inj_Coq.Init.Datatypes.inl',axiom,
    ! [Vvar__0__A__88845,Vvar__0__A__88846,Vvar__1__B__88847,Vvar__1__B__88848,Vvar__2___24Anonymous__88849,Vvar__2___24Anonymous__88850] :
      ( cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__88845,Vvar__1__B__88847,Vvar__2___24Anonymous__88849) = cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__88846,Vvar__1__B__88848,Vvar__2___24Anonymous__88850)
     => ( Vvar__2___24Anonymous__88849 = Vvar__2___24Anonymous__88850
        & Vvar__1__B__88847 = Vvar__1__B__88848
        & Vvar__0__A__88845 = Vvar__0__A__88846 ) ) ).

fof('$_inj_Coq.Init.Datatypes.inr',axiom,
    ! [Vvar__0__A__88851,Vvar__0__A__88852,Vvar__1__B__88853,Vvar__1__B__88854,Vvar__2___24Anonymous__88855,Vvar__2___24Anonymous__88856] :
      ( cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__88851,Vvar__1__B__88853,Vvar__2___24Anonymous__88855) = cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__88852,Vvar__1__B__88854,Vvar__2___24Anonymous__88856)
     => ( Vvar__2___24Anonymous__88855 = Vvar__2___24Anonymous__88856
        & Vvar__1__B__88853 = Vvar__1__B__88854
        & Vvar__0__A__88851 = Vvar__0__A__88852 ) ) ).

fof('$_inj_Coq.Init.Datatypes.nil',axiom,
    ! [Vvar__0__A__1147,Vvar__0__A__1148] :
      ( cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__1147) = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__1148)
     => Vvar__0__A__1147 = Vvar__0__A__1148 ) ).

fof('$_inj_Coq.Init.Datatypes.pair',axiom,
    ! [Vvar__0__A__1119,Vvar__0__A__1120,Vvar__1__B__1121,Vvar__1__B__1122,Vvar__2___24Anonymous__1123,Vvar__2___24Anonymous__1124,Vvar__3___24Anonymous__1125,Vvar__3___24Anonymous__1126] :
      ( cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__1119,Vvar__1__B__1121,Vvar__2___24Anonymous__1123,Vvar__3___24Anonymous__1125) = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__1120,Vvar__1__B__1122,Vvar__2___24Anonymous__1124,Vvar__3___24Anonymous__1126)
     => ( Vvar__3___24Anonymous__1125 = Vvar__3___24Anonymous__1126
        & Vvar__2___24Anonymous__1123 = Vvar__2___24Anonymous__1124
        & Vvar__1__B__1121 = Vvar__1__B__1122
        & Vvar__0__A__1119 = Vvar__0__A__1120 ) ) ).

fof('$_inj_Coq.Init.Decimal.D0',axiom,
    ! [Vvar__0___24Anonymous__75851,Vvar__0___24Anonymous__75852] :
      ( cCoq_2eInit_2eDecimal_2eD0___24a1(Vvar__0___24Anonymous__75851) = cCoq_2eInit_2eDecimal_2eD0___24a1(Vvar__0___24Anonymous__75852)
     => Vvar__0___24Anonymous__75851 = Vvar__0___24Anonymous__75852 ) ).

fof('$_inj_Coq.Init.Decimal.D1',axiom,
    ! [Vvar__0___24Anonymous__75853,Vvar__0___24Anonymous__75854] :
      ( cCoq_2eInit_2eDecimal_2eD1___24a1(Vvar__0___24Anonymous__75853) = cCoq_2eInit_2eDecimal_2eD1___24a1(Vvar__0___24Anonymous__75854)
     => Vvar__0___24Anonymous__75853 = Vvar__0___24Anonymous__75854 ) ).

fof('$_inj_Coq.Init.Decimal.D2',axiom,
    ! [Vvar__0___24Anonymous__75855,Vvar__0___24Anonymous__75856] :
      ( cCoq_2eInit_2eDecimal_2eD2___24a1(Vvar__0___24Anonymous__75855) = cCoq_2eInit_2eDecimal_2eD2___24a1(Vvar__0___24Anonymous__75856)
     => Vvar__0___24Anonymous__75855 = Vvar__0___24Anonymous__75856 ) ).

fof('$_inj_Coq.Init.Decimal.D3',axiom,
    ! [Vvar__0___24Anonymous__75857,Vvar__0___24Anonymous__75858] :
      ( cCoq_2eInit_2eDecimal_2eD3___24a1(Vvar__0___24Anonymous__75857) = cCoq_2eInit_2eDecimal_2eD3___24a1(Vvar__0___24Anonymous__75858)
     => Vvar__0___24Anonymous__75857 = Vvar__0___24Anonymous__75858 ) ).

fof('$_inj_Coq.Init.Decimal.D4',axiom,
    ! [Vvar__0___24Anonymous__75859,Vvar__0___24Anonymous__75860] :
      ( cCoq_2eInit_2eDecimal_2eD4___24a1(Vvar__0___24Anonymous__75859) = cCoq_2eInit_2eDecimal_2eD4___24a1(Vvar__0___24Anonymous__75860)
     => Vvar__0___24Anonymous__75859 = Vvar__0___24Anonymous__75860 ) ).

fof('$_inj_Coq.Init.Decimal.D5',axiom,
    ! [Vvar__0___24Anonymous__75861,Vvar__0___24Anonymous__75862] :
      ( cCoq_2eInit_2eDecimal_2eD5___24a1(Vvar__0___24Anonymous__75861) = cCoq_2eInit_2eDecimal_2eD5___24a1(Vvar__0___24Anonymous__75862)
     => Vvar__0___24Anonymous__75861 = Vvar__0___24Anonymous__75862 ) ).

fof('$_inj_Coq.Init.Decimal.D6',axiom,
    ! [Vvar__0___24Anonymous__75863,Vvar__0___24Anonymous__75864] :
      ( cCoq_2eInit_2eDecimal_2eD6___24a1(Vvar__0___24Anonymous__75863) = cCoq_2eInit_2eDecimal_2eD6___24a1(Vvar__0___24Anonymous__75864)
     => Vvar__0___24Anonymous__75863 = Vvar__0___24Anonymous__75864 ) ).

fof('$_inj_Coq.Init.Decimal.D7',axiom,
    ! [Vvar__0___24Anonymous__75865,Vvar__0___24Anonymous__75866] :
      ( cCoq_2eInit_2eDecimal_2eD7___24a1(Vvar__0___24Anonymous__75865) = cCoq_2eInit_2eDecimal_2eD7___24a1(Vvar__0___24Anonymous__75866)
     => Vvar__0___24Anonymous__75865 = Vvar__0___24Anonymous__75866 ) ).

fof('$_inj_Coq.Init.Decimal.D8',axiom,
    ! [Vvar__0___24Anonymous__75867,Vvar__0___24Anonymous__75868] :
      ( cCoq_2eInit_2eDecimal_2eD8___24a1(Vvar__0___24Anonymous__75867) = cCoq_2eInit_2eDecimal_2eD8___24a1(Vvar__0___24Anonymous__75868)
     => Vvar__0___24Anonymous__75867 = Vvar__0___24Anonymous__75868 ) ).

fof('$_inj_Coq.Init.Decimal.D9',axiom,
    ! [Vvar__0___24Anonymous__75869,Vvar__0___24Anonymous__75870] :
      ( cCoq_2eInit_2eDecimal_2eD9___24a1(Vvar__0___24Anonymous__75869) = cCoq_2eInit_2eDecimal_2eD9___24a1(Vvar__0___24Anonymous__75870)
     => Vvar__0___24Anonymous__75869 = Vvar__0___24Anonymous__75870 ) ).

fof('$_inj_Coq.Init.Decimal.Decimal',axiom,
    ! [Vvar__0__i__88878,Vvar__0__i__88879,Vvar__1__f__88880,Vvar__1__f__88881] :
      ( cCoq_2eInit_2eDecimal_2eDecimal___24a2(Vvar__0__i__88878,Vvar__1__f__88880) = cCoq_2eInit_2eDecimal_2eDecimal___24a2(Vvar__0__i__88879,Vvar__1__f__88881)
     => ( Vvar__1__f__88880 = Vvar__1__f__88881
        & Vvar__0__i__88878 = Vvar__0__i__88879 ) ) ).

fof('$_inj_Coq.Init.Decimal.DecimalExp',axiom,
    ! [Vvar__0__i__88882,Vvar__0__i__88883,Vvar__1__f__88884,Vvar__1__f__88885,Vvar__2__e__88886,Vvar__2__e__88887] :
      ( cCoq_2eInit_2eDecimal_2eDecimalExp___24a3(Vvar__0__i__88882,Vvar__1__f__88884,Vvar__2__e__88886) = cCoq_2eInit_2eDecimal_2eDecimalExp___24a3(Vvar__0__i__88883,Vvar__1__f__88885,Vvar__2__e__88887)
     => ( Vvar__2__e__88886 = Vvar__2__e__88887
        & Vvar__1__f__88884 = Vvar__1__f__88885
        & Vvar__0__i__88882 = Vvar__0__i__88883 ) ) ).

fof('$_inj_Coq.Init.Decimal.Neg',axiom,
    ! [Vvar__0__d__88865,Vvar__0__d__88866] :
      ( cCoq_2eInit_2eDecimal_2eNeg___24a1(Vvar__0__d__88865) = cCoq_2eInit_2eDecimal_2eNeg___24a1(Vvar__0__d__88866)
     => Vvar__0__d__88865 = Vvar__0__d__88866 ) ).

fof('$_inj_Coq.Init.Decimal.Pos',axiom,
    ! [Vvar__0__d__88863,Vvar__0__d__88864] :
      ( cCoq_2eInit_2eDecimal_2ePos___24a1(Vvar__0__d__88863) = cCoq_2eInit_2eDecimal_2ePos___24a1(Vvar__0__d__88864)
     => Vvar__0__d__88863 = Vvar__0__d__88864 ) ).

fof('$_inj_Coq.Init.Specif.exist',axiom,
    ! [Vvar__0__A__78064,Vvar__0__A__78065,Vvar__1__P__78066,Vvar__1__P__78067,Vvar__2__x__78068,Vvar__2__x__78069,Vvar__3___24Anonymous__78070,Vvar__3___24Anonymous__78071] :
      ( cCoq_2eInit_2eSpecif_2eexist___24a3(Vvar__0__A__78064,Vvar__1__P__78066,Vvar__2__x__78068) = cCoq_2eInit_2eSpecif_2eexist___24a3(Vvar__0__A__78065,Vvar__1__P__78067,Vvar__2__x__78069)
     => ( c_24Proof = c_24Proof
        & Vvar__2__x__78068 = Vvar__2__x__78069
        & Vvar__1__P__78066 = Vvar__1__P__78067
        & Vvar__0__A__78064 = Vvar__0__A__78065 ) ) ).

fof('$_inj_Coq.Init.Specif.exist2',axiom,
    ! [Vvar__0__A__91824,Vvar__0__A__91825,Vvar__1__P__91826,Vvar__1__P__91827,Vvar__2__Q__91828,Vvar__2__Q__91829,Vvar__3__x__91830,Vvar__3__x__91831,Vvar__4___24Anonymous__91832,Vvar__4___24Anonymous__91833,Vvar__5___24Anonymous__91834,Vvar__5___24Anonymous__91835] :
      ( cCoq_2eInit_2eSpecif_2eexist2___24a4(Vvar__0__A__91824,Vvar__1__P__91826,Vvar__2__Q__91828,Vvar__3__x__91830) = cCoq_2eInit_2eSpecif_2eexist2___24a4(Vvar__0__A__91825,Vvar__1__P__91827,Vvar__2__Q__91829,Vvar__3__x__91831)
     => ( c_24Proof = c_24Proof
        & c_24Proof = c_24Proof
        & Vvar__3__x__91830 = Vvar__3__x__91831
        & Vvar__2__Q__91828 = Vvar__2__Q__91829
        & Vvar__1__P__91826 = Vvar__1__P__91827
        & Vvar__0__A__91824 = Vvar__0__A__91825 ) ) ).

fof('$_inj_Coq.Init.Specif.existT',axiom,
    ! [Vvar__0__A__85974,Vvar__0__A__85975,Vvar__1__P__85976,Vvar__1__P__85977,Vvar__2__x__85978,Vvar__2__x__85979,Vvar__3___24Anonymous__85980,Vvar__3___24Anonymous__85981] :
      ( cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__85974,Vvar__1__P__85976,Vvar__2__x__85978,Vvar__3___24Anonymous__85980) = cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__85975,Vvar__1__P__85977,Vvar__2__x__85979,Vvar__3___24Anonymous__85981)
     => ( Vvar__3___24Anonymous__85980 = Vvar__3___24Anonymous__85981
        & Vvar__2__x__85978 = Vvar__2__x__85979
        & Vvar__1__P__85976 = Vvar__1__P__85977
        & Vvar__0__A__85974 = Vvar__0__A__85975 ) ) ).

fof('$_inj_Coq.Init.Specif.existT2',axiom,
    ! [Vvar__0__A__91880,Vvar__0__A__91881,Vvar__1__P__91882,Vvar__1__P__91883,Vvar__2__Q__91884,Vvar__2__Q__91885,Vvar__3__x__91886,Vvar__3__x__91887,Vvar__4___24Anonymous__91888,Vvar__4___24Anonymous__91889,Vvar__5___24Anonymous__91890,Vvar__5___24Anonymous__91891] :
      ( cCoq_2eInit_2eSpecif_2eexistT2___24a6(Vvar__0__A__91880,Vvar__1__P__91882,Vvar__2__Q__91884,Vvar__3__x__91886,Vvar__4___24Anonymous__91888,Vvar__5___24Anonymous__91890) = cCoq_2eInit_2eSpecif_2eexistT2___24a6(Vvar__0__A__91881,Vvar__1__P__91883,Vvar__2__Q__91885,Vvar__3__x__91887,Vvar__4___24Anonymous__91889,Vvar__5___24Anonymous__91891)
     => ( Vvar__5___24Anonymous__91890 = Vvar__5___24Anonymous__91891
        & Vvar__4___24Anonymous__91888 = Vvar__4___24Anonymous__91889
        & Vvar__3__x__91886 = Vvar__3__x__91887
        & Vvar__2__Q__91884 = Vvar__2__Q__91885
        & Vvar__1__P__91882 = Vvar__1__P__91883
        & Vvar__0__A__91880 = Vvar__0__A__91881 ) ) ).

fof('$_inj_Coq.Init.Specif.inleft',axiom,
    ! [Vvar__0__A__309,Vvar__0__A__310,Vvar__1__B__311,Vvar__1__B__312,Vvar__2___24Anonymous__313,Vvar__2___24Anonymous__314] :
      ( cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__309,Vvar__1__B__311,Vvar__2___24Anonymous__313) = cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__310,Vvar__1__B__312,Vvar__2___24Anonymous__314)
     => ( Vvar__2___24Anonymous__313 = Vvar__2___24Anonymous__314
        & Vvar__1__B__311 = Vvar__1__B__312
        & Vvar__0__A__309 = Vvar__0__A__310 ) ) ).

fof('$_inj_Coq.Init.Specif.inright',axiom,
    ! [Vvar__0__A__315,Vvar__0__A__316,Vvar__1__B__317,Vvar__1__B__318,Vvar__2___24Anonymous__319,Vvar__2___24Anonymous__320] :
      ( cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__315,Vvar__1__B__317) = cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__316,Vvar__1__B__318)
     => ( c_24Proof = c_24Proof
        & Vvar__1__B__317 = Vvar__1__B__318
        & Vvar__0__A__315 = Vvar__0__A__316 ) ) ).

fof('$_inj_Coq.Init.Specif.left',axiom,
    ! [Vvar__0__A__269,Vvar__0__A__270,Vvar__1__B__271,Vvar__1__B__272,Vvar__2___24Anonymous__273,Vvar__2___24Anonymous__274] :
      ( cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__269,Vvar__1__B__271) = cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__270,Vvar__1__B__272)
     => ( c_24Proof = c_24Proof
        & Vvar__1__B__271 = Vvar__1__B__272
        & Vvar__0__A__269 = Vvar__0__A__270 ) ) ).

fof('$_inj_Coq.Init.Specif.right',axiom,
    ! [Vvar__0__A__275,Vvar__0__A__276,Vvar__1__B__277,Vvar__1__B__278,Vvar__2___24Anonymous__279,Vvar__2___24Anonymous__280] :
      ( cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__275,Vvar__1__B__277) = cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__276,Vvar__1__B__278)
     => ( c_24Proof = c_24Proof
        & Vvar__1__B__277 = Vvar__1__B__278
        & Vvar__0__A__275 = Vvar__0__A__276 ) ) ).

fof('$_inj_Coq.Numbers.BinNums.Npos',axiom,
    ! [Vvar__0___24Anonymous__1092,Vvar__0___24Anonymous__1093] :
      ( cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__1092) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__1093)
     => Vvar__0___24Anonymous__1092 = Vvar__0___24Anonymous__1093 ) ).

fof('$_inj_Coq.Numbers.BinNums.Zneg',axiom,
    ! [Vvar__0___24Anonymous__1105,Vvar__0___24Anonymous__1106] :
      ( cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__1105) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__1106)
     => Vvar__0___24Anonymous__1105 = Vvar__0___24Anonymous__1106 ) ).

fof('$_inj_Coq.Numbers.BinNums.Zpos',axiom,
    ! [Vvar__0___24Anonymous__1103,Vvar__0___24Anonymous__1104] :
      ( cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__1103) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__1104)
     => Vvar__0___24Anonymous__1103 = Vvar__0___24Anonymous__1104 ) ).

fof('$_inj_Coq.Numbers.BinNums.xI',axiom,
    ! [Vvar__0___24Anonymous__1083,Vvar__0___24Anonymous__1084] :
      ( cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__1083) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__1084)
     => Vvar__0___24Anonymous__1083 = Vvar__0___24Anonymous__1084 ) ).

fof('$_inj_Coq.Numbers.BinNums.xO',axiom,
    ! [Vvar__0___24Anonymous__1085,Vvar__0___24Anonymous__1086] :
      ( cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__1085) = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__1086)
     => Vvar__0___24Anonymous__1085 = Vvar__0___24Anonymous__1086 ) ).

fof('$_inj_Coq.PArith.BinPos.Pos.IsPos',axiom,
    ! [Vvar__0___24Anonymous__200929,Vvar__0___24Anonymous__200930] :
      ( cCoq_2ePArith_2eBinPos_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__200929) = cCoq_2ePArith_2eBinPos_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__200930)
     => Vvar__0___24Anonymous__200929 = Vvar__0___24Anonymous__200930 ) ).

fof('$_inj_Coq.PArith.BinPos.Pos.PeanoSucc',axiom,
    ! [Vvar__0__p__109204,Vvar__0__p__109205,Vvar__1___24Anonymous__109206,Vvar__1___24Anonymous__109207] :
      ( cCoq_2ePArith_2eBinPos_2ePos_2ePeanoSucc___24a2(Vvar__0__p__109204,Vvar__1___24Anonymous__109206) = cCoq_2ePArith_2eBinPos_2ePos_2ePeanoSucc___24a2(Vvar__0__p__109205,Vvar__1___24Anonymous__109207)
     => ( Vvar__1___24Anonymous__109206 = Vvar__1___24Anonymous__109207
        & Vvar__0__p__109204 = Vvar__0__p__109205 ) ) ).

fof('$_inj_Coq.PArith.BinPosDef.Pos.IsPos',axiom,
    ! [Vvar__0___24Anonymous__88810,Vvar__0___24Anonymous__88811] :
      ( cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__88810) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__88811)
     => Vvar__0___24Anonymous__88810 = Vvar__0___24Anonymous__88811 ) ).

fof('$_inj_Coq.QArith.QArith_base.Qmake',axiom,
    ! [Vvar__0__Qnum__87815,Vvar__0__Qnum__87816,Vvar__1__Qden__87817,Vvar__1__Qden__87818] :
      ( cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__87815,Vvar__1__Qden__87817) = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__87816,Vvar__1__Qden__87818)
     => ( Vvar__1__Qden__87817 = Vvar__1__Qden__87818
        & Vvar__0__Qnum__87815 = Vvar__0__Qnum__87816 ) ) ).

fof('$_inj_Coq.Reals.RIneq.mknegreal',axiom,
    ! [Vvar__0__neg__85543,Vvar__0__neg__85544,Vvar__1__cond__neg__85545,Vvar__1__cond__neg__85546] :
      ( cCoq_2eReals_2eRIneq_2emknegreal___24a1(Vvar__0__neg__85543) = cCoq_2eReals_2eRIneq_2emknegreal___24a1(Vvar__0__neg__85544)
     => ( c_24Proof = c_24Proof
        & Vvar__0__neg__85543 = Vvar__0__neg__85544 ) ) ).

fof('$_inj_Coq.Reals.RIneq.mknonnegreal',axiom,
    ! [Vvar__0__nonneg__90966,Vvar__0__nonneg__90967,Vvar__1__cond__nonneg__90968,Vvar__1__cond__nonneg__90969] :
      ( cCoq_2eReals_2eRIneq_2emknonnegreal___24a1(Vvar__0__nonneg__90966) = cCoq_2eReals_2eRIneq_2emknonnegreal___24a1(Vvar__0__nonneg__90967)
     => ( c_24Proof = c_24Proof
        & Vvar__0__nonneg__90966 = Vvar__0__nonneg__90967 ) ) ).

fof('$_inj_Coq.Reals.RIneq.mknonposreal',axiom,
    ! [Vvar__0__nonpos__85536,Vvar__0__nonpos__85537,Vvar__1__cond__nonpos__85538,Vvar__1__cond__nonpos__85539] :
      ( cCoq_2eReals_2eRIneq_2emknonposreal___24a1(Vvar__0__nonpos__85536) = cCoq_2eReals_2eRIneq_2emknonposreal___24a1(Vvar__0__nonpos__85537)
     => ( c_24Proof = c_24Proof
        & Vvar__0__nonpos__85536 = Vvar__0__nonpos__85537 ) ) ).

fof('$_inj_Coq.Reals.RIneq.mknonzeroreal',axiom,
    ! [Vvar__0__nonzero__87822,Vvar__0__nonzero__87823,Vvar__1__cond__nonzero__87824,Vvar__1__cond__nonzero__87825] :
      ( cCoq_2eReals_2eRIneq_2emknonzeroreal___24a1(Vvar__0__nonzero__87822) = cCoq_2eReals_2eRIneq_2emknonzeroreal___24a1(Vvar__0__nonzero__87823)
     => ( c_24Proof = c_24Proof
        & Vvar__0__nonzero__87822 = Vvar__0__nonzero__87823 ) ) ).

fof('$_inj_Coq.Reals.RIneq.mkposreal',axiom,
    ! [Vvar__0__pos__90973,Vvar__0__pos__90974,Vvar__1__cond__pos__90975,Vvar__1__cond__pos__90976] :
      ( cCoq_2eReals_2eRIneq_2emkposreal___24a1(Vvar__0__pos__90973) = cCoq_2eReals_2eRIneq_2emkposreal___24a1(Vvar__0__pos__90974)
     => ( c_24Proof = c_24Proof
        & Vvar__0__pos__90973 = Vvar__0__pos__90974 ) ) ).

fof('$_inj_Coq.Reals.Rfunctions.ZintNeg',axiom,
    ! [Vvar__0__x__113370,Vvar__0__x__113371,Vvar__1__n__113372,Vvar__1__n__113373,Vvar__2___24Anonymous__113374,Vvar__2___24Anonymous__113375] :
      ( cCoq_2eReals_2eRfunctions_2eZintNeg___24a2(Vvar__0__x__113370,Vvar__1__n__113372) = cCoq_2eReals_2eRfunctions_2eZintNeg___24a2(Vvar__0__x__113371,Vvar__1__n__113373)
     => ( c_24Proof = c_24Proof
        & Vvar__1__n__113372 = Vvar__1__n__113373
        & Vvar__0__x__113370 = Vvar__0__x__113371 ) ) ).

fof('$_inj_Coq.Reals.Rfunctions.ZintNull',axiom,
    ! [Vvar__0__x__113360,Vvar__0__x__113361,Vvar__1___24Anonymous__113362,Vvar__1___24Anonymous__113363] :
      ( cCoq_2eReals_2eRfunctions_2eZintNull___24a1(Vvar__0__x__113360) = cCoq_2eReals_2eRfunctions_2eZintNull___24a1(Vvar__0__x__113361)
     => ( c_24Proof = c_24Proof
        & Vvar__0__x__113360 = Vvar__0__x__113361 ) ) ).

fof('$_inj_Coq.Reals.Rfunctions.ZintPos',axiom,
    ! [Vvar__0__x__113364,Vvar__0__x__113365,Vvar__1__n__113366,Vvar__1__n__113367,Vvar__2___24Anonymous__113368,Vvar__2___24Anonymous__113369] :
      ( cCoq_2eReals_2eRfunctions_2eZintPos___24a2(Vvar__0__x__113364,Vvar__1__n__113366) = cCoq_2eReals_2eRfunctions_2eZintPos___24a2(Vvar__0__x__113365,Vvar__1__n__113367)
     => ( c_24Proof = c_24Proof
        & Vvar__1__n__113366 = Vvar__1__n__113367
        & Vvar__0__x__113364 = Vvar__0__x__113365 ) ) ).

fof('$_inj_Coq.Strings.Ascii.Ascii',axiom,
    ! [Vvar__0___24Anonymous__2571,Vvar__0___24Anonymous__2572,Vvar__1___24Anonymous__2573,Vvar__1___24Anonymous__2574,Vvar__2___24Anonymous__2575,Vvar__2___24Anonymous__2576,Vvar__3___24Anonymous__2577,Vvar__3___24Anonymous__2578,Vvar__4___24Anonymous__2579,Vvar__4___24Anonymous__2580,Vvar__5___24Anonymous__2581,Vvar__5___24Anonymous__2582,Vvar__6___24Anonymous__2583,Vvar__6___24Anonymous__2584,Vvar__7___24Anonymous__2585,Vvar__7___24Anonymous__2586] :
      ( cCoq_2eStrings_2eAscii_2eAscii___24a8(Vvar__0___24Anonymous__2571,Vvar__1___24Anonymous__2573,Vvar__2___24Anonymous__2575,Vvar__3___24Anonymous__2577,Vvar__4___24Anonymous__2579,Vvar__5___24Anonymous__2581,Vvar__6___24Anonymous__2583,Vvar__7___24Anonymous__2585) = cCoq_2eStrings_2eAscii_2eAscii___24a8(Vvar__0___24Anonymous__2572,Vvar__1___24Anonymous__2574,Vvar__2___24Anonymous__2576,Vvar__3___24Anonymous__2578,Vvar__4___24Anonymous__2580,Vvar__5___24Anonymous__2582,Vvar__6___24Anonymous__2584,Vvar__7___24Anonymous__2586)
     => ( Vvar__7___24Anonymous__2585 = Vvar__7___24Anonymous__2586
        & Vvar__6___24Anonymous__2583 = Vvar__6___24Anonymous__2584
        & Vvar__5___24Anonymous__2581 = Vvar__5___24Anonymous__2582
        & Vvar__4___24Anonymous__2579 = Vvar__4___24Anonymous__2580
        & Vvar__3___24Anonymous__2577 = Vvar__3___24Anonymous__2578
        & Vvar__2___24Anonymous__2575 = Vvar__2___24Anonymous__2576
        & Vvar__1___24Anonymous__2573 = Vvar__1___24Anonymous__2574
        & Vvar__0___24Anonymous__2571 = Vvar__0___24Anonymous__2572 ) ) ).

fof('$_inj_Coq.Strings.String.String',axiom,
    ! [Vvar__0___24Anonymous__587,Vvar__0___24Anonymous__588,Vvar__1___24Anonymous__589,Vvar__1___24Anonymous__590] :
      ( cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__587,Vvar__1___24Anonymous__589) = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__588,Vvar__1___24Anonymous__590)
     => ( Vvar__1___24Anonymous__589 = Vvar__1___24Anonymous__590
        & Vvar__0___24Anonymous__587 = Vvar__0___24Anonymous__588 ) ) ).

fof('$_inj_Coq.Structures.OrderedType.EQ',axiom,
    ! [Vvar__0__X__90939,Vvar__0__X__90940,Vvar__1__lt__90941,Vvar__1__lt__90942,Vvar__2__eq__90943,Vvar__2__eq__90944,Vvar__3__x__90945,Vvar__3__x__90946,Vvar__4__y__90947,Vvar__4__y__90948,Vvar__5___24Anonymous__90949,Vvar__5___24Anonymous__90950] :
      ( cCoq_2eStructures_2eOrderedType_2eEQ___24a5(Vvar__0__X__90939,Vvar__1__lt__90941,Vvar__2__eq__90943,Vvar__3__x__90945,Vvar__4__y__90947) = cCoq_2eStructures_2eOrderedType_2eEQ___24a5(Vvar__0__X__90940,Vvar__1__lt__90942,Vvar__2__eq__90944,Vvar__3__x__90946,Vvar__4__y__90948)
     => ( c_24Proof = c_24Proof
        & Vvar__4__y__90947 = Vvar__4__y__90948
        & Vvar__3__x__90945 = Vvar__3__x__90946
        & Vvar__2__eq__90943 = Vvar__2__eq__90944
        & Vvar__1__lt__90941 = Vvar__1__lt__90942
        & Vvar__0__X__90939 = Vvar__0__X__90940 ) ) ).

fof('$_inj_Coq.Structures.OrderedType.GT',axiom,
    ! [Vvar__0__X__90951,Vvar__0__X__90952,Vvar__1__lt__90953,Vvar__1__lt__90954,Vvar__2__eq__90955,Vvar__2__eq__90956,Vvar__3__x__90957,Vvar__3__x__90958,Vvar__4__y__90959,Vvar__4__y__90960,Vvar__5___24Anonymous__90961,Vvar__5___24Anonymous__90962] :
      ( cCoq_2eStructures_2eOrderedType_2eGT___24a5(Vvar__0__X__90951,Vvar__1__lt__90953,Vvar__2__eq__90955,Vvar__3__x__90957,Vvar__4__y__90959) = cCoq_2eStructures_2eOrderedType_2eGT___24a5(Vvar__0__X__90952,Vvar__1__lt__90954,Vvar__2__eq__90956,Vvar__3__x__90958,Vvar__4__y__90960)
     => ( c_24Proof = c_24Proof
        & Vvar__4__y__90959 = Vvar__4__y__90960
        & Vvar__3__x__90957 = Vvar__3__x__90958
        & Vvar__2__eq__90955 = Vvar__2__eq__90956
        & Vvar__1__lt__90953 = Vvar__1__lt__90954
        & Vvar__0__X__90951 = Vvar__0__X__90952 ) ) ).

fof('$_inj_Coq.Structures.OrderedType.LT',axiom,
    ! [Vvar__0__X__90927,Vvar__0__X__90928,Vvar__1__lt__90929,Vvar__1__lt__90930,Vvar__2__eq__90931,Vvar__2__eq__90932,Vvar__3__x__90933,Vvar__3__x__90934,Vvar__4__y__90935,Vvar__4__y__90936,Vvar__5___24Anonymous__90937,Vvar__5___24Anonymous__90938] :
      ( cCoq_2eStructures_2eOrderedType_2eLT___24a5(Vvar__0__X__90927,Vvar__1__lt__90929,Vvar__2__eq__90931,Vvar__3__x__90933,Vvar__4__y__90935) = cCoq_2eStructures_2eOrderedType_2eLT___24a5(Vvar__0__X__90928,Vvar__1__lt__90930,Vvar__2__eq__90932,Vvar__3__x__90934,Vvar__4__y__90936)
     => ( c_24Proof = c_24Proof
        & Vvar__4__y__90935 = Vvar__4__y__90936
        & Vvar__3__x__90933 = Vvar__3__x__90934
        & Vvar__2__eq__90931 = Vvar__2__eq__90932
        & Vvar__1__lt__90929 = Vvar__1__lt__90930
        & Vvar__0__X__90927 = Vvar__0__X__90928 ) ) ).

fof('$_inj_Coq.Vectors.Fin.F1',axiom,
    ! [Vvar__0__n__18,Vvar__0__n__19] :
      ( cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__18) = cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__19)
     => Vvar__0__n__18 = Vvar__0__n__19 ) ).

fof('$_inj_Coq.Vectors.Fin.FS',axiom,
    ! [Vvar__0__n__20,Vvar__0__n__21,Vvar__1___24Anonymous__22,Vvar__1___24Anonymous__23] :
      ( cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__20,Vvar__1___24Anonymous__22) = cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__21,Vvar__1___24Anonymous__23)
     => ( Vvar__1___24Anonymous__22 = Vvar__1___24Anonymous__23
        & Vvar__0__n__20 = Vvar__0__n__21 ) ) ).

fof('$_inj_Coq.Vectors.Vector.cons',axiom,
    ! [Vvar__0__A__200652,Vvar__0__A__200653,Vvar__1__h__200654,Vvar__1__h__200655,Vvar__2__n__200656,Vvar__2__n__200657,Vvar__3___24Anonymous__200658,Vvar__3___24Anonymous__200659] :
      ( cCoq_2eVectors_2eVector_2econs___24a4(Vvar__0__A__200652,Vvar__1__h__200654,Vvar__2__n__200656,Vvar__3___24Anonymous__200658) = cCoq_2eVectors_2eVector_2econs___24a4(Vvar__0__A__200653,Vvar__1__h__200655,Vvar__2__n__200657,Vvar__3___24Anonymous__200659)
     => ( Vvar__3___24Anonymous__200658 = Vvar__3___24Anonymous__200659
        & Vvar__2__n__200656 = Vvar__2__n__200657
        & Vvar__1__h__200654 = Vvar__1__h__200655
        & Vvar__0__A__200652 = Vvar__0__A__200653 ) ) ).

fof('$_inj_Coq.Vectors.Vector.nil',axiom,
    ! [Vvar__0__A__200650,Vvar__0__A__200651] :
      ( cCoq_2eVectors_2eVector_2enil___24a1(Vvar__0__A__200650) = cCoq_2eVectors_2eVector_2enil___24a1(Vvar__0__A__200651)
     => Vvar__0__A__200650 = Vvar__0__A__200651 ) ).

fof('$_inj_Coq.Vectors.VectorDef.cons',axiom,
    ! [Vvar__0__A__2080,Vvar__0__A__2081,Vvar__1__h__2082,Vvar__1__h__2083,Vvar__2__n__2084,Vvar__2__n__2085,Vvar__3___24Anonymous__2086,Vvar__3___24Anonymous__2087] :
      ( cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__2080,Vvar__1__h__2082,Vvar__2__n__2084,Vvar__3___24Anonymous__2086) = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__2081,Vvar__1__h__2083,Vvar__2__n__2085,Vvar__3___24Anonymous__2087)
     => ( Vvar__3___24Anonymous__2086 = Vvar__3___24Anonymous__2087
        & Vvar__2__n__2084 = Vvar__2__n__2085
        & Vvar__1__h__2082 = Vvar__1__h__2083
        & Vvar__0__A__2080 = Vvar__0__A__2081 ) ) ).

fof('$_inj_Coq.Vectors.VectorDef.nil',axiom,
    ! [Vvar__0__A__2078,Vvar__0__A__2079] :
      ( cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__2078) = cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__2079)
     => Vvar__0__A__2078 = Vvar__0__A__2079 ) ).

fof('$_inj_Coq.ZArith.Znumtheory.Euclid_intro',axiom,
    ! [Vvar__0__a__113514,Vvar__0__a__113515,Vvar__1__b__113516,Vvar__1__b__113517,Vvar__2__u__113518,Vvar__2__u__113519,Vvar__3__v__113520,Vvar__3__v__113521,Vvar__4__d__113522,Vvar__4__d__113523,Vvar__5___24Anonymous__113524,Vvar__5___24Anonymous__113525,Vvar__6___24Anonymous__113526,Vvar__6___24Anonymous__113527] :
      ( cCoq_2eZArith_2eZnumtheory_2eEuclid__intro___24a5(Vvar__0__a__113514,Vvar__1__b__113516,Vvar__2__u__113518,Vvar__3__v__113520,Vvar__4__d__113522) = cCoq_2eZArith_2eZnumtheory_2eEuclid__intro___24a5(Vvar__0__a__113515,Vvar__1__b__113517,Vvar__2__u__113519,Vvar__3__v__113521,Vvar__4__d__113523)
     => ( c_24Proof = c_24Proof
        & c_24Proof = c_24Proof
        & Vvar__4__d__113522 = Vvar__4__d__113523
        & Vvar__3__v__113520 = Vvar__3__v__113521
        & Vvar__2__u__113518 = Vvar__2__u__113519
        & Vvar__1__b__113516 = Vvar__1__b__113517
        & Vvar__0__a__113514 = Vvar__0__a__113515 ) ) ).

fof('$_inj_Coq.ZArith.Zpower.Zdiv_rest_proof',axiom,
    ! [Vvar__0__x__113562,Vvar__0__x__113563,Vvar__1__p__113564,Vvar__1__p__113565,Vvar__2__q__113566,Vvar__2__q__113567,Vvar__3__r__113568,Vvar__3__r__113569,Vvar__4___24Anonymous__113570,Vvar__4___24Anonymous__113571,Vvar__5___24Anonymous__113572,Vvar__5___24Anonymous__113573,Vvar__6___24Anonymous__113574,Vvar__6___24Anonymous__113575] :
      ( cCoq_2eZArith_2eZpower_2eZdiv__rest__proof___24a4(Vvar__0__x__113562,Vvar__1__p__113564,Vvar__2__q__113566,Vvar__3__r__113568) = cCoq_2eZArith_2eZpower_2eZdiv__rest__proof___24a4(Vvar__0__x__113563,Vvar__1__p__113565,Vvar__2__q__113567,Vvar__3__r__113569)
     => ( c_24Proof = c_24Proof
        & c_24Proof = c_24Proof
        & c_24Proof = c_24Proof
        & Vvar__3__r__113568 = Vvar__3__r__113569
        & Vvar__2__q__113566 = Vvar__2__q__113567
        & Vvar__1__p__113564 = Vvar__1__p__113565
        & Vvar__0__x__113562 = Vvar__0__x__113563 ) ) ).

fof('$_inj_Coq.micromega.EnvRing.PEX',axiom,
    ! [Vvar__0__C__86594,Vvar__0__C__86595,Vvar__1___24Anonymous__86596,Vvar__1___24Anonymous__86597] :
      ( cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__86594,Vvar__1___24Anonymous__86596) = cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__86595,Vvar__1___24Anonymous__86597)
     => ( Vvar__1___24Anonymous__86596 = Vvar__1___24Anonymous__86597
        & Vvar__0__C__86594 = Vvar__0__C__86595 ) ) ).

fof('$_inj_Coq.micromega.EnvRing.PEadd',axiom,
    ! [Vvar__0__C__86598,Vvar__0__C__86599,Vvar__1___24Anonymous__86600,Vvar__1___24Anonymous__86601,Vvar__2___24Anonymous__86602,Vvar__2___24Anonymous__86603] :
      ( cCoq_2emicromega_2eEnvRing_2ePEadd___24a3(Vvar__0__C__86598,Vvar__1___24Anonymous__86600,Vvar__2___24Anonymous__86602) = cCoq_2emicromega_2eEnvRing_2ePEadd___24a3(Vvar__0__C__86599,Vvar__1___24Anonymous__86601,Vvar__2___24Anonymous__86603)
     => ( Vvar__2___24Anonymous__86602 = Vvar__2___24Anonymous__86603
        & Vvar__1___24Anonymous__86600 = Vvar__1___24Anonymous__86601
        & Vvar__0__C__86598 = Vvar__0__C__86599 ) ) ).

fof('$_inj_Coq.micromega.EnvRing.PEc',axiom,
    ! [Vvar__0__C__86590,Vvar__0__C__86591,Vvar__1___24Anonymous__86592,Vvar__1___24Anonymous__86593] :
      ( cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__86590,Vvar__1___24Anonymous__86592) = cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__86591,Vvar__1___24Anonymous__86593)
     => ( Vvar__1___24Anonymous__86592 = Vvar__1___24Anonymous__86593
        & Vvar__0__C__86590 = Vvar__0__C__86591 ) ) ).

fof('$_inj_Coq.micromega.EnvRing.PEmul',axiom,
    ! [Vvar__0__C__86610,Vvar__0__C__86611,Vvar__1___24Anonymous__86612,Vvar__1___24Anonymous__86613,Vvar__2___24Anonymous__86614,Vvar__2___24Anonymous__86615] :
      ( cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(Vvar__0__C__86610,Vvar__1___24Anonymous__86612,Vvar__2___24Anonymous__86614) = cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(Vvar__0__C__86611,Vvar__1___24Anonymous__86613,Vvar__2___24Anonymous__86615)
     => ( Vvar__2___24Anonymous__86614 = Vvar__2___24Anonymous__86615
        & Vvar__1___24Anonymous__86612 = Vvar__1___24Anonymous__86613
        & Vvar__0__C__86610 = Vvar__0__C__86611 ) ) ).

fof('$_inj_Coq.micromega.EnvRing.PEopp',axiom,
    ! [Vvar__0__C__86616,Vvar__0__C__86617,Vvar__1___24Anonymous__86618,Vvar__1___24Anonymous__86619] :
      ( cCoq_2emicromega_2eEnvRing_2ePEopp___24a2(Vvar__0__C__86616,Vvar__1___24Anonymous__86618) = cCoq_2emicromega_2eEnvRing_2ePEopp___24a2(Vvar__0__C__86617,Vvar__1___24Anonymous__86619)
     => ( Vvar__1___24Anonymous__86618 = Vvar__1___24Anonymous__86619
        & Vvar__0__C__86616 = Vvar__0__C__86617 ) ) ).

fof('$_inj_Coq.micromega.EnvRing.PEpow',axiom,
    ! [Vvar__0__C__86620,Vvar__0__C__86621,Vvar__1___24Anonymous__86622,Vvar__1___24Anonymous__86623,Vvar__2___24Anonymous__86624,Vvar__2___24Anonymous__86625] :
      ( cCoq_2emicromega_2eEnvRing_2ePEpow___24a3(Vvar__0__C__86620,Vvar__1___24Anonymous__86622,Vvar__2___24Anonymous__86624) = cCoq_2emicromega_2eEnvRing_2ePEpow___24a3(Vvar__0__C__86621,Vvar__1___24Anonymous__86623,Vvar__2___24Anonymous__86625)
     => ( Vvar__2___24Anonymous__86624 = Vvar__2___24Anonymous__86625
        & Vvar__1___24Anonymous__86622 = Vvar__1___24Anonymous__86623
        & Vvar__0__C__86620 = Vvar__0__C__86621 ) ) ).

fof('$_inj_Coq.micromega.EnvRing.PEsub',axiom,
    ! [Vvar__0__C__86604,Vvar__0__C__86605,Vvar__1___24Anonymous__86606,Vvar__1___24Anonymous__86607,Vvar__2___24Anonymous__86608,Vvar__2___24Anonymous__86609] :
      ( cCoq_2emicromega_2eEnvRing_2ePEsub___24a3(Vvar__0__C__86604,Vvar__1___24Anonymous__86606,Vvar__2___24Anonymous__86608) = cCoq_2emicromega_2eEnvRing_2ePEsub___24a3(Vvar__0__C__86605,Vvar__1___24Anonymous__86607,Vvar__2___24Anonymous__86609)
     => ( Vvar__2___24Anonymous__86608 = Vvar__2___24Anonymous__86609
        & Vvar__1___24Anonymous__86606 = Vvar__1___24Anonymous__86607
        & Vvar__0__C__86604 = Vvar__0__C__86605 ) ) ).

fof('$_inj_Coq.micromega.EnvRing.PX',axiom,
    ! [Vvar__0__C__88927,Vvar__0__C__88928,Vvar__1___24Anonymous__88929,Vvar__1___24Anonymous__88930,Vvar__2___24Anonymous__88931,Vvar__2___24Anonymous__88932,Vvar__3___24Anonymous__88933,Vvar__3___24Anonymous__88934] :
      ( cCoq_2emicromega_2eEnvRing_2ePX___24a4(Vvar__0__C__88927,Vvar__1___24Anonymous__88929,Vvar__2___24Anonymous__88931,Vvar__3___24Anonymous__88933) = cCoq_2emicromega_2eEnvRing_2ePX___24a4(Vvar__0__C__88928,Vvar__1___24Anonymous__88930,Vvar__2___24Anonymous__88932,Vvar__3___24Anonymous__88934)
     => ( Vvar__3___24Anonymous__88933 = Vvar__3___24Anonymous__88934
        & Vvar__2___24Anonymous__88931 = Vvar__2___24Anonymous__88932
        & Vvar__1___24Anonymous__88929 = Vvar__1___24Anonymous__88930
        & Vvar__0__C__88927 = Vvar__0__C__88928 ) ) ).

fof('$_inj_Coq.micromega.EnvRing.Pc',axiom,
    ! [Vvar__0__C__88917,Vvar__0__C__88918,Vvar__1___24Anonymous__88919,Vvar__1___24Anonymous__88920] :
      ( cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__88917,Vvar__1___24Anonymous__88919) = cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__88918,Vvar__1___24Anonymous__88920)
     => ( Vvar__1___24Anonymous__88919 = Vvar__1___24Anonymous__88920
        & Vvar__0__C__88917 = Vvar__0__C__88918 ) ) ).

fof('$_inj_Coq.micromega.EnvRing.Pinj',axiom,
    ! [Vvar__0__C__88921,Vvar__0__C__88922,Vvar__1___24Anonymous__88923,Vvar__1___24Anonymous__88924,Vvar__2___24Anonymous__88925,Vvar__2___24Anonymous__88926] :
      ( cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__88921,Vvar__1___24Anonymous__88923,Vvar__2___24Anonymous__88925) = cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__88922,Vvar__1___24Anonymous__88924,Vvar__2___24Anonymous__88926)
     => ( Vvar__2___24Anonymous__88925 = Vvar__2___24Anonymous__88926
        & Vvar__1___24Anonymous__88923 = Vvar__1___24Anonymous__88924
        & Vvar__0__C__88921 = Vvar__0__C__88922 ) ) ).

fof('$_inj_Coq.micromega.EnvRing.vmon',axiom,
    ! [Vvar__0___24Anonymous__85159,Vvar__0___24Anonymous__85160,Vvar__1___24Anonymous__85161,Vvar__1___24Anonymous__85162] :
      ( cCoq_2emicromega_2eEnvRing_2evmon___24a2(Vvar__0___24Anonymous__85159,Vvar__1___24Anonymous__85161) = cCoq_2emicromega_2eEnvRing_2evmon___24a2(Vvar__0___24Anonymous__85160,Vvar__1___24Anonymous__85162)
     => ( Vvar__1___24Anonymous__85161 = Vvar__1___24Anonymous__85162
        & Vvar__0___24Anonymous__85159 = Vvar__0___24Anonymous__85160 ) ) ).

fof('$_inj_Coq.micromega.EnvRing.zmon',axiom,
    ! [Vvar__0___24Anonymous__85155,Vvar__0___24Anonymous__85156,Vvar__1___24Anonymous__85157,Vvar__1___24Anonymous__85158] :
      ( cCoq_2emicromega_2eEnvRing_2ezmon___24a2(Vvar__0___24Anonymous__85155,Vvar__1___24Anonymous__85157) = cCoq_2emicromega_2eEnvRing_2ezmon___24a2(Vvar__0___24Anonymous__85156,Vvar__1___24Anonymous__85158)
     => ( Vvar__1___24Anonymous__85157 = Vvar__1___24Anonymous__85158
        & Vvar__0___24Anonymous__85155 = Vvar__0___24Anonymous__85156 ) ) ).

fof('$_inj_Coq.micromega.RMicromega.CInv',axiom,
    ! [Vvar__0__r__87967,Vvar__0__r__87968] :
      ( cCoq_2emicromega_2eRMicromega_2eCInv___24a1(Vvar__0__r__87967) = cCoq_2emicromega_2eRMicromega_2eCInv___24a1(Vvar__0__r__87968)
     => Vvar__0__r__87967 = Vvar__0__r__87968 ) ).

fof('$_inj_Coq.micromega.RMicromega.CMinus',axiom,
    ! [Vvar__0__r1__87955,Vvar__0__r1__87956,Vvar__1__r2__87957,Vvar__1__r2__87958] :
      ( cCoq_2emicromega_2eRMicromega_2eCMinus___24a2(Vvar__0__r1__87955,Vvar__1__r2__87957) = cCoq_2emicromega_2eRMicromega_2eCMinus___24a2(Vvar__0__r1__87956,Vvar__1__r2__87958)
     => ( Vvar__1__r2__87957 = Vvar__1__r2__87958
        & Vvar__0__r1__87955 = Vvar__0__r1__87956 ) ) ).

fof('$_inj_Coq.micromega.RMicromega.CMult',axiom,
    ! [Vvar__0__r1__87959,Vvar__0__r1__87960,Vvar__1__r2__87961,Vvar__1__r2__87962] :
      ( cCoq_2emicromega_2eRMicromega_2eCMult___24a2(Vvar__0__r1__87959,Vvar__1__r2__87961) = cCoq_2emicromega_2eRMicromega_2eCMult___24a2(Vvar__0__r1__87960,Vvar__1__r2__87962)
     => ( Vvar__1__r2__87961 = Vvar__1__r2__87962
        & Vvar__0__r1__87959 = Vvar__0__r1__87960 ) ) ).

fof('$_inj_Coq.micromega.RMicromega.COpp',axiom,
    ! [Vvar__0__r__87969,Vvar__0__r__87970] :
      ( cCoq_2emicromega_2eRMicromega_2eCOpp___24a1(Vvar__0__r__87969) = cCoq_2emicromega_2eRMicromega_2eCOpp___24a1(Vvar__0__r__87970)
     => Vvar__0__r__87969 = Vvar__0__r__87970 ) ).

fof('$_inj_Coq.micromega.RMicromega.CPlus',axiom,
    ! [Vvar__0__r1__87951,Vvar__0__r1__87952,Vvar__1__r2__87953,Vvar__1__r2__87954] :
      ( cCoq_2emicromega_2eRMicromega_2eCPlus___24a2(Vvar__0__r1__87951,Vvar__1__r2__87953) = cCoq_2emicromega_2eRMicromega_2eCPlus___24a2(Vvar__0__r1__87952,Vvar__1__r2__87954)
     => ( Vvar__1__r2__87953 = Vvar__1__r2__87954
        & Vvar__0__r1__87951 = Vvar__0__r1__87952 ) ) ).

fof('$_inj_Coq.micromega.RMicromega.CPow',axiom,
    ! [Vvar__0__r1__87963,Vvar__0__r1__87964,Vvar__1__z__87965,Vvar__1__z__87966] :
      ( cCoq_2emicromega_2eRMicromega_2eCPow___24a2(Vvar__0__r1__87963,Vvar__1__z__87965) = cCoq_2emicromega_2eRMicromega_2eCPow___24a2(Vvar__0__r1__87964,Vvar__1__z__87966)
     => ( Vvar__1__z__87965 = Vvar__1__z__87966
        & Vvar__0__r1__87963 = Vvar__0__r1__87964 ) ) ).

fof('$_inj_Coq.micromega.RMicromega.CQ',axiom,
    ! [Vvar__0__r__87947,Vvar__0__r__87948] :
      ( cCoq_2emicromega_2eRMicromega_2eCQ___24a1(Vvar__0__r__87947) = cCoq_2emicromega_2eRMicromega_2eCQ___24a1(Vvar__0__r__87948)
     => Vvar__0__r__87947 = Vvar__0__r__87948 ) ).

fof('$_inj_Coq.micromega.RMicromega.CZ',axiom,
    ! [Vvar__0__r__87949,Vvar__0__r__87950] :
      ( cCoq_2emicromega_2eRMicromega_2eCZ___24a1(Vvar__0__r__87949) = cCoq_2emicromega_2eRMicromega_2eCZ___24a1(Vvar__0__r__87950)
     => Vvar__0__r__87949 = Vvar__0__r__87950 ) ).

fof('$_inj_Coq.micromega.RingMicromega.Build_Formula',axiom,
    ! [Vvar__0__T__90989,Vvar__0__T__90990,Vvar__1__Flhs__90991,Vvar__1__Flhs__90992,Vvar__2__Fop__90993,Vvar__2__Fop__90994,Vvar__3__Frhs__90995,Vvar__3__Frhs__90996] :
      ( cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(Vvar__0__T__90989,Vvar__1__Flhs__90991,Vvar__2__Fop__90993,Vvar__3__Frhs__90995) = cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(Vvar__0__T__90990,Vvar__1__Flhs__90992,Vvar__2__Fop__90994,Vvar__3__Frhs__90996)
     => ( Vvar__3__Frhs__90995 = Vvar__3__Frhs__90996
        & Vvar__2__Fop__90993 = Vvar__2__Fop__90994
        & Vvar__1__Flhs__90991 = Vvar__1__Flhs__90992
        & Vvar__0__T__90989 = Vvar__0__T__90990 ) ) ).

fof('$_inj_Coq.micromega.RingMicromega.PsatzAdd',axiom,
    ! [Vvar__0__C__85683,Vvar__0__C__85684,Vvar__1___24Anonymous__85685,Vvar__1___24Anonymous__85686,Vvar__2___24Anonymous__85687,Vvar__2___24Anonymous__85688] :
      ( cCoq_2emicromega_2eRingMicromega_2ePsatzAdd___24a3(Vvar__0__C__85683,Vvar__1___24Anonymous__85685,Vvar__2___24Anonymous__85687) = cCoq_2emicromega_2eRingMicromega_2ePsatzAdd___24a3(Vvar__0__C__85684,Vvar__1___24Anonymous__85686,Vvar__2___24Anonymous__85688)
     => ( Vvar__2___24Anonymous__85687 = Vvar__2___24Anonymous__85688
        & Vvar__1___24Anonymous__85685 = Vvar__1___24Anonymous__85686
        & Vvar__0__C__85683 = Vvar__0__C__85684 ) ) ).

fof('$_inj_Coq.micromega.RingMicromega.PsatzC',axiom,
    ! [Vvar__0__C__85689,Vvar__0__C__85690,Vvar__1___24Anonymous__85691,Vvar__1___24Anonymous__85692] :
      ( cCoq_2emicromega_2eRingMicromega_2ePsatzC___24a2(Vvar__0__C__85689,Vvar__1___24Anonymous__85691) = cCoq_2emicromega_2eRingMicromega_2ePsatzC___24a2(Vvar__0__C__85690,Vvar__1___24Anonymous__85692)
     => ( Vvar__1___24Anonymous__85691 = Vvar__1___24Anonymous__85692
        & Vvar__0__C__85689 = Vvar__0__C__85690 ) ) ).

fof('$_inj_Coq.micromega.RingMicromega.PsatzIn',axiom,
    ! [Vvar__0__C__85663,Vvar__0__C__85664,Vvar__1___24Anonymous__85665,Vvar__1___24Anonymous__85666] :
      ( cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(Vvar__0__C__85663,Vvar__1___24Anonymous__85665) = cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(Vvar__0__C__85664,Vvar__1___24Anonymous__85666)
     => ( Vvar__1___24Anonymous__85665 = Vvar__1___24Anonymous__85666
        & Vvar__0__C__85663 = Vvar__0__C__85664 ) ) ).

fof('$_inj_Coq.micromega.RingMicromega.PsatzMulC',axiom,
    ! [Vvar__0__C__85671,Vvar__0__C__85672,Vvar__1___24Anonymous__85673,Vvar__1___24Anonymous__85674,Vvar__2___24Anonymous__85675,Vvar__2___24Anonymous__85676] :
      ( cCoq_2emicromega_2eRingMicromega_2ePsatzMulC___24a3(Vvar__0__C__85671,Vvar__1___24Anonymous__85673,Vvar__2___24Anonymous__85675) = cCoq_2emicromega_2eRingMicromega_2ePsatzMulC___24a3(Vvar__0__C__85672,Vvar__1___24Anonymous__85674,Vvar__2___24Anonymous__85676)
     => ( Vvar__2___24Anonymous__85675 = Vvar__2___24Anonymous__85676
        & Vvar__1___24Anonymous__85673 = Vvar__1___24Anonymous__85674
        & Vvar__0__C__85671 = Vvar__0__C__85672 ) ) ).

fof('$_inj_Coq.micromega.RingMicromega.PsatzMulE',axiom,
    ! [Vvar__0__C__85677,Vvar__0__C__85678,Vvar__1___24Anonymous__85679,Vvar__1___24Anonymous__85680,Vvar__2___24Anonymous__85681,Vvar__2___24Anonymous__85682] :
      ( cCoq_2emicromega_2eRingMicromega_2ePsatzMulE___24a3(Vvar__0__C__85677,Vvar__1___24Anonymous__85679,Vvar__2___24Anonymous__85681) = cCoq_2emicromega_2eRingMicromega_2ePsatzMulE___24a3(Vvar__0__C__85678,Vvar__1___24Anonymous__85680,Vvar__2___24Anonymous__85682)
     => ( Vvar__2___24Anonymous__85681 = Vvar__2___24Anonymous__85682
        & Vvar__1___24Anonymous__85679 = Vvar__1___24Anonymous__85680
        & Vvar__0__C__85677 = Vvar__0__C__85678 ) ) ).

fof('$_inj_Coq.micromega.RingMicromega.PsatzSquare',axiom,
    ! [Vvar__0__C__85667,Vvar__0__C__85668,Vvar__1___24Anonymous__85669,Vvar__1___24Anonymous__85670] :
      ( cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(Vvar__0__C__85667,Vvar__1___24Anonymous__85669) = cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(Vvar__0__C__85668,Vvar__1___24Anonymous__85670)
     => ( Vvar__1___24Anonymous__85669 = Vvar__1___24Anonymous__85670
        & Vvar__0__C__85667 = Vvar__0__C__85668 ) ) ).

fof('$_inj_Coq.micromega.RingMicromega.PsatzZ',axiom,
    ! [Vvar__0__C__85693,Vvar__0__C__85694] :
      ( cCoq_2emicromega_2eRingMicromega_2ePsatzZ___24a1(Vvar__0__C__85693) = cCoq_2emicromega_2eRingMicromega_2ePsatzZ___24a1(Vvar__0__C__85694)
     => Vvar__0__C__85693 = Vvar__0__C__85694 ) ).

fof('$_inj_Coq.micromega.Tauto.A',axiom,
    ! [Vvar__0__TA__86365,Vvar__0__TA__86366,Vvar__1__TX__86367,Vvar__1__TX__86368,Vvar__2__AA__86369,Vvar__2__AA__86370,Vvar__3__AF__86371,Vvar__3__AF__86372,Vvar__4___24Anonymous__86373,Vvar__4___24Anonymous__86374,Vvar__5___24Anonymous__86375,Vvar__5___24Anonymous__86376] :
      ( cCoq_2emicromega_2eTauto_2eA___24a6(Vvar__0__TA__86365,Vvar__1__TX__86367,Vvar__2__AA__86369,Vvar__3__AF__86371,Vvar__4___24Anonymous__86373,Vvar__5___24Anonymous__86375) = cCoq_2emicromega_2eTauto_2eA___24a6(Vvar__0__TA__86366,Vvar__1__TX__86368,Vvar__2__AA__86370,Vvar__3__AF__86372,Vvar__4___24Anonymous__86374,Vvar__5___24Anonymous__86376)
     => ( Vvar__5___24Anonymous__86375 = Vvar__5___24Anonymous__86376
        & Vvar__4___24Anonymous__86373 = Vvar__4___24Anonymous__86374
        & Vvar__3__AF__86371 = Vvar__3__AF__86372
        & Vvar__2__AA__86369 = Vvar__2__AA__86370
        & Vvar__1__TX__86367 = Vvar__1__TX__86368
        & Vvar__0__TA__86365 = Vvar__0__TA__86366 ) ) ).

fof('$_inj_Coq.micromega.Tauto.Cj',axiom,
    ! [Vvar__0__TA__86377,Vvar__0__TA__86378,Vvar__1__TX__86379,Vvar__1__TX__86380,Vvar__2__AA__86381,Vvar__2__AA__86382,Vvar__3__AF__86383,Vvar__3__AF__86384,Vvar__4___24Anonymous__86385,Vvar__4___24Anonymous__86386,Vvar__5___24Anonymous__86387,Vvar__5___24Anonymous__86388] :
      ( cCoq_2emicromega_2eTauto_2eCj___24a6(Vvar__0__TA__86377,Vvar__1__TX__86379,Vvar__2__AA__86381,Vvar__3__AF__86383,Vvar__4___24Anonymous__86385,Vvar__5___24Anonymous__86387) = cCoq_2emicromega_2eTauto_2eCj___24a6(Vvar__0__TA__86378,Vvar__1__TX__86380,Vvar__2__AA__86382,Vvar__3__AF__86384,Vvar__4___24Anonymous__86386,Vvar__5___24Anonymous__86388)
     => ( Vvar__5___24Anonymous__86387 = Vvar__5___24Anonymous__86388
        & Vvar__4___24Anonymous__86385 = Vvar__4___24Anonymous__86386
        & Vvar__3__AF__86383 = Vvar__3__AF__86384
        & Vvar__2__AA__86381 = Vvar__2__AA__86382
        & Vvar__1__TX__86379 = Vvar__1__TX__86380
        & Vvar__0__TA__86377 = Vvar__0__TA__86378 ) ) ).

fof('$_inj_Coq.micromega.Tauto.D',axiom,
    ! [Vvar__0__TA__86389,Vvar__0__TA__86390,Vvar__1__TX__86391,Vvar__1__TX__86392,Vvar__2__AA__86393,Vvar__2__AA__86394,Vvar__3__AF__86395,Vvar__3__AF__86396,Vvar__4___24Anonymous__86397,Vvar__4___24Anonymous__86398,Vvar__5___24Anonymous__86399,Vvar__5___24Anonymous__86400] :
      ( cCoq_2emicromega_2eTauto_2eD___24a6(Vvar__0__TA__86389,Vvar__1__TX__86391,Vvar__2__AA__86393,Vvar__3__AF__86395,Vvar__4___24Anonymous__86397,Vvar__5___24Anonymous__86399) = cCoq_2emicromega_2eTauto_2eD___24a6(Vvar__0__TA__86390,Vvar__1__TX__86392,Vvar__2__AA__86394,Vvar__3__AF__86396,Vvar__4___24Anonymous__86398,Vvar__5___24Anonymous__86400)
     => ( Vvar__5___24Anonymous__86399 = Vvar__5___24Anonymous__86400
        & Vvar__4___24Anonymous__86397 = Vvar__4___24Anonymous__86398
        & Vvar__3__AF__86395 = Vvar__3__AF__86396
        & Vvar__2__AA__86393 = Vvar__2__AA__86394
        & Vvar__1__TX__86391 = Vvar__1__TX__86392
        & Vvar__0__TA__86389 = Vvar__0__TA__86390 ) ) ).

fof('$_inj_Coq.micromega.Tauto.FF',axiom,
    ! [Vvar__0__TA__86347,Vvar__0__TA__86348,Vvar__1__TX__86349,Vvar__1__TX__86350,Vvar__2__AA__86351,Vvar__2__AA__86352,Vvar__3__AF__86353,Vvar__3__AF__86354] :
      ( cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__86347,Vvar__1__TX__86349,Vvar__2__AA__86351,Vvar__3__AF__86353) = cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__86348,Vvar__1__TX__86350,Vvar__2__AA__86352,Vvar__3__AF__86354)
     => ( Vvar__3__AF__86353 = Vvar__3__AF__86354
        & Vvar__2__AA__86351 = Vvar__2__AA__86352
        & Vvar__1__TX__86349 = Vvar__1__TX__86350
        & Vvar__0__TA__86347 = Vvar__0__TA__86348 ) ) ).

fof('$_inj_Coq.micromega.Tauto.I',axiom,
    ! [Vvar__0__TA__86411,Vvar__0__TA__86412,Vvar__1__TX__86413,Vvar__1__TX__86414,Vvar__2__AA__86415,Vvar__2__AA__86416,Vvar__3__AF__86417,Vvar__3__AF__86418,Vvar__4___24Anonymous__86419,Vvar__4___24Anonymous__86420,Vvar__5___24Anonymous__86421,Vvar__5___24Anonymous__86422,Vvar__6___24Anonymous__86423,Vvar__6___24Anonymous__86424] :
      ( cCoq_2emicromega_2eTauto_2eI___24a7(Vvar__0__TA__86411,Vvar__1__TX__86413,Vvar__2__AA__86415,Vvar__3__AF__86417,Vvar__4___24Anonymous__86419,Vvar__5___24Anonymous__86421,Vvar__6___24Anonymous__86423) = cCoq_2emicromega_2eTauto_2eI___24a7(Vvar__0__TA__86412,Vvar__1__TX__86414,Vvar__2__AA__86416,Vvar__3__AF__86418,Vvar__4___24Anonymous__86420,Vvar__5___24Anonymous__86422,Vvar__6___24Anonymous__86424)
     => ( Vvar__6___24Anonymous__86423 = Vvar__6___24Anonymous__86424
        & Vvar__5___24Anonymous__86421 = Vvar__5___24Anonymous__86422
        & Vvar__4___24Anonymous__86419 = Vvar__4___24Anonymous__86420
        & Vvar__3__AF__86417 = Vvar__3__AF__86418
        & Vvar__2__AA__86415 = Vvar__2__AA__86416
        & Vvar__1__TX__86413 = Vvar__1__TX__86414
        & Vvar__0__TA__86411 = Vvar__0__TA__86412 ) ) ).

fof('$_inj_Coq.micromega.Tauto.N',axiom,
    ! [Vvar__0__TA__86401,Vvar__0__TA__86402,Vvar__1__TX__86403,Vvar__1__TX__86404,Vvar__2__AA__86405,Vvar__2__AA__86406,Vvar__3__AF__86407,Vvar__3__AF__86408,Vvar__4___24Anonymous__86409,Vvar__4___24Anonymous__86410] :
      ( cCoq_2emicromega_2eTauto_2eN___24a5(Vvar__0__TA__86401,Vvar__1__TX__86403,Vvar__2__AA__86405,Vvar__3__AF__86407,Vvar__4___24Anonymous__86409) = cCoq_2emicromega_2eTauto_2eN___24a5(Vvar__0__TA__86402,Vvar__1__TX__86404,Vvar__2__AA__86406,Vvar__3__AF__86408,Vvar__4___24Anonymous__86410)
     => ( Vvar__4___24Anonymous__86409 = Vvar__4___24Anonymous__86410
        & Vvar__3__AF__86407 = Vvar__3__AF__86408
        & Vvar__2__AA__86405 = Vvar__2__AA__86406
        & Vvar__1__TX__86403 = Vvar__1__TX__86404
        & Vvar__0__TA__86401 = Vvar__0__TA__86402 ) ) ).

fof('$_inj_Coq.micromega.Tauto.TT',axiom,
    ! [Vvar__0__TA__86339,Vvar__0__TA__86340,Vvar__1__TX__86341,Vvar__1__TX__86342,Vvar__2__AA__86343,Vvar__2__AA__86344,Vvar__3__AF__86345,Vvar__3__AF__86346] :
      ( cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__86339,Vvar__1__TX__86341,Vvar__2__AA__86343,Vvar__3__AF__86345) = cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__86340,Vvar__1__TX__86342,Vvar__2__AA__86344,Vvar__3__AF__86346)
     => ( Vvar__3__AF__86345 = Vvar__3__AF__86346
        & Vvar__2__AA__86343 = Vvar__2__AA__86344
        & Vvar__1__TX__86341 = Vvar__1__TX__86342
        & Vvar__0__TA__86339 = Vvar__0__TA__86340 ) ) ).

fof('$_inj_Coq.micromega.Tauto.X',axiom,
    ! [Vvar__0__TA__86355,Vvar__0__TA__86356,Vvar__1__TX__86357,Vvar__1__TX__86358,Vvar__2__AA__86359,Vvar__2__AA__86360,Vvar__3__AF__86361,Vvar__3__AF__86362,Vvar__4___24Anonymous__86363,Vvar__4___24Anonymous__86364] :
      ( cCoq_2emicromega_2eTauto_2eX___24a5(Vvar__0__TA__86355,Vvar__1__TX__86357,Vvar__2__AA__86359,Vvar__3__AF__86361,Vvar__4___24Anonymous__86363) = cCoq_2emicromega_2eTauto_2eX___24a5(Vvar__0__TA__86356,Vvar__1__TX__86358,Vvar__2__AA__86360,Vvar__3__AF__86362,Vvar__4___24Anonymous__86364)
     => ( Vvar__4___24Anonymous__86363 = Vvar__4___24Anonymous__86364
        & Vvar__3__AF__86361 = Vvar__3__AF__86362
        & Vvar__2__AA__86359 = Vvar__2__AA__86360
        & Vvar__1__TX__86357 = Vvar__1__TX__86358
        & Vvar__0__TA__86355 = Vvar__0__TA__86356 ) ) ).

fof('$_inj_Coq.micromega.VarMap.Branch',axiom,
    ! [Vvar__0__A__86454,Vvar__0__A__86455,Vvar__1___24Anonymous__86456,Vvar__1___24Anonymous__86457,Vvar__2___24Anonymous__86458,Vvar__2___24Anonymous__86459,Vvar__3___24Anonymous__86460,Vvar__3___24Anonymous__86461] :
      ( cCoq_2emicromega_2eVarMap_2eBranch___24a4(Vvar__0__A__86454,Vvar__1___24Anonymous__86456,Vvar__2___24Anonymous__86458,Vvar__3___24Anonymous__86460) = cCoq_2emicromega_2eVarMap_2eBranch___24a4(Vvar__0__A__86455,Vvar__1___24Anonymous__86457,Vvar__2___24Anonymous__86459,Vvar__3___24Anonymous__86461)
     => ( Vvar__3___24Anonymous__86460 = Vvar__3___24Anonymous__86461
        & Vvar__2___24Anonymous__86458 = Vvar__2___24Anonymous__86459
        & Vvar__1___24Anonymous__86456 = Vvar__1___24Anonymous__86457
        & Vvar__0__A__86454 = Vvar__0__A__86455 ) ) ).

fof('$_inj_Coq.micromega.VarMap.Elt',axiom,
    ! [Vvar__0__A__86450,Vvar__0__A__86451,Vvar__1___24Anonymous__86452,Vvar__1___24Anonymous__86453] :
      ( cCoq_2emicromega_2eVarMap_2eElt___24a2(Vvar__0__A__86450,Vvar__1___24Anonymous__86452) = cCoq_2emicromega_2eVarMap_2eElt___24a2(Vvar__0__A__86451,Vvar__1___24Anonymous__86453)
     => ( Vvar__1___24Anonymous__86452 = Vvar__1___24Anonymous__86453
        & Vvar__0__A__86450 = Vvar__0__A__86451 ) ) ).

fof('$_inj_Coq.micromega.VarMap.Empty',axiom,
    ! [Vvar__0__A__86448,Vvar__0__A__86449] :
      ( cCoq_2emicromega_2eVarMap_2eEmpty___24a1(Vvar__0__A__86448) = cCoq_2emicromega_2eVarMap_2eEmpty___24a1(Vvar__0__A__86449)
     => Vvar__0__A__86448 = Vvar__0__A__86449 ) ).

fof('$_inj_Coq.micromega.ZMicromega.CutProof',axiom,
    ! [Vvar__0___24Anonymous__83828,Vvar__0___24Anonymous__83829,Vvar__1___24Anonymous__83830,Vvar__1___24Anonymous__83831] :
      ( cCoq_2emicromega_2eZMicromega_2eCutProof___24a2(Vvar__0___24Anonymous__83828,Vvar__1___24Anonymous__83830) = cCoq_2emicromega_2eZMicromega_2eCutProof___24a2(Vvar__0___24Anonymous__83829,Vvar__1___24Anonymous__83831)
     => ( Vvar__1___24Anonymous__83830 = Vvar__1___24Anonymous__83831
        & Vvar__0___24Anonymous__83828 = Vvar__0___24Anonymous__83829 ) ) ).

fof('$_inj_Coq.micromega.ZMicromega.EnumProof',axiom,
    ! [Vvar__0___24Anonymous__83832,Vvar__0___24Anonymous__83833,Vvar__1___24Anonymous__83834,Vvar__1___24Anonymous__83835,Vvar__2___24Anonymous__83836,Vvar__2___24Anonymous__83837] :
      ( cCoq_2emicromega_2eZMicromega_2eEnumProof___24a3(Vvar__0___24Anonymous__83832,Vvar__1___24Anonymous__83834,Vvar__2___24Anonymous__83836) = cCoq_2emicromega_2eZMicromega_2eEnumProof___24a3(Vvar__0___24Anonymous__83833,Vvar__1___24Anonymous__83835,Vvar__2___24Anonymous__83837)
     => ( Vvar__2___24Anonymous__83836 = Vvar__2___24Anonymous__83837
        & Vvar__1___24Anonymous__83834 = Vvar__1___24Anonymous__83835
        & Vvar__0___24Anonymous__83832 = Vvar__0___24Anonymous__83833 ) ) ).

fof('$_inj_Coq.micromega.ZMicromega.RatProof',axiom,
    ! [Vvar__0___24Anonymous__83824,Vvar__0___24Anonymous__83825,Vvar__1___24Anonymous__83826,Vvar__1___24Anonymous__83827] :
      ( cCoq_2emicromega_2eZMicromega_2eRatProof___24a2(Vvar__0___24Anonymous__83824,Vvar__1___24Anonymous__83826) = cCoq_2emicromega_2eZMicromega_2eRatProof___24a2(Vvar__0___24Anonymous__83825,Vvar__1___24Anonymous__83827)
     => ( Vvar__1___24Anonymous__83826 = Vvar__1___24Anonymous__83827
        & Vvar__0___24Anonymous__83824 = Vvar__0___24Anonymous__83825 ) ) ).

fof('$_inj_Coq.micromega.ZMicromega.Vars.Node',axiom,
    ! [Vvar__0___24Anonymous__200968,Vvar__0___24Anonymous__200969,Vvar__1___24Anonymous__200970,Vvar__1___24Anonymous__200971,Vvar__2___24Anonymous__200972,Vvar__2___24Anonymous__200973] :
      ( cCoq_2emicromega_2eZMicromega_2eVars_2eNode___24a3(Vvar__0___24Anonymous__200968,Vvar__1___24Anonymous__200970,Vvar__2___24Anonymous__200972) = cCoq_2emicromega_2eZMicromega_2eVars_2eNode___24a3(Vvar__0___24Anonymous__200969,Vvar__1___24Anonymous__200971,Vvar__2___24Anonymous__200973)
     => ( Vvar__2___24Anonymous__200972 = Vvar__2___24Anonymous__200973
        & Vvar__1___24Anonymous__200970 = Vvar__1___24Anonymous__200971
        & Vvar__0___24Anonymous__200968 = Vvar__0___24Anonymous__200969 ) ) ).

fof('$_inj_Coq.setoid_ring.Field_theory.FEI',axiom,
    ! [Vvar__0__C__85466,Vvar__0__C__85467] :
      ( cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__85466) = cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__85467)
     => Vvar__0__C__85466 = Vvar__0__C__85467 ) ).

fof('$_inj_Coq.setoid_ring.Field_theory.FEO',axiom,
    ! [Vvar__0__C__85464,Vvar__0__C__85465] :
      ( cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__85464) = cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__85465)
     => Vvar__0__C__85464 = Vvar__0__C__85465 ) ).

fof('$_inj_Coq.setoid_ring.Field_theory.FEX',axiom,
    ! [Vvar__0__C__85472,Vvar__0__C__85473,Vvar__1___24Anonymous__85474,Vvar__1___24Anonymous__85475] :
      ( cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(Vvar__0__C__85472,Vvar__1___24Anonymous__85474) = cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(Vvar__0__C__85473,Vvar__1___24Anonymous__85475)
     => ( Vvar__1___24Anonymous__85474 = Vvar__1___24Anonymous__85475
        & Vvar__0__C__85472 = Vvar__0__C__85473 ) ) ).

fof('$_inj_Coq.setoid_ring.Field_theory.FEadd',axiom,
    ! [Vvar__0__C__85476,Vvar__0__C__85477,Vvar__1___24Anonymous__85478,Vvar__1___24Anonymous__85479,Vvar__2___24Anonymous__85480,Vvar__2___24Anonymous__85481] :
      ( cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(Vvar__0__C__85476,Vvar__1___24Anonymous__85478,Vvar__2___24Anonymous__85480) = cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(Vvar__0__C__85477,Vvar__1___24Anonymous__85479,Vvar__2___24Anonymous__85481)
     => ( Vvar__2___24Anonymous__85480 = Vvar__2___24Anonymous__85481
        & Vvar__1___24Anonymous__85478 = Vvar__1___24Anonymous__85479
        & Vvar__0__C__85476 = Vvar__0__C__85477 ) ) ).

fof('$_inj_Coq.setoid_ring.Field_theory.FEc',axiom,
    ! [Vvar__0__C__85468,Vvar__0__C__85469,Vvar__1___24Anonymous__85470,Vvar__1___24Anonymous__85471] :
      ( cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(Vvar__0__C__85468,Vvar__1___24Anonymous__85470) = cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(Vvar__0__C__85469,Vvar__1___24Anonymous__85471)
     => ( Vvar__1___24Anonymous__85470 = Vvar__1___24Anonymous__85471
        & Vvar__0__C__85468 = Vvar__0__C__85469 ) ) ).

fof('$_inj_Coq.setoid_ring.Field_theory.FEdiv',axiom,
    ! [Vvar__0__C__85502,Vvar__0__C__85503,Vvar__1___24Anonymous__85504,Vvar__1___24Anonymous__85505,Vvar__2___24Anonymous__85506,Vvar__2___24Anonymous__85507] :
      ( cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(Vvar__0__C__85502,Vvar__1___24Anonymous__85504,Vvar__2___24Anonymous__85506) = cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(Vvar__0__C__85503,Vvar__1___24Anonymous__85505,Vvar__2___24Anonymous__85507)
     => ( Vvar__2___24Anonymous__85506 = Vvar__2___24Anonymous__85507
        & Vvar__1___24Anonymous__85504 = Vvar__1___24Anonymous__85505
        & Vvar__0__C__85502 = Vvar__0__C__85503 ) ) ).

fof('$_inj_Coq.setoid_ring.Field_theory.FEinv',axiom,
    ! [Vvar__0__C__85498,Vvar__0__C__85499,Vvar__1___24Anonymous__85500,Vvar__1___24Anonymous__85501] :
      ( cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(Vvar__0__C__85498,Vvar__1___24Anonymous__85500) = cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(Vvar__0__C__85499,Vvar__1___24Anonymous__85501)
     => ( Vvar__1___24Anonymous__85500 = Vvar__1___24Anonymous__85501
        & Vvar__0__C__85498 = Vvar__0__C__85499 ) ) ).

fof('$_inj_Coq.setoid_ring.Field_theory.FEmul',axiom,
    ! [Vvar__0__C__85488,Vvar__0__C__85489,Vvar__1___24Anonymous__85490,Vvar__1___24Anonymous__85491,Vvar__2___24Anonymous__85492,Vvar__2___24Anonymous__85493] :
      ( cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(Vvar__0__C__85488,Vvar__1___24Anonymous__85490,Vvar__2___24Anonymous__85492) = cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(Vvar__0__C__85489,Vvar__1___24Anonymous__85491,Vvar__2___24Anonymous__85493)
     => ( Vvar__2___24Anonymous__85492 = Vvar__2___24Anonymous__85493
        & Vvar__1___24Anonymous__85490 = Vvar__1___24Anonymous__85491
        & Vvar__0__C__85488 = Vvar__0__C__85489 ) ) ).

fof('$_inj_Coq.setoid_ring.Field_theory.FEopp',axiom,
    ! [Vvar__0__C__85494,Vvar__0__C__85495,Vvar__1___24Anonymous__85496,Vvar__1___24Anonymous__85497] :
      ( cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(Vvar__0__C__85494,Vvar__1___24Anonymous__85496) = cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(Vvar__0__C__85495,Vvar__1___24Anonymous__85497)
     => ( Vvar__1___24Anonymous__85496 = Vvar__1___24Anonymous__85497
        & Vvar__0__C__85494 = Vvar__0__C__85495 ) ) ).

fof('$_inj_Coq.setoid_ring.Field_theory.FEpow',axiom,
    ! [Vvar__0__C__85508,Vvar__0__C__85509,Vvar__1___24Anonymous__85510,Vvar__1___24Anonymous__85511,Vvar__2___24Anonymous__85512,Vvar__2___24Anonymous__85513] :
      ( cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(Vvar__0__C__85508,Vvar__1___24Anonymous__85510,Vvar__2___24Anonymous__85512) = cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(Vvar__0__C__85509,Vvar__1___24Anonymous__85511,Vvar__2___24Anonymous__85513)
     => ( Vvar__2___24Anonymous__85512 = Vvar__2___24Anonymous__85513
        & Vvar__1___24Anonymous__85510 = Vvar__1___24Anonymous__85511
        & Vvar__0__C__85508 = Vvar__0__C__85509 ) ) ).

fof('$_inj_Coq.setoid_ring.Field_theory.FEsub',axiom,
    ! [Vvar__0__C__85482,Vvar__0__C__85483,Vvar__1___24Anonymous__85484,Vvar__1___24Anonymous__85485,Vvar__2___24Anonymous__85486,Vvar__2___24Anonymous__85487] :
      ( cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(Vvar__0__C__85482,Vvar__1___24Anonymous__85484,Vvar__2___24Anonymous__85486) = cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(Vvar__0__C__85483,Vvar__1___24Anonymous__85485,Vvar__2___24Anonymous__85487)
     => ( Vvar__2___24Anonymous__85486 = Vvar__2___24Anonymous__85487
        & Vvar__1___24Anonymous__85484 = Vvar__1___24Anonymous__85485
        & Vvar__0__C__85482 = Vvar__0__C__85483 ) ) ).

fof('$_inj_Coq.setoid_ring.Field_theory.mk_linear',axiom,
    ! [Vvar__0__C__85520,Vvar__0__C__85521,Vvar__1__num__85522,Vvar__1__num__85523,Vvar__2__denum__85524,Vvar__2__denum__85525,Vvar__3__condition__85526,Vvar__3__condition__85527] :
      ( cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(Vvar__0__C__85520,Vvar__1__num__85522,Vvar__2__denum__85524,Vvar__3__condition__85526) = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(Vvar__0__C__85521,Vvar__1__num__85523,Vvar__2__denum__85525,Vvar__3__condition__85527)
     => ( Vvar__3__condition__85526 = Vvar__3__condition__85527
        & Vvar__2__denum__85524 = Vvar__2__denum__85525
        & Vvar__1__num__85522 = Vvar__1__num__85523
        & Vvar__0__C__85520 = Vvar__0__C__85521 ) ) ).

fof('$_inj_Coq.setoid_ring.Field_theory.mk_rsplit',axiom,
    ! [Vvar__0__C__86660,Vvar__0__C__86661,Vvar__1__rsplit__left__86662,Vvar__1__rsplit__left__86663,Vvar__2__rsplit__common__86664,Vvar__2__rsplit__common__86665,Vvar__3__rsplit__right__86666,Vvar__3__rsplit__right__86667] :
      ( cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(Vvar__0__C__86660,Vvar__1__rsplit__left__86662,Vvar__2__rsplit__common__86664,Vvar__3__rsplit__right__86666) = cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(Vvar__0__C__86661,Vvar__1__rsplit__left__86663,Vvar__2__rsplit__common__86665,Vvar__3__rsplit__right__86667)
     => ( Vvar__3__rsplit__right__86666 = Vvar__3__rsplit__right__86667
        & Vvar__2__rsplit__common__86664 = Vvar__2__rsplit__common__86665
        & Vvar__1__rsplit__left__86662 = Vvar__1__rsplit__left__86663
        & Vvar__0__C__86660 = Vvar__0__C__86661 ) ) ).

fof('$_inj_Coq.setoid_ring.InitialRing.mkhypo',axiom,
    ! [Vvar__0__hypo__type__89674,Vvar__0__hypo__type__89675,Vvar__1__hypo__proof__89676,Vvar__1__hypo__proof__89677] :
      ( cCoq_2esetoid__ring_2eInitialRing_2emkhypo___24a2(Vvar__0__hypo__type__89674,Vvar__1__hypo__proof__89676) = cCoq_2esetoid__ring_2eInitialRing_2emkhypo___24a2(Vvar__0__hypo__type__89675,Vvar__1__hypo__proof__89677)
     => ( Vvar__1__hypo__proof__89676 = Vvar__1__hypo__proof__89677
        & Vvar__0__hypo__type__89674 = Vvar__0__hypo__type__89675 ) ) ).

fof('$_inj_Coq.setoid_ring.Ring_polynom.PEI',axiom,
    ! [Vvar__0__C__1593,Vvar__0__C__1594] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__1593) = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__1594)
     => Vvar__0__C__1593 = Vvar__0__C__1594 ) ).

fof('$_inj_Coq.setoid_ring.Ring_polynom.PEO',axiom,
    ! [Vvar__0__C__1591,Vvar__0__C__1592] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__1591) = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__1592)
     => Vvar__0__C__1591 = Vvar__0__C__1592 ) ).

fof('$_inj_Coq.setoid_ring.Ring_polynom.PEX',axiom,
    ! [Vvar__0__C__1599,Vvar__0__C__1600,Vvar__1___24Anonymous__1601,Vvar__1___24Anonymous__1602] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(Vvar__0__C__1599,Vvar__1___24Anonymous__1601) = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(Vvar__0__C__1600,Vvar__1___24Anonymous__1602)
     => ( Vvar__1___24Anonymous__1601 = Vvar__1___24Anonymous__1602
        & Vvar__0__C__1599 = Vvar__0__C__1600 ) ) ).

fof('$_inj_Coq.setoid_ring.Ring_polynom.PEadd',axiom,
    ! [Vvar__0__C__1603,Vvar__0__C__1604,Vvar__1___24Anonymous__1605,Vvar__1___24Anonymous__1606,Vvar__2___24Anonymous__1607,Vvar__2___24Anonymous__1608] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(Vvar__0__C__1603,Vvar__1___24Anonymous__1605,Vvar__2___24Anonymous__1607) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(Vvar__0__C__1604,Vvar__1___24Anonymous__1606,Vvar__2___24Anonymous__1608)
     => ( Vvar__2___24Anonymous__1607 = Vvar__2___24Anonymous__1608
        & Vvar__1___24Anonymous__1605 = Vvar__1___24Anonymous__1606
        & Vvar__0__C__1603 = Vvar__0__C__1604 ) ) ).

fof('$_inj_Coq.setoid_ring.Ring_polynom.PEc',axiom,
    ! [Vvar__0__C__1595,Vvar__0__C__1596,Vvar__1___24Anonymous__1597,Vvar__1___24Anonymous__1598] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(Vvar__0__C__1595,Vvar__1___24Anonymous__1597) = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(Vvar__0__C__1596,Vvar__1___24Anonymous__1598)
     => ( Vvar__1___24Anonymous__1597 = Vvar__1___24Anonymous__1598
        & Vvar__0__C__1595 = Vvar__0__C__1596 ) ) ).

fof('$_inj_Coq.setoid_ring.Ring_polynom.PEmul',axiom,
    ! [Vvar__0__C__1615,Vvar__0__C__1616,Vvar__1___24Anonymous__1617,Vvar__1___24Anonymous__1618,Vvar__2___24Anonymous__1619,Vvar__2___24Anonymous__1620] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(Vvar__0__C__1615,Vvar__1___24Anonymous__1617,Vvar__2___24Anonymous__1619) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(Vvar__0__C__1616,Vvar__1___24Anonymous__1618,Vvar__2___24Anonymous__1620)
     => ( Vvar__2___24Anonymous__1619 = Vvar__2___24Anonymous__1620
        & Vvar__1___24Anonymous__1617 = Vvar__1___24Anonymous__1618
        & Vvar__0__C__1615 = Vvar__0__C__1616 ) ) ).

fof('$_inj_Coq.setoid_ring.Ring_polynom.PEopp',axiom,
    ! [Vvar__0__C__1621,Vvar__0__C__1622,Vvar__1___24Anonymous__1623,Vvar__1___24Anonymous__1624] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(Vvar__0__C__1621,Vvar__1___24Anonymous__1623) = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(Vvar__0__C__1622,Vvar__1___24Anonymous__1624)
     => ( Vvar__1___24Anonymous__1623 = Vvar__1___24Anonymous__1624
        & Vvar__0__C__1621 = Vvar__0__C__1622 ) ) ).

fof('$_inj_Coq.setoid_ring.Ring_polynom.PEpow',axiom,
    ! [Vvar__0__C__1625,Vvar__0__C__1626,Vvar__1___24Anonymous__1627,Vvar__1___24Anonymous__1628,Vvar__2___24Anonymous__1629,Vvar__2___24Anonymous__1630] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(Vvar__0__C__1625,Vvar__1___24Anonymous__1627,Vvar__2___24Anonymous__1629) = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(Vvar__0__C__1626,Vvar__1___24Anonymous__1628,Vvar__2___24Anonymous__1630)
     => ( Vvar__2___24Anonymous__1629 = Vvar__2___24Anonymous__1630
        & Vvar__1___24Anonymous__1627 = Vvar__1___24Anonymous__1628
        & Vvar__0__C__1625 = Vvar__0__C__1626 ) ) ).

fof('$_inj_Coq.setoid_ring.Ring_polynom.PEsub',axiom,
    ! [Vvar__0__C__1609,Vvar__0__C__1610,Vvar__1___24Anonymous__1611,Vvar__1___24Anonymous__1612,Vvar__2___24Anonymous__1613,Vvar__2___24Anonymous__1614] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(Vvar__0__C__1609,Vvar__1___24Anonymous__1611,Vvar__2___24Anonymous__1613) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(Vvar__0__C__1610,Vvar__1___24Anonymous__1612,Vvar__2___24Anonymous__1614)
     => ( Vvar__2___24Anonymous__1613 = Vvar__2___24Anonymous__1614
        & Vvar__1___24Anonymous__1611 = Vvar__1___24Anonymous__1612
        & Vvar__0__C__1609 = Vvar__0__C__1610 ) ) ).

fof('$_inj_Coq.setoid_ring.Ring_polynom.PX',axiom,
    ! [Vvar__0__C__1246,Vvar__0__C__1247,Vvar__1___24Anonymous__1248,Vvar__1___24Anonymous__1249,Vvar__2___24Anonymous__1250,Vvar__2___24Anonymous__1251,Vvar__3___24Anonymous__1252,Vvar__3___24Anonymous__1253] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(Vvar__0__C__1246,Vvar__1___24Anonymous__1248,Vvar__2___24Anonymous__1250,Vvar__3___24Anonymous__1252) = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(Vvar__0__C__1247,Vvar__1___24Anonymous__1249,Vvar__2___24Anonymous__1251,Vvar__3___24Anonymous__1253)
     => ( Vvar__3___24Anonymous__1252 = Vvar__3___24Anonymous__1253
        & Vvar__2___24Anonymous__1250 = Vvar__2___24Anonymous__1251
        & Vvar__1___24Anonymous__1248 = Vvar__1___24Anonymous__1249
        & Vvar__0__C__1246 = Vvar__0__C__1247 ) ) ).

fof('$_inj_Coq.setoid_ring.Ring_polynom.Pc',axiom,
    ! [Vvar__0__C__1236,Vvar__0__C__1237,Vvar__1___24Anonymous__1238,Vvar__1___24Anonymous__1239] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__1236,Vvar__1___24Anonymous__1238) = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__1237,Vvar__1___24Anonymous__1239)
     => ( Vvar__1___24Anonymous__1238 = Vvar__1___24Anonymous__1239
        & Vvar__0__C__1236 = Vvar__0__C__1237 ) ) ).

fof('$_inj_Coq.setoid_ring.Ring_polynom.Pinj',axiom,
    ! [Vvar__0__C__1240,Vvar__0__C__1241,Vvar__1___24Anonymous__1242,Vvar__1___24Anonymous__1243,Vvar__2___24Anonymous__1244,Vvar__2___24Anonymous__1245] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__1240,Vvar__1___24Anonymous__1242,Vvar__2___24Anonymous__1244) = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__1241,Vvar__1___24Anonymous__1243,Vvar__2___24Anonymous__1245)
     => ( Vvar__2___24Anonymous__1244 = Vvar__2___24Anonymous__1245
        & Vvar__1___24Anonymous__1242 = Vvar__1___24Anonymous__1243
        & Vvar__0__C__1240 = Vvar__0__C__1241 ) ) ).

fof('$_inj_Coq.setoid_ring.Ring_polynom.vmon',axiom,
    ! [Vvar__0___24Anonymous__1405,Vvar__0___24Anonymous__1406,Vvar__1___24Anonymous__1407,Vvar__1___24Anonymous__1408] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(Vvar__0___24Anonymous__1405,Vvar__1___24Anonymous__1407) = cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(Vvar__0___24Anonymous__1406,Vvar__1___24Anonymous__1408)
     => ( Vvar__1___24Anonymous__1407 = Vvar__1___24Anonymous__1408
        & Vvar__0___24Anonymous__1405 = Vvar__0___24Anonymous__1406 ) ) ).

fof('$_inj_Coq.setoid_ring.Ring_polynom.zmon',axiom,
    ! [Vvar__0___24Anonymous__1401,Vvar__0___24Anonymous__1402,Vvar__1___24Anonymous__1403,Vvar__1___24Anonymous__1404] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__1401,Vvar__1___24Anonymous__1403) = cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__1402,Vvar__1___24Anonymous__1404)
     => ( Vvar__1___24Anonymous__1403 = Vvar__1___24Anonymous__1404
        & Vvar__0___24Anonymous__1401 = Vvar__0___24Anonymous__1402 ) ) ).

fof('$_inj_Coq.setoid_ring.Ring_theory.Computational',axiom,
    ! [Vvar__0__R__85861,Vvar__0__R__85862,Vvar__1__req__85863,Vvar__1__req__85864,Vvar__2__reqb__85865,Vvar__2__reqb__85866,Vvar__3___24Anonymous__85867,Vvar__3___24Anonymous__85868] :
      ( cCoq_2esetoid__ring_2eRing__theory_2eComputational___24a3(Vvar__0__R__85861,Vvar__1__req__85863,Vvar__2__reqb__85865) = cCoq_2esetoid__ring_2eRing__theory_2eComputational___24a3(Vvar__0__R__85862,Vvar__1__req__85864,Vvar__2__reqb__85866)
     => ( c_24Proof = c_24Proof
        & Vvar__2__reqb__85865 = Vvar__2__reqb__85866
        & Vvar__1__req__85863 = Vvar__1__req__85864
        & Vvar__0__R__85861 = Vvar__0__R__85862 ) ) ).

fof('$_inj_Coq.setoid_ring.Ring_theory.Morphism',axiom,
    ! [Vvar__0__R__85869,Vvar__0__R__85870,Vvar__1__rO__85871,Vvar__1__rO__85872,Vvar__2__rI__85873,Vvar__2__rI__85874,Vvar__3__radd__85875,Vvar__3__radd__85876,Vvar__4__rmul__85877,Vvar__4__rmul__85878,Vvar__5__rsub__85879,Vvar__5__rsub__85880,Vvar__6__ropp__85881,Vvar__6__ropp__85882,Vvar__7__req__85883,Vvar__7__req__85884,Vvar__8__C__85885,Vvar__8__C__85886,Vvar__9__cO__85887,Vvar__9__cO__85888,Vvar__10__cI__85889,Vvar__10__cI__85890,Vvar__11__cadd__85891,Vvar__11__cadd__85892,Vvar__12__cmul__85893,Vvar__12__cmul__85894,Vvar__13__csub__85895,Vvar__13__csub__85896,Vvar__14__copp__85897,Vvar__14__copp__85898,Vvar__15__ceqb__85899,Vvar__15__ceqb__85900,Vvar__16__phi__85901,Vvar__16__phi__85902,Vvar__17___24Anonymous__85903,Vvar__17___24Anonymous__85904] :
      ( cCoq_2esetoid__ring_2eRing__theory_2eMorphism___24a17(Vvar__0__R__85869,Vvar__1__rO__85871,Vvar__2__rI__85873,Vvar__3__radd__85875,Vvar__4__rmul__85877,Vvar__5__rsub__85879,Vvar__6__ropp__85881,Vvar__7__req__85883,Vvar__8__C__85885,Vvar__9__cO__85887,Vvar__10__cI__85889,Vvar__11__cadd__85891,Vvar__12__cmul__85893,Vvar__13__csub__85895,Vvar__14__copp__85897,Vvar__15__ceqb__85899,Vvar__16__phi__85901) = cCoq_2esetoid__ring_2eRing__theory_2eMorphism___24a17(Vvar__0__R__85870,Vvar__1__rO__85872,Vvar__2__rI__85874,Vvar__3__radd__85876,Vvar__4__rmul__85878,Vvar__5__rsub__85880,Vvar__6__ropp__85882,Vvar__7__req__85884,Vvar__8__C__85886,Vvar__9__cO__85888,Vvar__10__cI__85890,Vvar__11__cadd__85892,Vvar__12__cmul__85894,Vvar__13__csub__85896,Vvar__14__copp__85898,Vvar__15__ceqb__85900,Vvar__16__phi__85902)
     => ( c_24Proof = c_24Proof
        & Vvar__16__phi__85901 = Vvar__16__phi__85902
        & Vvar__15__ceqb__85899 = Vvar__15__ceqb__85900
        & Vvar__14__copp__85897 = Vvar__14__copp__85898
        & Vvar__13__csub__85895 = Vvar__13__csub__85896
        & Vvar__12__cmul__85893 = Vvar__12__cmul__85894
        & Vvar__11__cadd__85891 = Vvar__11__cadd__85892
        & Vvar__10__cI__85889 = Vvar__10__cI__85890
        & Vvar__9__cO__85887 = Vvar__9__cO__85888
        & Vvar__8__C__85885 = Vvar__8__C__85886
        & Vvar__7__req__85883 = Vvar__7__req__85884
        & Vvar__6__ropp__85881 = Vvar__6__ropp__85882
        & Vvar__5__rsub__85879 = Vvar__5__rsub__85880
        & Vvar__4__rmul__85877 = Vvar__4__rmul__85878
        & Vvar__3__radd__85875 = Vvar__3__radd__85876
        & Vvar__2__rI__85873 = Vvar__2__rI__85874
        & Vvar__1__rO__85871 = Vvar__1__rO__85872
        & Vvar__0__R__85869 = Vvar__0__R__85870 ) ) ).

fof('$_inj_PLF.Imp.AExp.AMinus',axiom,
    ! [Vvar__0__a1__79403,Vvar__0__a1__79404,Vvar__1__a2__79405,Vvar__1__a2__79406] :
      ( cPLF_2eImp_2eAExp_2eAMinus___24a2(Vvar__0__a1__79403,Vvar__1__a2__79405) = cPLF_2eImp_2eAExp_2eAMinus___24a2(Vvar__0__a1__79404,Vvar__1__a2__79406)
     => ( Vvar__1__a2__79405 = Vvar__1__a2__79406
        & Vvar__0__a1__79403 = Vvar__0__a1__79404 ) ) ).

fof('$_inj_PLF.Imp.AExp.AMult',axiom,
    ! [Vvar__0__a1__79407,Vvar__0__a1__79408,Vvar__1__a2__79409,Vvar__1__a2__79410] :
      ( cPLF_2eImp_2eAExp_2eAMult___24a2(Vvar__0__a1__79407,Vvar__1__a2__79409) = cPLF_2eImp_2eAExp_2eAMult___24a2(Vvar__0__a1__79408,Vvar__1__a2__79410)
     => ( Vvar__1__a2__79409 = Vvar__1__a2__79410
        & Vvar__0__a1__79407 = Vvar__0__a1__79408 ) ) ).

fof('$_inj_PLF.Imp.AExp.ANum',axiom,
    ! [Vvar__0__n__79397,Vvar__0__n__79398] :
      ( cPLF_2eImp_2eAExp_2eANum___24a1(Vvar__0__n__79397) = cPLF_2eImp_2eAExp_2eANum___24a1(Vvar__0__n__79398)
     => Vvar__0__n__79397 = Vvar__0__n__79398 ) ).

fof('$_inj_PLF.Imp.AExp.APlus',axiom,
    ! [Vvar__0__a1__79399,Vvar__0__a1__79400,Vvar__1__a2__79401,Vvar__1__a2__79402] :
      ( cPLF_2eImp_2eAExp_2eAPlus___24a2(Vvar__0__a1__79399,Vvar__1__a2__79401) = cPLF_2eImp_2eAExp_2eAPlus___24a2(Vvar__0__a1__79400,Vvar__1__a2__79402)
     => ( Vvar__1__a2__79401 = Vvar__1__a2__79402
        & Vvar__0__a1__79399 = Vvar__0__a1__79400 ) ) ).

fof('$_inj_PLF.Imp.AExp.BAnd',axiom,
    ! [Vvar__0__b1__91949,Vvar__0__b1__91950,Vvar__1__b2__91951,Vvar__1__b2__91952] :
      ( cPLF_2eImp_2eAExp_2eBAnd___24a2(Vvar__0__b1__91949,Vvar__1__b2__91951) = cPLF_2eImp_2eAExp_2eBAnd___24a2(Vvar__0__b1__91950,Vvar__1__b2__91952)
     => ( Vvar__1__b2__91951 = Vvar__1__b2__91952
        & Vvar__0__b1__91949 = Vvar__0__b1__91950 ) ) ).

fof('$_inj_PLF.Imp.AExp.BEq',axiom,
    ! [Vvar__0__a1__91939,Vvar__0__a1__91940,Vvar__1__a2__91941,Vvar__1__a2__91942] :
      ( cPLF_2eImp_2eAExp_2eBEq___24a2(Vvar__0__a1__91939,Vvar__1__a2__91941) = cPLF_2eImp_2eAExp_2eBEq___24a2(Vvar__0__a1__91940,Vvar__1__a2__91942)
     => ( Vvar__1__a2__91941 = Vvar__1__a2__91942
        & Vvar__0__a1__91939 = Vvar__0__a1__91940 ) ) ).

fof('$_inj_PLF.Imp.AExp.BLe',axiom,
    ! [Vvar__0__a1__91943,Vvar__0__a1__91944,Vvar__1__a2__91945,Vvar__1__a2__91946] :
      ( cPLF_2eImp_2eAExp_2eBLe___24a2(Vvar__0__a1__91943,Vvar__1__a2__91945) = cPLF_2eImp_2eAExp_2eBLe___24a2(Vvar__0__a1__91944,Vvar__1__a2__91946)
     => ( Vvar__1__a2__91945 = Vvar__1__a2__91946
        & Vvar__0__a1__91943 = Vvar__0__a1__91944 ) ) ).

fof('$_inj_PLF.Imp.AExp.BNot',axiom,
    ! [Vvar__0__b__91947,Vvar__0__b__91948] :
      ( cPLF_2eImp_2eAExp_2eBNot___24a1(Vvar__0__b__91947) = cPLF_2eImp_2eAExp_2eBNot___24a1(Vvar__0__b__91948)
     => Vvar__0__b__91947 = Vvar__0__b__91948 ) ).

fof('$_inj_PLF.Imp.AId',axiom,
    ! [Vvar__0__x__377,Vvar__0__x__378] :
      ( cPLF_2eImp_2eAId___24a1(Vvar__0__x__377) = cPLF_2eImp_2eAId___24a1(Vvar__0__x__378)
     => Vvar__0__x__377 = Vvar__0__x__378 ) ).

fof('$_inj_PLF.Imp.AMinus',axiom,
    ! [Vvar__0__a1__383,Vvar__0__a1__384,Vvar__1__a2__385,Vvar__1__a2__386] :
      ( cPLF_2eImp_2eAMinus___24a2(Vvar__0__a1__383,Vvar__1__a2__385) = cPLF_2eImp_2eAMinus___24a2(Vvar__0__a1__384,Vvar__1__a2__386)
     => ( Vvar__1__a2__385 = Vvar__1__a2__386
        & Vvar__0__a1__383 = Vvar__0__a1__384 ) ) ).

fof('$_inj_PLF.Imp.AMult',axiom,
    ! [Vvar__0__a1__387,Vvar__0__a1__388,Vvar__1__a2__389,Vvar__1__a2__390] :
      ( cPLF_2eImp_2eAMult___24a2(Vvar__0__a1__387,Vvar__1__a2__389) = cPLF_2eImp_2eAMult___24a2(Vvar__0__a1__388,Vvar__1__a2__390)
     => ( Vvar__1__a2__389 = Vvar__1__a2__390
        & Vvar__0__a1__387 = Vvar__0__a1__388 ) ) ).

fof('$_inj_PLF.Imp.ANum',axiom,
    ! [Vvar__0__n__375,Vvar__0__n__376] :
      ( cPLF_2eImp_2eANum___24a1(Vvar__0__n__375) = cPLF_2eImp_2eANum___24a1(Vvar__0__n__376)
     => Vvar__0__n__375 = Vvar__0__n__376 ) ).

fof('$_inj_PLF.Imp.APlus',axiom,
    ! [Vvar__0__a1__379,Vvar__0__a1__380,Vvar__1__a2__381,Vvar__1__a2__382] :
      ( cPLF_2eImp_2eAPlus___24a2(Vvar__0__a1__379,Vvar__1__a2__381) = cPLF_2eImp_2eAPlus___24a2(Vvar__0__a1__380,Vvar__1__a2__382)
     => ( Vvar__1__a2__381 = Vvar__1__a2__382
        & Vvar__0__a1__379 = Vvar__0__a1__380 ) ) ).

fof('$_inj_PLF.Imp.BAnd',axiom,
    ! [Vvar__0__b1__451,Vvar__0__b1__452,Vvar__1__b2__453,Vvar__1__b2__454] :
      ( cPLF_2eImp_2eBAnd___24a2(Vvar__0__b1__451,Vvar__1__b2__453) = cPLF_2eImp_2eBAnd___24a2(Vvar__0__b1__452,Vvar__1__b2__454)
     => ( Vvar__1__b2__453 = Vvar__1__b2__454
        & Vvar__0__b1__451 = Vvar__0__b1__452 ) ) ).

fof('$_inj_PLF.Imp.BEq',axiom,
    ! [Vvar__0__a1__441,Vvar__0__a1__442,Vvar__1__a2__443,Vvar__1__a2__444] :
      ( cPLF_2eImp_2eBEq___24a2(Vvar__0__a1__441,Vvar__1__a2__443) = cPLF_2eImp_2eBEq___24a2(Vvar__0__a1__442,Vvar__1__a2__444)
     => ( Vvar__1__a2__443 = Vvar__1__a2__444
        & Vvar__0__a1__441 = Vvar__0__a1__442 ) ) ).

fof('$_inj_PLF.Imp.BLe',axiom,
    ! [Vvar__0__a1__445,Vvar__0__a1__446,Vvar__1__a2__447,Vvar__1__a2__448] :
      ( cPLF_2eImp_2eBLe___24a2(Vvar__0__a1__445,Vvar__1__a2__447) = cPLF_2eImp_2eBLe___24a2(Vvar__0__a1__446,Vvar__1__a2__448)
     => ( Vvar__1__a2__447 = Vvar__1__a2__448
        & Vvar__0__a1__445 = Vvar__0__a1__446 ) ) ).

fof('$_inj_PLF.Imp.BNot',axiom,
    ! [Vvar__0__b__449,Vvar__0__b__450] :
      ( cPLF_2eImp_2eBNot___24a1(Vvar__0__b__449) = cPLF_2eImp_2eBNot___24a1(Vvar__0__b__450)
     => Vvar__0__b__449 = Vvar__0__b__450 ) ).

fof('$_inj_PLF.Imp.BreakImp.CAss',axiom,
    ! [Vvar__0__x__92008,Vvar__0__x__92009,Vvar__1__a__92010,Vvar__1__a__92011] :
      ( cPLF_2eImp_2eBreakImp_2eCAss___24a2(Vvar__0__x__92008,Vvar__1__a__92010) = cPLF_2eImp_2eBreakImp_2eCAss___24a2(Vvar__0__x__92009,Vvar__1__a__92011)
     => ( Vvar__1__a__92010 = Vvar__1__a__92011
        & Vvar__0__x__92008 = Vvar__0__x__92009 ) ) ).

fof('$_inj_PLF.Imp.BreakImp.CIf',axiom,
    ! [Vvar__0__b__92016,Vvar__0__b__92017,Vvar__1__c1__92018,Vvar__1__c1__92019,Vvar__2__c2__92020,Vvar__2__c2__92021] :
      ( cPLF_2eImp_2eBreakImp_2eCIf___24a3(Vvar__0__b__92016,Vvar__1__c1__92018,Vvar__2__c2__92020) = cPLF_2eImp_2eBreakImp_2eCIf___24a3(Vvar__0__b__92017,Vvar__1__c1__92019,Vvar__2__c2__92021)
     => ( Vvar__2__c2__92020 = Vvar__2__c2__92021
        & Vvar__1__c1__92018 = Vvar__1__c1__92019
        & Vvar__0__b__92016 = Vvar__0__b__92017 ) ) ).

fof('$_inj_PLF.Imp.BreakImp.CSeq',axiom,
    ! [Vvar__0__c1__92012,Vvar__0__c1__92013,Vvar__1__c2__92014,Vvar__1__c2__92015] :
      ( cPLF_2eImp_2eBreakImp_2eCSeq___24a2(Vvar__0__c1__92012,Vvar__1__c2__92014) = cPLF_2eImp_2eBreakImp_2eCSeq___24a2(Vvar__0__c1__92013,Vvar__1__c2__92015)
     => ( Vvar__1__c2__92014 = Vvar__1__c2__92015
        & Vvar__0__c1__92012 = Vvar__0__c1__92013 ) ) ).

fof('$_inj_PLF.Imp.BreakImp.CWhile',axiom,
    ! [Vvar__0__b__92022,Vvar__0__b__92023,Vvar__1__c__92024,Vvar__1__c__92025] :
      ( cPLF_2eImp_2eBreakImp_2eCWhile___24a2(Vvar__0__b__92022,Vvar__1__c__92024) = cPLF_2eImp_2eBreakImp_2eCWhile___24a2(Vvar__0__b__92023,Vvar__1__c__92025)
     => ( Vvar__1__c__92024 = Vvar__1__c__92025
        & Vvar__0__b__92022 = Vvar__0__b__92023 ) ) ).

fof('$_inj_PLF.Imp.CAss',axiom,
    ! [Vvar__0__x__530,Vvar__0__x__531,Vvar__1__a__532,Vvar__1__a__533] :
      ( cPLF_2eImp_2eCAss___24a2(Vvar__0__x__530,Vvar__1__a__532) = cPLF_2eImp_2eCAss___24a2(Vvar__0__x__531,Vvar__1__a__533)
     => ( Vvar__1__a__532 = Vvar__1__a__533
        & Vvar__0__x__530 = Vvar__0__x__531 ) ) ).

fof('$_inj_PLF.Imp.CIf',axiom,
    ! [Vvar__0__b__538,Vvar__0__b__539,Vvar__1__c1__540,Vvar__1__c1__541,Vvar__2__c2__542,Vvar__2__c2__543] :
      ( cPLF_2eImp_2eCIf___24a3(Vvar__0__b__538,Vvar__1__c1__540,Vvar__2__c2__542) = cPLF_2eImp_2eCIf___24a3(Vvar__0__b__539,Vvar__1__c1__541,Vvar__2__c2__543)
     => ( Vvar__2__c2__542 = Vvar__2__c2__543
        & Vvar__1__c1__540 = Vvar__1__c1__541
        & Vvar__0__b__538 = Vvar__0__b__539 ) ) ).

fof('$_inj_PLF.Imp.CSeq',axiom,
    ! [Vvar__0__c1__534,Vvar__0__c1__535,Vvar__1__c2__536,Vvar__1__c2__537] :
      ( cPLF_2eImp_2eCSeq___24a2(Vvar__0__c1__534,Vvar__1__c2__536) = cPLF_2eImp_2eCSeq___24a2(Vvar__0__c1__535,Vvar__1__c2__537)
     => ( Vvar__1__c2__536 = Vvar__1__c2__537
        & Vvar__0__c1__534 = Vvar__0__c1__535 ) ) ).

fof('$_inj_PLF.Imp.CWhile',axiom,
    ! [Vvar__0__b__544,Vvar__0__b__545,Vvar__1__c__546,Vvar__1__c__547] :
      ( cPLF_2eImp_2eCWhile___24a2(Vvar__0__b__544,Vvar__1__c__546) = cPLF_2eImp_2eCWhile___24a2(Vvar__0__b__545,Vvar__1__c__547)
     => ( Vvar__1__c__546 = Vvar__1__c__547
        & Vvar__0__b__544 = Vvar__0__b__545 ) ) ).

fof('$_inj_PLF.Imp.SLoad',axiom,
    ! [Vvar__0__x__76442,Vvar__0__x__76443] :
      ( cPLF_2eImp_2eSLoad___24a1(Vvar__0__x__76442) = cPLF_2eImp_2eSLoad___24a1(Vvar__0__x__76443)
     => Vvar__0__x__76442 = Vvar__0__x__76443 ) ).

fof('$_inj_PLF.Imp.SPush',axiom,
    ! [Vvar__0__n__76440,Vvar__0__n__76441] :
      ( cPLF_2eImp_2eSPush___24a1(Vvar__0__n__76440) = cPLF_2eImp_2eSPush___24a1(Vvar__0__n__76441)
     => Vvar__0__n__76440 = Vvar__0__n__76441 ) ).

fof('$_inj_PLF.Imp.aevalR_division.ADiv',axiom,
    ! [Vvar__0__a1__83947,Vvar__0__a1__83948,Vvar__1__a2__83949,Vvar__1__a2__83950] :
      ( cPLF_2eImp_2eaevalR__division_2eADiv___24a2(Vvar__0__a1__83947,Vvar__1__a2__83949) = cPLF_2eImp_2eaevalR__division_2eADiv___24a2(Vvar__0__a1__83948,Vvar__1__a2__83950)
     => ( Vvar__1__a2__83949 = Vvar__1__a2__83950
        & Vvar__0__a1__83947 = Vvar__0__a1__83948 ) ) ).

fof('$_inj_PLF.Imp.aevalR_division.AMinus',axiom,
    ! [Vvar__0__a1__83939,Vvar__0__a1__83940,Vvar__1__a2__83941,Vvar__1__a2__83942] :
      ( cPLF_2eImp_2eaevalR__division_2eAMinus___24a2(Vvar__0__a1__83939,Vvar__1__a2__83941) = cPLF_2eImp_2eaevalR__division_2eAMinus___24a2(Vvar__0__a1__83940,Vvar__1__a2__83942)
     => ( Vvar__1__a2__83941 = Vvar__1__a2__83942
        & Vvar__0__a1__83939 = Vvar__0__a1__83940 ) ) ).

fof('$_inj_PLF.Imp.aevalR_division.AMult',axiom,
    ! [Vvar__0__a1__83943,Vvar__0__a1__83944,Vvar__1__a2__83945,Vvar__1__a2__83946] :
      ( cPLF_2eImp_2eaevalR__division_2eAMult___24a2(Vvar__0__a1__83943,Vvar__1__a2__83945) = cPLF_2eImp_2eaevalR__division_2eAMult___24a2(Vvar__0__a1__83944,Vvar__1__a2__83946)
     => ( Vvar__1__a2__83945 = Vvar__1__a2__83946
        & Vvar__0__a1__83943 = Vvar__0__a1__83944 ) ) ).

fof('$_inj_PLF.Imp.aevalR_division.ANum',axiom,
    ! [Vvar__0__n__83933,Vvar__0__n__83934] :
      ( cPLF_2eImp_2eaevalR__division_2eANum___24a1(Vvar__0__n__83933) = cPLF_2eImp_2eaevalR__division_2eANum___24a1(Vvar__0__n__83934)
     => Vvar__0__n__83933 = Vvar__0__n__83934 ) ).

fof('$_inj_PLF.Imp.aevalR_division.APlus',axiom,
    ! [Vvar__0__a1__83935,Vvar__0__a1__83936,Vvar__1__a2__83937,Vvar__1__a2__83938] :
      ( cPLF_2eImp_2eaevalR__division_2eAPlus___24a2(Vvar__0__a1__83935,Vvar__1__a2__83937) = cPLF_2eImp_2eaevalR__division_2eAPlus___24a2(Vvar__0__a1__83936,Vvar__1__a2__83938)
     => ( Vvar__1__a2__83937 = Vvar__1__a2__83938
        & Vvar__0__a1__83935 = Vvar__0__a1__83936 ) ) ).

fof('$_inj_PLF.Imp.aevalR_extended.AMinus',axiom,
    ! [Vvar__0__a1__92241,Vvar__0__a1__92242,Vvar__1__a2__92243,Vvar__1__a2__92244] :
      ( cPLF_2eImp_2eaevalR__extended_2eAMinus___24a2(Vvar__0__a1__92241,Vvar__1__a2__92243) = cPLF_2eImp_2eaevalR__extended_2eAMinus___24a2(Vvar__0__a1__92242,Vvar__1__a2__92244)
     => ( Vvar__1__a2__92243 = Vvar__1__a2__92244
        & Vvar__0__a1__92241 = Vvar__0__a1__92242 ) ) ).

fof('$_inj_PLF.Imp.aevalR_extended.AMult',axiom,
    ! [Vvar__0__a1__92245,Vvar__0__a1__92246,Vvar__1__a2__92247,Vvar__1__a2__92248] :
      ( cPLF_2eImp_2eaevalR__extended_2eAMult___24a2(Vvar__0__a1__92245,Vvar__1__a2__92247) = cPLF_2eImp_2eaevalR__extended_2eAMult___24a2(Vvar__0__a1__92246,Vvar__1__a2__92248)
     => ( Vvar__1__a2__92247 = Vvar__1__a2__92248
        & Vvar__0__a1__92245 = Vvar__0__a1__92246 ) ) ).

fof('$_inj_PLF.Imp.aevalR_extended.ANum',axiom,
    ! [Vvar__0__n__92235,Vvar__0__n__92236] :
      ( cPLF_2eImp_2eaevalR__extended_2eANum___24a1(Vvar__0__n__92235) = cPLF_2eImp_2eaevalR__extended_2eANum___24a1(Vvar__0__n__92236)
     => Vvar__0__n__92235 = Vvar__0__n__92236 ) ).

fof('$_inj_PLF.Imp.aevalR_extended.APlus',axiom,
    ! [Vvar__0__a1__92237,Vvar__0__a1__92238,Vvar__1__a2__92239,Vvar__1__a2__92240] :
      ( cPLF_2eImp_2eaevalR__extended_2eAPlus___24a2(Vvar__0__a1__92237,Vvar__1__a2__92239) = cPLF_2eImp_2eaevalR__extended_2eAPlus___24a2(Vvar__0__a1__92238,Vvar__1__a2__92240)
     => ( Vvar__1__a2__92239 = Vvar__1__a2__92240
        & Vvar__0__a1__92237 = Vvar__0__a1__92238 ) ) ).

fof('$_inj_PLF.LibTactics.boxer',axiom,
    ! [Vvar__0__A__87804,Vvar__0__A__87805,Vvar__1___24Anonymous__87806,Vvar__1___24Anonymous__87807] :
      ( cPLF_2eLibTactics_2eboxer___24a2(Vvar__0__A__87804,Vvar__1___24Anonymous__87806) = cPLF_2eLibTactics_2eboxer___24a2(Vvar__0__A__87805,Vvar__1___24Anonymous__87807)
     => ( Vvar__1___24Anonymous__87806 = Vvar__1___24Anonymous__87807
        & Vvar__0__A__87804 = Vvar__0__A__87805 ) ) ).

fof('$_inj_PLF.References.STLCRef.Arrow',axiom,
    ! [Vvar__0___24Anonymous__203376,Vvar__0___24Anonymous__203377,Vvar__1___24Anonymous__203378,Vvar__1___24Anonymous__203379] :
      ( cPLF_2eReferences_2eSTLCRef_2eArrow___24a2(Vvar__0___24Anonymous__203376,Vvar__1___24Anonymous__203378) = cPLF_2eReferences_2eSTLCRef_2eArrow___24a2(Vvar__0___24Anonymous__203377,Vvar__1___24Anonymous__203379)
     => ( Vvar__1___24Anonymous__203378 = Vvar__1___24Anonymous__203379
        & Vvar__0___24Anonymous__203376 = Vvar__0___24Anonymous__203377 ) ) ).

fof('$_inj_PLF.References.STLCRef.Ref',axiom,
    ! [Vvar__0___24Anonymous__203380,Vvar__0___24Anonymous__203381] :
      ( cPLF_2eReferences_2eSTLCRef_2eRef___24a1(Vvar__0___24Anonymous__203380) = cPLF_2eReferences_2eSTLCRef_2eRef___24a1(Vvar__0___24Anonymous__203381)
     => Vvar__0___24Anonymous__203380 = Vvar__0___24Anonymous__203381 ) ).

fof('$_inj_PLF.References.STLCRef.abs',axiom,
    ! [Vvar__0___24Anonymous__203641,Vvar__0___24Anonymous__203642,Vvar__1___24Anonymous__203643,Vvar__1___24Anonymous__203644,Vvar__2___24Anonymous__203645,Vvar__2___24Anonymous__203646] :
      ( cPLF_2eReferences_2eSTLCRef_2eabs___24a3(Vvar__0___24Anonymous__203641,Vvar__1___24Anonymous__203643,Vvar__2___24Anonymous__203645) = cPLF_2eReferences_2eSTLCRef_2eabs___24a3(Vvar__0___24Anonymous__203642,Vvar__1___24Anonymous__203644,Vvar__2___24Anonymous__203646)
     => ( Vvar__2___24Anonymous__203645 = Vvar__2___24Anonymous__203646
        & Vvar__1___24Anonymous__203643 = Vvar__1___24Anonymous__203644
        & Vvar__0___24Anonymous__203641 = Vvar__0___24Anonymous__203642 ) ) ).

fof('$_inj_PLF.References.STLCRef.app',axiom,
    ! [Vvar__0___24Anonymous__203637,Vvar__0___24Anonymous__203638,Vvar__1___24Anonymous__203639,Vvar__1___24Anonymous__203640] :
      ( cPLF_2eReferences_2eSTLCRef_2eapp___24a2(Vvar__0___24Anonymous__203637,Vvar__1___24Anonymous__203639) = cPLF_2eReferences_2eSTLCRef_2eapp___24a2(Vvar__0___24Anonymous__203638,Vvar__1___24Anonymous__203640)
     => ( Vvar__1___24Anonymous__203639 = Vvar__1___24Anonymous__203640
        & Vvar__0___24Anonymous__203637 = Vvar__0___24Anonymous__203638 ) ) ).

fof('$_inj_PLF.References.STLCRef.assign',axiom,
    ! [Vvar__0___24Anonymous__203667,Vvar__0___24Anonymous__203668,Vvar__1___24Anonymous__203669,Vvar__1___24Anonymous__203670] :
      ( cPLF_2eReferences_2eSTLCRef_2eassign___24a2(Vvar__0___24Anonymous__203667,Vvar__1___24Anonymous__203669) = cPLF_2eReferences_2eSTLCRef_2eassign___24a2(Vvar__0___24Anonymous__203668,Vvar__1___24Anonymous__203670)
     => ( Vvar__1___24Anonymous__203669 = Vvar__1___24Anonymous__203670
        & Vvar__0___24Anonymous__203667 = Vvar__0___24Anonymous__203668 ) ) ).

fof('$_inj_PLF.References.STLCRef.const',axiom,
    ! [Vvar__0___24Anonymous__203647,Vvar__0___24Anonymous__203648] :
      ( cPLF_2eReferences_2eSTLCRef_2econst___24a1(Vvar__0___24Anonymous__203647) = cPLF_2eReferences_2eSTLCRef_2econst___24a1(Vvar__0___24Anonymous__203648)
     => Vvar__0___24Anonymous__203647 = Vvar__0___24Anonymous__203648 ) ).

fof('$_inj_PLF.References.STLCRef.deref',axiom,
    ! [Vvar__0___24Anonymous__203665,Vvar__0___24Anonymous__203666] :
      ( cPLF_2eReferences_2eSTLCRef_2ederef___24a1(Vvar__0___24Anonymous__203665) = cPLF_2eReferences_2eSTLCRef_2ederef___24a1(Vvar__0___24Anonymous__203666)
     => Vvar__0___24Anonymous__203665 = Vvar__0___24Anonymous__203666 ) ).

fof('$_inj_PLF.References.STLCRef.loc',axiom,
    ! [Vvar__0___24Anonymous__203671,Vvar__0___24Anonymous__203672] :
      ( cPLF_2eReferences_2eSTLCRef_2eloc___24a1(Vvar__0___24Anonymous__203671) = cPLF_2eReferences_2eSTLCRef_2eloc___24a1(Vvar__0___24Anonymous__203672)
     => Vvar__0___24Anonymous__203671 = Vvar__0___24Anonymous__203672 ) ).

fof('$_inj_PLF.References.STLCRef.mlt',axiom,
    ! [Vvar__0___24Anonymous__203653,Vvar__0___24Anonymous__203654,Vvar__1___24Anonymous__203655,Vvar__1___24Anonymous__203656] :
      ( cPLF_2eReferences_2eSTLCRef_2emlt___24a2(Vvar__0___24Anonymous__203653,Vvar__1___24Anonymous__203655) = cPLF_2eReferences_2eSTLCRef_2emlt___24a2(Vvar__0___24Anonymous__203654,Vvar__1___24Anonymous__203656)
     => ( Vvar__1___24Anonymous__203655 = Vvar__1___24Anonymous__203656
        & Vvar__0___24Anonymous__203653 = Vvar__0___24Anonymous__203654 ) ) ).

fof('$_inj_PLF.References.STLCRef.prd',axiom,
    ! [Vvar__0___24Anonymous__203651,Vvar__0___24Anonymous__203652] :
      ( cPLF_2eReferences_2eSTLCRef_2eprd___24a1(Vvar__0___24Anonymous__203651) = cPLF_2eReferences_2eSTLCRef_2eprd___24a1(Vvar__0___24Anonymous__203652)
     => Vvar__0___24Anonymous__203651 = Vvar__0___24Anonymous__203652 ) ).

fof('$_inj_PLF.References.STLCRef.ref',axiom,
    ! [Vvar__0___24Anonymous__203663,Vvar__0___24Anonymous__203664] :
      ( cPLF_2eReferences_2eSTLCRef_2eref___24a1(Vvar__0___24Anonymous__203663) = cPLF_2eReferences_2eSTLCRef_2eref___24a1(Vvar__0___24Anonymous__203664)
     => Vvar__0___24Anonymous__203663 = Vvar__0___24Anonymous__203664 ) ).

fof('$_inj_PLF.References.STLCRef.scc',axiom,
    ! [Vvar__0___24Anonymous__203649,Vvar__0___24Anonymous__203650] :
      ( cPLF_2eReferences_2eSTLCRef_2escc___24a1(Vvar__0___24Anonymous__203649) = cPLF_2eReferences_2eSTLCRef_2escc___24a1(Vvar__0___24Anonymous__203650)
     => Vvar__0___24Anonymous__203649 = Vvar__0___24Anonymous__203650 ) ).

fof('$_inj_PLF.References.STLCRef.test0',axiom,
    ! [Vvar__0___24Anonymous__203657,Vvar__0___24Anonymous__203658,Vvar__1___24Anonymous__203659,Vvar__1___24Anonymous__203660,Vvar__2___24Anonymous__203661,Vvar__2___24Anonymous__203662] :
      ( cPLF_2eReferences_2eSTLCRef_2etest0___24a3(Vvar__0___24Anonymous__203657,Vvar__1___24Anonymous__203659,Vvar__2___24Anonymous__203661) = cPLF_2eReferences_2eSTLCRef_2etest0___24a3(Vvar__0___24Anonymous__203658,Vvar__1___24Anonymous__203660,Vvar__2___24Anonymous__203662)
     => ( Vvar__2___24Anonymous__203661 = Vvar__2___24Anonymous__203662
        & Vvar__1___24Anonymous__203659 = Vvar__1___24Anonymous__203660
        & Vvar__0___24Anonymous__203657 = Vvar__0___24Anonymous__203658 ) ) ).

fof('$_inj_PLF.References.STLCRef.var',axiom,
    ! [Vvar__0___24Anonymous__203635,Vvar__0___24Anonymous__203636] :
      ( cPLF_2eReferences_2eSTLCRef_2evar___24a1(Vvar__0___24Anonymous__203635) = cPLF_2eReferences_2eSTLCRef_2evar___24a1(Vvar__0___24Anonymous__203636)
     => Vvar__0___24Anonymous__203635 = Vvar__0___24Anonymous__203636 ) ).

fof('$_inj_PLF.Smallstep.C',axiom,
    ! [Vvar__0___24Anonymous__943,Vvar__0___24Anonymous__944] :
      ( cPLF_2eSmallstep_2eC___24a1(Vvar__0___24Anonymous__943) = cPLF_2eSmallstep_2eC___24a1(Vvar__0___24Anonymous__944)
     => Vvar__0___24Anonymous__943 = Vvar__0___24Anonymous__944 ) ).

fof('$_inj_PLF.Smallstep.CImp.CAss',axiom,
    ! [Vvar__0___24Anonymous__79542,Vvar__0___24Anonymous__79543,Vvar__1___24Anonymous__79544,Vvar__1___24Anonymous__79545] :
      ( cPLF_2eSmallstep_2eCImp_2eCAss___24a2(Vvar__0___24Anonymous__79542,Vvar__1___24Anonymous__79544) = cPLF_2eSmallstep_2eCImp_2eCAss___24a2(Vvar__0___24Anonymous__79543,Vvar__1___24Anonymous__79545)
     => ( Vvar__1___24Anonymous__79544 = Vvar__1___24Anonymous__79545
        & Vvar__0___24Anonymous__79542 = Vvar__0___24Anonymous__79543 ) ) ).

fof('$_inj_PLF.Smallstep.CImp.CIf',axiom,
    ! [Vvar__0___24Anonymous__79550,Vvar__0___24Anonymous__79551,Vvar__1___24Anonymous__79552,Vvar__1___24Anonymous__79553,Vvar__2___24Anonymous__79554,Vvar__2___24Anonymous__79555] :
      ( cPLF_2eSmallstep_2eCImp_2eCIf___24a3(Vvar__0___24Anonymous__79550,Vvar__1___24Anonymous__79552,Vvar__2___24Anonymous__79554) = cPLF_2eSmallstep_2eCImp_2eCIf___24a3(Vvar__0___24Anonymous__79551,Vvar__1___24Anonymous__79553,Vvar__2___24Anonymous__79555)
     => ( Vvar__2___24Anonymous__79554 = Vvar__2___24Anonymous__79555
        & Vvar__1___24Anonymous__79552 = Vvar__1___24Anonymous__79553
        & Vvar__0___24Anonymous__79550 = Vvar__0___24Anonymous__79551 ) ) ).

fof('$_inj_PLF.Smallstep.CImp.CPar',axiom,
    ! [Vvar__0___24Anonymous__79560,Vvar__0___24Anonymous__79561,Vvar__1___24Anonymous__79562,Vvar__1___24Anonymous__79563] :
      ( cPLF_2eSmallstep_2eCImp_2eCPar___24a2(Vvar__0___24Anonymous__79560,Vvar__1___24Anonymous__79562) = cPLF_2eSmallstep_2eCImp_2eCPar___24a2(Vvar__0___24Anonymous__79561,Vvar__1___24Anonymous__79563)
     => ( Vvar__1___24Anonymous__79562 = Vvar__1___24Anonymous__79563
        & Vvar__0___24Anonymous__79560 = Vvar__0___24Anonymous__79561 ) ) ).

fof('$_inj_PLF.Smallstep.CImp.CSeq',axiom,
    ! [Vvar__0___24Anonymous__79546,Vvar__0___24Anonymous__79547,Vvar__1___24Anonymous__79548,Vvar__1___24Anonymous__79549] :
      ( cPLF_2eSmallstep_2eCImp_2eCSeq___24a2(Vvar__0___24Anonymous__79546,Vvar__1___24Anonymous__79548) = cPLF_2eSmallstep_2eCImp_2eCSeq___24a2(Vvar__0___24Anonymous__79547,Vvar__1___24Anonymous__79549)
     => ( Vvar__1___24Anonymous__79548 = Vvar__1___24Anonymous__79549
        & Vvar__0___24Anonymous__79546 = Vvar__0___24Anonymous__79547 ) ) ).

fof('$_inj_PLF.Smallstep.CImp.CWhile',axiom,
    ! [Vvar__0___24Anonymous__79556,Vvar__0___24Anonymous__79557,Vvar__1___24Anonymous__79558,Vvar__1___24Anonymous__79559] :
      ( cPLF_2eSmallstep_2eCImp_2eCWhile___24a2(Vvar__0___24Anonymous__79556,Vvar__1___24Anonymous__79558) = cPLF_2eSmallstep_2eCImp_2eCWhile___24a2(Vvar__0___24Anonymous__79557,Vvar__1___24Anonymous__79559)
     => ( Vvar__1___24Anonymous__79558 = Vvar__1___24Anonymous__79559
        & Vvar__0___24Anonymous__79556 = Vvar__0___24Anonymous__79557 ) ) ).

fof('$_inj_PLF.Smallstep.Combined.C',axiom,
    ! [Vvar__0___24Anonymous__92058,Vvar__0___24Anonymous__92059] :
      ( cPLF_2eSmallstep_2eCombined_2eC___24a1(Vvar__0___24Anonymous__92058) = cPLF_2eSmallstep_2eCombined_2eC___24a1(Vvar__0___24Anonymous__92059)
     => Vvar__0___24Anonymous__92058 = Vvar__0___24Anonymous__92059 ) ).

fof('$_inj_PLF.Smallstep.Combined.P',axiom,
    ! [Vvar__0___24Anonymous__92060,Vvar__0___24Anonymous__92061,Vvar__1___24Anonymous__92062,Vvar__1___24Anonymous__92063] :
      ( cPLF_2eSmallstep_2eCombined_2eP___24a2(Vvar__0___24Anonymous__92060,Vvar__1___24Anonymous__92062) = cPLF_2eSmallstep_2eCombined_2eP___24a2(Vvar__0___24Anonymous__92061,Vvar__1___24Anonymous__92063)
     => ( Vvar__1___24Anonymous__92062 = Vvar__1___24Anonymous__92063
        & Vvar__0___24Anonymous__92060 = Vvar__0___24Anonymous__92061 ) ) ).

fof('$_inj_PLF.Smallstep.Combined.test',axiom,
    ! [Vvar__0___24Anonymous__92064,Vvar__0___24Anonymous__92065,Vvar__1___24Anonymous__92066,Vvar__1___24Anonymous__92067,Vvar__2___24Anonymous__92068,Vvar__2___24Anonymous__92069] :
      ( cPLF_2eSmallstep_2eCombined_2etest___24a3(Vvar__0___24Anonymous__92064,Vvar__1___24Anonymous__92066,Vvar__2___24Anonymous__92068) = cPLF_2eSmallstep_2eCombined_2etest___24a3(Vvar__0___24Anonymous__92065,Vvar__1___24Anonymous__92067,Vvar__2___24Anonymous__92069)
     => ( Vvar__2___24Anonymous__92068 = Vvar__2___24Anonymous__92069
        & Vvar__1___24Anonymous__92066 = Vvar__1___24Anonymous__92067
        & Vvar__0___24Anonymous__92064 = Vvar__0___24Anonymous__92065 ) ) ).

fof('$_inj_PLF.Smallstep.P',axiom,
    ! [Vvar__0___24Anonymous__945,Vvar__0___24Anonymous__946,Vvar__1___24Anonymous__947,Vvar__1___24Anonymous__948] :
      ( cPLF_2eSmallstep_2eP___24a2(Vvar__0___24Anonymous__945,Vvar__1___24Anonymous__947) = cPLF_2eSmallstep_2eP___24a2(Vvar__0___24Anonymous__946,Vvar__1___24Anonymous__948)
     => ( Vvar__1___24Anonymous__947 = Vvar__1___24Anonymous__948
        & Vvar__0___24Anonymous__945 = Vvar__0___24Anonymous__946 ) ) ).

fof('$_inj_PLF.Smallstep.Temp4.test',axiom,
    ! [Vvar__0___24Anonymous__88822,Vvar__0___24Anonymous__88823,Vvar__1___24Anonymous__88824,Vvar__1___24Anonymous__88825,Vvar__2___24Anonymous__88826,Vvar__2___24Anonymous__88827] :
      ( cPLF_2eSmallstep_2eTemp4_2etest___24a3(Vvar__0___24Anonymous__88822,Vvar__1___24Anonymous__88824,Vvar__2___24Anonymous__88826) = cPLF_2eSmallstep_2eTemp4_2etest___24a3(Vvar__0___24Anonymous__88823,Vvar__1___24Anonymous__88825,Vvar__2___24Anonymous__88827)
     => ( Vvar__2___24Anonymous__88826 = Vvar__2___24Anonymous__88827
        & Vvar__1___24Anonymous__88824 = Vvar__1___24Anonymous__88825
        & Vvar__0___24Anonymous__88822 = Vvar__0___24Anonymous__88823 ) ) ).

fof('$_inj_PLF.Stlc.STLC.Arrow',axiom,
    ! [Vvar__0___24Anonymous__92122,Vvar__0___24Anonymous__92123,Vvar__1___24Anonymous__92124,Vvar__1___24Anonymous__92125] :
      ( cPLF_2eStlc_2eSTLC_2eArrow___24a2(Vvar__0___24Anonymous__92122,Vvar__1___24Anonymous__92124) = cPLF_2eStlc_2eSTLC_2eArrow___24a2(Vvar__0___24Anonymous__92123,Vvar__1___24Anonymous__92125)
     => ( Vvar__1___24Anonymous__92124 = Vvar__1___24Anonymous__92125
        & Vvar__0___24Anonymous__92122 = Vvar__0___24Anonymous__92123 ) ) ).

fof('$_inj_PLF.Stlc.STLC.abs',axiom,
    ! [Vvar__0___24Anonymous__92187,Vvar__0___24Anonymous__92188,Vvar__1___24Anonymous__92189,Vvar__1___24Anonymous__92190,Vvar__2___24Anonymous__92191,Vvar__2___24Anonymous__92192] :
      ( cPLF_2eStlc_2eSTLC_2eabs___24a3(Vvar__0___24Anonymous__92187,Vvar__1___24Anonymous__92189,Vvar__2___24Anonymous__92191) = cPLF_2eStlc_2eSTLC_2eabs___24a3(Vvar__0___24Anonymous__92188,Vvar__1___24Anonymous__92190,Vvar__2___24Anonymous__92192)
     => ( Vvar__2___24Anonymous__92191 = Vvar__2___24Anonymous__92192
        & Vvar__1___24Anonymous__92189 = Vvar__1___24Anonymous__92190
        & Vvar__0___24Anonymous__92187 = Vvar__0___24Anonymous__92188 ) ) ).

fof('$_inj_PLF.Stlc.STLC.app',axiom,
    ! [Vvar__0___24Anonymous__92183,Vvar__0___24Anonymous__92184,Vvar__1___24Anonymous__92185,Vvar__1___24Anonymous__92186] :
      ( cPLF_2eStlc_2eSTLC_2eapp___24a2(Vvar__0___24Anonymous__92183,Vvar__1___24Anonymous__92185) = cPLF_2eStlc_2eSTLC_2eapp___24a2(Vvar__0___24Anonymous__92184,Vvar__1___24Anonymous__92186)
     => ( Vvar__1___24Anonymous__92185 = Vvar__1___24Anonymous__92186
        & Vvar__0___24Anonymous__92183 = Vvar__0___24Anonymous__92184 ) ) ).

fof('$_inj_PLF.Stlc.STLC.test',axiom,
    ! [Vvar__0___24Anonymous__92193,Vvar__0___24Anonymous__92194,Vvar__1___24Anonymous__92195,Vvar__1___24Anonymous__92196,Vvar__2___24Anonymous__92197,Vvar__2___24Anonymous__92198] :
      ( cPLF_2eStlc_2eSTLC_2etest___24a3(Vvar__0___24Anonymous__92193,Vvar__1___24Anonymous__92195,Vvar__2___24Anonymous__92197) = cPLF_2eStlc_2eSTLC_2etest___24a3(Vvar__0___24Anonymous__92194,Vvar__1___24Anonymous__92196,Vvar__2___24Anonymous__92198)
     => ( Vvar__2___24Anonymous__92197 = Vvar__2___24Anonymous__92198
        & Vvar__1___24Anonymous__92195 = Vvar__1___24Anonymous__92196
        & Vvar__0___24Anonymous__92193 = Vvar__0___24Anonymous__92194 ) ) ).

fof('$_inj_PLF.Stlc.STLC.var',axiom,
    ! [Vvar__0___24Anonymous__92181,Vvar__0___24Anonymous__92182] :
      ( cPLF_2eStlc_2eSTLC_2evar___24a1(Vvar__0___24Anonymous__92181) = cPLF_2eStlc_2eSTLC_2evar___24a1(Vvar__0___24Anonymous__92182)
     => Vvar__0___24Anonymous__92181 = Vvar__0___24Anonymous__92182 ) ).

fof('$_inj_PLF.StlcProp.STLCArith.Arrow',axiom,
    ! [Vvar__0___24Anonymous__200667,Vvar__0___24Anonymous__200668,Vvar__1___24Anonymous__200669,Vvar__1___24Anonymous__200670] :
      ( cPLF_2eStlcProp_2eSTLCArith_2eArrow___24a2(Vvar__0___24Anonymous__200667,Vvar__1___24Anonymous__200669) = cPLF_2eStlcProp_2eSTLCArith_2eArrow___24a2(Vvar__0___24Anonymous__200668,Vvar__1___24Anonymous__200670)
     => ( Vvar__1___24Anonymous__200669 = Vvar__1___24Anonymous__200670
        & Vvar__0___24Anonymous__200667 = Vvar__0___24Anonymous__200668 ) ) ).

fof('$_inj_PLF.StlcProp.STLCArith.abs',axiom,
    ! [Vvar__0___24Anonymous__200790,Vvar__0___24Anonymous__200791,Vvar__1___24Anonymous__200792,Vvar__1___24Anonymous__200793,Vvar__2___24Anonymous__200794,Vvar__2___24Anonymous__200795] :
      ( cPLF_2eStlcProp_2eSTLCArith_2eabs___24a3(Vvar__0___24Anonymous__200790,Vvar__1___24Anonymous__200792,Vvar__2___24Anonymous__200794) = cPLF_2eStlcProp_2eSTLCArith_2eabs___24a3(Vvar__0___24Anonymous__200791,Vvar__1___24Anonymous__200793,Vvar__2___24Anonymous__200795)
     => ( Vvar__2___24Anonymous__200794 = Vvar__2___24Anonymous__200795
        & Vvar__1___24Anonymous__200792 = Vvar__1___24Anonymous__200793
        & Vvar__0___24Anonymous__200790 = Vvar__0___24Anonymous__200791 ) ) ).

fof('$_inj_PLF.StlcProp.STLCArith.app',axiom,
    ! [Vvar__0___24Anonymous__200786,Vvar__0___24Anonymous__200787,Vvar__1___24Anonymous__200788,Vvar__1___24Anonymous__200789] :
      ( cPLF_2eStlcProp_2eSTLCArith_2eapp___24a2(Vvar__0___24Anonymous__200786,Vvar__1___24Anonymous__200788) = cPLF_2eStlcProp_2eSTLCArith_2eapp___24a2(Vvar__0___24Anonymous__200787,Vvar__1___24Anonymous__200789)
     => ( Vvar__1___24Anonymous__200788 = Vvar__1___24Anonymous__200789
        & Vvar__0___24Anonymous__200786 = Vvar__0___24Anonymous__200787 ) ) ).

fof('$_inj_PLF.StlcProp.STLCArith.const',axiom,
    ! [Vvar__0___24Anonymous__200796,Vvar__0___24Anonymous__200797] :
      ( cPLF_2eStlcProp_2eSTLCArith_2econst___24a1(Vvar__0___24Anonymous__200796) = cPLF_2eStlcProp_2eSTLCArith_2econst___24a1(Vvar__0___24Anonymous__200797)
     => Vvar__0___24Anonymous__200796 = Vvar__0___24Anonymous__200797 ) ).

fof('$_inj_PLF.StlcProp.STLCArith.mlt',axiom,
    ! [Vvar__0___24Anonymous__200802,Vvar__0___24Anonymous__200803,Vvar__1___24Anonymous__200804,Vvar__1___24Anonymous__200805] :
      ( cPLF_2eStlcProp_2eSTLCArith_2emlt___24a2(Vvar__0___24Anonymous__200802,Vvar__1___24Anonymous__200804) = cPLF_2eStlcProp_2eSTLCArith_2emlt___24a2(Vvar__0___24Anonymous__200803,Vvar__1___24Anonymous__200805)
     => ( Vvar__1___24Anonymous__200804 = Vvar__1___24Anonymous__200805
        & Vvar__0___24Anonymous__200802 = Vvar__0___24Anonymous__200803 ) ) ).

fof('$_inj_PLF.StlcProp.STLCArith.prd',axiom,
    ! [Vvar__0___24Anonymous__200800,Vvar__0___24Anonymous__200801] :
      ( cPLF_2eStlcProp_2eSTLCArith_2eprd___24a1(Vvar__0___24Anonymous__200800) = cPLF_2eStlcProp_2eSTLCArith_2eprd___24a1(Vvar__0___24Anonymous__200801)
     => Vvar__0___24Anonymous__200800 = Vvar__0___24Anonymous__200801 ) ).

fof('$_inj_PLF.StlcProp.STLCArith.scc',axiom,
    ! [Vvar__0___24Anonymous__200798,Vvar__0___24Anonymous__200799] :
      ( cPLF_2eStlcProp_2eSTLCArith_2escc___24a1(Vvar__0___24Anonymous__200798) = cPLF_2eStlcProp_2eSTLCArith_2escc___24a1(Vvar__0___24Anonymous__200799)
     => Vvar__0___24Anonymous__200798 = Vvar__0___24Anonymous__200799 ) ).

fof('$_inj_PLF.StlcProp.STLCArith.test0',axiom,
    ! [Vvar__0___24Anonymous__200806,Vvar__0___24Anonymous__200807,Vvar__1___24Anonymous__200808,Vvar__1___24Anonymous__200809,Vvar__2___24Anonymous__200810,Vvar__2___24Anonymous__200811] :
      ( cPLF_2eStlcProp_2eSTLCArith_2etest0___24a3(Vvar__0___24Anonymous__200806,Vvar__1___24Anonymous__200808,Vvar__2___24Anonymous__200810) = cPLF_2eStlcProp_2eSTLCArith_2etest0___24a3(Vvar__0___24Anonymous__200807,Vvar__1___24Anonymous__200809,Vvar__2___24Anonymous__200811)
     => ( Vvar__2___24Anonymous__200810 = Vvar__2___24Anonymous__200811
        & Vvar__1___24Anonymous__200808 = Vvar__1___24Anonymous__200809
        & Vvar__0___24Anonymous__200806 = Vvar__0___24Anonymous__200807 ) ) ).

fof('$_inj_PLF.StlcProp.STLCArith.var',axiom,
    ! [Vvar__0___24Anonymous__200784,Vvar__0___24Anonymous__200785] :
      ( cPLF_2eStlcProp_2eSTLCArith_2evar___24a1(Vvar__0___24Anonymous__200784) = cPLF_2eStlcProp_2eSTLCArith_2evar___24a1(Vvar__0___24Anonymous__200785)
     => Vvar__0___24Anonymous__200784 = Vvar__0___24Anonymous__200785 ) ).

fof('$_inj_PLF.Types.iszro',axiom,
    ! [Vvar__0___24Anonymous__199823,Vvar__0___24Anonymous__199824] :
      ( cPLF_2eTypes_2eiszro___24a1(Vvar__0___24Anonymous__199823) = cPLF_2eTypes_2eiszro___24a1(Vvar__0___24Anonymous__199824)
     => Vvar__0___24Anonymous__199823 = Vvar__0___24Anonymous__199824 ) ).

fof('$_inj_PLF.Types.prd',axiom,
    ! [Vvar__0___24Anonymous__199821,Vvar__0___24Anonymous__199822] :
      ( cPLF_2eTypes_2eprd___24a1(Vvar__0___24Anonymous__199821) = cPLF_2eTypes_2eprd___24a1(Vvar__0___24Anonymous__199822)
     => Vvar__0___24Anonymous__199821 = Vvar__0___24Anonymous__199822 ) ).

fof('$_inj_PLF.Types.scc',axiom,
    ! [Vvar__0___24Anonymous__199819,Vvar__0___24Anonymous__199820] :
      ( cPLF_2eTypes_2escc___24a1(Vvar__0___24Anonymous__199819) = cPLF_2eTypes_2escc___24a1(Vvar__0___24Anonymous__199820)
     => Vvar__0___24Anonymous__199819 = Vvar__0___24Anonymous__199820 ) ).

fof('$_inj_PLF.Types.test',axiom,
    ! [Vvar__0___24Anonymous__199813,Vvar__0___24Anonymous__199814,Vvar__1___24Anonymous__199815,Vvar__1___24Anonymous__199816,Vvar__2___24Anonymous__199817,Vvar__2___24Anonymous__199818] :
      ( cPLF_2eTypes_2etest___24a3(Vvar__0___24Anonymous__199813,Vvar__1___24Anonymous__199815,Vvar__2___24Anonymous__199817) = cPLF_2eTypes_2etest___24a3(Vvar__0___24Anonymous__199814,Vvar__1___24Anonymous__199816,Vvar__2___24Anonymous__199818)
     => ( Vvar__2___24Anonymous__199817 = Vvar__2___24Anonymous__199818
        & Vvar__1___24Anonymous__199815 = Vvar__1___24Anonymous__199816
        & Vvar__0___24Anonymous__199813 = Vvar__0___24Anonymous__199814 ) ) ).

fof('$_inversion_Coq.Arith.Between.P_nth',axiom,
    ! [Vvar__0__P__83560,Vvar__1__Q__83562,Vvar__2__init__83565,Vvar__3___24Anonymous__83566,Vvar__4___24Anonymous__83567] :
      ( c_24__type__83593___24t(Vvar__0__P__83560,Vvar__1__Q__83562,Vvar__2__init__83565,Vvar__3___24Anonymous__83566,Vvar__4___24Anonymous__83567,Vvar__0__P__83560)
     => ( c_24__type__83601___24t(Vvar__0__P__83560,Vvar__1__Q__83562,Vvar__2__init__83565,Vvar__3___24Anonymous__83566,Vvar__4___24Anonymous__83567,Vvar__1__Q__83562)
       => ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__init__83565)
         => ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__3___24Anonymous__83566)
           => ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__4___24Anonymous__83567)
             => ( cCoq_2eArith_2eBetween_2eP__nth___24a5(Vvar__0__P__83560,Vvar__1__Q__83562,Vvar__2__init__83565,Vvar__3___24Anonymous__83566,Vvar__4___24Anonymous__83567)
               => ( ( Vvar__4___24Anonymous__83567 = cCoq_2eInit_2eDatatypes_2eO
                    & Vvar__3___24Anonymous__83566 = Vvar__2__init__83565 )
                  | ? [Vvar__3__k__83581] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__3__k__83581)
                      & ? [Vvar__4__l__83582] :
                          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__4__l__83582)
                          & ? [Vvar__5__n__83583] :
                              ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__5__n__83583)
                              & cCoq_2eArith_2eBetween_2eP__nth___24a5(Vvar__0__P__83560,Vvar__1__Q__83562,Vvar__2__init__83565,Vvar__3__k__83581,Vvar__5__n__83583)
                              & cCoq_2eArith_2eBetween_2ebetween___24a3(Vvar__0__P__83560,cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__3__k__83581),Vvar__4__l__83582)
                              & p(happ(Vvar__1__Q__83562,Vvar__4__l__83582))
                              & Vvar__4___24Anonymous__83567 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__5__n__83583)
                              & Vvar__3___24Anonymous__83566 = Vvar__4__l__83582 ) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Arith.Between.between',axiom,
    ! [Vvar__0__P__83517,Vvar__1__k__83519,Vvar__2___24Anonymous__83520] :
      ( c_24__type__83534___24t(Vvar__0__P__83517,Vvar__1__k__83519,Vvar__2___24Anonymous__83520,Vvar__0__P__83517)
     => ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__k__83519)
       => ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2___24Anonymous__83520)
         => ( cCoq_2eArith_2eBetween_2ebetween___24a3(Vvar__0__P__83517,Vvar__1__k__83519,Vvar__2___24Anonymous__83520)
           => ( Vvar__2___24Anonymous__83520 = Vvar__1__k__83519
              | ? [Vvar__2__l__83528] :
                  ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__l__83528)
                  & cCoq_2eArith_2eBetween_2ebetween___24a3(Vvar__0__P__83517,Vvar__1__k__83519,Vvar__2__l__83528)
                  & p(happ(Vvar__0__P__83517,Vvar__2__l__83528))
                  & Vvar__2___24Anonymous__83520 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__l__83528) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Arith.Between.exists_between',axiom,
    ! [Vvar__0__Q__83536,Vvar__1__k__83538,Vvar__2___24Anonymous__83539] :
      ( c_24__type__83555___24t(Vvar__0__Q__83536,Vvar__1__k__83538,Vvar__2___24Anonymous__83539,Vvar__0__Q__83536)
     => ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__k__83538)
       => ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2___24Anonymous__83539)
         => ( cCoq_2eArith_2eBetween_2eexists__between___24a3(Vvar__0__Q__83536,Vvar__1__k__83538,Vvar__2___24Anonymous__83539)
           => ( ? [Vvar__2__l__83544] :
                  ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__l__83544)
                  & cCoq_2eArith_2eBetween_2eexists__between___24a3(Vvar__0__Q__83536,Vvar__1__k__83538,Vvar__2__l__83544)
                  & Vvar__2___24Anonymous__83539 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__l__83544) )
              | ? [Vvar__2__l__83549] :
                  ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__l__83549)
                  & cCoq_2eInit_2ePeano_2ele___24a2(Vvar__1__k__83538,Vvar__2__l__83549)
                  & p(happ(Vvar__0__Q__83536,Vvar__2__l__83549))
                  & Vvar__2___24Anonymous__83539 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__l__83549) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Arith.Even.even',axiom,
    ! [Vvar__0___24Anonymous__75879] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__75879)
     => ( cCoq_2eArith_2eEven_2eeven___24a1(Vvar__0___24Anonymous__75879)
       => ( Vvar__0___24Anonymous__75879 = cCoq_2eInit_2eDatatypes_2eO
          | ? [Vvar__0__n__75881] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__75881)
              & cCoq_2eArith_2eEven_2eodd___24a1(Vvar__0__n__75881)
              & Vvar__0___24Anonymous__75879 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0__n__75881) ) ) ) ) ).

fof('$_inversion_Coq.Arith.Even.odd',axiom,
    ! [Vvar__0___24Anonymous__75883] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__75883)
     => ( cCoq_2eArith_2eEven_2eodd___24a1(Vvar__0___24Anonymous__75883)
       => ? [Vvar__0__n__75885] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__75885)
            & cCoq_2eArith_2eEven_2eeven___24a1(Vvar__0__n__75885)
            & Vvar__0___24Anonymous__75883 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0__n__75885) ) ) ) ).

fof('$_inversion_Coq.Bool.Bool.reflect',axiom,
    ! [Vvar__0__P__92253,Vvar__1___24Anonymous__92254,VX92255] :
      ( cProp___24t(Vvar__0__P__92253)
     => ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__92254)
       => ( cCoq_2eBool_2eBool_2ereflect___24t(Vvar__0__P__92253,Vvar__1___24Anonymous__92254,VX92255)
         => ( ( p(Vvar__0__P__92253)
              & Vvar__1___24Anonymous__92254 = cCoq_2eInit_2eDatatypes_2etrue
              & VX92255 = cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__92253) )
            | ( ~ p(Vvar__0__P__92253)
              & Vvar__1___24Anonymous__92254 = cCoq_2eInit_2eDatatypes_2efalse
              & VX92255 = cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__92253) ) ) ) ) ) ).

fof('$_inversion_Coq.FSets.FSetPositive.PositiveSet.ct',axiom,
    ! [Vvar__0___24Anonymous__109339,Vvar__1___24Anonymous__109340,Vvar__2___24Anonymous__109341] :
      ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__0___24Anonymous__109339)
     => ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__1___24Anonymous__109340)
       => ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__2___24Anonymous__109341)
         => ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2ect___24a3(Vvar__0___24Anonymous__109339,Vvar__1___24Anonymous__109340,Vvar__2___24Anonymous__109341)
           => ( ? [Vvar__0__x__109343] :
                  ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__0__x__109343)
                  & Vvar__2___24Anonymous__109341 = Vvar__0__x__109343
                  & Vvar__1___24Anonymous__109340 = Vvar__0__x__109343
                  & Vvar__0___24Anonymous__109339 = Vvar__0__x__109343 )
              | ? [Vvar__0__x__109344] :
                  ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__0__x__109344)
                  & Vvar__2___24Anonymous__109341 = Vvar__0__x__109344
                  & Vvar__1___24Anonymous__109340 = cCoq_2eInit_2eDatatypes_2eEq
                  & Vvar__0___24Anonymous__109339 = Vvar__0__x__109344 )
              | ? [Vvar__0__x__109345] :
                  ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__0__x__109345)
                  & Vvar__2___24Anonymous__109341 = Vvar__0__x__109345
                  & Vvar__1___24Anonymous__109340 = Vvar__0__x__109345
                  & Vvar__0___24Anonymous__109339 = cCoq_2eInit_2eDatatypes_2eEq )
              | ? [Vvar__0__x__109346] :
                  ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__0__x__109346)
                  & Vvar__2___24Anonymous__109341 = Vvar__0__x__109346
                  & Vvar__1___24Anonymous__109340 = cCoq_2eInit_2eDatatypes_2eLt
                  & Vvar__0___24Anonymous__109339 = cCoq_2eInit_2eDatatypes_2eGt )
              | ? [Vvar__0__x__109347] :
                  ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__0__x__109347)
                  & Vvar__2___24Anonymous__109341 = Vvar__0__x__109347
                  & Vvar__1___24Anonymous__109340 = cCoq_2eInit_2eDatatypes_2eGt
                  & Vvar__0___24Anonymous__109339 = cCoq_2eInit_2eDatatypes_2eLt ) ) ) ) ) ) ).

fof('$_inversion_Coq.FSets.FSetPositive.PositiveSet.tree',axiom,
    ! [VX82627] :
      ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(VX82627)
     => ( VX82627 = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf
        | ? [Vvar__0___24Anonymous__82628] :
            ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__0___24Anonymous__82628)
            & ? [Vvar__1___24Anonymous__82629] :
                ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__82629)
                & ? [Vvar__2___24Anonymous__82630] :
                    ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__2___24Anonymous__82630)
                    & VX82627 = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__82628,Vvar__1___24Anonymous__82629,Vvar__2___24Anonymous__82630) ) ) ) ) ) ).

fof('$_inversion_Coq.Init.Byte.byte',axiom,
    ! [VX2706] :
      ( cCoq_2eInit_2eByte_2ebyte___24t(VX2706)
     => ( VX2706 = cCoq_2eInit_2eByte_2ex00
        | VX2706 = cCoq_2eInit_2eByte_2ex01
        | VX2706 = cCoq_2eInit_2eByte_2ex02
        | VX2706 = cCoq_2eInit_2eByte_2ex03
        | VX2706 = cCoq_2eInit_2eByte_2ex04
        | VX2706 = cCoq_2eInit_2eByte_2ex05
        | VX2706 = cCoq_2eInit_2eByte_2ex06
        | VX2706 = cCoq_2eInit_2eByte_2ex07
        | VX2706 = cCoq_2eInit_2eByte_2ex08
        | VX2706 = cCoq_2eInit_2eByte_2ex09
        | VX2706 = cCoq_2eInit_2eByte_2ex0a
        | VX2706 = cCoq_2eInit_2eByte_2ex0b
        | VX2706 = cCoq_2eInit_2eByte_2ex0c
        | VX2706 = cCoq_2eInit_2eByte_2ex0d
        | VX2706 = cCoq_2eInit_2eByte_2ex0e
        | VX2706 = cCoq_2eInit_2eByte_2ex0f
        | VX2706 = cCoq_2eInit_2eByte_2ex10
        | VX2706 = cCoq_2eInit_2eByte_2ex11
        | VX2706 = cCoq_2eInit_2eByte_2ex12
        | VX2706 = cCoq_2eInit_2eByte_2ex13
        | VX2706 = cCoq_2eInit_2eByte_2ex14
        | VX2706 = cCoq_2eInit_2eByte_2ex15
        | VX2706 = cCoq_2eInit_2eByte_2ex16
        | VX2706 = cCoq_2eInit_2eByte_2ex17
        | VX2706 = cCoq_2eInit_2eByte_2ex18
        | VX2706 = cCoq_2eInit_2eByte_2ex19
        | VX2706 = cCoq_2eInit_2eByte_2ex1a
        | VX2706 = cCoq_2eInit_2eByte_2ex1b
        | VX2706 = cCoq_2eInit_2eByte_2ex1c
        | VX2706 = cCoq_2eInit_2eByte_2ex1d
        | VX2706 = cCoq_2eInit_2eByte_2ex1e
        | VX2706 = cCoq_2eInit_2eByte_2ex1f
        | VX2706 = cCoq_2eInit_2eByte_2ex20
        | VX2706 = cCoq_2eInit_2eByte_2ex21
        | VX2706 = cCoq_2eInit_2eByte_2ex22
        | VX2706 = cCoq_2eInit_2eByte_2ex23
        | VX2706 = cCoq_2eInit_2eByte_2ex24
        | VX2706 = cCoq_2eInit_2eByte_2ex25
        | VX2706 = cCoq_2eInit_2eByte_2ex26
        | VX2706 = cCoq_2eInit_2eByte_2ex27
        | VX2706 = cCoq_2eInit_2eByte_2ex28
        | VX2706 = cCoq_2eInit_2eByte_2ex29
        | VX2706 = cCoq_2eInit_2eByte_2ex2a
        | VX2706 = cCoq_2eInit_2eByte_2ex2b
        | VX2706 = cCoq_2eInit_2eByte_2ex2c
        | VX2706 = cCoq_2eInit_2eByte_2ex2d
        | VX2706 = cCoq_2eInit_2eByte_2ex2e
        | VX2706 = cCoq_2eInit_2eByte_2ex2f
        | VX2706 = cCoq_2eInit_2eByte_2ex30
        | VX2706 = cCoq_2eInit_2eByte_2ex31
        | VX2706 = cCoq_2eInit_2eByte_2ex32
        | VX2706 = cCoq_2eInit_2eByte_2ex33
        | VX2706 = cCoq_2eInit_2eByte_2ex34
        | VX2706 = cCoq_2eInit_2eByte_2ex35
        | VX2706 = cCoq_2eInit_2eByte_2ex36
        | VX2706 = cCoq_2eInit_2eByte_2ex37
        | VX2706 = cCoq_2eInit_2eByte_2ex38
        | VX2706 = cCoq_2eInit_2eByte_2ex39
        | VX2706 = cCoq_2eInit_2eByte_2ex3a
        | VX2706 = cCoq_2eInit_2eByte_2ex3b
        | VX2706 = cCoq_2eInit_2eByte_2ex3c
        | VX2706 = cCoq_2eInit_2eByte_2ex3d
        | VX2706 = cCoq_2eInit_2eByte_2ex3e
        | VX2706 = cCoq_2eInit_2eByte_2ex3f
        | VX2706 = cCoq_2eInit_2eByte_2ex40
        | VX2706 = cCoq_2eInit_2eByte_2ex41
        | VX2706 = cCoq_2eInit_2eByte_2ex42
        | VX2706 = cCoq_2eInit_2eByte_2ex43
        | VX2706 = cCoq_2eInit_2eByte_2ex44
        | VX2706 = cCoq_2eInit_2eByte_2ex45
        | VX2706 = cCoq_2eInit_2eByte_2ex46
        | VX2706 = cCoq_2eInit_2eByte_2ex47
        | VX2706 = cCoq_2eInit_2eByte_2ex48
        | VX2706 = cCoq_2eInit_2eByte_2ex49
        | VX2706 = cCoq_2eInit_2eByte_2ex4a
        | VX2706 = cCoq_2eInit_2eByte_2ex4b
        | VX2706 = cCoq_2eInit_2eByte_2ex4c
        | VX2706 = cCoq_2eInit_2eByte_2ex4d
        | VX2706 = cCoq_2eInit_2eByte_2ex4e
        | VX2706 = cCoq_2eInit_2eByte_2ex4f
        | VX2706 = cCoq_2eInit_2eByte_2ex50
        | VX2706 = cCoq_2eInit_2eByte_2ex51
        | VX2706 = cCoq_2eInit_2eByte_2ex52
        | VX2706 = cCoq_2eInit_2eByte_2ex53
        | VX2706 = cCoq_2eInit_2eByte_2ex54
        | VX2706 = cCoq_2eInit_2eByte_2ex55
        | VX2706 = cCoq_2eInit_2eByte_2ex56
        | VX2706 = cCoq_2eInit_2eByte_2ex57
        | VX2706 = cCoq_2eInit_2eByte_2ex58
        | VX2706 = cCoq_2eInit_2eByte_2ex59
        | VX2706 = cCoq_2eInit_2eByte_2ex5a
        | VX2706 = cCoq_2eInit_2eByte_2ex5b
        | VX2706 = cCoq_2eInit_2eByte_2ex5c
        | VX2706 = cCoq_2eInit_2eByte_2ex5d
        | VX2706 = cCoq_2eInit_2eByte_2ex5e
        | VX2706 = cCoq_2eInit_2eByte_2ex5f
        | VX2706 = cCoq_2eInit_2eByte_2ex60
        | VX2706 = cCoq_2eInit_2eByte_2ex61
        | VX2706 = cCoq_2eInit_2eByte_2ex62
        | VX2706 = cCoq_2eInit_2eByte_2ex63
        | VX2706 = cCoq_2eInit_2eByte_2ex64
        | VX2706 = cCoq_2eInit_2eByte_2ex65
        | VX2706 = cCoq_2eInit_2eByte_2ex66
        | VX2706 = cCoq_2eInit_2eByte_2ex67
        | VX2706 = cCoq_2eInit_2eByte_2ex68
        | VX2706 = cCoq_2eInit_2eByte_2ex69
        | VX2706 = cCoq_2eInit_2eByte_2ex6a
        | VX2706 = cCoq_2eInit_2eByte_2ex6b
        | VX2706 = cCoq_2eInit_2eByte_2ex6c
        | VX2706 = cCoq_2eInit_2eByte_2ex6d
        | VX2706 = cCoq_2eInit_2eByte_2ex6e
        | VX2706 = cCoq_2eInit_2eByte_2ex6f
        | VX2706 = cCoq_2eInit_2eByte_2ex70
        | VX2706 = cCoq_2eInit_2eByte_2ex71
        | VX2706 = cCoq_2eInit_2eByte_2ex72
        | VX2706 = cCoq_2eInit_2eByte_2ex73
        | VX2706 = cCoq_2eInit_2eByte_2ex74
        | VX2706 = cCoq_2eInit_2eByte_2ex75
        | VX2706 = cCoq_2eInit_2eByte_2ex76
        | VX2706 = cCoq_2eInit_2eByte_2ex77
        | VX2706 = cCoq_2eInit_2eByte_2ex78
        | VX2706 = cCoq_2eInit_2eByte_2ex79
        | VX2706 = cCoq_2eInit_2eByte_2ex7a
        | VX2706 = cCoq_2eInit_2eByte_2ex7b
        | VX2706 = cCoq_2eInit_2eByte_2ex7c
        | VX2706 = cCoq_2eInit_2eByte_2ex7d
        | VX2706 = cCoq_2eInit_2eByte_2ex7e
        | VX2706 = cCoq_2eInit_2eByte_2ex7f
        | VX2706 = cCoq_2eInit_2eByte_2ex80
        | VX2706 = cCoq_2eInit_2eByte_2ex81
        | VX2706 = cCoq_2eInit_2eByte_2ex82
        | VX2706 = cCoq_2eInit_2eByte_2ex83
        | VX2706 = cCoq_2eInit_2eByte_2ex84
        | VX2706 = cCoq_2eInit_2eByte_2ex85
        | VX2706 = cCoq_2eInit_2eByte_2ex86
        | VX2706 = cCoq_2eInit_2eByte_2ex87
        | VX2706 = cCoq_2eInit_2eByte_2ex88
        | VX2706 = cCoq_2eInit_2eByte_2ex89
        | VX2706 = cCoq_2eInit_2eByte_2ex8a
        | VX2706 = cCoq_2eInit_2eByte_2ex8b
        | VX2706 = cCoq_2eInit_2eByte_2ex8c
        | VX2706 = cCoq_2eInit_2eByte_2ex8d
        | VX2706 = cCoq_2eInit_2eByte_2ex8e
        | VX2706 = cCoq_2eInit_2eByte_2ex8f
        | VX2706 = cCoq_2eInit_2eByte_2ex90
        | VX2706 = cCoq_2eInit_2eByte_2ex91
        | VX2706 = cCoq_2eInit_2eByte_2ex92
        | VX2706 = cCoq_2eInit_2eByte_2ex93
        | VX2706 = cCoq_2eInit_2eByte_2ex94
        | VX2706 = cCoq_2eInit_2eByte_2ex95
        | VX2706 = cCoq_2eInit_2eByte_2ex96
        | VX2706 = cCoq_2eInit_2eByte_2ex97
        | VX2706 = cCoq_2eInit_2eByte_2ex98
        | VX2706 = cCoq_2eInit_2eByte_2ex99
        | VX2706 = cCoq_2eInit_2eByte_2ex9a
        | VX2706 = cCoq_2eInit_2eByte_2ex9b
        | VX2706 = cCoq_2eInit_2eByte_2ex9c
        | VX2706 = cCoq_2eInit_2eByte_2ex9d
        | VX2706 = cCoq_2eInit_2eByte_2ex9e
        | VX2706 = cCoq_2eInit_2eByte_2ex9f
        | VX2706 = cCoq_2eInit_2eByte_2exa0
        | VX2706 = cCoq_2eInit_2eByte_2exa1
        | VX2706 = cCoq_2eInit_2eByte_2exa2
        | VX2706 = cCoq_2eInit_2eByte_2exa3
        | VX2706 = cCoq_2eInit_2eByte_2exa4
        | VX2706 = cCoq_2eInit_2eByte_2exa5
        | VX2706 = cCoq_2eInit_2eByte_2exa6
        | VX2706 = cCoq_2eInit_2eByte_2exa7
        | VX2706 = cCoq_2eInit_2eByte_2exa8
        | VX2706 = cCoq_2eInit_2eByte_2exa9
        | VX2706 = cCoq_2eInit_2eByte_2exaa
        | VX2706 = cCoq_2eInit_2eByte_2exab
        | VX2706 = cCoq_2eInit_2eByte_2exac
        | VX2706 = cCoq_2eInit_2eByte_2exad
        | VX2706 = cCoq_2eInit_2eByte_2exae
        | VX2706 = cCoq_2eInit_2eByte_2exaf
        | VX2706 = cCoq_2eInit_2eByte_2exb0
        | VX2706 = cCoq_2eInit_2eByte_2exb1
        | VX2706 = cCoq_2eInit_2eByte_2exb2
        | VX2706 = cCoq_2eInit_2eByte_2exb3
        | VX2706 = cCoq_2eInit_2eByte_2exb4
        | VX2706 = cCoq_2eInit_2eByte_2exb5
        | VX2706 = cCoq_2eInit_2eByte_2exb6
        | VX2706 = cCoq_2eInit_2eByte_2exb7
        | VX2706 = cCoq_2eInit_2eByte_2exb8
        | VX2706 = cCoq_2eInit_2eByte_2exb9
        | VX2706 = cCoq_2eInit_2eByte_2exba
        | VX2706 = cCoq_2eInit_2eByte_2exbb
        | VX2706 = cCoq_2eInit_2eByte_2exbc
        | VX2706 = cCoq_2eInit_2eByte_2exbd
        | VX2706 = cCoq_2eInit_2eByte_2exbe
        | VX2706 = cCoq_2eInit_2eByte_2exbf
        | VX2706 = cCoq_2eInit_2eByte_2exc0
        | VX2706 = cCoq_2eInit_2eByte_2exc1
        | VX2706 = cCoq_2eInit_2eByte_2exc2
        | VX2706 = cCoq_2eInit_2eByte_2exc3
        | VX2706 = cCoq_2eInit_2eByte_2exc4
        | VX2706 = cCoq_2eInit_2eByte_2exc5
        | VX2706 = cCoq_2eInit_2eByte_2exc6
        | VX2706 = cCoq_2eInit_2eByte_2exc7
        | VX2706 = cCoq_2eInit_2eByte_2exc8
        | VX2706 = cCoq_2eInit_2eByte_2exc9
        | VX2706 = cCoq_2eInit_2eByte_2exca
        | VX2706 = cCoq_2eInit_2eByte_2excb
        | VX2706 = cCoq_2eInit_2eByte_2excc
        | VX2706 = cCoq_2eInit_2eByte_2excd
        | VX2706 = cCoq_2eInit_2eByte_2exce
        | VX2706 = cCoq_2eInit_2eByte_2excf
        | VX2706 = cCoq_2eInit_2eByte_2exd0
        | VX2706 = cCoq_2eInit_2eByte_2exd1
        | VX2706 = cCoq_2eInit_2eByte_2exd2
        | VX2706 = cCoq_2eInit_2eByte_2exd3
        | VX2706 = cCoq_2eInit_2eByte_2exd4
        | VX2706 = cCoq_2eInit_2eByte_2exd5
        | VX2706 = cCoq_2eInit_2eByte_2exd6
        | VX2706 = cCoq_2eInit_2eByte_2exd7
        | VX2706 = cCoq_2eInit_2eByte_2exd8
        | VX2706 = cCoq_2eInit_2eByte_2exd9
        | VX2706 = cCoq_2eInit_2eByte_2exda
        | VX2706 = cCoq_2eInit_2eByte_2exdb
        | VX2706 = cCoq_2eInit_2eByte_2exdc
        | VX2706 = cCoq_2eInit_2eByte_2exdd
        | VX2706 = cCoq_2eInit_2eByte_2exde
        | VX2706 = cCoq_2eInit_2eByte_2exdf
        | VX2706 = cCoq_2eInit_2eByte_2exe0
        | VX2706 = cCoq_2eInit_2eByte_2exe1
        | VX2706 = cCoq_2eInit_2eByte_2exe2
        | VX2706 = cCoq_2eInit_2eByte_2exe3
        | VX2706 = cCoq_2eInit_2eByte_2exe4
        | VX2706 = cCoq_2eInit_2eByte_2exe5
        | VX2706 = cCoq_2eInit_2eByte_2exe6
        | VX2706 = cCoq_2eInit_2eByte_2exe7
        | VX2706 = cCoq_2eInit_2eByte_2exe8
        | VX2706 = cCoq_2eInit_2eByte_2exe9
        | VX2706 = cCoq_2eInit_2eByte_2exea
        | VX2706 = cCoq_2eInit_2eByte_2exeb
        | VX2706 = cCoq_2eInit_2eByte_2exec
        | VX2706 = cCoq_2eInit_2eByte_2exed
        | VX2706 = cCoq_2eInit_2eByte_2exee
        | VX2706 = cCoq_2eInit_2eByte_2exef
        | VX2706 = cCoq_2eInit_2eByte_2exf0
        | VX2706 = cCoq_2eInit_2eByte_2exf1
        | VX2706 = cCoq_2eInit_2eByte_2exf2
        | VX2706 = cCoq_2eInit_2eByte_2exf3
        | VX2706 = cCoq_2eInit_2eByte_2exf4
        | VX2706 = cCoq_2eInit_2eByte_2exf5
        | VX2706 = cCoq_2eInit_2eByte_2exf6
        | VX2706 = cCoq_2eInit_2eByte_2exf7
        | VX2706 = cCoq_2eInit_2eByte_2exf8
        | VX2706 = cCoq_2eInit_2eByte_2exf9
        | VX2706 = cCoq_2eInit_2eByte_2exfa
        | VX2706 = cCoq_2eInit_2eByte_2exfb
        | VX2706 = cCoq_2eInit_2eByte_2exfc
        | VX2706 = cCoq_2eInit_2eByte_2exfd
        | VX2706 = cCoq_2eInit_2eByte_2exfe
        | VX2706 = cCoq_2eInit_2eByte_2exff ) ) ).

fof('$_inversion_Coq.Init.Datatypes.BoolSpec',axiom,
    ! [Vvar__0__P__80608,Vvar__1__Q__80609,Vvar__2___24Anonymous__80610] :
      ( cProp___24t(Vvar__0__P__80608)
     => ( cProp___24t(Vvar__1__Q__80609)
       => ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__2___24Anonymous__80610)
         => ( cCoq_2eInit_2eDatatypes_2eBoolSpec___24a3(Vvar__0__P__80608,Vvar__1__Q__80609,Vvar__2___24Anonymous__80610)
           => ( ( p(Vvar__0__P__80608)
                & Vvar__2___24Anonymous__80610 = cCoq_2eInit_2eDatatypes_2etrue )
              | ( p(Vvar__1__Q__80609)
                & Vvar__2___24Anonymous__80610 = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ).

fof('$_inversion_Coq.Init.Datatypes.CompareSpec',axiom,
    ! [Vvar__0__Peq__75721,Vvar__1__Plt__75722,Vvar__2__Pgt__75723,Vvar__3___24Anonymous__75724] :
      ( cProp___24t(Vvar__0__Peq__75721)
     => ( cProp___24t(Vvar__1__Plt__75722)
       => ( cProp___24t(Vvar__2__Pgt__75723)
         => ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__3___24Anonymous__75724)
           => ( cCoq_2eInit_2eDatatypes_2eCompareSpec___24a4(Vvar__0__Peq__75721,Vvar__1__Plt__75722,Vvar__2__Pgt__75723,Vvar__3___24Anonymous__75724)
             => ( ( p(Vvar__0__Peq__75721)
                  & Vvar__3___24Anonymous__75724 = cCoq_2eInit_2eDatatypes_2eEq )
                | ( p(Vvar__1__Plt__75722)
                  & Vvar__3___24Anonymous__75724 = cCoq_2eInit_2eDatatypes_2eLt )
                | ( p(Vvar__2__Pgt__75723)
                  & Vvar__3___24Anonymous__75724 = cCoq_2eInit_2eDatatypes_2eGt ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Init.Datatypes.CompareSpecT',axiom,
    ! [Vvar__0__Peq__112810,Vvar__1__Plt__112811,Vvar__2__Pgt__112812,Vvar__3___24Anonymous__112813,VX112814] :
      ( cProp___24t(Vvar__0__Peq__112810)
     => ( cProp___24t(Vvar__1__Plt__112811)
       => ( cProp___24t(Vvar__2__Pgt__112812)
         => ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__3___24Anonymous__112813)
           => ( cCoq_2eInit_2eDatatypes_2eCompareSpecT___24t(Vvar__0__Peq__112810,Vvar__1__Plt__112811,Vvar__2__Pgt__112812,Vvar__3___24Anonymous__112813,VX112814)
             => ( ( p(Vvar__0__Peq__112810)
                  & Vvar__3___24Anonymous__112813 = cCoq_2eInit_2eDatatypes_2eEq
                  & VX112814 = cCoq_2eInit_2eDatatypes_2eCompEqT___24a3(Vvar__0__Peq__112810,Vvar__1__Plt__112811,Vvar__2__Pgt__112812) )
                | ( p(Vvar__1__Plt__112811)
                  & Vvar__3___24Anonymous__112813 = cCoq_2eInit_2eDatatypes_2eLt
                  & VX112814 = cCoq_2eInit_2eDatatypes_2eCompLtT___24a3(Vvar__0__Peq__112810,Vvar__1__Plt__112811,Vvar__2__Pgt__112812) )
                | ( p(Vvar__2__Pgt__112812)
                  & Vvar__3___24Anonymous__112813 = cCoq_2eInit_2eDatatypes_2eGt
                  & VX112814 = cCoq_2eInit_2eDatatypes_2eCompGtT___24a3(Vvar__0__Peq__112810,Vvar__1__Plt__112811,Vvar__2__Pgt__112812) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Init.Datatypes.bool',axiom,
    ! [VX332] :
      ( cCoq_2eInit_2eDatatypes_2ebool___24t(VX332)
     => ( VX332 = cCoq_2eInit_2eDatatypes_2etrue
        | VX332 = cCoq_2eInit_2eDatatypes_2efalse ) ) ).

fof('$_inversion_Coq.Init.Datatypes.comparison',axiom,
    ! [VX75720] :
      ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(VX75720)
     => ( VX75720 = cCoq_2eInit_2eDatatypes_2eEq
        | VX75720 = cCoq_2eInit_2eDatatypes_2eLt
        | VX75720 = cCoq_2eInit_2eDatatypes_2eGt ) ) ).

fof('$_inversion_Coq.Init.Datatypes.eq_true',axiom,
    ! [Vvar__0___24Anonymous__112808] :
      ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__0___24Anonymous__112808)
     => ( cCoq_2eInit_2eDatatypes_2eeq__true___24a1(Vvar__0___24Anonymous__112808)
       => Vvar__0___24Anonymous__112808 = cCoq_2eInit_2eDatatypes_2etrue ) ) ).

fof('$_inversion_Coq.Init.Datatypes.identity',axiom,
    ! [Vvar__0__A__85131,Vvar__1__a__85132,Vvar__2___24Anonymous__85133] :
      ( cType___24t(Vvar__0__A__85131)
     => ( t(Vvar__1__a__85132,Vvar__0__A__85131)
       => ( t(Vvar__2___24Anonymous__85133,Vvar__0__A__85131)
         => ( cCoq_2eInit_2eDatatypes_2eidentity___24a3(Vvar__0__A__85131,Vvar__1__a__85132,Vvar__2___24Anonymous__85133)
           => Vvar__2___24Anonymous__85133 = Vvar__1__a__85132 ) ) ) ) ).

fof('$_inversion_Coq.Init.Datatypes.list',axiom,
    ! [Vvar__0__A__1135,VX1136] :
      ( cType___24t(Vvar__0__A__1135)
     => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__1135,VX1136)
       => ( VX1136 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__1135)
          | ? [Vvar__1___24Anonymous__1139] :
              ( t(Vvar__1___24Anonymous__1139,Vvar__0__A__1135)
              & ? [Vvar__2___24Anonymous__1140] :
                  ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__1135,Vvar__2___24Anonymous__1140)
                  & VX1136 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__1135,Vvar__1___24Anonymous__1139,Vvar__2___24Anonymous__1140) ) ) ) ) ) ).

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

fof('$_inversion_Coq.Init.Datatypes.option',axiom,
    ! [Vvar__0__A__75631,VX75632] :
      ( cType___24t(Vvar__0__A__75631)
     => ( cCoq_2eInit_2eDatatypes_2eoption___24t(Vvar__0__A__75631,VX75632)
       => ( ? [Vvar__1___24Anonymous__75634] :
              ( t(Vvar__1___24Anonymous__75634,Vvar__0__A__75631)
              & VX75632 = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__75631,Vvar__1___24Anonymous__75634) )
          | VX75632 = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__75631) ) ) ) ).

fof('$_inversion_Coq.Init.Datatypes.prod',axiom,
    ! [Vvar__0__A__1109,Vvar__1__B__1110,VX1111] :
      ( cType___24t(Vvar__0__A__1109)
     => ( cType___24t(Vvar__1__B__1110)
       => ( cCoq_2eInit_2eDatatypes_2eprod___24t(Vvar__0__A__1109,Vvar__1__B__1110,VX1111)
         => ? [Vvar__2___24Anonymous__1114] :
              ( t(Vvar__2___24Anonymous__1114,Vvar__0__A__1109)
              & ? [Vvar__3___24Anonymous__1115] :
                  ( t(Vvar__3___24Anonymous__1115,Vvar__1__B__1110)
                  & VX1111 = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__1109,Vvar__1__B__1110,Vvar__2___24Anonymous__1114,Vvar__3___24Anonymous__1115) ) ) ) ) ) ).

fof('$_inversion_Coq.Init.Datatypes.sum',axiom,
    ! [Vvar__0__A__88829,Vvar__1__B__88830,VX88831] :
      ( cType___24t(Vvar__0__A__88829)
     => ( cType___24t(Vvar__1__B__88830)
       => ( cCoq_2eInit_2eDatatypes_2esum___24t(Vvar__0__A__88829,Vvar__1__B__88830,VX88831)
         => ( ? [Vvar__2___24Anonymous__88834] :
                ( t(Vvar__2___24Anonymous__88834,Vvar__0__A__88829)
                & VX88831 = cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__88829,Vvar__1__B__88830,Vvar__2___24Anonymous__88834) )
            | ? [Vvar__2___24Anonymous__88837] :
                ( t(Vvar__2___24Anonymous__88837,Vvar__1__B__88830)
                & VX88831 = cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__88829,Vvar__1__B__88830,Vvar__2___24Anonymous__88837) ) ) ) ) ) ).

fof('$_inversion_Coq.Init.Datatypes.unit',axiom,
    ! [VX594] :
      ( cCoq_2eInit_2eDatatypes_2eunit___24t(VX594)
     => VX594 = cCoq_2eInit_2eDatatypes_2ett ) ).

fof('$_inversion_Coq.Init.Decimal.decimal',axiom,
    ! [VX88867] :
      ( cCoq_2eInit_2eDecimal_2edecimal___24t(VX88867)
     => ( ? [Vvar__0__i__88868] :
            ( cCoq_2eInit_2eDecimal_2eint___24t(Vvar__0__i__88868)
            & ? [Vvar__1__f__88869] :
                ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__1__f__88869)
                & VX88867 = cCoq_2eInit_2eDecimal_2eDecimal___24a2(Vvar__0__i__88868,Vvar__1__f__88869) ) )
        | ? [Vvar__0__i__88870] :
            ( cCoq_2eInit_2eDecimal_2eint___24t(Vvar__0__i__88870)
            & ? [Vvar__1__f__88871] :
                ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__1__f__88871)
                & ? [Vvar__2__e__88872] :
                    ( cCoq_2eInit_2eDecimal_2eint___24t(Vvar__2__e__88872)
                    & VX88867 = cCoq_2eInit_2eDecimal_2eDecimalExp___24a3(Vvar__0__i__88870,Vvar__1__f__88871,Vvar__2__e__88872) ) ) ) ) ) ).

fof('$_inversion_Coq.Init.Decimal.int',axiom,
    ! [VX88858] :
      ( cCoq_2eInit_2eDecimal_2eint___24t(VX88858)
     => ( ? [Vvar__0__d__88859] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0__d__88859)
            & VX88858 = cCoq_2eInit_2eDecimal_2ePos___24a1(Vvar__0__d__88859) )
        | ? [Vvar__0__d__88860] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0__d__88860)
            & VX88858 = cCoq_2eInit_2eDecimal_2eNeg___24a1(Vvar__0__d__88860) ) ) ) ).

fof('$_inversion_Coq.Init.Decimal.uint',axiom,
    ! [VX75740] :
      ( cCoq_2eInit_2eDecimal_2euint___24t(VX75740)
     => ( VX75740 = cCoq_2eInit_2eDecimal_2eNil
        | ? [Vvar__0___24Anonymous__75741] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__75741)
            & VX75740 = cCoq_2eInit_2eDecimal_2eD0___24a1(Vvar__0___24Anonymous__75741) )
        | ? [Vvar__0___24Anonymous__75742] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__75742)
            & VX75740 = cCoq_2eInit_2eDecimal_2eD1___24a1(Vvar__0___24Anonymous__75742) )
        | ? [Vvar__0___24Anonymous__75743] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__75743)
            & VX75740 = cCoq_2eInit_2eDecimal_2eD2___24a1(Vvar__0___24Anonymous__75743) )
        | ? [Vvar__0___24Anonymous__75744] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__75744)
            & VX75740 = cCoq_2eInit_2eDecimal_2eD3___24a1(Vvar__0___24Anonymous__75744) )
        | ? [Vvar__0___24Anonymous__75745] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__75745)
            & VX75740 = cCoq_2eInit_2eDecimal_2eD4___24a1(Vvar__0___24Anonymous__75745) )
        | ? [Vvar__0___24Anonymous__75746] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__75746)
            & VX75740 = cCoq_2eInit_2eDecimal_2eD5___24a1(Vvar__0___24Anonymous__75746) )
        | ? [Vvar__0___24Anonymous__75747] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__75747)
            & VX75740 = cCoq_2eInit_2eDecimal_2eD6___24a1(Vvar__0___24Anonymous__75747) )
        | ? [Vvar__0___24Anonymous__75748] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__75748)
            & VX75740 = cCoq_2eInit_2eDecimal_2eD7___24a1(Vvar__0___24Anonymous__75748) )
        | ? [Vvar__0___24Anonymous__75749] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__75749)
            & VX75740 = cCoq_2eInit_2eDecimal_2eD8___24a1(Vvar__0___24Anonymous__75749) )
        | ? [Vvar__0___24Anonymous__75750] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__75750)
            & VX75740 = cCoq_2eInit_2eDecimal_2eD9___24a1(Vvar__0___24Anonymous__75750) ) ) ) ).

fof('$_inversion_Coq.Init.Peano.le',axiom,
    ! [Vvar__0__n__572,Vvar__1___24Anonymous__573] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__572)
     => ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__573)
       => ( cCoq_2eInit_2ePeano_2ele___24a2(Vvar__0__n__572,Vvar__1___24Anonymous__573)
         => ( Vvar__1___24Anonymous__573 = Vvar__0__n__572
            | ? [Vvar__1__m__577] :
                ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__m__577)
                & cCoq_2eInit_2ePeano_2ele___24a2(Vvar__0__n__572,Vvar__1__m__577)
                & Vvar__1___24Anonymous__573 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__1__m__577) ) ) ) ) ) ).

fof('$_inversion_Coq.Init.Specif.sig',axiom,
    ! [Vvar__0__A__78041,Vvar__1__P__78042,VX78045] :
      ( cType___24t(Vvar__0__A__78041)
     => ( c_24__type__78055___24t(Vvar__0__A__78041,Vvar__1__P__78042,Vvar__1__P__78042)
       => ( cCoq_2eInit_2eSpecif_2esig___24t(Vvar__0__A__78041,Vvar__1__P__78042,VX78045)
         => ? [Vvar__2__x__78050] :
              ( t(Vvar__2__x__78050,Vvar__0__A__78041)
              & p(happ(Vvar__1__P__78042,Vvar__2__x__78050))
              & VX78045 = cCoq_2eInit_2eSpecif_2eexist___24a3(Vvar__0__A__78041,Vvar__1__P__78042,Vvar__2__x__78050) ) ) ) ) ).

fof('$_inversion_Coq.Init.Specif.sig2',axiom,
    ! [Vvar__0__A__91780,Vvar__1__P__91781,Vvar__2__Q__91784,VX91787] :
      ( cType___24t(Vvar__0__A__91780)
     => ( c_24__type__91804___24t(Vvar__0__A__91780,Vvar__1__P__91781,Vvar__2__Q__91784,Vvar__1__P__91781)
       => ( c_24__type__91812___24t(Vvar__0__A__91780,Vvar__1__P__91781,Vvar__2__Q__91784,Vvar__2__Q__91784)
         => ( cCoq_2eInit_2eSpecif_2esig2___24t(Vvar__0__A__91780,Vvar__1__P__91781,Vvar__2__Q__91784,VX91787)
           => ? [Vvar__3__x__91795] :
                ( t(Vvar__3__x__91795,Vvar__0__A__91780)
                & p(happ(Vvar__1__P__91781,Vvar__3__x__91795))
                & p(happ(Vvar__2__Q__91784,Vvar__3__x__91795))
                & VX91787 = cCoq_2eInit_2eSpecif_2eexist2___24a4(Vvar__0__A__91780,Vvar__1__P__91781,Vvar__2__Q__91784,Vvar__3__x__91795) ) ) ) ) ) ).

fof('$_inversion_Coq.Init.Specif.sigT',axiom,
    ! [Vvar__0__A__85953,Vvar__1__P__85954,VX85957] :
      ( cType___24t(Vvar__0__A__85953)
     => ( c_24__type__85967___24t(Vvar__0__A__85953,Vvar__1__P__85954,Vvar__1__P__85954)
       => ( cCoq_2eInit_2eSpecif_2esigT___24t(Vvar__0__A__85953,Vvar__1__P__85954,VX85957)
         => ? [Vvar__2__x__85962] :
              ( t(Vvar__2__x__85962,Vvar__0__A__85953)
              & ? [Vvar__3___24Anonymous__85963] :
                  ( t(Vvar__3___24Anonymous__85963,happ(Vvar__1__P__85954,Vvar__2__x__85962))
                  & VX85957 = cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__85953,Vvar__1__P__85954,Vvar__2__x__85962,Vvar__3___24Anonymous__85963) ) ) ) ) ) ).

fof('$_inversion_Coq.Init.Specif.sigT2',axiom,
    ! [Vvar__0__A__91836,Vvar__1__P__91837,Vvar__2__Q__91840,VX91843] :
      ( cType___24t(Vvar__0__A__91836)
     => ( c_24__type__91860___24t(Vvar__0__A__91836,Vvar__1__P__91837,Vvar__2__Q__91840,Vvar__1__P__91837)
       => ( c_24__type__91868___24t(Vvar__0__A__91836,Vvar__1__P__91837,Vvar__2__Q__91840,Vvar__2__Q__91840)
         => ( cCoq_2eInit_2eSpecif_2esigT2___24t(Vvar__0__A__91836,Vvar__1__P__91837,Vvar__2__Q__91840,VX91843)
           => ? [Vvar__3__x__91851] :
                ( t(Vvar__3__x__91851,Vvar__0__A__91836)
                & ? [Vvar__4___24Anonymous__91852] :
                    ( t(Vvar__4___24Anonymous__91852,happ(Vvar__1__P__91837,Vvar__3__x__91851))
                    & ? [Vvar__5___24Anonymous__91853] :
                        ( t(Vvar__5___24Anonymous__91853,happ(Vvar__2__Q__91840,Vvar__3__x__91851))
                        & VX91843 = cCoq_2eInit_2eSpecif_2eexistT2___24a6(Vvar__0__A__91836,Vvar__1__P__91837,Vvar__2__Q__91840,Vvar__3__x__91851,Vvar__4___24Anonymous__91852,Vvar__5___24Anonymous__91853) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Init.Specif.sumbool',axiom,
    ! [Vvar__0__A__251,Vvar__1__B__252,VX253] :
      ( cProp___24t(Vvar__0__A__251)
     => ( cProp___24t(Vvar__1__B__252)
       => ( cCoq_2eInit_2eSpecif_2esumbool___24t(Vvar__0__A__251,Vvar__1__B__252,VX253)
         => ( ( p(Vvar__0__A__251)
              & VX253 = cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__251,Vvar__1__B__252) )
            | ( p(Vvar__1__B__252)
              & VX253 = cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__251,Vvar__1__B__252) ) ) ) ) ) ).

fof('$_inversion_Coq.Init.Specif.sumor',axiom,
    ! [Vvar__0__A__291,Vvar__1__B__292,VX293] :
      ( cType___24t(Vvar__0__A__291)
     => ( cProp___24t(Vvar__1__B__292)
       => ( cCoq_2eInit_2eSpecif_2esumor___24t(Vvar__0__A__291,Vvar__1__B__292,VX293)
         => ( ? [Vvar__2___24Anonymous__296] :
                ( t(Vvar__2___24Anonymous__296,Vvar__0__A__291)
                & VX293 = cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__291,Vvar__1__B__292,Vvar__2___24Anonymous__296) )
            | ( p(Vvar__1__B__292)
              & VX293 = cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__291,Vvar__1__B__292) ) ) ) ) ) ).

fof('$_inversion_Coq.Init.Wf.Acc',axiom,
    ! [Vvar__0__A__83729,Vvar__1__R__83730,Vvar__2__x__83735] :
      ( cType___24t(Vvar__0__A__83729)
     => ( c_24__type__83764___24t(Vvar__0__A__83729,Vvar__1__R__83730,Vvar__2__x__83735,Vvar__1__R__83730)
       => ( t(Vvar__2__x__83735,Vvar__0__A__83729)
         => ( cCoq_2eInit_2eWf_2eAcc___24a3(Vvar__0__A__83729,Vvar__1__R__83730,Vvar__2__x__83735)
           => ( ! [Vvar__var__var__var__var__3__y__83745__83747__83749__83751__83753] :
                  ( t(Vvar__var__var__var__var__3__y__83745__83747__83749__83751__83753,Vvar__0__A__83729)
                 => ( p(happ(happ(Vvar__1__R__83730,Vvar__var__var__var__var__3__y__83745__83747__83749__83751__83753),Vvar__2__x__83735))
                   => cCoq_2eInit_2eWf_2eAcc___24a3(Vvar__0__A__83729,Vvar__1__R__83730,Vvar__var__var__var__var__3__y__83745__83747__83749__83751__83753) ) )
              & p(c_24True) ) ) ) ) ) ).

fof('$_inversion_Coq.Lists.List.Exists',axiom,
    ! [Vvar__0__A__113798,Vvar__1__P__113799,Vvar__2___24Anonymous__113802] :
      ( cType___24t(Vvar__0__A__113798)
     => ( c_24__type__113822___24t(Vvar__0__A__113798,Vvar__1__P__113799,Vvar__2___24Anonymous__113802,Vvar__1__P__113799)
       => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__113798,Vvar__2___24Anonymous__113802)
         => ( cCoq_2eLists_2eList_2eExists___24a3(Vvar__0__A__113798,Vvar__1__P__113799,Vvar__2___24Anonymous__113802)
           => ( ? [Vvar__2__x__113808] :
                  ( t(Vvar__2__x__113808,Vvar__0__A__113798)
                  & ? [Vvar__3__l__113809] :
                      ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__113798,Vvar__3__l__113809)
                      & p(happ(Vvar__1__P__113799,Vvar__2__x__113808))
                      & Vvar__2___24Anonymous__113802 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__113798,Vvar__2__x__113808,Vvar__3__l__113809) ) )
              | ? [Vvar__2__x__113815] :
                  ( t(Vvar__2__x__113815,Vvar__0__A__113798)
                  & ? [Vvar__3__l__113816] :
                      ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__113798,Vvar__3__l__113816)
                      & cCoq_2eLists_2eList_2eExists___24a3(Vvar__0__A__113798,Vvar__1__P__113799,Vvar__3__l__113816)
                      & Vvar__2___24Anonymous__113802 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__113798,Vvar__2__x__113815,Vvar__3__l__113816) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Lists.List.Forall',axiom,
    ! [Vvar__0__A__96800,Vvar__1__P__96801,Vvar__2___24Anonymous__96804] :
      ( cType___24t(Vvar__0__A__96800)
     => ( c_24__type__96822___24t(Vvar__0__A__96800,Vvar__1__P__96801,Vvar__2___24Anonymous__96804,Vvar__1__P__96801)
       => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__96800,Vvar__2___24Anonymous__96804)
         => ( cCoq_2eLists_2eList_2eForall___24a3(Vvar__0__A__96800,Vvar__1__P__96801,Vvar__2___24Anonymous__96804)
           => ( Vvar__2___24Anonymous__96804 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__96800)
              | ? [Vvar__2__x__96814] :
                  ( t(Vvar__2__x__96814,Vvar__0__A__96800)
                  & ? [Vvar__3__l__96815] :
                      ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__96800,Vvar__3__l__96815)
                      & p(happ(Vvar__1__P__96801,Vvar__2__x__96814))
                      & cCoq_2eLists_2eList_2eForall___24a3(Vvar__0__A__96800,Vvar__1__P__96801,Vvar__3__l__96815)
                      & Vvar__2___24Anonymous__96804 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__96800,Vvar__2__x__96814,Vvar__3__l__96815) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Lists.List.Forall2',axiom,
    ! [Vvar__0__A__113824,Vvar__1__B__113825,Vvar__2__R__113826,Vvar__3___24Anonymous__113831,Vvar__4___24Anonymous__113832] :
      ( cType___24t(Vvar__0__A__113824)
     => ( cType___24t(Vvar__1__B__113825)
       => ( c_24__type__113869___24t(Vvar__0__A__113824,Vvar__1__B__113825,Vvar__2__R__113826,Vvar__3___24Anonymous__113831,Vvar__4___24Anonymous__113832,Vvar__2__R__113826)
         => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__113824,Vvar__3___24Anonymous__113831)
           => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__1__B__113825,Vvar__4___24Anonymous__113832)
             => ( cCoq_2eLists_2eList_2eForall2___24a5(Vvar__0__A__113824,Vvar__1__B__113825,Vvar__2__R__113826,Vvar__3___24Anonymous__113831,Vvar__4___24Anonymous__113832)
               => ( ( Vvar__4___24Anonymous__113832 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__1__B__113825)
                    & Vvar__3___24Anonymous__113831 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__113824) )
                  | ? [Vvar__3__x__113848] :
                      ( t(Vvar__3__x__113848,Vvar__0__A__113824)
                      & ? [Vvar__4__y__113849] :
                          ( t(Vvar__4__y__113849,Vvar__1__B__113825)
                          & ? [Vvar__5__l__113850] :
                              ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__113824,Vvar__5__l__113850)
                              & ? [Vvar__6__l_27__113851] :
                                  ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__1__B__113825,Vvar__6__l_27__113851)
                                  & p(happ(happ(Vvar__2__R__113826,Vvar__3__x__113848),Vvar__4__y__113849))
                                  & cCoq_2eLists_2eList_2eForall2___24a5(Vvar__0__A__113824,Vvar__1__B__113825,Vvar__2__R__113826,Vvar__5__l__113850,Vvar__6__l_27__113851)
                                  & Vvar__4___24Anonymous__113832 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__1__B__113825,Vvar__4__y__113849,Vvar__6__l_27__113851)
                                  & Vvar__3___24Anonymous__113831 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__113824,Vvar__3__x__113848,Vvar__5__l__113850) ) ) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Lists.List.NoDup',axiom,
    ! [Vvar__0__A__76632,Vvar__1___24Anonymous__76633] :
      ( cType___24t(Vvar__0__A__76632)
     => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__76632,Vvar__1___24Anonymous__76633)
       => ( cCoq_2eLists_2eList_2eNoDup___24a2(Vvar__0__A__76632,Vvar__1___24Anonymous__76633)
         => ( Vvar__1___24Anonymous__76633 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__76632)
            | ? [Vvar__1__x__76637] :
                ( t(Vvar__1__x__76637,Vvar__0__A__76632)
                & ? [Vvar__2__l__76638] :
                    ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__76632,Vvar__2__l__76638)
                    & ~ cCoq_2eLists_2eList_2eIn___24a3(Vvar__0__A__76632,Vvar__1__x__76637,Vvar__2__l__76638)
                    & cCoq_2eLists_2eList_2eNoDup___24a2(Vvar__0__A__76632,Vvar__2__l__76638)
                    & Vvar__1___24Anonymous__76633 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__76632,Vvar__1__x__76637,Vvar__2__l__76638) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Lists.SetoidList.InA',axiom,
    ! [Vvar__0__A__113418,Vvar__1__eqA__113419,Vvar__2__x__113424,Vvar__3___24Anonymous__113425] :
      ( cType___24t(Vvar__0__A__113418)
     => ( c_24__type__113458___24t(Vvar__0__A__113418,Vvar__1__eqA__113419,Vvar__2__x__113424,Vvar__3___24Anonymous__113425,Vvar__1__eqA__113419)
       => ( t(Vvar__2__x__113424,Vvar__0__A__113418)
         => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__113418,Vvar__3___24Anonymous__113425)
           => ( cCoq_2eLists_2eSetoidList_2eInA___24a4(Vvar__0__A__113418,Vvar__1__eqA__113419,Vvar__2__x__113424,Vvar__3___24Anonymous__113425)
             => ( ? [Vvar__3__y__113434] :
                    ( t(Vvar__3__y__113434,Vvar__0__A__113418)
                    & ? [Vvar__4__l__113435] :
                        ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__113418,Vvar__4__l__113435)
                        & p(happ(happ(Vvar__1__eqA__113419,Vvar__2__x__113424),Vvar__3__y__113434))
                        & Vvar__3___24Anonymous__113425 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__113418,Vvar__3__y__113434,Vvar__4__l__113435) ) )
                | ? [Vvar__3__y__113444] :
                    ( t(Vvar__3__y__113444,Vvar__0__A__113418)
                    & ? [Vvar__4__l__113445] :
                        ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__113418,Vvar__4__l__113445)
                        & cCoq_2eLists_2eSetoidList_2eInA___24a4(Vvar__0__A__113418,Vvar__1__eqA__113419,Vvar__2__x__113424,Vvar__4__l__113445)
                        & Vvar__3___24Anonymous__113425 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__113418,Vvar__3__y__113444,Vvar__4__l__113445) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Lists.SetoidList.NoDupA',axiom,
    ! [Vvar__0__A__115577,Vvar__1__eqA__115578,Vvar__2___24Anonymous__115583] :
      ( cType___24t(Vvar__0__A__115577)
     => ( c_24__type__115610___24t(Vvar__0__A__115577,Vvar__1__eqA__115578,Vvar__2___24Anonymous__115583,Vvar__1__eqA__115578)
       => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__115577,Vvar__2___24Anonymous__115583)
         => ( cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(Vvar__0__A__115577,Vvar__1__eqA__115578,Vvar__2___24Anonymous__115583)
           => ( Vvar__2___24Anonymous__115583 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__115577)
              | ? [Vvar__2__x__115597] :
                  ( t(Vvar__2__x__115597,Vvar__0__A__115577)
                  & ? [Vvar__3__l__115598] :
                      ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__115577,Vvar__3__l__115598)
                      & ~ cCoq_2eLists_2eSetoidList_2eInA___24a4(Vvar__0__A__115577,Vvar__1__eqA__115578,Vvar__2__x__115597,Vvar__3__l__115598)
                      & cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(Vvar__0__A__115577,Vvar__1__eqA__115578,Vvar__3__l__115598)
                      & Vvar__2___24Anonymous__115583 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__115577,Vvar__2__x__115597,Vvar__3__l__115598) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Lists.SetoidList.eqlistA',axiom,
    ! [Vvar__0__A__115612,Vvar__1__eqA__115613,Vvar__2___24Anonymous__115618,Vvar__3___24Anonymous__115619] :
      ( cType___24t(Vvar__0__A__115612)
     => ( c_24__type__115650___24t(Vvar__0__A__115612,Vvar__1__eqA__115613,Vvar__2___24Anonymous__115618,Vvar__3___24Anonymous__115619,Vvar__1__eqA__115613)
       => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__115612,Vvar__2___24Anonymous__115618)
         => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__115612,Vvar__3___24Anonymous__115619)
           => ( cCoq_2eLists_2eSetoidList_2eeqlistA___24a4(Vvar__0__A__115612,Vvar__1__eqA__115613,Vvar__2___24Anonymous__115618,Vvar__3___24Anonymous__115619)
             => ( ( Vvar__3___24Anonymous__115619 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__115612)
                  & Vvar__2___24Anonymous__115618 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__115612) )
                | ? [Vvar__2__x__115633] :
                    ( t(Vvar__2__x__115633,Vvar__0__A__115612)
                    & ? [Vvar__3__x_27__115634] :
                        ( t(Vvar__3__x_27__115634,Vvar__0__A__115612)
                        & ? [Vvar__4__l__115635] :
                            ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__115612,Vvar__4__l__115635)
                            & ? [Vvar__5__l_27__115636] :
                                ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__115612,Vvar__5__l_27__115636)
                                & p(happ(happ(Vvar__1__eqA__115613,Vvar__2__x__115633),Vvar__3__x_27__115634))
                                & cCoq_2eLists_2eSetoidList_2eeqlistA___24a4(Vvar__0__A__115612,Vvar__1__eqA__115613,Vvar__4__l__115635,Vvar__5__l_27__115636)
                                & Vvar__3___24Anonymous__115619 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__115612,Vvar__3__x_27__115634,Vvar__5__l_27__115636)
                                & Vvar__2___24Anonymous__115618 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__115612,Vvar__2__x__115633,Vvar__4__l__115635) ) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Logic.EqdepFacts.eq_dep',axiom,
    ! [Vvar__0__U__85163,Vvar__1__P__85164,Vvar__2__p__85167,Vvar__3__x__85168,Vvar__4__q__85169,Vvar__5___24Anonymous__85170] :
      ( cType___24t(Vvar__0__U__85163)
     => ( c_24__type__85185___24t(Vvar__0__U__85163,Vvar__1__P__85164,Vvar__2__p__85167,Vvar__3__x__85168,Vvar__4__q__85169,Vvar__5___24Anonymous__85170,Vvar__1__P__85164)
       => ( t(Vvar__2__p__85167,Vvar__0__U__85163)
         => ( t(Vvar__3__x__85168,happ(Vvar__1__P__85164,Vvar__2__p__85167))
           => ( t(Vvar__4__q__85169,Vvar__0__U__85163)
             => ( t(Vvar__5___24Anonymous__85170,happ(Vvar__1__P__85164,Vvar__4__q__85169))
               => ( cCoq_2eLogic_2eEqdepFacts_2eeq__dep___24a6(Vvar__0__U__85163,Vvar__1__P__85164,Vvar__2__p__85167,Vvar__3__x__85168,Vvar__4__q__85169,Vvar__5___24Anonymous__85170)
                 => ( Vvar__5___24Anonymous__85170 = Vvar__3__x__85168
                    & Vvar__4__q__85169 = Vvar__2__p__85167 ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Logic.EqdepFacts.eq_dep1',axiom,
    ! [Vvar__0__U__86626,Vvar__1__P__86627,Vvar__2__p__86630,Vvar__3__x__86631,Vvar__4__q__86632,Vvar__5__y__86633] :
      ( cType___24t(Vvar__0__U__86626)
     => ( c_24__type__86652___24t(Vvar__0__U__86626,Vvar__1__P__86627,Vvar__2__p__86630,Vvar__3__x__86631,Vvar__4__q__86632,Vvar__5__y__86633,Vvar__1__P__86627)
       => ( t(Vvar__2__p__86630,Vvar__0__U__86626)
         => ( t(Vvar__3__x__86631,happ(Vvar__1__P__86627,Vvar__2__p__86630))
           => ( t(Vvar__4__q__86632,Vvar__0__U__86626)
             => ( t(Vvar__5__y__86633,happ(Vvar__1__P__86627,Vvar__4__q__86632))
               => ( cCoq_2eLogic_2eEqdepFacts_2eeq__dep1___24a6(Vvar__0__U__86626,Vvar__1__P__86627,Vvar__2__p__86630,Vvar__3__x__86631,Vvar__4__q__86632,Vvar__5__y__86633)
                 => ( Vvar__4__q__86632 = Vvar__2__p__86630
                    & Vvar__3__x__86631 = cCoq_2eInit_2eLogic_2eeq__rect___24a5(Vvar__0__U__86626,Vvar__4__q__86632,Vvar__1__P__86627,Vvar__5__y__86633,Vvar__2__p__86630)
                    & p(c_24True) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Logic.JMeq.JMeq',axiom,
    ! [Vvar__0__A__89678,Vvar__1__x__89679,Vvar__2__B__89680,Vvar__3___24Anonymous__89681] :
      ( cType___24t(Vvar__0__A__89678)
     => ( t(Vvar__1__x__89679,Vvar__0__A__89678)
       => ( cType___24t(Vvar__2__B__89680)
         => ( t(Vvar__3___24Anonymous__89681,Vvar__2__B__89680)
           => ( cCoq_2eLogic_2eJMeq_2eJMeq___24a4(Vvar__0__A__89678,Vvar__1__x__89679,Vvar__2__B__89680,Vvar__3___24Anonymous__89681)
             => ( Vvar__3___24Anonymous__89681 = Vvar__1__x__89679
                & Vvar__2__B__89680 = Vvar__0__A__89678 ) ) ) ) ) ) ).

fof('$_inversion_Coq.Numbers.BinNums.N',axiom,
    ! [VX1089] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(VX1089)
     => ( VX1089 = cCoq_2eNumbers_2eBinNums_2eN0
        | ? [Vvar__0___24Anonymous__1090] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1090)
            & VX1089 = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__1090) ) ) ) ).

fof('$_inversion_Coq.Numbers.BinNums.Z',axiom,
    ! [VX1096] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(VX1096)
     => ( VX1096 = cCoq_2eNumbers_2eBinNums_2eZ0
        | ? [Vvar__0___24Anonymous__1097] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1097)
            & VX1096 = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__1097) )
        | ? [Vvar__0___24Anonymous__1098] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1098)
            & VX1096 = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__1098) ) ) ) ).

fof('$_inversion_Coq.Numbers.BinNums.positive',axiom,
    ! [VX1076] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(VX1076)
     => ( ? [Vvar__0___24Anonymous__1077] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1077)
            & VX1076 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__1077) )
        | ? [Vvar__0___24Anonymous__1078] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1078)
            & VX1076 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__1078) )
        | VX1076 = cCoq_2eNumbers_2eBinNums_2exH ) ) ).

fof('$_inversion_Coq.PArith.BinPos.Pos.PeanoView',axiom,
    ! [Vvar__0___24Anonymous__109143,VX109144] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__109143)
     => ( cCoq_2ePArith_2eBinPos_2ePos_2ePeanoView___24t(Vvar__0___24Anonymous__109143,VX109144)
       => ( ( Vvar__0___24Anonymous__109143 = cCoq_2eNumbers_2eBinNums_2exH
            & VX109144 = cCoq_2ePArith_2eBinPos_2ePos_2ePeanoOne )
          | ? [Vvar__0__p__109145] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0__p__109145)
              & ? [Vvar__1___24Anonymous__109146] :
                  ( cCoq_2ePArith_2eBinPos_2ePos_2ePeanoView___24t(Vvar__0__p__109145,Vvar__1___24Anonymous__109146)
                  & Vvar__0___24Anonymous__109143 = c_24__case__Coq_2eNumbers_2eBinNums_2epositive_24109181___24a2(Vvar__0___24Anonymous__109143,Vvar__0__p__109145)
                  & VX109144 = cCoq_2ePArith_2eBinPos_2ePos_2ePeanoSucc___24a2(Vvar__0__p__109145,Vvar__1___24Anonymous__109146) ) ) ) ) ) ).

fof('$_inversion_Coq.PArith.BinPos.Pos.SqrtSpec',axiom,
    ! [Vvar__0___24Anonymous__93929,Vvar__1___24Anonymous__93930] :
      ( cCoq_2eInit_2eDatatypes_2eprod___24t(cCoq_2eNumbers_2eBinNums_2epositive,cCoq_2ePArith_2eBinPosDef_2ePos_2emask,Vvar__0___24Anonymous__93929)
     => ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__93930)
       => ( cCoq_2ePArith_2eBinPos_2ePos_2eSqrtSpec___24a2(Vvar__0___24Anonymous__93929,Vvar__1___24Anonymous__93930)
         => ( ? [Vvar__0__s__93932] :
                ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0__s__93932)
                & ? [Vvar__1__x__93933] :
                    ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__x__93933)
                    & Vvar__1__x__93933 = cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0__s__93932,Vvar__0__s__93932)
                    & Vvar__1___24Anonymous__93930 = Vvar__1__x__93933
                    & Vvar__0___24Anonymous__93929 = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2epositive,cCoq_2ePArith_2eBinPosDef_2ePos_2emask,Vvar__0__s__93932,cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNul) ) )
            | ? [Vvar__0__s__93935] :
                ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0__s__93935)
                & ? [Vvar__1__r__93936] :
                    ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__r__93936)
                    & ? [Vvar__2__x__93937] :
                        ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2__x__93937)
                        & Vvar__2__x__93937 = cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0__s__93935,Vvar__0__s__93935),Vvar__1__r__93936)
                        & cCoq_2ePArith_2eBinPos_2ePos_2ele___24a2(Vvar__1__r__93936,cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0__s__93935))
                        & Vvar__1___24Anonymous__93930 = Vvar__2__x__93937
                        & Vvar__0___24Anonymous__93929 = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2epositive,cCoq_2ePArith_2eBinPosDef_2ePos_2emask,Vvar__0__s__93935,cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__1__r__93936)) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.PArith.BinPos.Pos.mask',axiom,
    ! [VX200925] :
      ( cCoq_2ePArith_2eBinPos_2ePos_2emask___24t(VX200925)
     => ( VX200925 = cCoq_2ePArith_2eBinPos_2ePos_2eIsNul
        | ? [Vvar__0___24Anonymous__200926] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__200926)
            & VX200925 = cCoq_2ePArith_2eBinPos_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__200926) )
        | VX200925 = cCoq_2ePArith_2eBinPos_2ePos_2eIsNeg ) ) ).

fof('$_inversion_Coq.PArith.BinPosDef.Pos.mask',axiom,
    ! [VX88806] :
      ( cCoq_2ePArith_2eBinPosDef_2ePos_2emask___24t(VX88806)
     => ( VX88806 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNul
        | ? [Vvar__0___24Anonymous__88807] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__88807)
            & VX88806 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__88807) )
        | VX88806 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNeg ) ) ).

fof('$_inversion_Coq.QArith.QArith_base.Q',axiom,
    ! [VX87812] :
      ( cCoq_2eQArith_2eQArith__base_2eQ___24t(VX87812)
     => ? [Vvar__0__Qnum__87813] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__Qnum__87813)
          & ? [Vvar__1__Qden__87814] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__Qden__87814)
              & VX87812 = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__87813,Vvar__1__Qden__87814) ) ) ) ).

fof('$_inversion_Coq.Reals.RIneq.negreal',axiom,
    ! [VX85540] :
      ( cCoq_2eReals_2eRIneq_2enegreal___24t(VX85540)
     => ? [Vvar__0__neg__85541] :
          ( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0__neg__85541)
          & cCoq_2eReals_2eRdefinitions_2eRlt___24a2(Vvar__0__neg__85541,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0))
          & VX85540 = cCoq_2eReals_2eRIneq_2emknegreal___24a1(Vvar__0__neg__85541) ) ) ).

fof('$_inversion_Coq.Reals.RIneq.nonnegreal',axiom,
    ! [VX90963] :
      ( cCoq_2eReals_2eRIneq_2enonnegreal___24t(VX90963)
     => ? [Vvar__0__nonneg__90964] :
          ( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0__nonneg__90964)
          & cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),Vvar__0__nonneg__90964)
          & VX90963 = cCoq_2eReals_2eRIneq_2emknonnegreal___24a1(Vvar__0__nonneg__90964) ) ) ).

fof('$_inversion_Coq.Reals.RIneq.nonposreal',axiom,
    ! [VX85533] :
      ( cCoq_2eReals_2eRIneq_2enonposreal___24t(VX85533)
     => ? [Vvar__0__nonpos__85534] :
          ( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0__nonpos__85534)
          & cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vvar__0__nonpos__85534,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0))
          & VX85533 = cCoq_2eReals_2eRIneq_2emknonposreal___24a1(Vvar__0__nonpos__85534) ) ) ).

fof('$_inversion_Coq.Reals.RIneq.nonzeroreal',axiom,
    ! [VX87819] :
      ( cCoq_2eReals_2eRIneq_2enonzeroreal___24t(VX87819)
     => ? [Vvar__0__nonzero__87820] :
          ( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0__nonzero__87820)
          & Vvar__0__nonzero__87820 != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
          & VX87819 = cCoq_2eReals_2eRIneq_2emknonzeroreal___24a1(Vvar__0__nonzero__87820) ) ) ).

fof('$_inversion_Coq.Reals.RIneq.posreal',axiom,
    ! [VX90970] :
      ( cCoq_2eReals_2eRIneq_2eposreal___24t(VX90970)
     => ? [Vvar__0__pos__90971] :
          ( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0__pos__90971)
          & cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),Vvar__0__pos__90971)
          & VX90970 = cCoq_2eReals_2eRIneq_2emkposreal___24a1(Vvar__0__pos__90971) ) ) ).

fof('$_inversion_Coq.Reals.Rfunctions.Z_spec',axiom,
    ! [Vvar__0__x__113287,Vvar__1___24Anonymous__113288,VX113289] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__x__113287)
     => ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__1___24Anonymous__113288)
       => ( cCoq_2eReals_2eRfunctions_2eZ__spec___24t(Vvar__0__x__113287,Vvar__1___24Anonymous__113288,VX113289)
         => ( ( Vvar__0__x__113287 = cCoq_2eNumbers_2eBinNums_2eZ0
              & Vvar__1___24Anonymous__113288 = cCoq_2eNumbers_2eBinNums_2eZ0
              & VX113289 = cCoq_2eReals_2eRfunctions_2eZintNull___24a1(Vvar__0__x__113287) )
            | ? [Vvar__1__n__113293] :
                ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__n__113293)
                & Vvar__0__x__113287 = cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(Vvar__1__n__113293)
                & Vvar__1___24Anonymous__113288 = c_24__case__Coq_2eInit_2eDatatypes_2enat_24113313___24a3(Vvar__0__x__113287,Vvar__1___24Anonymous__113288,Vvar__1__n__113293)
                & VX113289 = cCoq_2eReals_2eRfunctions_2eZintPos___24a2(Vvar__0__x__113287,Vvar__1__n__113293) )
            | ? [Vvar__1__n__113298] :
                ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__n__113298)
                & Vvar__0__x__113287 = cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(Vvar__1__n__113298))
                & Vvar__1___24Anonymous__113288 = c_24__case__Coq_2eNumbers_2eBinNums_2eZ_24113330___24a3(Vvar__0__x__113287,Vvar__1___24Anonymous__113288,Vvar__1__n__113298)
                & VX113289 = cCoq_2eReals_2eRfunctions_2eZintNeg___24a2(Vvar__0__x__113287,Vvar__1__n__113298) ) ) ) ) ) ).

fof('$_inversion_Coq.Relations.Relation_Operators.Desc',axiom,
    ! [Vvar__0__A__114965,Vvar__1__leA__114966,Vvar__2___24Anonymous__114971] :
      ( cType___24t(Vvar__0__A__114965)
     => ( c_24__type__115061___24t(Vvar__0__A__114965,Vvar__1__leA__114966,Vvar__2___24Anonymous__114971,Vvar__1__leA__114966)
       => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__114965,Vvar__2___24Anonymous__114971)
         => ( cCoq_2eRelations_2eRelation__Operators_2eDesc___24a3(Vvar__0__A__114965,Vvar__1__leA__114966,Vvar__2___24Anonymous__114971)
           => ( Vvar__2___24Anonymous__114971 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__114965)
              | ? [Vvar__2__x__114985] :
                  ( t(Vvar__2__x__114985,Vvar__0__A__114965)
                  & Vvar__2___24Anonymous__114971 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__114965,Vvar__2__x__114985,cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__114965)) )
              | ? [Vvar__2__x__114992] :
                  ( t(Vvar__2__x__114992,Vvar__0__A__114965)
                  & ? [Vvar__3__y__114993] :
                      ( t(Vvar__3__y__114993,Vvar__0__A__114965)
                      & ? [Vvar__4__l__114994] :
                          ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__114965,Vvar__4__l__114994)
                          & cCoq_2eRelations_2eRelation__Operators_2eclos__refl___24a4(Vvar__0__A__114965,Vvar__1__leA__114966,Vvar__2__x__114992,Vvar__3__y__114993)
                          & cCoq_2eRelations_2eRelation__Operators_2eDesc___24a3(Vvar__0__A__114965,Vvar__1__leA__114966,cCoq_2eInit_2eDatatypes_2eapp___24a3(Vvar__0__A__114965,Vvar__4__l__114994,cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__114965,Vvar__3__y__114993,cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__114965))))
                          & Vvar__2___24Anonymous__114971 = c_24__case__Coq_2eInit_2eDatatypes_2elist_24115259___24a6(Vvar__0__A__114965,Vvar__1__leA__114966,Vvar__2___24Anonymous__114971,Vvar__2__x__114992,Vvar__3__y__114993,Vvar__4__l__114994) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Relations.Relation_Operators.swapprod',axiom,
    ! [Vvar__0__A__114872,Vvar__1__R__114873,Vvar__2___24Anonymous__114878,Vvar__3___24Anonymous__114879] :
      ( cType___24t(Vvar__0__A__114872)
     => ( c_24__type__114912___24t(Vvar__0__A__114872,Vvar__1__R__114873,Vvar__2___24Anonymous__114878,Vvar__3___24Anonymous__114879,Vvar__1__R__114873)
       => ( cCoq_2eInit_2eDatatypes_2eprod___24t(Vvar__0__A__114872,Vvar__0__A__114872,Vvar__2___24Anonymous__114878)
         => ( cCoq_2eInit_2eDatatypes_2eprod___24t(Vvar__0__A__114872,Vvar__0__A__114872,Vvar__3___24Anonymous__114879)
           => ( cCoq_2eRelations_2eRelation__Operators_2eswapprod___24a4(Vvar__0__A__114872,Vvar__1__R__114873,Vvar__2___24Anonymous__114878,Vvar__3___24Anonymous__114879)
             => ( ? [Vvar__2__x__114887] :
                    ( t(Vvar__2__x__114887,Vvar__0__A__114872)
                    & ? [Vvar__3__y__114888] :
                        ( t(Vvar__3__y__114888,Vvar__0__A__114872)
                        & ? [Vvar__4__p__114889] :
                            ( cCoq_2eInit_2eDatatypes_2eprod___24t(Vvar__0__A__114872,Vvar__0__A__114872,Vvar__4__p__114889)
                            & cCoq_2eRelations_2eRelation__Operators_2esymprod___24a6(Vvar__0__A__114872,Vvar__0__A__114872,Vvar__1__R__114873,Vvar__1__R__114873,cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__114872,Vvar__0__A__114872,Vvar__2__x__114887,Vvar__3__y__114888),Vvar__4__p__114889)
                            & Vvar__3___24Anonymous__114879 = Vvar__4__p__114889
                            & Vvar__2___24Anonymous__114878 = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__114872,Vvar__0__A__114872,Vvar__2__x__114887,Vvar__3__y__114888) ) ) )
                | ? [Vvar__2__x__114897] :
                    ( t(Vvar__2__x__114897,Vvar__0__A__114872)
                    & ? [Vvar__3__y__114898] :
                        ( t(Vvar__3__y__114898,Vvar__0__A__114872)
                        & ? [Vvar__4__p__114899] :
                            ( cCoq_2eInit_2eDatatypes_2eprod___24t(Vvar__0__A__114872,Vvar__0__A__114872,Vvar__4__p__114899)
                            & cCoq_2eRelations_2eRelation__Operators_2esymprod___24a6(Vvar__0__A__114872,Vvar__0__A__114872,Vvar__1__R__114873,Vvar__1__R__114873,cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__114872,Vvar__0__A__114872,Vvar__2__x__114897,Vvar__3__y__114898),Vvar__4__p__114899)
                            & Vvar__3___24Anonymous__114879 = Vvar__4__p__114899
                            & Vvar__2___24Anonymous__114878 = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__114872,Vvar__0__A__114872,Vvar__3__y__114898,Vvar__2__x__114897) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Relations.Relation_Operators.symprod',axiom,
    ! [Vvar__0__A__114775,Vvar__1__B__114776,Vvar__2__leA__114777,Vvar__3__leB__114782,Vvar__4___24Anonymous__114787,Vvar__5___24Anonymous__114788] :
      ( cType___24t(Vvar__0__A__114775)
     => ( cType___24t(Vvar__1__B__114776)
       => ( c_24__type__114845___24t(Vvar__0__A__114775,Vvar__1__B__114776,Vvar__2__leA__114777,Vvar__3__leB__114782,Vvar__4___24Anonymous__114787,Vvar__5___24Anonymous__114788,Vvar__2__leA__114777)
         => ( c_24__type__114870___24t(Vvar__0__A__114775,Vvar__1__B__114776,Vvar__2__leA__114777,Vvar__3__leB__114782,Vvar__4___24Anonymous__114787,Vvar__5___24Anonymous__114788,Vvar__3__leB__114782)
           => ( cCoq_2eInit_2eDatatypes_2eprod___24t(Vvar__0__A__114775,Vvar__1__B__114776,Vvar__4___24Anonymous__114787)
             => ( cCoq_2eInit_2eDatatypes_2eprod___24t(Vvar__0__A__114775,Vvar__1__B__114776,Vvar__5___24Anonymous__114788)
               => ( cCoq_2eRelations_2eRelation__Operators_2esymprod___24a6(Vvar__0__A__114775,Vvar__1__B__114776,Vvar__2__leA__114777,Vvar__3__leB__114782,Vvar__4___24Anonymous__114787,Vvar__5___24Anonymous__114788)
                 => ( ? [Vvar__4__x__114802] :
                        ( t(Vvar__4__x__114802,Vvar__0__A__114775)
                        & ? [Vvar__5__x_27__114803] :
                            ( t(Vvar__5__x_27__114803,Vvar__0__A__114775)
                            & p(happ(happ(Vvar__2__leA__114777,Vvar__4__x__114802),Vvar__5__x_27__114803))
                            & ? [Vvar__7__y__114805] :
                                ( t(Vvar__7__y__114805,Vvar__1__B__114776)
                                & Vvar__5___24Anonymous__114788 = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__114775,Vvar__1__B__114776,Vvar__5__x_27__114803,Vvar__7__y__114805)
                                & Vvar__4___24Anonymous__114787 = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__114775,Vvar__1__B__114776,Vvar__4__x__114802,Vvar__7__y__114805) ) ) )
                    | ? [Vvar__4__y__114818] :
                        ( t(Vvar__4__y__114818,Vvar__1__B__114776)
                        & ? [Vvar__5__y_27__114819] :
                            ( t(Vvar__5__y_27__114819,Vvar__1__B__114776)
                            & p(happ(happ(Vvar__3__leB__114782,Vvar__4__y__114818),Vvar__5__y_27__114819))
                            & ? [Vvar__7__x__114821] :
                                ( t(Vvar__7__x__114821,Vvar__0__A__114775)
                                & Vvar__5___24Anonymous__114788 = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__114775,Vvar__1__B__114776,Vvar__7__x__114821,Vvar__5__y_27__114819)
                                & Vvar__4___24Anonymous__114787 = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__114775,Vvar__1__B__114776,Vvar__7__x__114821,Vvar__4__y__114818) ) ) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Sorting.Sorted.HdRel',axiom,
    ! [Vvar__0__A__115699,Vvar__1__R__115700,Vvar__2__a__115705,Vvar__3___24Anonymous__115706] :
      ( cType___24t(Vvar__0__A__115699)
     => ( c_24__type__115736___24t(Vvar__0__A__115699,Vvar__1__R__115700,Vvar__2__a__115705,Vvar__3___24Anonymous__115706,Vvar__1__R__115700)
       => ( t(Vvar__2__a__115705,Vvar__0__A__115699)
         => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__115699,Vvar__3___24Anonymous__115706)
           => ( cCoq_2eSorting_2eSorted_2eHdRel___24a4(Vvar__0__A__115699,Vvar__1__R__115700,Vvar__2__a__115705,Vvar__3___24Anonymous__115706)
             => ( Vvar__3___24Anonymous__115706 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__115699)
                | ? [Vvar__3__b__115722] :
                    ( t(Vvar__3__b__115722,Vvar__0__A__115699)
                    & ? [Vvar__4__l__115723] :
                        ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__115699,Vvar__4__l__115723)
                        & p(happ(happ(Vvar__1__R__115700,Vvar__2__a__115705),Vvar__3__b__115722))
                        & Vvar__3___24Anonymous__115706 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__115699,Vvar__3__b__115722,Vvar__4__l__115723) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Sorting.Sorted.LocallySorted',axiom,
    ! [Vvar__0__A__115656,Vvar__1__R__115657,Vvar__2___24Anonymous__115662] :
      ( cType___24t(Vvar__0__A__115656)
     => ( c_24__type__115697___24t(Vvar__0__A__115656,Vvar__1__R__115657,Vvar__2___24Anonymous__115662,Vvar__1__R__115657)
       => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__115656,Vvar__2___24Anonymous__115662)
         => ( cCoq_2eSorting_2eSorted_2eLocallySorted___24a3(Vvar__0__A__115656,Vvar__1__R__115657,Vvar__2___24Anonymous__115662)
           => ( Vvar__2___24Anonymous__115662 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__115656)
              | ? [Vvar__2__a__115676] :
                  ( t(Vvar__2__a__115676,Vvar__0__A__115656)
                  & Vvar__2___24Anonymous__115662 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__115656,Vvar__2__a__115676,cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__115656)) )
              | ? [Vvar__2__a__115683] :
                  ( t(Vvar__2__a__115683,Vvar__0__A__115656)
                  & ? [Vvar__3__b__115684] :
                      ( t(Vvar__3__b__115684,Vvar__0__A__115656)
                      & ? [Vvar__4__l__115685] :
                          ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__115656,Vvar__4__l__115685)
                          & cCoq_2eSorting_2eSorted_2eLocallySorted___24a3(Vvar__0__A__115656,Vvar__1__R__115657,cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__115656,Vvar__3__b__115684,Vvar__4__l__115685))
                          & p(happ(happ(Vvar__1__R__115657,Vvar__2__a__115683),Vvar__3__b__115684))
                          & Vvar__2___24Anonymous__115662 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__115656,Vvar__2__a__115683,cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__115656,Vvar__3__b__115684,Vvar__4__l__115685)) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Sorting.Sorted.Sorted',axiom,
    ! [Vvar__0__A__115738,Vvar__1__R__115739,Vvar__2___24Anonymous__115744] :
      ( cType___24t(Vvar__0__A__115738)
     => ( c_24__type__115771___24t(Vvar__0__A__115738,Vvar__1__R__115739,Vvar__2___24Anonymous__115744,Vvar__1__R__115739)
       => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__115738,Vvar__2___24Anonymous__115744)
         => ( cCoq_2eSorting_2eSorted_2eSorted___24a3(Vvar__0__A__115738,Vvar__1__R__115739,Vvar__2___24Anonymous__115744)
           => ( Vvar__2___24Anonymous__115744 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__115738)
              | ? [Vvar__2__a__115758] :
                  ( t(Vvar__2__a__115758,Vvar__0__A__115738)
                  & ? [Vvar__3__l__115759] :
                      ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__115738,Vvar__3__l__115759)
                      & cCoq_2eSorting_2eSorted_2eSorted___24a3(Vvar__0__A__115738,Vvar__1__R__115739,Vvar__3__l__115759)
                      & cCoq_2eSorting_2eSorted_2eHdRel___24a4(Vvar__0__A__115738,Vvar__1__R__115739,Vvar__2__a__115758,Vvar__3__l__115759)
                      & Vvar__2___24Anonymous__115744 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__115738,Vvar__2__a__115758,Vvar__3__l__115759) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Strings.Ascii.ascii',axiom,
    ! [VX2562] :
      ( cCoq_2eStrings_2eAscii_2eascii___24t(VX2562)
     => ? [Vvar__0___24Anonymous__2563] :
          ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__0___24Anonymous__2563)
          & ? [Vvar__1___24Anonymous__2564] :
              ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__2564)
              & ? [Vvar__2___24Anonymous__2565] :
                  ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__2___24Anonymous__2565)
                  & ? [Vvar__3___24Anonymous__2566] :
                      ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__3___24Anonymous__2566)
                      & ? [Vvar__4___24Anonymous__2567] :
                          ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__4___24Anonymous__2567)
                          & ? [Vvar__5___24Anonymous__2568] :
                              ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__5___24Anonymous__2568)
                              & ? [Vvar__6___24Anonymous__2569] :
                                  ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__6___24Anonymous__2569)
                                  & ? [Vvar__7___24Anonymous__2570] :
                                      ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__7___24Anonymous__2570)
                                      & VX2562 = cCoq_2eStrings_2eAscii_2eAscii___24a8(Vvar__0___24Anonymous__2563,Vvar__1___24Anonymous__2564,Vvar__2___24Anonymous__2565,Vvar__3___24Anonymous__2566,Vvar__4___24Anonymous__2567,Vvar__5___24Anonymous__2568,Vvar__6___24Anonymous__2569,Vvar__7___24Anonymous__2570) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Strings.String.string',axiom,
    ! [VX582] :
      ( cCoq_2eStrings_2eString_2estring___24t(VX582)
     => ( VX582 = cCoq_2eStrings_2eString_2eEmptyString
        | ? [Vvar__0___24Anonymous__583] :
            ( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__0___24Anonymous__583)
            & ? [Vvar__1___24Anonymous__584] :
                ( cCoq_2eStrings_2eString_2estring___24t(Vvar__1___24Anonymous__584)
                & VX582 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__583,Vvar__1___24Anonymous__584) ) ) ) ) ).

fof('$_inversion_Coq.Structures.OrderedType.Compare',axiom,
    ! [Vvar__0__X__90771,Vvar__1__lt__90772,Vvar__2__eq__90777,Vvar__3__x__90782,Vvar__4__y__90783,VX90784] :
      ( cType___24t(Vvar__0__X__90771)
     => ( c_24__type__90844___24t(Vvar__0__X__90771,Vvar__1__lt__90772,Vvar__2__eq__90777,Vvar__3__x__90782,Vvar__4__y__90783,Vvar__1__lt__90772)
       => ( c_24__type__90863___24t(Vvar__0__X__90771,Vvar__1__lt__90772,Vvar__2__eq__90777,Vvar__3__x__90782,Vvar__4__y__90783,Vvar__2__eq__90777)
         => ( t(Vvar__3__x__90782,Vvar__0__X__90771)
           => ( t(Vvar__4__y__90783,Vvar__0__X__90771)
             => ( cCoq_2eStructures_2eOrderedType_2eCompare___24t(Vvar__0__X__90771,Vvar__1__lt__90772,Vvar__2__eq__90777,Vvar__3__x__90782,Vvar__4__y__90783,VX90784)
               => ( ( p(happ(happ(Vvar__1__lt__90772,Vvar__3__x__90782),Vvar__4__y__90783))
                    & VX90784 = cCoq_2eStructures_2eOrderedType_2eLT___24a5(Vvar__0__X__90771,Vvar__1__lt__90772,Vvar__2__eq__90777,Vvar__3__x__90782,Vvar__4__y__90783) )
                  | ( p(happ(happ(Vvar__2__eq__90777,Vvar__3__x__90782),Vvar__4__y__90783))
                    & VX90784 = cCoq_2eStructures_2eOrderedType_2eEQ___24a5(Vvar__0__X__90771,Vvar__1__lt__90772,Vvar__2__eq__90777,Vvar__3__x__90782,Vvar__4__y__90783) )
                  | ( p(happ(happ(Vvar__1__lt__90772,Vvar__4__y__90783),Vvar__3__x__90782))
                    & VX90784 = cCoq_2eStructures_2eOrderedType_2eGT___24a5(Vvar__0__X__90771,Vvar__1__lt__90772,Vvar__2__eq__90777,Vvar__3__x__90782,Vvar__4__y__90783) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Structures.OrderedTypeEx.String_as_OT.lts',axiom,
    ! [Vvar__0___24Anonymous__113597,Vvar__1___24Anonymous__113598] :
      ( cCoq_2eStrings_2eString_2estring___24t(Vvar__0___24Anonymous__113597)
     => ( cCoq_2eStrings_2eString_2estring___24t(Vvar__1___24Anonymous__113598)
       => ( cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2elts___24a2(Vvar__0___24Anonymous__113597,Vvar__1___24Anonymous__113598)
         => ( ? [Vvar__0__a__113600] :
                ( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__0__a__113600)
                & ? [Vvar__1__s__113601] :
                    ( cCoq_2eStrings_2eString_2estring___24t(Vvar__1__s__113601)
                    & Vvar__1___24Anonymous__113598 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0__a__113600,Vvar__1__s__113601)
                    & Vvar__0___24Anonymous__113597 = cCoq_2eStrings_2eString_2eEmptyString ) )
            | ? [Vvar__0__a__113602] :
                ( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__0__a__113602)
                & ? [Vvar__1__s1__113603] :
                    ( cCoq_2eStrings_2eString_2estring___24t(Vvar__1__s1__113603)
                    & ? [Vvar__2__s2__113604] :
                        ( cCoq_2eStrings_2eString_2estring___24t(Vvar__2__s2__113604)
                        & cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2elts___24a2(Vvar__1__s1__113603,Vvar__2__s2__113604)
                        & Vvar__1___24Anonymous__113598 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0__a__113602,Vvar__2__s2__113604)
                        & Vvar__0___24Anonymous__113597 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0__a__113602,Vvar__1__s1__113603) ) ) )
            | ? [Vvar__0__a__113606] :
                ( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__0__a__113606)
                & ? [Vvar__1__b__113607] :
                    ( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__1__b__113607)
                    & ? [Vvar__2__s1__113608] :
                        ( cCoq_2eStrings_2eString_2estring___24t(Vvar__2__s1__113608)
                        & ? [Vvar__3__s2__113609] :
                            ( cCoq_2eStrings_2eString_2estring___24t(Vvar__3__s2__113609)
                            & p(cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eStrings_2eAscii_2enat__of__ascii___24a1(Vvar__0__a__113606),cCoq_2eStrings_2eAscii_2enat__of__ascii___24a1(Vvar__1__b__113607)))
                            & Vvar__1___24Anonymous__113598 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__1__b__113607,Vvar__3__s2__113609)
                            & Vvar__0___24Anonymous__113597 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0__a__113606,Vvar__2__s1__113608) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Structures.OrdersTac.ord',axiom,
    ! [VX87811] :
      ( cCoq_2eStructures_2eOrdersTac_2eord___24t(VX87811)
     => ( VX87811 = cCoq_2eStructures_2eOrdersTac_2eOEQ
        | VX87811 = cCoq_2eStructures_2eOrdersTac_2eOLT
        | VX87811 = cCoq_2eStructures_2eOrdersTac_2eOLE ) ) ).

fof('$_inversion_Coq.Vectors.Fin.t',axiom,
    ! [Vvar__0___24Anonymous__8,VX9] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__8)
     => ( cCoq_2eVectors_2eFin_2et___24t(Vvar__0___24Anonymous__8,VX9)
       => ( ? [Vvar__0__n__10] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__10)
              & Vvar__0___24Anonymous__8 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0__n__10)
              & VX9 = cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__10) )
          | ? [Vvar__0__n__11] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__11)
              & ? [Vvar__1___24Anonymous__12] :
                  ( cCoq_2eVectors_2eFin_2et___24t(Vvar__0__n__11,Vvar__1___24Anonymous__12)
                  & Vvar__0___24Anonymous__8 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0__n__11)
                  & VX9 = cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__11,Vvar__1___24Anonymous__12) ) ) ) ) ) ).

fof('$_inversion_Coq.Vectors.Vector.t',axiom,
    ! [Vvar__0__A__200636,Vvar__1___24Anonymous__200637,VX200638] :
      ( cType___24t(Vvar__0__A__200636)
     => ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__200637)
       => ( cCoq_2eVectors_2eVector_2et___24t(Vvar__0__A__200636,Vvar__1___24Anonymous__200637,VX200638)
         => ( ( Vvar__1___24Anonymous__200637 = cCoq_2eInit_2eDatatypes_2eO
              & VX200638 = cCoq_2eVectors_2eVector_2enil___24a1(Vvar__0__A__200636) )
            | ? [Vvar__1__h__200641] :
                ( t(Vvar__1__h__200641,Vvar__0__A__200636)
                & ? [Vvar__2__n__200642] :
                    ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__200642)
                    & ? [Vvar__3___24Anonymous__200643] :
                        ( cCoq_2eVectors_2eVector_2et___24t(Vvar__0__A__200636,Vvar__2__n__200642,Vvar__3___24Anonymous__200643)
                        & Vvar__1___24Anonymous__200637 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__n__200642)
                        & VX200638 = cCoq_2eVectors_2eVector_2econs___24a4(Vvar__0__A__200636,Vvar__1__h__200641,Vvar__2__n__200642,Vvar__3___24Anonymous__200643) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Vectors.VectorDef.t',axiom,
    ! [Vvar__0__A__2062,Vvar__1___24Anonymous__2063,VX2064] :
      ( cType___24t(Vvar__0__A__2062)
     => ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__2063)
       => ( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__2062,Vvar__1___24Anonymous__2063,VX2064)
         => ( ( Vvar__1___24Anonymous__2063 = cCoq_2eInit_2eDatatypes_2eO
              & VX2064 = cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__2062) )
            | ? [Vvar__1__h__2067] :
                ( t(Vvar__1__h__2067,Vvar__0__A__2062)
                & ? [Vvar__2__n__2068] :
                    ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__2068)
                    & ? [Vvar__3___24Anonymous__2069] :
                        ( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__2062,Vvar__2__n__2068,Vvar__3___24Anonymous__2069)
                        & Vvar__1___24Anonymous__2063 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__n__2068)
                        & VX2064 = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__2062,Vvar__1__h__2067,Vvar__2__n__2068,Vvar__3___24Anonymous__2069) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.ZArith.Znumtheory.Bezout',axiom,
    ! [Vvar__0__a__113528,Vvar__1__b__113529,Vvar__2__d__113530] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__a__113528)
     => ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__1__b__113529)
       => ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2__d__113530)
         => ( cCoq_2eZArith_2eZnumtheory_2eBezout___24a3(Vvar__0__a__113528,Vvar__1__b__113529,Vvar__2__d__113530)
           => ? [Vvar__3__u__113535] :
                ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3__u__113535)
                & ? [Vvar__4__v__113536] :
                    ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__4__v__113536)
                    & cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__3__u__113535,Vvar__0__a__113528),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__4__v__113536,Vvar__1__b__113529)) = Vvar__2__d__113530
                    & p(c_24True) ) ) ) ) ) ) ).

fof('$_inversion_Coq.ZArith.Znumtheory.Euclid',axiom,
    ! [Vvar__0__a__113503,Vvar__1__b__113504,VX113505] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__a__113503)
     => ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__1__b__113504)
       => ( cCoq_2eZArith_2eZnumtheory_2eEuclid___24t(Vvar__0__a__113503,Vvar__1__b__113504,VX113505)
         => ? [Vvar__2__u__113508] :
              ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2__u__113508)
              & ? [Vvar__3__v__113509] :
                  ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3__v__113509)
                  & ? [Vvar__4__d__113510] :
                      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__4__d__113510)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__2__u__113508,Vvar__0__a__113503),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__3__v__113509,Vvar__1__b__113504)) = Vvar__4__d__113510
                      & cCoq_2eZArith_2eZnumtheory_2eZis__gcd___24a3(Vvar__0__a__113503,Vvar__1__b__113504,Vvar__4__d__113510)
                      & VX113505 = cCoq_2eZArith_2eZnumtheory_2eEuclid__intro___24a5(Vvar__0__a__113503,Vvar__1__b__113504,Vvar__2__u__113508,Vvar__3__v__113509,Vvar__4__d__113510) ) ) ) ) ) ) ).

fof('$_inversion_Coq.ZArith.Znumtheory.Zis_gcd',axiom,
    ! [Vvar__0__a__113475,Vvar__1__b__113476,Vvar__2__g__113477] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__a__113475)
     => ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__1__b__113476)
       => ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2__g__113477)
         => ( cCoq_2eZArith_2eZnumtheory_2eZis__gcd___24a3(Vvar__0__a__113475,Vvar__1__b__113476,Vvar__2__g__113477)
           => ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__2__g__113477,Vvar__0__a__113475)
              & cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__2__g__113477,Vvar__1__b__113476)
              & ! [Vvar__var__var__var__var__5__x__113485__113488__113491__113494__113497] :
                  ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__var__var__var__var__5__x__113485__113488__113491__113494__113497)
                 => ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__var__var__var__var__5__x__113485__113488__113491__113494__113497,Vvar__0__a__113475)
                   => ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__var__var__var__var__5__x__113485__113488__113491__113494__113497,Vvar__1__b__113476)
                     => cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__var__var__var__var__5__x__113485__113488__113491__113494__113497,Vvar__2__g__113477) ) ) )
              & p(c_24True) ) ) ) ) ) ).

fof('$_inversion_Coq.ZArith.Znumtheory.prime',axiom,
    ! [Vvar__0__p__108718] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__p__108718)
     => ( cCoq_2eZArith_2eZnumtheory_2eprime___24a1(Vvar__0__p__108718)
       => ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),Vvar__0__p__108718))
          & ! [Vvar__var__var__2__n__108723__108725__108727] :
              ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__var__var__2__n__108723__108725__108727)
             => ( ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),Vvar__var__var__2__n__108723__108725__108727))
                  & p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(Vvar__var__var__2__n__108723__108725__108727,Vvar__0__p__108718)) )
               => cCoq_2eZArith_2eZnumtheory_2erel__prime___24a2(Vvar__var__var__2__n__108723__108725__108727,Vvar__0__p__108718) ) )
          & p(c_24True) ) ) ) ).

fof('$_inversion_Coq.ZArith.Zpower.Zdiv_rest_proofs',axiom,
    ! [Vvar__0__x__113538,Vvar__1__p__113539,VX113540] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__x__113538)
     => ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__p__113539)
       => ( cCoq_2eZArith_2eZpower_2eZdiv__rest__proofs___24t(Vvar__0__x__113538,Vvar__1__p__113539,VX113540)
         => ? [Vvar__2__q__113543] :
              ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2__q__113543)
              & ? [Vvar__3__r__113544] :
                  ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3__r__113544)
                  & Vvar__0__x__113538 = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__2__q__113543,cCoq_2eZArith_2eZpower_2etwo__power__pos___24a1(Vvar__1__p__113539)),Vvar__3__r__113544)
                  & p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,Vvar__3__r__113544))
                  & p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(Vvar__3__r__113544,cCoq_2eZArith_2eZpower_2etwo__power__pos___24a1(Vvar__1__p__113539)))
                  & VX113540 = cCoq_2eZArith_2eZpower_2eZdiv__rest__proof___24a4(Vvar__0__x__113538,Vvar__1__p__113539,Vvar__2__q__113543,Vvar__3__r__113544) ) ) ) ) ) ).

fof('$_inversion_Coq.micromega.DeclConstant.DeclaredConstant',axiom,
    ! [Vvar__0__T__83613,Vvar__1__F__83614] :
      ( cType___24t(Vvar__0__T__83613)
     => ( t(Vvar__1__F__83614,Vvar__0__T__83613)
       => ( cCoq_2emicromega_2eDeclConstant_2eDeclaredConstant___24a2(Vvar__0__T__83613,Vvar__1__F__83614)
         => p(c_24True) ) ) ) ).

fof('$_inversion_Coq.micromega.DeclConstant.GT',axiom,
    ! [Vvar__0__T__85137,Vvar__1__F__85138] :
      ( cType___24t(Vvar__0__T__85137)
     => ( t(Vvar__1__F__85138,Vvar__0__T__85137)
       => ( cCoq_2emicromega_2eDeclConstant_2eGT___24a2(Vvar__0__T__85137,Vvar__1__F__85138)
         => p(c_24True) ) ) ) ).

fof('$_inversion_Coq.micromega.EnvRing.Mon',axiom,
    ! [VX85142] :
      ( cCoq_2emicromega_2eEnvRing_2eMon___24t(VX85142)
     => ( VX85142 = cCoq_2emicromega_2eEnvRing_2emon0
        | ? [Vvar__0___24Anonymous__85143] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__85143)
            & ? [Vvar__1___24Anonymous__85144] :
                ( cCoq_2emicromega_2eEnvRing_2eMon___24t(Vvar__1___24Anonymous__85144)
                & VX85142 = cCoq_2emicromega_2eEnvRing_2ezmon___24a2(Vvar__0___24Anonymous__85143,Vvar__1___24Anonymous__85144) ) )
        | ? [Vvar__0___24Anonymous__85145] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__85145)
            & ? [Vvar__1___24Anonymous__85146] :
                ( cCoq_2emicromega_2eEnvRing_2eMon___24t(Vvar__1___24Anonymous__85146)
                & VX85142 = cCoq_2emicromega_2eEnvRing_2evmon___24a2(Vvar__0___24Anonymous__85145,Vvar__1___24Anonymous__85146) ) ) ) ) ).

fof('$_inversion_Coq.micromega.EnvRing.PExpr',axiom,
    ! [Vvar__0__C__86462,VX86463] :
      ( cType___24t(Vvar__0__C__86462)
     => ( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__86462,VX86463)
       => ( ? [Vvar__1___24Anonymous__86465] :
              ( t(Vvar__1___24Anonymous__86465,Vvar__0__C__86462)
              & VX86463 = cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__86462,Vvar__1___24Anonymous__86465) )
          | ? [Vvar__1___24Anonymous__86467] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__86467)
              & VX86463 = cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__86462,Vvar__1___24Anonymous__86467) )
          | ? [Vvar__1___24Anonymous__86469] :
              ( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__86462,Vvar__1___24Anonymous__86469)
              & ? [Vvar__2___24Anonymous__86470] :
                  ( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__86462,Vvar__2___24Anonymous__86470)
                  & VX86463 = cCoq_2emicromega_2eEnvRing_2ePEadd___24a3(Vvar__0__C__86462,Vvar__1___24Anonymous__86469,Vvar__2___24Anonymous__86470) ) )
          | ? [Vvar__1___24Anonymous__86472] :
              ( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__86462,Vvar__1___24Anonymous__86472)
              & ? [Vvar__2___24Anonymous__86473] :
                  ( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__86462,Vvar__2___24Anonymous__86473)
                  & VX86463 = cCoq_2emicromega_2eEnvRing_2ePEsub___24a3(Vvar__0__C__86462,Vvar__1___24Anonymous__86472,Vvar__2___24Anonymous__86473) ) )
          | ? [Vvar__1___24Anonymous__86475] :
              ( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__86462,Vvar__1___24Anonymous__86475)
              & ? [Vvar__2___24Anonymous__86476] :
                  ( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__86462,Vvar__2___24Anonymous__86476)
                  & VX86463 = cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(Vvar__0__C__86462,Vvar__1___24Anonymous__86475,Vvar__2___24Anonymous__86476) ) )
          | ? [Vvar__1___24Anonymous__86478] :
              ( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__86462,Vvar__1___24Anonymous__86478)
              & VX86463 = cCoq_2emicromega_2eEnvRing_2ePEopp___24a2(Vvar__0__C__86462,Vvar__1___24Anonymous__86478) )
          | ? [Vvar__1___24Anonymous__86480] :
              ( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__86462,Vvar__1___24Anonymous__86480)
              & ? [Vvar__2___24Anonymous__86481] :
                  ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__86481)
                  & VX86463 = cCoq_2emicromega_2eEnvRing_2ePEpow___24a3(Vvar__0__C__86462,Vvar__1___24Anonymous__86480,Vvar__2___24Anonymous__86481) ) ) ) ) ) ).

fof('$_inversion_Coq.micromega.EnvRing.Pol',axiom,
    ! [Vvar__0__C__88888,VX88889] :
      ( cType___24t(Vvar__0__C__88888)
     => ( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__88888,VX88889)
       => ( ? [Vvar__1___24Anonymous__88891] :
              ( t(Vvar__1___24Anonymous__88891,Vvar__0__C__88888)
              & VX88889 = cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__88888,Vvar__1___24Anonymous__88891) )
          | ? [Vvar__1___24Anonymous__88893] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__88893)
              & ? [Vvar__2___24Anonymous__88894] :
                  ( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__88888,Vvar__2___24Anonymous__88894)
                  & VX88889 = cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__88888,Vvar__1___24Anonymous__88893,Vvar__2___24Anonymous__88894) ) )
          | ? [Vvar__1___24Anonymous__88896] :
              ( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__88888,Vvar__1___24Anonymous__88896)
              & ? [Vvar__2___24Anonymous__88897] :
                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__88897)
                  & ? [Vvar__3___24Anonymous__88898] :
                      ( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__88888,Vvar__3___24Anonymous__88898)
                      & VX88889 = cCoq_2emicromega_2eEnvRing_2ePX___24a4(Vvar__0__C__88888,Vvar__1___24Anonymous__88896,Vvar__2___24Anonymous__88897,Vvar__3___24Anonymous__88898) ) ) ) ) ) ) ).

fof('$_inversion_Coq.micromega.OrderedRing.SOR',axiom,
    ! [Vvar__0__R__89693,Vvar__1__rO__89694,Vvar__2__rI__89695,Vvar__3__rplus__89696,Vvar__4__rtimes__89701,Vvar__5__rminus__89706,Vvar__6__ropp__89711,Vvar__7__req__89714,Vvar__8__rle__89719,Vvar__9__rlt__89724] :
      ( cType___24t(Vvar__0__R__89693)
     => ( t(Vvar__1__rO__89694,Vvar__0__R__89693)
       => ( t(Vvar__2__rI__89695,Vvar__0__R__89693)
         => ( c_24__type__90125___24t(Vvar__0__R__89693,Vvar__1__rO__89694,Vvar__2__rI__89695,Vvar__3__rplus__89696,Vvar__4__rtimes__89701,Vvar__5__rminus__89706,Vvar__6__ropp__89711,Vvar__7__req__89714,Vvar__8__rle__89719,Vvar__9__rlt__89724,Vvar__3__rplus__89696)
           => ( c_24__type__90226___24t(Vvar__0__R__89693,Vvar__1__rO__89694,Vvar__2__rI__89695,Vvar__3__rplus__89696,Vvar__4__rtimes__89701,Vvar__5__rminus__89706,Vvar__6__ropp__89711,Vvar__7__req__89714,Vvar__8__rle__89719,Vvar__9__rlt__89724,Vvar__4__rtimes__89701)
             => ( c_24__type__90327___24t(Vvar__0__R__89693,Vvar__1__rO__89694,Vvar__2__rI__89695,Vvar__3__rplus__89696,Vvar__4__rtimes__89701,Vvar__5__rminus__89706,Vvar__6__ropp__89711,Vvar__7__req__89714,Vvar__8__rle__89719,Vvar__9__rlt__89724,Vvar__5__rminus__89706)
               => ( c_24__type__90417___24t(Vvar__0__R__89693,Vvar__1__rO__89694,Vvar__2__rI__89695,Vvar__3__rplus__89696,Vvar__4__rtimes__89701,Vvar__5__rminus__89706,Vvar__6__ropp__89711,Vvar__7__req__89714,Vvar__8__rle__89719,Vvar__9__rlt__89724,Vvar__6__ropp__89711)
                 => ( c_24__type__90518___24t(Vvar__0__R__89693,Vvar__1__rO__89694,Vvar__2__rI__89695,Vvar__3__rplus__89696,Vvar__4__rtimes__89701,Vvar__5__rminus__89706,Vvar__6__ropp__89711,Vvar__7__req__89714,Vvar__8__rle__89719,Vvar__9__rlt__89724,Vvar__7__req__89714)
                   => ( c_24__type__90619___24t(Vvar__0__R__89693,Vvar__1__rO__89694,Vvar__2__rI__89695,Vvar__3__rplus__89696,Vvar__4__rtimes__89701,Vvar__5__rminus__89706,Vvar__6__ropp__89711,Vvar__7__req__89714,Vvar__8__rle__89719,Vvar__9__rlt__89724,Vvar__8__rle__89719)
                     => ( c_24__type__90720___24t(Vvar__0__R__89693,Vvar__1__rO__89694,Vvar__2__rI__89695,Vvar__3__rplus__89696,Vvar__4__rtimes__89701,Vvar__5__rminus__89706,Vvar__6__ropp__89711,Vvar__7__req__89714,Vvar__8__rle__89719,Vvar__9__rlt__89724,Vvar__9__rlt__89724)
                       => ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(Vvar__0__R__89693,Vvar__1__rO__89694,Vvar__2__rI__89695,Vvar__3__rplus__89696,Vvar__4__rtimes__89701,Vvar__5__rminus__89706,Vvar__6__ropp__89711,Vvar__7__req__89714,Vvar__8__rle__89719,Vvar__9__rlt__89724)
                         => ( cCoq_2eSetoids_2eSetoid_2eSetoid__Theory___24a2(Vvar__0__R__89693,Vvar__7__req__89714)
                            & ! [Vvar__var__var__var__var__11__x1__89768__89774__89879__89885__89891] :
                                ( t(Vvar__var__var__var__var__11__x1__89768__89774__89879__89885__89891,Vvar__0__R__89693)
                               => ! [Vvar__var__var__var__var__12__x2__89769__89775__89880__89886__89892] :
                                    ( t(Vvar__var__var__var__var__12__x2__89769__89775__89880__89886__89892,Vvar__0__R__89693)
                                   => ( p(happ(happ(Vvar__7__req__89714,Vvar__var__var__var__var__11__x1__89768__89774__89879__89885__89891),Vvar__var__var__var__var__12__x2__89769__89775__89880__89886__89892))
                                     => ! [Vvar__var__var__var__var__14__y1__89770__89776__89881__89887__89893] :
                                          ( t(Vvar__var__var__var__var__14__y1__89770__89776__89881__89887__89893,Vvar__0__R__89693)
                                         => ! [Vvar__var__var__var__var__15__y2__89771__89777__89882__89888__89894] :
                                              ( t(Vvar__var__var__var__var__15__y2__89771__89777__89882__89888__89894,Vvar__0__R__89693)
                                             => ( p(happ(happ(Vvar__7__req__89714,Vvar__var__var__var__var__14__y1__89770__89776__89881__89887__89893),Vvar__var__var__var__var__15__y2__89771__89777__89882__89888__89894))
                                               => p(happ(happ(Vvar__7__req__89714,happ(happ(Vvar__3__rplus__89696,Vvar__var__var__var__var__11__x1__89768__89774__89879__89885__89891),Vvar__var__var__var__var__14__y1__89770__89776__89881__89887__89893)),happ(happ(Vvar__3__rplus__89696,Vvar__var__var__var__var__12__x2__89769__89775__89880__89886__89892),Vvar__var__var__var__var__15__y2__89771__89777__89882__89888__89894))) ) ) ) ) ) )
                            & ! [Vvar__var__var__var__var__12__x1__89781__89787__89897__89903__89909] :
                                ( t(Vvar__var__var__var__var__12__x1__89781__89787__89897__89903__89909,Vvar__0__R__89693)
                               => ! [Vvar__var__var__var__var__13__x2__89782__89788__89898__89904__89910] :
                                    ( t(Vvar__var__var__var__var__13__x2__89782__89788__89898__89904__89910,Vvar__0__R__89693)
                                   => ( p(happ(happ(Vvar__7__req__89714,Vvar__var__var__var__var__12__x1__89781__89787__89897__89903__89909),Vvar__var__var__var__var__13__x2__89782__89788__89898__89904__89910))
                                     => ! [Vvar__var__var__var__var__15__y1__89783__89789__89899__89905__89911] :
                                          ( t(Vvar__var__var__var__var__15__y1__89783__89789__89899__89905__89911,Vvar__0__R__89693)
                                         => ! [Vvar__var__var__var__var__16__y2__89784__89790__89900__89906__89912] :
                                              ( t(Vvar__var__var__var__var__16__y2__89784__89790__89900__89906__89912,Vvar__0__R__89693)
                                             => ( p(happ(happ(Vvar__7__req__89714,Vvar__var__var__var__var__15__y1__89783__89789__89899__89905__89911),Vvar__var__var__var__var__16__y2__89784__89790__89900__89906__89912))
                                               => p(happ(happ(Vvar__7__req__89714,happ(happ(Vvar__4__rtimes__89701,Vvar__var__var__var__var__12__x1__89781__89787__89897__89903__89909),Vvar__var__var__var__var__15__y1__89783__89789__89899__89905__89911)),happ(happ(Vvar__4__rtimes__89701,Vvar__var__var__var__var__13__x2__89782__89788__89898__89904__89910),Vvar__var__var__var__var__16__y2__89784__89790__89900__89906__89912))) ) ) ) ) ) )
                            & ! [Vvar__var__var__var__var__13__x1__89794__89797__89915__89918__89921] :
                                ( t(Vvar__var__var__var__var__13__x1__89794__89797__89915__89918__89921,Vvar__0__R__89693)
                               => ! [Vvar__var__var__var__var__14__x2__89795__89798__89916__89919__89922] :
                                    ( t(Vvar__var__var__var__var__14__x2__89795__89798__89916__89919__89922,Vvar__0__R__89693)
                                   => ( p(happ(happ(Vvar__7__req__89714,Vvar__var__var__var__var__13__x1__89794__89797__89915__89918__89921),Vvar__var__var__var__var__14__x2__89795__89798__89916__89919__89922))
                                     => p(happ(happ(Vvar__7__req__89714,happ(Vvar__6__ropp__89711,Vvar__var__var__var__var__13__x1__89794__89797__89915__89918__89921)),happ(Vvar__6__ropp__89711,Vvar__var__var__var__var__14__x2__89795__89798__89916__89919__89922))) ) ) )
                            & ! [Vvar__var__var__var__var__14__x1__89801__89807__89924__89930__89936] :
                                ( t(Vvar__var__var__var__var__14__x1__89801__89807__89924__89930__89936,Vvar__0__R__89693)
                               => ! [Vvar__var__var__var__var__15__x2__89802__89808__89925__89931__89937] :
                                    ( t(Vvar__var__var__var__var__15__x2__89802__89808__89925__89931__89937,Vvar__0__R__89693)
                                   => ( p(happ(happ(Vvar__7__req__89714,Vvar__var__var__var__var__14__x1__89801__89807__89924__89930__89936),Vvar__var__var__var__var__15__x2__89802__89808__89925__89931__89937))
                                     => ! [Vvar__var__var__var__var__17__y1__89803__89809__89926__89932__89938] :
                                          ( t(Vvar__var__var__var__var__17__y1__89803__89809__89926__89932__89938,Vvar__0__R__89693)
                                         => ! [Vvar__var__var__var__var__18__y2__89804__89810__89927__89933__89939] :
                                              ( t(Vvar__var__var__var__var__18__y2__89804__89810__89927__89933__89939,Vvar__0__R__89693)
                                             => ( p(happ(happ(Vvar__7__req__89714,Vvar__var__var__var__var__17__y1__89803__89809__89926__89932__89938),Vvar__var__var__var__var__18__y2__89804__89810__89927__89933__89939))
                                               => ( p(happ(happ(Vvar__8__rle__89719,Vvar__var__var__var__var__14__x1__89801__89807__89924__89930__89936),Vvar__var__var__var__var__17__y1__89803__89809__89926__89932__89938))
                                                <=> p(happ(happ(Vvar__8__rle__89719,Vvar__var__var__var__var__15__x2__89802__89808__89925__89931__89937),Vvar__var__var__var__var__18__y2__89804__89810__89927__89933__89939)) ) ) ) ) ) ) )
                            & ! [Vvar__var__var__var__var__15__x1__89814__89820__89942__89948__89954] :
                                ( t(Vvar__var__var__var__var__15__x1__89814__89820__89942__89948__89954,Vvar__0__R__89693)
                               => ! [Vvar__var__var__var__var__16__x2__89815__89821__89943__89949__89955] :
                                    ( t(Vvar__var__var__var__var__16__x2__89815__89821__89943__89949__89955,Vvar__0__R__89693)
                                   => ( p(happ(happ(Vvar__7__req__89714,Vvar__var__var__var__var__15__x1__89814__89820__89942__89948__89954),Vvar__var__var__var__var__16__x2__89815__89821__89943__89949__89955))
                                     => ! [Vvar__var__var__var__var__18__y1__89816__89822__89944__89950__89956] :
                                          ( t(Vvar__var__var__var__var__18__y1__89816__89822__89944__89950__89956,Vvar__0__R__89693)
                                         => ! [Vvar__var__var__var__var__19__y2__89817__89823__89945__89951__89957] :
                                              ( t(Vvar__var__var__var__var__19__y2__89817__89823__89945__89951__89957,Vvar__0__R__89693)
                                             => ( p(happ(happ(Vvar__7__req__89714,Vvar__var__var__var__var__18__y1__89816__89822__89944__89950__89956),Vvar__var__var__var__var__19__y2__89817__89823__89945__89951__89957))
                                               => ( p(happ(happ(Vvar__9__rlt__89724,Vvar__var__var__var__var__15__x1__89814__89820__89942__89948__89954),Vvar__var__var__var__var__18__y1__89816__89822__89944__89950__89956))
                                                <=> p(happ(happ(Vvar__9__rlt__89724,Vvar__var__var__var__var__16__x2__89815__89821__89943__89949__89955),Vvar__var__var__var__var__19__y2__89817__89823__89945__89951__89957)) ) ) ) ) ) ) )
                            & cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(Vvar__0__R__89693,Vvar__1__rO__89694,Vvar__2__rI__89695,Vvar__3__rplus__89696,Vvar__4__rtimes__89701,Vvar__5__rminus__89706,Vvar__6__ropp__89711,Vvar__7__req__89714)
                            & ! [Vvar__var__var__var__17__n__89828__89829__89960__89961] :
                                ( t(Vvar__var__var__var__17__n__89828__89829__89960__89961,Vvar__0__R__89693)
                               => p(happ(happ(Vvar__8__rle__89719,Vvar__var__var__var__17__n__89828__89829__89960__89961),Vvar__var__var__var__17__n__89828__89829__89960__89961)) )
                            & ! [Vvar__var__var__var__var__18__n__89831__89835__89962__89966__89970] :
                                ( t(Vvar__var__var__var__var__18__n__89831__89835__89962__89966__89970,Vvar__0__R__89693)
                               => ! [Vvar__var__var__var__var__19__m__89832__89836__89963__89967__89971] :
                                    ( t(Vvar__var__var__var__var__19__m__89832__89836__89963__89967__89971,Vvar__0__R__89693)
                                   => ( p(happ(happ(Vvar__8__rle__89719,Vvar__var__var__var__var__18__n__89831__89835__89962__89966__89970),Vvar__var__var__var__var__19__m__89832__89836__89963__89967__89971))
                                     => ( p(happ(happ(Vvar__8__rle__89719,Vvar__var__var__var__var__19__m__89832__89836__89963__89967__89971),Vvar__var__var__var__var__18__n__89831__89835__89962__89966__89970))
                                       => p(happ(happ(Vvar__7__req__89714,Vvar__var__var__var__var__18__n__89831__89835__89962__89966__89970),Vvar__var__var__var__var__19__m__89832__89836__89963__89967__89971)) ) ) ) )
                            & ! [Vvar__var__var__var__19__n__89840__89845__89974__89979] :
                                ( t(Vvar__var__var__var__19__n__89840__89845__89974__89979,Vvar__0__R__89693)
                               => ! [Vvar__var__var__var__20__m__89841__89846__89975__89980] :
                                    ( t(Vvar__var__var__var__20__m__89841__89846__89975__89980,Vvar__0__R__89693)
                                   => ! [Vvar__var__var__var__21__p__89842__89847__89976__89981] :
                                        ( t(Vvar__var__var__var__21__p__89842__89847__89976__89981,Vvar__0__R__89693)
                                       => ( p(happ(happ(Vvar__8__rle__89719,Vvar__var__var__var__19__n__89840__89845__89974__89979),Vvar__var__var__var__20__m__89841__89846__89975__89980))
                                         => ( p(happ(happ(Vvar__8__rle__89719,Vvar__var__var__var__20__m__89841__89846__89975__89980),Vvar__var__var__var__21__p__89842__89847__89976__89981))
                                           => p(happ(happ(Vvar__8__rle__89719,Vvar__var__var__var__19__n__89840__89845__89974__89979),Vvar__var__var__var__21__p__89842__89847__89976__89981)) ) ) ) ) )
                            & ! [Vvar__var__var__var__var__var__20__n__89851__89853__89984__89986__89988__89990] :
                                ( t(Vvar__var__var__var__var__var__20__n__89851__89853__89984__89986__89988__89990,Vvar__0__R__89693)
                               => ! [Vvar__var__var__var__var__var__21__m__89852__89854__89985__89987__89989__89991] :
                                    ( t(Vvar__var__var__var__var__var__21__m__89852__89854__89985__89987__89989__89991,Vvar__0__R__89693)
                                   => ( p(happ(happ(Vvar__9__rlt__89724,Vvar__var__var__var__var__var__20__n__89851__89853__89984__89986__89988__89990),Vvar__var__var__var__var__var__21__m__89852__89854__89985__89987__89989__89991))
                                    <=> ( p(happ(happ(Vvar__8__rle__89719,Vvar__var__var__var__var__var__20__n__89851__89853__89984__89986__89988__89990),Vvar__var__var__var__var__var__21__m__89852__89854__89985__89987__89989__89991))
                                        & ~ p(happ(happ(Vvar__7__req__89714,Vvar__var__var__var__var__var__20__n__89851__89853__89984__89986__89988__89990),Vvar__var__var__var__var__var__21__m__89852__89854__89985__89987__89989__89991)) ) ) ) )
                            & ! [Vvar__var__var__var__var__21__n__89856__89858__89992__89994__89996] :
                                ( t(Vvar__var__var__var__var__21__n__89856__89858__89992__89994__89996,Vvar__0__R__89693)
                               => ! [Vvar__var__var__var__var__22__m__89857__89859__89993__89995__89997] :
                                    ( t(Vvar__var__var__var__var__22__m__89857__89859__89993__89995__89997,Vvar__0__R__89693)
                                   => ( p(happ(happ(Vvar__9__rlt__89724,Vvar__var__var__var__var__21__n__89856__89858__89992__89994__89996),Vvar__var__var__var__var__22__m__89857__89859__89993__89995__89997))
                                      | p(happ(happ(Vvar__7__req__89714,Vvar__var__var__var__var__21__n__89856__89858__89992__89994__89996),Vvar__var__var__var__var__22__m__89857__89859__89993__89995__89997))
                                      | p(happ(happ(Vvar__9__rlt__89724,Vvar__var__var__var__var__22__m__89857__89859__89993__89995__89997),Vvar__var__var__var__var__21__n__89856__89858__89992__89994__89996)) ) ) )
                            & ! [Vvar__var__var__var__var__22__n__89861__89865__89998__90002__90006] :
                                ( t(Vvar__var__var__var__var__22__n__89861__89865__89998__90002__90006,Vvar__0__R__89693)
                               => ! [Vvar__var__var__var__var__23__m__89862__89866__89999__90003__90007] :
                                    ( t(Vvar__var__var__var__var__23__m__89862__89866__89999__90003__90007,Vvar__0__R__89693)
                                   => ! [Vvar__var__var__var__var__24__p__89863__89867__90000__90004__90008] :
                                        ( t(Vvar__var__var__var__var__24__p__89863__89867__90000__90004__90008,Vvar__0__R__89693)
                                       => ( p(happ(happ(Vvar__8__rle__89719,Vvar__var__var__var__var__22__n__89861__89865__89998__90002__90006),Vvar__var__var__var__var__23__m__89862__89866__89999__90003__90007))
                                         => p(happ(happ(Vvar__8__rle__89719,happ(happ(Vvar__3__rplus__89696,Vvar__var__var__var__var__24__p__89863__89867__90000__90004__90008),Vvar__var__var__var__var__22__n__89861__89865__89998__90002__90006)),happ(happ(Vvar__3__rplus__89696,Vvar__var__var__var__var__24__p__89863__89867__90000__90004__90008),Vvar__var__var__var__var__23__m__89862__89866__89999__90003__90007))) ) ) ) )
                            & ! [Vvar__var__var__var__var__var__23__n__89870__89874__90010__90014__90018__90022] :
                                ( t(Vvar__var__var__var__var__var__23__n__89870__89874__90010__90014__90018__90022,Vvar__0__R__89693)
                               => ! [Vvar__var__var__var__var__var__24__m__89871__89875__90011__90015__90019__90023] :
                                    ( t(Vvar__var__var__var__var__var__24__m__89871__89875__90011__90015__90019__90023,Vvar__0__R__89693)
                                   => ( p(happ(happ(Vvar__9__rlt__89724,Vvar__1__rO__89694),Vvar__var__var__var__var__var__23__n__89870__89874__90010__90014__90018__90022))
                                     => ( p(happ(happ(Vvar__9__rlt__89724,Vvar__1__rO__89694),Vvar__var__var__var__var__var__24__m__89871__89875__90011__90015__90019__90023))
                                       => p(happ(happ(Vvar__9__rlt__89724,Vvar__1__rO__89694),happ(happ(Vvar__4__rtimes__89701,Vvar__var__var__var__var__var__23__n__89870__89874__90010__90014__90018__90022),Vvar__var__var__var__var__var__24__m__89871__89875__90011__90015__90019__90023))) ) ) ) )
                            & ~ p(happ(happ(Vvar__7__req__89714,Vvar__1__rO__89694),Vvar__2__rI__89695))
                            & p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.micromega.RMicromega.Rcst',axiom,
    ! [VX87826] :
      ( cCoq_2emicromega_2eRMicromega_2eRcst___24t(VX87826)
     => ( VX87826 = cCoq_2emicromega_2eRMicromega_2eC0
        | VX87826 = cCoq_2emicromega_2eRMicromega_2eC1
        | ? [Vvar__0__r__87827] :
            ( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vvar__0__r__87827)
            & VX87826 = cCoq_2emicromega_2eRMicromega_2eCQ___24a1(Vvar__0__r__87827) )
        | ? [Vvar__0__r__87828] :
            ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__r__87828)
            & VX87826 = cCoq_2emicromega_2eRMicromega_2eCZ___24a1(Vvar__0__r__87828) )
        | ? [Vvar__0__r1__87829] :
            ( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r1__87829)
            & ? [Vvar__1__r2__87830] :
                ( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__1__r2__87830)
                & VX87826 = cCoq_2emicromega_2eRMicromega_2eCPlus___24a2(Vvar__0__r1__87829,Vvar__1__r2__87830) ) )
        | ? [Vvar__0__r1__87831] :
            ( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r1__87831)
            & ? [Vvar__1__r2__87832] :
                ( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__1__r2__87832)
                & VX87826 = cCoq_2emicromega_2eRMicromega_2eCMinus___24a2(Vvar__0__r1__87831,Vvar__1__r2__87832) ) )
        | ? [Vvar__0__r1__87833] :
            ( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r1__87833)
            & ? [Vvar__1__r2__87834] :
                ( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__1__r2__87834)
                & VX87826 = cCoq_2emicromega_2eRMicromega_2eCMult___24a2(Vvar__0__r1__87833,Vvar__1__r2__87834) ) )
        | ? [Vvar__0__r1__87835] :
            ( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r1__87835)
            & ? [Vvar__1__z__87836] :
                ( cCoq_2eInit_2eDatatypes_2esum___24t(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eInit_2eDatatypes_2enat,Vvar__1__z__87836)
                & VX87826 = cCoq_2emicromega_2eRMicromega_2eCPow___24a2(Vvar__0__r1__87835,Vvar__1__z__87836) ) )
        | ? [Vvar__0__r__87837] :
            ( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r__87837)
            & VX87826 = cCoq_2emicromega_2eRMicromega_2eCInv___24a1(Vvar__0__r__87837) )
        | ? [Vvar__0__r__87838] :
            ( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r__87838)
            & VX87826 = cCoq_2emicromega_2eRMicromega_2eCOpp___24a1(Vvar__0__r__87838) ) ) ) ).

fof('$_inversion_Coq.micromega.RingMicromega.Formula',axiom,
    ! [Vvar__0__T__90983,VX90984] :
      ( cType___24t(Vvar__0__T__90983)
     => ( cCoq_2emicromega_2eRingMicromega_2eFormula___24t(Vvar__0__T__90983,VX90984)
       => ? [Vvar__1__Flhs__90986] :
            ( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__T__90983,Vvar__1__Flhs__90986)
            & ? [Vvar__2__Fop__90987] :
                ( cCoq_2emicromega_2eRingMicromega_2eOp2___24t(Vvar__2__Fop__90987)
                & ? [Vvar__3__Frhs__90988] :
                    ( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__T__90983,Vvar__3__Frhs__90988)
                    & VX90984 = cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(Vvar__0__T__90983,Vvar__1__Flhs__90986,Vvar__2__Fop__90987,Vvar__3__Frhs__90988) ) ) ) ) ) ).

fof('$_inversion_Coq.micromega.RingMicromega.Op1',axiom,
    ! [VX85548] :
      ( cCoq_2emicromega_2eRingMicromega_2eOp1___24t(VX85548)
     => ( VX85548 = cCoq_2emicromega_2eRingMicromega_2eEqual
        | VX85548 = cCoq_2emicromega_2eRingMicromega_2eNonEqual
        | VX85548 = cCoq_2emicromega_2eRingMicromega_2eStrict
        | VX85548 = cCoq_2emicromega_2eRingMicromega_2eNonStrict ) ) ).

fof('$_inversion_Coq.micromega.RingMicromega.Op2',axiom,
    ! [VX85695] :
      ( cCoq_2emicromega_2eRingMicromega_2eOp2___24t(VX85695)
     => ( VX85695 = cCoq_2emicromega_2eRingMicromega_2eOpEq
        | VX85695 = cCoq_2emicromega_2eRingMicromega_2eOpNEq
        | VX85695 = cCoq_2emicromega_2eRingMicromega_2eOpLe
        | VX85695 = cCoq_2emicromega_2eRingMicromega_2eOpGe
        | VX85695 = cCoq_2emicromega_2eRingMicromega_2eOpLt
        | VX85695 = cCoq_2emicromega_2eRingMicromega_2eOpGt ) ) ).

fof('$_inversion_Coq.micromega.RingMicromega.Psatz',axiom,
    ! [Vvar__0__C__85549,VX85550] :
      ( cType___24t(Vvar__0__C__85549)
     => ( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__85549,VX85550)
       => ( ? [Vvar__1___24Anonymous__85552] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__85552)
              & VX85550 = cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(Vvar__0__C__85549,Vvar__1___24Anonymous__85552) )
          | ? [Vvar__1___24Anonymous__85554] :
              ( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(Vvar__0__C__85549,Vvar__1___24Anonymous__85554)
              & VX85550 = cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(Vvar__0__C__85549,Vvar__1___24Anonymous__85554) )
          | ? [Vvar__1___24Anonymous__85556] :
              ( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(Vvar__0__C__85549,Vvar__1___24Anonymous__85556)
              & ? [Vvar__2___24Anonymous__85557] :
                  ( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__85549,Vvar__2___24Anonymous__85557)
                  & VX85550 = cCoq_2emicromega_2eRingMicromega_2ePsatzMulC___24a3(Vvar__0__C__85549,Vvar__1___24Anonymous__85556,Vvar__2___24Anonymous__85557) ) )
          | ? [Vvar__1___24Anonymous__85559] :
              ( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__85549,Vvar__1___24Anonymous__85559)
              & ? [Vvar__2___24Anonymous__85560] :
                  ( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__85549,Vvar__2___24Anonymous__85560)
                  & VX85550 = cCoq_2emicromega_2eRingMicromega_2ePsatzMulE___24a3(Vvar__0__C__85549,Vvar__1___24Anonymous__85559,Vvar__2___24Anonymous__85560) ) )
          | ? [Vvar__1___24Anonymous__85562] :
              ( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__85549,Vvar__1___24Anonymous__85562)
              & ? [Vvar__2___24Anonymous__85563] :
                  ( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__85549,Vvar__2___24Anonymous__85563)
                  & VX85550 = cCoq_2emicromega_2eRingMicromega_2ePsatzAdd___24a3(Vvar__0__C__85549,Vvar__1___24Anonymous__85562,Vvar__2___24Anonymous__85563) ) )
          | ? [Vvar__1___24Anonymous__85565] :
              ( t(Vvar__1___24Anonymous__85565,Vvar__0__C__85549)
              & VX85550 = cCoq_2emicromega_2eRingMicromega_2ePsatzC___24a2(Vvar__0__C__85549,Vvar__1___24Anonymous__85565) )
          | VX85550 = cCoq_2emicromega_2eRingMicromega_2ePsatzZ___24a1(Vvar__0__C__85549) ) ) ) ).

fof('$_inversion_Coq.micromega.RingMicromega.SORaddon',axiom,
    ! [Vvar__0__R__97026,Vvar__1__rO__97027,Vvar__2__rI__97028,Vvar__3__rplus__97029,Vvar__4__rtimes__97034,Vvar__5__rminus__97039,Vvar__6__ropp__97044,Vvar__7__req__97047,Vvar__8__rle__97052,Vvar__9__C__97057,Vvar__10__cO__97058,Vvar__11__cI__97059,Vvar__12__cplus__97060,Vvar__13__ctimes__97065,Vvar__14__cminus__97070,Vvar__15__copp__97075,Vvar__16__ceqb__97078,Vvar__17__cleb__97083,Vvar__18__phi__97088,Vvar__19__E__97091,Vvar__20__pow__phi__97092,Vvar__21__rpow__97095] :
      ( cType___24t(Vvar__0__R__97026)
     => ( t(Vvar__1__rO__97027,Vvar__0__R__97026)
       => ( t(Vvar__2__rI__97028,Vvar__0__R__97026)
         => ( c_24__type__97559___24t(Vvar__0__R__97026,Vvar__1__rO__97027,Vvar__2__rI__97028,Vvar__3__rplus__97029,Vvar__4__rtimes__97034,Vvar__5__rminus__97039,Vvar__6__ropp__97044,Vvar__7__req__97047,Vvar__8__rle__97052,Vvar__9__C__97057,Vvar__10__cO__97058,Vvar__11__cI__97059,Vvar__12__cplus__97060,Vvar__13__ctimes__97065,Vvar__14__cminus__97070,Vvar__15__copp__97075,Vvar__16__ceqb__97078,Vvar__17__cleb__97083,Vvar__18__phi__97088,Vvar__19__E__97091,Vvar__20__pow__phi__97092,Vvar__21__rpow__97095,Vvar__3__rplus__97029)
           => ( c_24__type__97905___24t(Vvar__0__R__97026,Vvar__1__rO__97027,Vvar__2__rI__97028,Vvar__3__rplus__97029,Vvar__4__rtimes__97034,Vvar__5__rminus__97039,Vvar__6__ropp__97044,Vvar__7__req__97047,Vvar__8__rle__97052,Vvar__9__C__97057,Vvar__10__cO__97058,Vvar__11__cI__97059,Vvar__12__cplus__97060,Vvar__13__ctimes__97065,Vvar__14__cminus__97070,Vvar__15__copp__97075,Vvar__16__ceqb__97078,Vvar__17__cleb__97083,Vvar__18__phi__97088,Vvar__19__E__97091,Vvar__20__pow__phi__97092,Vvar__21__rpow__97095,Vvar__4__rtimes__97034)
             => ( c_24__type__98251___24t(Vvar__0__R__97026,Vvar__1__rO__97027,Vvar__2__rI__97028,Vvar__3__rplus__97029,Vvar__4__rtimes__97034,Vvar__5__rminus__97039,Vvar__6__ropp__97044,Vvar__7__req__97047,Vvar__8__rle__97052,Vvar__9__C__97057,Vvar__10__cO__97058,Vvar__11__cI__97059,Vvar__12__cplus__97060,Vvar__13__ctimes__97065,Vvar__14__cminus__97070,Vvar__15__copp__97075,Vvar__16__ceqb__97078,Vvar__17__cleb__97083,Vvar__18__phi__97088,Vvar__19__E__97091,Vvar__20__pow__phi__97092,Vvar__21__rpow__97095,Vvar__5__rminus__97039)
               => ( c_24__type__98574___24t(Vvar__0__R__97026,Vvar__1__rO__97027,Vvar__2__rI__97028,Vvar__3__rplus__97029,Vvar__4__rtimes__97034,Vvar__5__rminus__97039,Vvar__6__ropp__97044,Vvar__7__req__97047,Vvar__8__rle__97052,Vvar__9__C__97057,Vvar__10__cO__97058,Vvar__11__cI__97059,Vvar__12__cplus__97060,Vvar__13__ctimes__97065,Vvar__14__cminus__97070,Vvar__15__copp__97075,Vvar__16__ceqb__97078,Vvar__17__cleb__97083,Vvar__18__phi__97088,Vvar__19__E__97091,Vvar__20__pow__phi__97092,Vvar__21__rpow__97095,Vvar__6__ropp__97044)
                 => ( c_24__type__98920___24t(Vvar__0__R__97026,Vvar__1__rO__97027,Vvar__2__rI__97028,Vvar__3__rplus__97029,Vvar__4__rtimes__97034,Vvar__5__rminus__97039,Vvar__6__ropp__97044,Vvar__7__req__97047,Vvar__8__rle__97052,Vvar__9__C__97057,Vvar__10__cO__97058,Vvar__11__cI__97059,Vvar__12__cplus__97060,Vvar__13__ctimes__97065,Vvar__14__cminus__97070,Vvar__15__copp__97075,Vvar__16__ceqb__97078,Vvar__17__cleb__97083,Vvar__18__phi__97088,Vvar__19__E__97091,Vvar__20__pow__phi__97092,Vvar__21__rpow__97095,Vvar__7__req__97047)
                   => ( c_24__type__99266___24t(Vvar__0__R__97026,Vvar__1__rO__97027,Vvar__2__rI__97028,Vvar__3__rplus__97029,Vvar__4__rtimes__97034,Vvar__5__rminus__97039,Vvar__6__ropp__97044,Vvar__7__req__97047,Vvar__8__rle__97052,Vvar__9__C__97057,Vvar__10__cO__97058,Vvar__11__cI__97059,Vvar__12__cplus__97060,Vvar__13__ctimes__97065,Vvar__14__cminus__97070,Vvar__15__copp__97075,Vvar__16__ceqb__97078,Vvar__17__cleb__97083,Vvar__18__phi__97088,Vvar__19__E__97091,Vvar__20__pow__phi__97092,Vvar__21__rpow__97095,Vvar__8__rle__97052)
                     => ( cType___24t(Vvar__9__C__97057)
                       => ( t(Vvar__10__cO__97058,Vvar__9__C__97057)
                         => ( t(Vvar__11__cI__97059,Vvar__9__C__97057)
                           => ( c_24__type__99612___24t(Vvar__0__R__97026,Vvar__1__rO__97027,Vvar__2__rI__97028,Vvar__3__rplus__97029,Vvar__4__rtimes__97034,Vvar__5__rminus__97039,Vvar__6__ropp__97044,Vvar__7__req__97047,Vvar__8__rle__97052,Vvar__9__C__97057,Vvar__10__cO__97058,Vvar__11__cI__97059,Vvar__12__cplus__97060,Vvar__13__ctimes__97065,Vvar__14__cminus__97070,Vvar__15__copp__97075,Vvar__16__ceqb__97078,Vvar__17__cleb__97083,Vvar__18__phi__97088,Vvar__19__E__97091,Vvar__20__pow__phi__97092,Vvar__21__rpow__97095,Vvar__12__cplus__97060)
                             => ( c_24__type__99958___24t(Vvar__0__R__97026,Vvar__1__rO__97027,Vvar__2__rI__97028,Vvar__3__rplus__97029,Vvar__4__rtimes__97034,Vvar__5__rminus__97039,Vvar__6__ropp__97044,Vvar__7__req__97047,Vvar__8__rle__97052,Vvar__9__C__97057,Vvar__10__cO__97058,Vvar__11__cI__97059,Vvar__12__cplus__97060,Vvar__13__ctimes__97065,Vvar__14__cminus__97070,Vvar__15__copp__97075,Vvar__16__ceqb__97078,Vvar__17__cleb__97083,Vvar__18__phi__97088,Vvar__19__E__97091,Vvar__20__pow__phi__97092,Vvar__21__rpow__97095,Vvar__13__ctimes__97065)
                               => ( c_24__type__100304___24t(Vvar__0__R__97026,Vvar__1__rO__97027,Vvar__2__rI__97028,Vvar__3__rplus__97029,Vvar__4__rtimes__97034,Vvar__5__rminus__97039,Vvar__6__ropp__97044,Vvar__7__req__97047,Vvar__8__rle__97052,Vvar__9__C__97057,Vvar__10__cO__97058,Vvar__11__cI__97059,Vvar__12__cplus__97060,Vvar__13__ctimes__97065,Vvar__14__cminus__97070,Vvar__15__copp__97075,Vvar__16__ceqb__97078,Vvar__17__cleb__97083,Vvar__18__phi__97088,Vvar__19__E__97091,Vvar__20__pow__phi__97092,Vvar__21__rpow__97095,Vvar__14__cminus__97070)
                                 => ( c_24__type__100627___24t(Vvar__0__R__97026,Vvar__1__rO__97027,Vvar__2__rI__97028,Vvar__3__rplus__97029,Vvar__4__rtimes__97034,Vvar__5__rminus__97039,Vvar__6__ropp__97044,Vvar__7__req__97047,Vvar__8__rle__97052,Vvar__9__C__97057,Vvar__10__cO__97058,Vvar__11__cI__97059,Vvar__12__cplus__97060,Vvar__13__ctimes__97065,Vvar__14__cminus__97070,Vvar__15__copp__97075,Vvar__16__ceqb__97078,Vvar__17__cleb__97083,Vvar__18__phi__97088,Vvar__19__E__97091,Vvar__20__pow__phi__97092,Vvar__21__rpow__97095,Vvar__15__copp__97075)
                                   => ( c_24__type__100973___24t(Vvar__0__R__97026,Vvar__1__rO__97027,Vvar__2__rI__97028,Vvar__3__rplus__97029,Vvar__4__rtimes__97034,Vvar__5__rminus__97039,Vvar__6__ropp__97044,Vvar__7__req__97047,Vvar__8__rle__97052,Vvar__9__C__97057,Vvar__10__cO__97058,Vvar__11__cI__97059,Vvar__12__cplus__97060,Vvar__13__ctimes__97065,Vvar__14__cminus__97070,Vvar__15__copp__97075,Vvar__16__ceqb__97078,Vvar__17__cleb__97083,Vvar__18__phi__97088,Vvar__19__E__97091,Vvar__20__pow__phi__97092,Vvar__21__rpow__97095,Vvar__16__ceqb__97078)
                                     => ( c_24__type__101319___24t(Vvar__0__R__97026,Vvar__1__rO__97027,Vvar__2__rI__97028,Vvar__3__rplus__97029,Vvar__4__rtimes__97034,Vvar__5__rminus__97039,Vvar__6__ropp__97044,Vvar__7__req__97047,Vvar__8__rle__97052,Vvar__9__C__97057,Vvar__10__cO__97058,Vvar__11__cI__97059,Vvar__12__cplus__97060,Vvar__13__ctimes__97065,Vvar__14__cminus__97070,Vvar__15__copp__97075,Vvar__16__ceqb__97078,Vvar__17__cleb__97083,Vvar__18__phi__97088,Vvar__19__E__97091,Vvar__20__pow__phi__97092,Vvar__21__rpow__97095,Vvar__17__cleb__97083)
                                       => ( c_24__type__101642___24t(Vvar__0__R__97026,Vvar__1__rO__97027,Vvar__2__rI__97028,Vvar__3__rplus__97029,Vvar__4__rtimes__97034,Vvar__5__rminus__97039,Vvar__6__ropp__97044,Vvar__7__req__97047,Vvar__8__rle__97052,Vvar__9__C__97057,Vvar__10__cO__97058,Vvar__11__cI__97059,Vvar__12__cplus__97060,Vvar__13__ctimes__97065,Vvar__14__cminus__97070,Vvar__15__copp__97075,Vvar__16__ceqb__97078,Vvar__17__cleb__97083,Vvar__18__phi__97088,Vvar__19__E__97091,Vvar__20__pow__phi__97092,Vvar__21__rpow__97095,Vvar__18__phi__97088)
                                         => ( cType___24t(Vvar__19__E__97091)
                                           => ( c_24__type__101965___24t(Vvar__0__R__97026,Vvar__1__rO__97027,Vvar__2__rI__97028,Vvar__3__rplus__97029,Vvar__4__rtimes__97034,Vvar__5__rminus__97039,Vvar__6__ropp__97044,Vvar__7__req__97047,Vvar__8__rle__97052,Vvar__9__C__97057,Vvar__10__cO__97058,Vvar__11__cI__97059,Vvar__12__cplus__97060,Vvar__13__ctimes__97065,Vvar__14__cminus__97070,Vvar__15__copp__97075,Vvar__16__ceqb__97078,Vvar__17__cleb__97083,Vvar__18__phi__97088,Vvar__19__E__97091,Vvar__20__pow__phi__97092,Vvar__21__rpow__97095,Vvar__20__pow__phi__97092)
                                             => ( c_24__type__102311___24t(Vvar__0__R__97026,Vvar__1__rO__97027,Vvar__2__rI__97028,Vvar__3__rplus__97029,Vvar__4__rtimes__97034,Vvar__5__rminus__97039,Vvar__6__ropp__97044,Vvar__7__req__97047,Vvar__8__rle__97052,Vvar__9__C__97057,Vvar__10__cO__97058,Vvar__11__cI__97059,Vvar__12__cplus__97060,Vvar__13__ctimes__97065,Vvar__14__cminus__97070,Vvar__15__copp__97075,Vvar__16__ceqb__97078,Vvar__17__cleb__97083,Vvar__18__phi__97088,Vvar__19__E__97091,Vvar__20__pow__phi__97092,Vvar__21__rpow__97095,Vvar__21__rpow__97095)
                                               => ( cCoq_2emicromega_2eRingMicromega_2eSORaddon___24a22(Vvar__0__R__97026,Vvar__1__rO__97027,Vvar__2__rI__97028,Vvar__3__rplus__97029,Vvar__4__rtimes__97034,Vvar__5__rminus__97039,Vvar__6__ropp__97044,Vvar__7__req__97047,Vvar__8__rle__97052,Vvar__9__C__97057,Vvar__10__cO__97058,Vvar__11__cI__97059,Vvar__12__cplus__97060,Vvar__13__ctimes__97065,Vvar__14__cminus__97070,Vvar__15__copp__97075,Vvar__16__ceqb__97078,Vvar__17__cleb__97083,Vvar__18__phi__97088,Vvar__19__E__97091,Vvar__20__pow__phi__97092,Vvar__21__rpow__97095)
                                                 => ( cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(Vvar__0__R__97026,Vvar__1__rO__97027,Vvar__2__rI__97028,Vvar__3__rplus__97029,Vvar__4__rtimes__97034,Vvar__5__rminus__97039,Vvar__6__ropp__97044,Vvar__7__req__97047,Vvar__9__C__97057,Vvar__10__cO__97058,Vvar__11__cI__97059,Vvar__12__cplus__97060,Vvar__13__ctimes__97065,Vvar__14__cminus__97070,Vvar__15__copp__97075,Vvar__16__ceqb__97078,Vvar__18__phi__97088)
                                                    & cCoq_2esetoid__ring_2eRing__theory_2epower__theory___24a7(Vvar__0__R__97026,Vvar__2__rI__97028,Vvar__4__rtimes__97034,Vvar__7__req__97047,Vvar__19__E__97091,Vvar__20__pow__phi__97092,Vvar__21__rpow__97095)
                                                    & ! [Vvar__var__var__var__var__var__24__x__97178__97181__97191__97194__97197__97200] :
                                                        ( t(Vvar__var__var__var__var__var__24__x__97178__97181__97191__97194__97197__97200,Vvar__9__C__97057)
                                                       => ! [Vvar__var__var__var__var__var__25__y__97179__97182__97192__97195__97198__97201] :
                                                            ( t(Vvar__var__var__var__var__var__25__y__97179__97182__97192__97195__97198__97201,Vvar__9__C__97057)
                                                           => ( happ(happ(Vvar__16__ceqb__97078,Vvar__var__var__var__var__var__24__x__97178__97181__97191__97194__97197__97200),Vvar__var__var__var__var__var__25__y__97179__97182__97192__97195__97198__97201) = cCoq_2eInit_2eDatatypes_2efalse
                                                             => ~ p(happ(happ(Vvar__7__req__97047,happ(Vvar__18__phi__97088,Vvar__var__var__var__var__var__24__x__97178__97181__97191__97194__97197__97200)),happ(Vvar__18__phi__97088,Vvar__var__var__var__var__var__25__y__97179__97182__97192__97195__97198__97201))) ) ) )
                                                    & ! [Vvar__var__var__var__var__var__25__x__97185__97188__97203__97206__97209__97212] :
                                                        ( t(Vvar__var__var__var__var__var__25__x__97185__97188__97203__97206__97209__97212,Vvar__9__C__97057)
                                                       => ! [Vvar__var__var__var__var__var__26__y__97186__97189__97204__97207__97210__97213] :
                                                            ( t(Vvar__var__var__var__var__var__26__y__97186__97189__97204__97207__97210__97213,Vvar__9__C__97057)
                                                           => ( happ(happ(Vvar__17__cleb__97083,Vvar__var__var__var__var__var__25__x__97185__97188__97203__97206__97209__97212),Vvar__var__var__var__var__var__26__y__97186__97189__97204__97207__97210__97213) = cCoq_2eInit_2eDatatypes_2etrue
                                                             => p(happ(happ(Vvar__8__rle__97052,happ(Vvar__18__phi__97088,Vvar__var__var__var__var__var__25__x__97185__97188__97203__97206__97209__97212)),happ(Vvar__18__phi__97088,Vvar__var__var__var__var__var__26__y__97186__97189__97204__97207__97210__97213))) ) ) )
                                                    & p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.micromega.Tauto.GFormula',axiom,
    ! [Vvar__0__TA__85982,Vvar__1__TX__85983,Vvar__2__AA__85984,Vvar__3__AF__85985,VX85986] :
      ( cType___24t(Vvar__0__TA__85982)
     => ( cType___24t(Vvar__1__TX__85983)
       => ( cType___24t(Vvar__2__AA__85984)
         => ( cType___24t(Vvar__3__AF__85985)
           => ( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__85982,Vvar__1__TX__85983,Vvar__2__AA__85984,Vvar__3__AF__85985,VX85986)
             => ( VX85986 = cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__85982,Vvar__1__TX__85983,Vvar__2__AA__85984,Vvar__3__AF__85985)
                | VX85986 = cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__85982,Vvar__1__TX__85983,Vvar__2__AA__85984,Vvar__3__AF__85985)
                | ? [Vvar__4___24Anonymous__85999] :
                    ( t(Vvar__4___24Anonymous__85999,Vvar__1__TX__85983)
                    & VX85986 = cCoq_2emicromega_2eTauto_2eX___24a5(Vvar__0__TA__85982,Vvar__1__TX__85983,Vvar__2__AA__85984,Vvar__3__AF__85985,Vvar__4___24Anonymous__85999) )
                | ? [Vvar__4___24Anonymous__86004] :
                    ( t(Vvar__4___24Anonymous__86004,Vvar__0__TA__85982)
                    & ? [Vvar__5___24Anonymous__86005] :
                        ( t(Vvar__5___24Anonymous__86005,Vvar__2__AA__85984)
                        & VX85986 = cCoq_2emicromega_2eTauto_2eA___24a6(Vvar__0__TA__85982,Vvar__1__TX__85983,Vvar__2__AA__85984,Vvar__3__AF__85985,Vvar__4___24Anonymous__86004,Vvar__5___24Anonymous__86005) ) )
                | ? [Vvar__4___24Anonymous__86010] :
                    ( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__85982,Vvar__1__TX__85983,Vvar__2__AA__85984,Vvar__3__AF__85985,Vvar__4___24Anonymous__86010)
                    & ? [Vvar__5___24Anonymous__86011] :
                        ( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__85982,Vvar__1__TX__85983,Vvar__2__AA__85984,Vvar__3__AF__85985,Vvar__5___24Anonymous__86011)
                        & VX85986 = cCoq_2emicromega_2eTauto_2eCj___24a6(Vvar__0__TA__85982,Vvar__1__TX__85983,Vvar__2__AA__85984,Vvar__3__AF__85985,Vvar__4___24Anonymous__86010,Vvar__5___24Anonymous__86011) ) )
                | ? [Vvar__4___24Anonymous__86016] :
                    ( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__85982,Vvar__1__TX__85983,Vvar__2__AA__85984,Vvar__3__AF__85985,Vvar__4___24Anonymous__86016)
                    & ? [Vvar__5___24Anonymous__86017] :
                        ( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__85982,Vvar__1__TX__85983,Vvar__2__AA__85984,Vvar__3__AF__85985,Vvar__5___24Anonymous__86017)
                        & VX85986 = cCoq_2emicromega_2eTauto_2eD___24a6(Vvar__0__TA__85982,Vvar__1__TX__85983,Vvar__2__AA__85984,Vvar__3__AF__85985,Vvar__4___24Anonymous__86016,Vvar__5___24Anonymous__86017) ) )
                | ? [Vvar__4___24Anonymous__86022] :
                    ( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__85982,Vvar__1__TX__85983,Vvar__2__AA__85984,Vvar__3__AF__85985,Vvar__4___24Anonymous__86022)
                    & VX85986 = cCoq_2emicromega_2eTauto_2eN___24a5(Vvar__0__TA__85982,Vvar__1__TX__85983,Vvar__2__AA__85984,Vvar__3__AF__85985,Vvar__4___24Anonymous__86022) )
                | ? [Vvar__4___24Anonymous__86027] :
                    ( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__85982,Vvar__1__TX__85983,Vvar__2__AA__85984,Vvar__3__AF__85985,Vvar__4___24Anonymous__86027)
                    & ? [Vvar__5___24Anonymous__86028] :
                        ( cCoq_2eInit_2eDatatypes_2eoption___24t(Vvar__3__AF__85985,Vvar__5___24Anonymous__86028)
                        & ? [Vvar__6___24Anonymous__86029] :
                            ( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__85982,Vvar__1__TX__85983,Vvar__2__AA__85984,Vvar__3__AF__85985,Vvar__6___24Anonymous__86029)
                            & VX85986 = cCoq_2emicromega_2eTauto_2eI___24a7(Vvar__0__TA__85982,Vvar__1__TX__85983,Vvar__2__AA__85984,Vvar__3__AF__85985,Vvar__4___24Anonymous__86027,Vvar__5___24Anonymous__86028,Vvar__6___24Anonymous__86029) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.micromega.VarMap.t',axiom,
    ! [Vvar__0__A__86425,VX86426] :
      ( cType___24t(Vvar__0__A__86425)
     => ( cCoq_2emicromega_2eVarMap_2et___24t(Vvar__0__A__86425,VX86426)
       => ( VX86426 = cCoq_2emicromega_2eVarMap_2eEmpty___24a1(Vvar__0__A__86425)
          | ? [Vvar__1___24Anonymous__86429] :
              ( t(Vvar__1___24Anonymous__86429,Vvar__0__A__86425)
              & VX86426 = cCoq_2emicromega_2eVarMap_2eElt___24a2(Vvar__0__A__86425,Vvar__1___24Anonymous__86429) )
          | ? [Vvar__1___24Anonymous__86431] :
              ( cCoq_2emicromega_2eVarMap_2et___24t(Vvar__0__A__86425,Vvar__1___24Anonymous__86431)
              & ? [Vvar__2___24Anonymous__86432] :
                  ( t(Vvar__2___24Anonymous__86432,Vvar__0__A__86425)
                  & ? [Vvar__3___24Anonymous__86433] :
                      ( cCoq_2emicromega_2eVarMap_2et___24t(Vvar__0__A__86425,Vvar__3___24Anonymous__86433)
                      & VX86426 = cCoq_2emicromega_2eVarMap_2eBranch___24a4(Vvar__0__A__86425,Vvar__1___24Anonymous__86431,Vvar__2___24Anonymous__86432,Vvar__3___24Anonymous__86433) ) ) ) ) ) ) ).

fof('$_inversion_Coq.micromega.ZMicromega.Vars.Facts.MP.Dec.FSetDecideAuxiliary.FSet_Prop',axiom,
    ! [Vvar__0___24Anonymous__92101] :
      ( cProp___24t(Vvar__0___24Anonymous__92101)
     => ( cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__Prop___24a1(Vvar__0___24Anonymous__92101)
       => ( ? [Vvar__0__P__92103] :
              ( cProp___24t(Vvar__0__P__92103)
              & cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__92103)
              & Vvar__0___24Anonymous__92101 = Vvar__0__P__92103 )
          | ? [Vvar__0__s__92105] :
              ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__0__s__92105)
              & Vvar__0___24Anonymous__92101 = c_24__prop__92114___24a2(Vvar__0___24Anonymous__92101,Vvar__0__s__92105) )
          | ? [Vvar__0__s1__92107] :
              ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__0__s1__92107)
              & ? [Vvar__1__s2__92108] :
                  ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__1__s2__92108)
                  & Vvar__0___24Anonymous__92101 = c_24__prop__92115___24a3(Vvar__0___24Anonymous__92101,Vvar__0__s1__92107,Vvar__1__s2__92108) ) )
          | ? [Vvar__0__s1__92111] :
              ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__0__s1__92111)
              & ? [Vvar__1__s2__92112] :
                  ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__1__s2__92112)
                  & Vvar__0___24Anonymous__92101 = c_24__prop__92116___24a3(Vvar__0___24Anonymous__92101,Vvar__0__s1__92111,Vvar__1__s2__92112) ) ) ) ) ) ).

fof('$_inversion_Coq.micromega.ZMicromega.Vars.Facts.MP.Dec.FSetDecideAuxiliary.FSet_elt_Prop',axiom,
    ! [Vvar__0___24Anonymous__92070] :
      ( cProp___24t(Vvar__0___24Anonymous__92070)
     => ( cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0___24Anonymous__92070)
       => ( ? [Vvar__0__S__92072] :
              ( cType___24t(Vvar__0__S__92072)
              & ? [Vvar__1__x__92073] :
                  ( t(Vvar__1__x__92073,Vvar__0__S__92072)
                  & ? [Vvar__2__y__92074] :
                      ( t(Vvar__2__y__92074,Vvar__0__S__92072)
                      & Vvar__0___24Anonymous__92070 = c_24__prop__92094___24a4(Vvar__0___24Anonymous__92070,Vvar__0__S__92072,Vvar__1__x__92073,Vvar__2__y__92074) ) ) )
          | ? [Vvar__0__x__92075] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0__x__92075)
              & ? [Vvar__1__y__92076] :
                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__y__92076)
                  & Vvar__0___24Anonymous__92070 = c_24__prop__92095___24a3(Vvar__0___24Anonymous__92070,Vvar__0__x__92075,Vvar__1__y__92076) ) )
          | ? [Vvar__0__x__92077] :
              ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vvar__0__x__92077)
              & ? [Vvar__1__s__92078] :
                  ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__1__s__92078)
                  & Vvar__0___24Anonymous__92070 = c_24__prop__92096___24a3(Vvar__0___24Anonymous__92070,Vvar__0__x__92077,Vvar__1__s__92078) ) )
          | Vvar__0___24Anonymous__92070 = c_24True
          | Vvar__0___24Anonymous__92070 = c_24False
          | ? [Vvar__0__P__92079] :
              ( cProp___24t(Vvar__0__P__92079)
              & ? [Vvar__1__Q__92080] :
                  ( cProp___24t(Vvar__1__Q__92080)
                  & cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__92079)
                  & cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__1__Q__92080)
                  & Vvar__0___24Anonymous__92070 = c_24__prop__92097___24a3(Vvar__0___24Anonymous__92070,Vvar__0__P__92079,Vvar__1__Q__92080) ) )
          | ? [Vvar__0__P__92083] :
              ( cProp___24t(Vvar__0__P__92083)
              & ? [Vvar__1__Q__92084] :
                  ( cProp___24t(Vvar__1__Q__92084)
                  & cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__92083)
                  & cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__1__Q__92084)
                  & Vvar__0___24Anonymous__92070 = c_24__prop__92098___24a3(Vvar__0___24Anonymous__92070,Vvar__0__P__92083,Vvar__1__Q__92084) ) )
          | ? [Vvar__0__P__92087] :
              ( cProp___24t(Vvar__0__P__92087)
              & ? [Vvar__1__Q__92088] :
                  ( cProp___24t(Vvar__1__Q__92088)
                  & cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__92087)
                  & cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__1__Q__92088)
                  & Vvar__0___24Anonymous__92070 = c_24__prop__92099___24a3(Vvar__0___24Anonymous__92070,Vvar__0__P__92087,Vvar__1__Q__92088) ) )
          | ? [Vvar__0__P__92092] :
              ( cProp___24t(Vvar__0__P__92092)
              & cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__92092)
              & Vvar__0___24Anonymous__92070 = c_24__prop__92100___24a2(Vvar__0___24Anonymous__92070,Vvar__0__P__92092) ) ) ) ) ).

fof('$_inversion_Coq.micromega.ZMicromega.Vars.ct',axiom,
    ! [Vvar__0___24Anonymous__200557,Vvar__1___24Anonymous__200558,Vvar__2___24Anonymous__200559] :
      ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__0___24Anonymous__200557)
     => ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__1___24Anonymous__200558)
       => ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__2___24Anonymous__200559)
         => ( cCoq_2emicromega_2eZMicromega_2eVars_2ect___24a3(Vvar__0___24Anonymous__200557,Vvar__1___24Anonymous__200558,Vvar__2___24Anonymous__200559)
           => ( ? [Vvar__0__x__200561] :
                  ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__0__x__200561)
                  & Vvar__2___24Anonymous__200559 = Vvar__0__x__200561
                  & Vvar__1___24Anonymous__200558 = Vvar__0__x__200561
                  & Vvar__0___24Anonymous__200557 = Vvar__0__x__200561 )
              | ? [Vvar__0__x__200562] :
                  ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__0__x__200562)
                  & Vvar__2___24Anonymous__200559 = Vvar__0__x__200562
                  & Vvar__1___24Anonymous__200558 = cCoq_2eInit_2eDatatypes_2eEq
                  & Vvar__0___24Anonymous__200557 = Vvar__0__x__200562 )
              | ? [Vvar__0__x__200563] :
                  ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__0__x__200563)
                  & Vvar__2___24Anonymous__200559 = Vvar__0__x__200563
                  & Vvar__1___24Anonymous__200558 = Vvar__0__x__200563
                  & Vvar__0___24Anonymous__200557 = cCoq_2eInit_2eDatatypes_2eEq )
              | ? [Vvar__0__x__200564] :
                  ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__0__x__200564)
                  & Vvar__2___24Anonymous__200559 = Vvar__0__x__200564
                  & Vvar__1___24Anonymous__200558 = cCoq_2eInit_2eDatatypes_2eLt
                  & Vvar__0___24Anonymous__200557 = cCoq_2eInit_2eDatatypes_2eGt )
              | ? [Vvar__0__x__200565] :
                  ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__0__x__200565)
                  & Vvar__2___24Anonymous__200559 = Vvar__0__x__200565
                  & Vvar__1___24Anonymous__200558 = cCoq_2eInit_2eDatatypes_2eGt
                  & Vvar__0___24Anonymous__200557 = cCoq_2eInit_2eDatatypes_2eLt ) ) ) ) ) ) ).

fof('$_inversion_Coq.micromega.ZMicromega.Vars.tree',axiom,
    ! [VX200961] :
      ( cCoq_2emicromega_2eZMicromega_2eVars_2etree___24t(VX200961)
     => ( VX200961 = cCoq_2emicromega_2eZMicromega_2eVars_2eLeaf
        | ? [Vvar__0___24Anonymous__200962] :
            ( cCoq_2emicromega_2eZMicromega_2eVars_2etree___24t(Vvar__0___24Anonymous__200962)
            & ? [Vvar__1___24Anonymous__200963] :
                ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__200963)
                & ? [Vvar__2___24Anonymous__200964] :
                    ( cCoq_2emicromega_2eZMicromega_2eVars_2etree___24t(Vvar__2___24Anonymous__200964)
                    & VX200961 = cCoq_2emicromega_2eZMicromega_2eVars_2eNode___24a3(Vvar__0___24Anonymous__200962,Vvar__1___24Anonymous__200963,Vvar__2___24Anonymous__200964) ) ) ) ) ) ).

fof('$_inversion_Coq.micromega.ZMicromega.ZArithProof',axiom,
    ! [VX83795] :
      ( cCoq_2emicromega_2eZMicromega_2eZArithProof___24t(VX83795)
     => ( VX83795 = cCoq_2emicromega_2eZMicromega_2eDoneProof
        | ? [Vvar__0___24Anonymous__83796] :
            ( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__0___24Anonymous__83796)
            & ? [Vvar__1___24Anonymous__83797] :
                ( cCoq_2emicromega_2eZMicromega_2eZArithProof___24t(Vvar__1___24Anonymous__83797)
                & VX83795 = cCoq_2emicromega_2eZMicromega_2eRatProof___24a2(Vvar__0___24Anonymous__83796,Vvar__1___24Anonymous__83797) ) )
        | ? [Vvar__0___24Anonymous__83798] :
            ( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__0___24Anonymous__83798)
            & ? [Vvar__1___24Anonymous__83799] :
                ( cCoq_2emicromega_2eZMicromega_2eZArithProof___24t(Vvar__1___24Anonymous__83799)
                & VX83795 = cCoq_2emicromega_2eZMicromega_2eCutProof___24a2(Vvar__0___24Anonymous__83798,Vvar__1___24Anonymous__83799) ) )
        | ? [Vvar__0___24Anonymous__83800] :
            ( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__0___24Anonymous__83800)
            & ? [Vvar__1___24Anonymous__83801] :
                ( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__1___24Anonymous__83801)
                & ? [Vvar__2___24Anonymous__83802] :
                    ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2emicromega_2eZMicromega_2eZArithProof,Vvar__2___24Anonymous__83802)
                    & VX83795 = cCoq_2emicromega_2eZMicromega_2eEnumProof___24a3(Vvar__0___24Anonymous__83800,Vvar__1___24Anonymous__83801,Vvar__2___24Anonymous__83802) ) ) ) ) ) ).

fof('$_inversion_Coq.micromega.ZMicromega.Zdivide_pol',axiom,
    ! [Vvar__0__x__218528,Vvar__1___24Anonymous__218529] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__x__218528)
     => ( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(cCoq_2eNumbers_2eBinNums_2eZ,Vvar__1___24Anonymous__218529)
       => ( cCoq_2emicromega_2eZMicromega_2eZdivide__pol___24a2(Vvar__0__x__218528,Vvar__1___24Anonymous__218529)
         => ( ? [Vvar__1__c__218532] :
                ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__1__c__218532)
                & cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__0__x__218528,Vvar__1__c__218532)
                & Vvar__1___24Anonymous__218529 = cCoq_2emicromega_2eEnvRing_2ePc___24a2(cCoq_2eNumbers_2eBinNums_2eZ,Vvar__1__c__218532) )
            | ? [Vvar__1__p__218535] :
                ( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(cCoq_2eNumbers_2eBinNums_2eZ,Vvar__1__p__218535)
                & cCoq_2emicromega_2eZMicromega_2eZdivide__pol___24a2(Vvar__0__x__218528,Vvar__1__p__218535)
                & ? [Vvar__3__j__218537] :
                    ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__3__j__218537)
                    & Vvar__1___24Anonymous__218529 = cCoq_2emicromega_2eEnvRing_2ePinj___24a3(cCoq_2eNumbers_2eBinNums_2eZ,Vvar__3__j__218537,Vvar__1__p__218535) ) )
            | ? [Vvar__1__p__218539] :
                ( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(cCoq_2eNumbers_2eBinNums_2eZ,Vvar__1__p__218539)
                & ? [Vvar__2__q__218540] :
                    ( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(cCoq_2eNumbers_2eBinNums_2eZ,Vvar__2__q__218540)
                    & cCoq_2emicromega_2eZMicromega_2eZdivide__pol___24a2(Vvar__0__x__218528,Vvar__1__p__218539)
                    & cCoq_2emicromega_2eZMicromega_2eZdivide__pol___24a2(Vvar__0__x__218528,Vvar__2__q__218540)
                    & ? [Vvar__5__j__218543] :
                        ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__5__j__218543)
                        & Vvar__1___24Anonymous__218529 = cCoq_2emicromega_2eEnvRing_2ePX___24a4(cCoq_2eNumbers_2eBinNums_2eZ,Vvar__1__p__218539,Vvar__5__j__218543,Vvar__2__q__218540) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.micromega.ZMicromega.is_diff_env_elt',axiom,
    ! [Vvar__0__fr__115914,Vvar__1__env__115915,Vvar__2__env_27__115918,Vvar__3__x__115921] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0__fr__115914)
     => ( c_24__type__115942___24t(Vvar__0__fr__115914,Vvar__1__env__115915,Vvar__2__env_27__115918,Vvar__3__x__115921,Vvar__1__env__115915)
       => ( c_24__type__115951___24t(Vvar__0__fr__115914,Vvar__1__env__115915,Vvar__2__env_27__115918,Vvar__3__x__115921,Vvar__2__env_27__115918)
         => ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__3__x__115921)
           => ( cCoq_2emicromega_2eZMicromega_2eis__diff__env__elt___24a4(Vvar__0__fr__115914,Vvar__1__env__115915,Vvar__2__env_27__115918,Vvar__3__x__115921)
             => ( happ(Vvar__1__env__115915,Vvar__3__x__115921) = happ(Vvar__2__env_27__115918,Vvar__3__x__115921)
                & happ(Vvar__1__env__115915,Vvar__3__x__115921) = cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(happ(Vvar__2__env_27__115918,cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0__fr__115914,Vvar__3__x__115921))),happ(Vvar__2__env_27__115918,cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0__fr__115914,Vvar__3__x__115921))))
                & p(cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(happ(Vvar__2__env_27__115918,cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0__fr__115914,Vvar__3__x__115921))),cCoq_2eNumbers_2eBinNums_2eZ0))
                & p(cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(happ(Vvar__2__env_27__115918,cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0__fr__115914,Vvar__3__x__115921))),cCoq_2eNumbers_2eBinNums_2eZ0))
                & p(c_24True) ) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Field_theory.FExpr',axiom,
    ! [Vvar__0__C__85187,VX85188] :
      ( cType___24t(Vvar__0__C__85187)
     => ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__85187,VX85188)
       => ( VX85188 = cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__85187)
          | VX85188 = cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__85187)
          | ? [Vvar__1___24Anonymous__85192] :
              ( t(Vvar__1___24Anonymous__85192,Vvar__0__C__85187)
              & VX85188 = cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(Vvar__0__C__85187,Vvar__1___24Anonymous__85192) )
          | ? [Vvar__1___24Anonymous__85194] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__85194)
              & VX85188 = cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(Vvar__0__C__85187,Vvar__1___24Anonymous__85194) )
          | ? [Vvar__1___24Anonymous__85196] :
              ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__85187,Vvar__1___24Anonymous__85196)
              & ? [Vvar__2___24Anonymous__85197] :
                  ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__85187,Vvar__2___24Anonymous__85197)
                  & VX85188 = cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(Vvar__0__C__85187,Vvar__1___24Anonymous__85196,Vvar__2___24Anonymous__85197) ) )
          | ? [Vvar__1___24Anonymous__85199] :
              ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__85187,Vvar__1___24Anonymous__85199)
              & ? [Vvar__2___24Anonymous__85200] :
                  ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__85187,Vvar__2___24Anonymous__85200)
                  & VX85188 = cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(Vvar__0__C__85187,Vvar__1___24Anonymous__85199,Vvar__2___24Anonymous__85200) ) )
          | ? [Vvar__1___24Anonymous__85202] :
              ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__85187,Vvar__1___24Anonymous__85202)
              & ? [Vvar__2___24Anonymous__85203] :
                  ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__85187,Vvar__2___24Anonymous__85203)
                  & VX85188 = cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(Vvar__0__C__85187,Vvar__1___24Anonymous__85202,Vvar__2___24Anonymous__85203) ) )
          | ? [Vvar__1___24Anonymous__85205] :
              ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__85187,Vvar__1___24Anonymous__85205)
              & VX85188 = cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(Vvar__0__C__85187,Vvar__1___24Anonymous__85205) )
          | ? [Vvar__1___24Anonymous__85207] :
              ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__85187,Vvar__1___24Anonymous__85207)
              & VX85188 = cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(Vvar__0__C__85187,Vvar__1___24Anonymous__85207) )
          | ? [Vvar__1___24Anonymous__85209] :
              ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__85187,Vvar__1___24Anonymous__85209)
              & ? [Vvar__2___24Anonymous__85210] :
                  ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__85187,Vvar__2___24Anonymous__85210)
                  & VX85188 = cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(Vvar__0__C__85187,Vvar__1___24Anonymous__85209,Vvar__2___24Anonymous__85210) ) )
          | ? [Vvar__1___24Anonymous__85212] :
              ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__85187,Vvar__1___24Anonymous__85212)
              & ? [Vvar__2___24Anonymous__85213] :
                  ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__85213)
                  & VX85188 = cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(Vvar__0__C__85187,Vvar__1___24Anonymous__85212,Vvar__2___24Anonymous__85213) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Field_theory.almost_field_theory',axiom,
    ! [Vvar__0__R__88935,Vvar__1__rO__88936,Vvar__2__rI__88937,Vvar__3__radd__88938,Vvar__4__rmul__88943,Vvar__5__rsub__88948,Vvar__6__ropp__88953,Vvar__7__rdiv__88956,Vvar__8__rinv__88961,Vvar__9__req__88964] :
      ( cType___24t(Vvar__0__R__88935)
     => ( t(Vvar__1__rO__88936,Vvar__0__R__88935)
       => ( t(Vvar__2__rI__88937,Vvar__0__R__88935)
         => ( c_24__type__89129___24t(Vvar__0__R__88935,Vvar__1__rO__88936,Vvar__2__rI__88937,Vvar__3__radd__88938,Vvar__4__rmul__88943,Vvar__5__rsub__88948,Vvar__6__ropp__88953,Vvar__7__rdiv__88956,Vvar__8__rinv__88961,Vvar__9__req__88964,Vvar__3__radd__88938)
           => ( c_24__type__89222___24t(Vvar__0__R__88935,Vvar__1__rO__88936,Vvar__2__rI__88937,Vvar__3__radd__88938,Vvar__4__rmul__88943,Vvar__5__rsub__88948,Vvar__6__ropp__88953,Vvar__7__rdiv__88956,Vvar__8__rinv__88961,Vvar__9__req__88964,Vvar__4__rmul__88943)
             => ( c_24__type__89315___24t(Vvar__0__R__88935,Vvar__1__rO__88936,Vvar__2__rI__88937,Vvar__3__radd__88938,Vvar__4__rmul__88943,Vvar__5__rsub__88948,Vvar__6__ropp__88953,Vvar__7__rdiv__88956,Vvar__8__rinv__88961,Vvar__9__req__88964,Vvar__5__rsub__88948)
               => ( c_24__type__89397___24t(Vvar__0__R__88935,Vvar__1__rO__88936,Vvar__2__rI__88937,Vvar__3__radd__88938,Vvar__4__rmul__88943,Vvar__5__rsub__88948,Vvar__6__ropp__88953,Vvar__7__rdiv__88956,Vvar__8__rinv__88961,Vvar__9__req__88964,Vvar__6__ropp__88953)
                 => ( c_24__type__89490___24t(Vvar__0__R__88935,Vvar__1__rO__88936,Vvar__2__rI__88937,Vvar__3__radd__88938,Vvar__4__rmul__88943,Vvar__5__rsub__88948,Vvar__6__ropp__88953,Vvar__7__rdiv__88956,Vvar__8__rinv__88961,Vvar__9__req__88964,Vvar__7__rdiv__88956)
                   => ( c_24__type__89572___24t(Vvar__0__R__88935,Vvar__1__rO__88936,Vvar__2__rI__88937,Vvar__3__radd__88938,Vvar__4__rmul__88943,Vvar__5__rsub__88948,Vvar__6__ropp__88953,Vvar__7__rdiv__88956,Vvar__8__rinv__88961,Vvar__9__req__88964,Vvar__8__rinv__88961)
                     => ( c_24__type__89665___24t(Vvar__0__R__88935,Vvar__1__rO__88936,Vvar__2__rI__88937,Vvar__3__radd__88938,Vvar__4__rmul__88943,Vvar__5__rsub__88948,Vvar__6__ropp__88953,Vvar__7__rdiv__88956,Vvar__8__rinv__88961,Vvar__9__req__88964,Vvar__9__req__88964)
                       => ( cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(Vvar__0__R__88935,Vvar__1__rO__88936,Vvar__2__rI__88937,Vvar__3__radd__88938,Vvar__4__rmul__88943,Vvar__5__rsub__88948,Vvar__6__ropp__88953,Vvar__7__rdiv__88956,Vvar__8__rinv__88961,Vvar__9__req__88964)
                         => ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(Vvar__0__R__88935,Vvar__1__rO__88936,Vvar__2__rI__88937,Vvar__3__radd__88938,Vvar__4__rmul__88943,Vvar__5__rsub__88948,Vvar__6__ropp__88953,Vvar__9__req__88964)
                            & ~ p(happ(happ(Vvar__9__req__88964,Vvar__2__rI__88937),Vvar__1__rO__88936))
                            & ! [Vvar__var__var__var__var__var__var__12__p__89007__89009__89016__89018__89020__89022__89024] :
                                ( t(Vvar__var__var__var__var__var__var__12__p__89007__89009__89016__89018__89020__89022__89024,Vvar__0__R__88935)
                               => ! [Vvar__var__var__var__var__var__var__13__q__89008__89010__89017__89019__89021__89023__89025] :
                                    ( t(Vvar__var__var__var__var__var__var__13__q__89008__89010__89017__89019__89021__89023__89025,Vvar__0__R__88935)
                                   => p(happ(happ(Vvar__9__req__88964,happ(happ(Vvar__7__rdiv__88956,Vvar__var__var__var__var__var__var__12__p__89007__89009__89016__89018__89020__89022__89024),Vvar__var__var__var__var__var__var__13__q__89008__89010__89017__89019__89021__89023__89025)),happ(happ(Vvar__4__rmul__88943,Vvar__var__var__var__var__var__var__12__p__89007__89009__89016__89018__89020__89022__89024),happ(Vvar__8__rinv__88961,Vvar__var__var__var__var__var__var__13__q__89008__89010__89017__89019__89021__89023__89025)))) ) )
                            & ! [Vvar__var__var__var__var__var__var__var__13__p__89012__89014__89026__89028__89030__89032__89034__89036] :
                                ( t(Vvar__var__var__var__var__var__var__var__13__p__89012__89014__89026__89028__89030__89032__89034__89036,Vvar__0__R__88935)
                               => ( ~ p(happ(happ(Vvar__9__req__88964,Vvar__var__var__var__var__var__var__var__13__p__89012__89014__89026__89028__89030__89032__89034__89036),Vvar__1__rO__88936))
                                 => p(happ(happ(Vvar__9__req__88964,happ(happ(Vvar__4__rmul__88943,happ(Vvar__8__rinv__88961,Vvar__var__var__var__var__var__var__var__13__p__89012__89014__89026__89028__89030__89032__89034__89036)),Vvar__var__var__var__var__var__var__var__13__p__89012__89014__89026__89028__89030__89032__89034__89036)),Vvar__2__rI__88937)) ) )
                            & p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Field_theory.field_theory',axiom,
    ! [Vvar__0__R__86668,Vvar__1__rO__86669,Vvar__2__rI__86670,Vvar__3__radd__86671,Vvar__4__rmul__86676,Vvar__5__rsub__86681,Vvar__6__ropp__86686,Vvar__7__rdiv__86689,Vvar__8__rinv__86694,Vvar__9__req__86697] :
      ( cType___24t(Vvar__0__R__86668)
     => ( t(Vvar__1__rO__86669,Vvar__0__R__86668)
       => ( t(Vvar__2__rI__86670,Vvar__0__R__86668)
         => ( c_24__type__86862___24t(Vvar__0__R__86668,Vvar__1__rO__86669,Vvar__2__rI__86670,Vvar__3__radd__86671,Vvar__4__rmul__86676,Vvar__5__rsub__86681,Vvar__6__ropp__86686,Vvar__7__rdiv__86689,Vvar__8__rinv__86694,Vvar__9__req__86697,Vvar__3__radd__86671)
           => ( c_24__type__86955___24t(Vvar__0__R__86668,Vvar__1__rO__86669,Vvar__2__rI__86670,Vvar__3__radd__86671,Vvar__4__rmul__86676,Vvar__5__rsub__86681,Vvar__6__ropp__86686,Vvar__7__rdiv__86689,Vvar__8__rinv__86694,Vvar__9__req__86697,Vvar__4__rmul__86676)
             => ( c_24__type__87048___24t(Vvar__0__R__86668,Vvar__1__rO__86669,Vvar__2__rI__86670,Vvar__3__radd__86671,Vvar__4__rmul__86676,Vvar__5__rsub__86681,Vvar__6__ropp__86686,Vvar__7__rdiv__86689,Vvar__8__rinv__86694,Vvar__9__req__86697,Vvar__5__rsub__86681)
               => ( c_24__type__87130___24t(Vvar__0__R__86668,Vvar__1__rO__86669,Vvar__2__rI__86670,Vvar__3__radd__86671,Vvar__4__rmul__86676,Vvar__5__rsub__86681,Vvar__6__ropp__86686,Vvar__7__rdiv__86689,Vvar__8__rinv__86694,Vvar__9__req__86697,Vvar__6__ropp__86686)
                 => ( c_24__type__87223___24t(Vvar__0__R__86668,Vvar__1__rO__86669,Vvar__2__rI__86670,Vvar__3__radd__86671,Vvar__4__rmul__86676,Vvar__5__rsub__86681,Vvar__6__ropp__86686,Vvar__7__rdiv__86689,Vvar__8__rinv__86694,Vvar__9__req__86697,Vvar__7__rdiv__86689)
                   => ( c_24__type__87305___24t(Vvar__0__R__86668,Vvar__1__rO__86669,Vvar__2__rI__86670,Vvar__3__radd__86671,Vvar__4__rmul__86676,Vvar__5__rsub__86681,Vvar__6__ropp__86686,Vvar__7__rdiv__86689,Vvar__8__rinv__86694,Vvar__9__req__86697,Vvar__8__rinv__86694)
                     => ( c_24__type__87398___24t(Vvar__0__R__86668,Vvar__1__rO__86669,Vvar__2__rI__86670,Vvar__3__radd__86671,Vvar__4__rmul__86676,Vvar__5__rsub__86681,Vvar__6__ropp__86686,Vvar__7__rdiv__86689,Vvar__8__rinv__86694,Vvar__9__req__86697,Vvar__9__req__86697)
                       => ( cCoq_2esetoid__ring_2eField__theory_2efield__theory___24a10(Vvar__0__R__86668,Vvar__1__rO__86669,Vvar__2__rI__86670,Vvar__3__radd__86671,Vvar__4__rmul__86676,Vvar__5__rsub__86681,Vvar__6__ropp__86686,Vvar__7__rdiv__86689,Vvar__8__rinv__86694,Vvar__9__req__86697)
                         => ( cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(Vvar__0__R__86668,Vvar__1__rO__86669,Vvar__2__rI__86670,Vvar__3__radd__86671,Vvar__4__rmul__86676,Vvar__5__rsub__86681,Vvar__6__ropp__86686,Vvar__9__req__86697)
                            & ~ p(happ(happ(Vvar__9__req__86697,Vvar__2__rI__86670),Vvar__1__rO__86669))
                            & ! [Vvar__var__var__var__var__var__var__12__p__86740__86742__86749__86751__86753__86755__86757] :
                                ( t(Vvar__var__var__var__var__var__var__12__p__86740__86742__86749__86751__86753__86755__86757,Vvar__0__R__86668)
                               => ! [Vvar__var__var__var__var__var__var__13__q__86741__86743__86750__86752__86754__86756__86758] :
                                    ( t(Vvar__var__var__var__var__var__var__13__q__86741__86743__86750__86752__86754__86756__86758,Vvar__0__R__86668)
                                   => p(happ(happ(Vvar__9__req__86697,happ(happ(Vvar__7__rdiv__86689,Vvar__var__var__var__var__var__var__12__p__86740__86742__86749__86751__86753__86755__86757),Vvar__var__var__var__var__var__var__13__q__86741__86743__86750__86752__86754__86756__86758)),happ(happ(Vvar__4__rmul__86676,Vvar__var__var__var__var__var__var__12__p__86740__86742__86749__86751__86753__86755__86757),happ(Vvar__8__rinv__86694,Vvar__var__var__var__var__var__var__13__q__86741__86743__86750__86752__86754__86756__86758)))) ) )
                            & ! [Vvar__var__var__var__var__var__var__var__13__p__86745__86747__86759__86761__86763__86765__86767__86769] :
                                ( t(Vvar__var__var__var__var__var__var__var__13__p__86745__86747__86759__86761__86763__86765__86767__86769,Vvar__0__R__86668)
                               => ( ~ p(happ(happ(Vvar__9__req__86697,Vvar__var__var__var__var__var__var__var__13__p__86745__86747__86759__86761__86763__86765__86767__86769),Vvar__1__rO__86669))
                                 => p(happ(happ(Vvar__9__req__86697,happ(happ(Vvar__4__rmul__86676,happ(Vvar__8__rinv__86694,Vvar__var__var__var__var__var__var__var__13__p__86745__86747__86759__86761__86763__86765__86767__86769)),Vvar__var__var__var__var__var__var__var__13__p__86745__86747__86759__86761__86763__86765__86767__86769)),Vvar__2__rI__86670)) ) )
                            & p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Field_theory.linear',axiom,
    ! [Vvar__0__C__85514,VX85515] :
      ( cType___24t(Vvar__0__C__85514)
     => ( cCoq_2esetoid__ring_2eField__theory_2elinear___24t(Vvar__0__C__85514,VX85515)
       => ? [Vvar__1__num__85517] :
            ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__85514,Vvar__1__num__85517)
            & ? [Vvar__2__denum__85518] :
                ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__85514,Vvar__2__denum__85518)
                & ? [Vvar__3__condition__85519] :
                    ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vvar__0__C__85514),Vvar__3__condition__85519)
                    & VX85515 = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(Vvar__0__C__85514,Vvar__1__num__85517,Vvar__2__denum__85518,Vvar__3__condition__85519) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Field_theory.rsplit',axiom,
    ! [Vvar__0__C__86654,VX86655] :
      ( cType___24t(Vvar__0__C__86654)
     => ( cCoq_2esetoid__ring_2eField__theory_2ersplit___24t(Vvar__0__C__86654,VX86655)
       => ? [Vvar__1__rsplit__left__86657] :
            ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__86654,Vvar__1__rsplit__left__86657)
            & ? [Vvar__2__rsplit__common__86658] :
                ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__86654,Vvar__2__rsplit__common__86658)
                & ? [Vvar__3__rsplit__right__86659] :
                    ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__86654,Vvar__3__rsplit__right__86659)
                    & VX86655 = cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(Vvar__0__C__86654,Vvar__1__rsplit__left__86657,Vvar__2__rsplit__common__86658,Vvar__3__rsplit__right__86659) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Field_theory.semi_field_theory',axiom,
    ! [Vvar__0__R__87404,Vvar__1__rO__87405,Vvar__2__rI__87406,Vvar__3__radd__87407,Vvar__4__rmul__87412,Vvar__5__rdiv__87417,Vvar__6__rinv__87422,Vvar__7__req__87425] :
      ( cType___24t(Vvar__0__R__87404)
     => ( t(Vvar__1__rO__87405,Vvar__0__R__87404)
       => ( t(Vvar__2__rI__87406,Vvar__0__R__87404)
         => ( c_24__type__87552___24t(Vvar__0__R__87404,Vvar__1__rO__87405,Vvar__2__rI__87406,Vvar__3__radd__87407,Vvar__4__rmul__87412,Vvar__5__rdiv__87417,Vvar__6__rinv__87422,Vvar__7__req__87425,Vvar__3__radd__87407)
           => ( c_24__type__87615___24t(Vvar__0__R__87404,Vvar__1__rO__87405,Vvar__2__rI__87406,Vvar__3__radd__87407,Vvar__4__rmul__87412,Vvar__5__rdiv__87417,Vvar__6__rinv__87422,Vvar__7__req__87425,Vvar__4__rmul__87412)
             => ( c_24__type__87678___24t(Vvar__0__R__87404,Vvar__1__rO__87405,Vvar__2__rI__87406,Vvar__3__radd__87407,Vvar__4__rmul__87412,Vvar__5__rdiv__87417,Vvar__6__rinv__87422,Vvar__7__req__87425,Vvar__5__rdiv__87417)
               => ( c_24__type__87732___24t(Vvar__0__R__87404,Vvar__1__rO__87405,Vvar__2__rI__87406,Vvar__3__radd__87407,Vvar__4__rmul__87412,Vvar__5__rdiv__87417,Vvar__6__rinv__87422,Vvar__7__req__87425,Vvar__6__rinv__87422)
                 => ( c_24__type__87795___24t(Vvar__0__R__87404,Vvar__1__rO__87405,Vvar__2__rI__87406,Vvar__3__radd__87407,Vvar__4__rmul__87412,Vvar__5__rdiv__87417,Vvar__6__rinv__87422,Vvar__7__req__87425,Vvar__7__req__87425)
                   => ( cCoq_2esetoid__ring_2eField__theory_2esemi__field__theory___24a8(Vvar__0__R__87404,Vvar__1__rO__87405,Vvar__2__rI__87406,Vvar__3__radd__87407,Vvar__4__rmul__87412,Vvar__5__rdiv__87417,Vvar__6__rinv__87422,Vvar__7__req__87425)
                     => ( cCoq_2esetoid__ring_2eRing__theory_2esemi__ring__theory___24a6(Vvar__0__R__87404,Vvar__1__rO__87405,Vvar__2__rI__87406,Vvar__3__radd__87407,Vvar__4__rmul__87412,Vvar__7__req__87425)
                        & ~ p(happ(happ(Vvar__7__req__87425,Vvar__2__rI__87406),Vvar__1__rO__87405))
                        & ! [Vvar__var__var__var__var__var__var__10__p__87460__87462__87469__87471__87473__87475__87477] :
                            ( t(Vvar__var__var__var__var__var__var__10__p__87460__87462__87469__87471__87473__87475__87477,Vvar__0__R__87404)
                           => ! [Vvar__var__var__var__var__var__var__11__q__87461__87463__87470__87472__87474__87476__87478] :
                                ( t(Vvar__var__var__var__var__var__var__11__q__87461__87463__87470__87472__87474__87476__87478,Vvar__0__R__87404)
                               => p(happ(happ(Vvar__7__req__87425,happ(happ(Vvar__5__rdiv__87417,Vvar__var__var__var__var__var__var__10__p__87460__87462__87469__87471__87473__87475__87477),Vvar__var__var__var__var__var__var__11__q__87461__87463__87470__87472__87474__87476__87478)),happ(happ(Vvar__4__rmul__87412,Vvar__var__var__var__var__var__var__10__p__87460__87462__87469__87471__87473__87475__87477),happ(Vvar__6__rinv__87422,Vvar__var__var__var__var__var__var__11__q__87461__87463__87470__87472__87474__87476__87478)))) ) )
                        & ! [Vvar__var__var__var__var__var__var__var__11__p__87465__87467__87479__87481__87483__87485__87487__87489] :
                            ( t(Vvar__var__var__var__var__var__var__var__11__p__87465__87467__87479__87481__87483__87485__87487__87489,Vvar__0__R__87404)
                           => ( ~ p(happ(happ(Vvar__7__req__87425,Vvar__var__var__var__var__var__var__var__11__p__87465__87467__87479__87481__87483__87485__87487__87489),Vvar__1__rO__87405))
                             => p(happ(happ(Vvar__7__req__87425,happ(happ(Vvar__4__rmul__87412,happ(Vvar__6__rinv__87422,Vvar__var__var__var__var__var__var__var__11__p__87465__87467__87479__87481__87483__87485__87487__87489)),Vvar__var__var__var__var__var__var__var__11__p__87465__87467__87479__87481__87483__87485__87487__87489)),Vvar__2__rI__87406)) ) )
                        & p(c_24True) ) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.InitialRing.hypo',axiom,
    ! [VX89671] :
      ( cCoq_2esetoid__ring_2eInitialRing_2ehypo___24t(VX89671)
     => ? [Vvar__0__hypo__type__89672] :
          ( cType___24t(Vvar__0__hypo__type__89672)
          & ? [Vvar__1__hypo__proof__89673] :
              ( t(Vvar__1__hypo__proof__89673,Vvar__0__hypo__type__89672)
              & VX89671 = cCoq_2esetoid__ring_2eInitialRing_2emkhypo___24a2(Vvar__0__hypo__type__89672,Vvar__1__hypo__proof__89673) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Ring_polynom.Mon',axiom,
    ! [VX1388] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(VX1388)
     => ( VX1388 = cCoq_2esetoid__ring_2eRing__polynom_2emon0
        | ? [Vvar__0___24Anonymous__1389] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1389)
            & ? [Vvar__1___24Anonymous__1390] :
                ( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(Vvar__1___24Anonymous__1390)
                & VX1388 = cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__1389,Vvar__1___24Anonymous__1390) ) )
        | ? [Vvar__0___24Anonymous__1391] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__1391)
            & ? [Vvar__1___24Anonymous__1392] :
                ( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(Vvar__1___24Anonymous__1392)
                & VX1388 = cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(Vvar__0___24Anonymous__1391,Vvar__1___24Anonymous__1392) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Ring_polynom.PExpr',axiom,
    ! [Vvar__0__C__1409,VX1410] :
      ( cType___24t(Vvar__0__C__1409)
     => ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__1409,VX1410)
       => ( VX1410 = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__1409)
          | VX1410 = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__1409)
          | ? [Vvar__1___24Anonymous__1414] :
              ( t(Vvar__1___24Anonymous__1414,Vvar__0__C__1409)
              & VX1410 = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(Vvar__0__C__1409,Vvar__1___24Anonymous__1414) )
          | ? [Vvar__1___24Anonymous__1416] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__1416)
              & VX1410 = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(Vvar__0__C__1409,Vvar__1___24Anonymous__1416) )
          | ? [Vvar__1___24Anonymous__1418] :
              ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__1409,Vvar__1___24Anonymous__1418)
              & ? [Vvar__2___24Anonymous__1419] :
                  ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__1409,Vvar__2___24Anonymous__1419)
                  & VX1410 = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(Vvar__0__C__1409,Vvar__1___24Anonymous__1418,Vvar__2___24Anonymous__1419) ) )
          | ? [Vvar__1___24Anonymous__1421] :
              ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__1409,Vvar__1___24Anonymous__1421)
              & ? [Vvar__2___24Anonymous__1422] :
                  ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__1409,Vvar__2___24Anonymous__1422)
                  & VX1410 = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(Vvar__0__C__1409,Vvar__1___24Anonymous__1421,Vvar__2___24Anonymous__1422) ) )
          | ? [Vvar__1___24Anonymous__1424] :
              ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__1409,Vvar__1___24Anonymous__1424)
              & ? [Vvar__2___24Anonymous__1425] :
                  ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__1409,Vvar__2___24Anonymous__1425)
                  & VX1410 = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(Vvar__0__C__1409,Vvar__1___24Anonymous__1424,Vvar__2___24Anonymous__1425) ) )
          | ? [Vvar__1___24Anonymous__1427] :
              ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__1409,Vvar__1___24Anonymous__1427)
              & VX1410 = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(Vvar__0__C__1409,Vvar__1___24Anonymous__1427) )
          | ? [Vvar__1___24Anonymous__1429] :
              ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__1409,Vvar__1___24Anonymous__1429)
              & ? [Vvar__2___24Anonymous__1430] :
                  ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__1430)
                  & VX1410 = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(Vvar__0__C__1409,Vvar__1___24Anonymous__1429,Vvar__2___24Anonymous__1430) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Ring_polynom.Pol',axiom,
    ! [Vvar__0__C__1207,VX1208] :
      ( cType___24t(Vvar__0__C__1207)
     => ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__1207,VX1208)
       => ( ? [Vvar__1___24Anonymous__1210] :
              ( t(Vvar__1___24Anonymous__1210,Vvar__0__C__1207)
              & VX1208 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__1207,Vvar__1___24Anonymous__1210) )
          | ? [Vvar__1___24Anonymous__1212] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__1212)
              & ? [Vvar__2___24Anonymous__1213] :
                  ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__1207,Vvar__2___24Anonymous__1213)
                  & VX1208 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__1207,Vvar__1___24Anonymous__1212,Vvar__2___24Anonymous__1213) ) )
          | ? [Vvar__1___24Anonymous__1215] :
              ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__1207,Vvar__1___24Anonymous__1215)
              & ? [Vvar__2___24Anonymous__1216] :
                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__1216)
                  & ? [Vvar__3___24Anonymous__1217] :
                      ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__1207,Vvar__3___24Anonymous__1217)
                      & VX1208 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(Vvar__0__C__1207,Vvar__1___24Anonymous__1215,Vvar__2___24Anonymous__1216,Vvar__3___24Anonymous__1217) ) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Ring_theory.almost_ring_theory',axiom,
    ! [Vvar__0__R__90997,Vvar__1__rO__90998,Vvar__2__rI__90999,Vvar__3__radd__91000,Vvar__4__rmul__91005,Vvar__5__rsub__91010,Vvar__6__ropp__91015,Vvar__7__req__91018] :
      ( cType___24t(Vvar__0__R__90997)
     => ( t(Vvar__1__rO__90998,Vvar__0__R__90997)
       => ( t(Vvar__2__rI__90999,Vvar__0__R__90997)
         => ( c_24__type__91246___24t(Vvar__0__R__90997,Vvar__1__rO__90998,Vvar__2__rI__90999,Vvar__3__radd__91000,Vvar__4__rmul__91005,Vvar__5__rsub__91010,Vvar__6__ropp__91015,Vvar__7__req__91018,Vvar__3__radd__91000)
           => ( c_24__type__91309___24t(Vvar__0__R__90997,Vvar__1__rO__90998,Vvar__2__rI__90999,Vvar__3__radd__91000,Vvar__4__rmul__91005,Vvar__5__rsub__91010,Vvar__6__ropp__91015,Vvar__7__req__91018,Vvar__4__rmul__91005)
             => ( c_24__type__91372___24t(Vvar__0__R__90997,Vvar__1__rO__90998,Vvar__2__rI__90999,Vvar__3__radd__91000,Vvar__4__rmul__91005,Vvar__5__rsub__91010,Vvar__6__ropp__91015,Vvar__7__req__91018,Vvar__5__rsub__91010)
               => ( c_24__type__91426___24t(Vvar__0__R__90997,Vvar__1__rO__90998,Vvar__2__rI__90999,Vvar__3__radd__91000,Vvar__4__rmul__91005,Vvar__5__rsub__91010,Vvar__6__ropp__91015,Vvar__7__req__91018,Vvar__6__ropp__91015)
                 => ( c_24__type__91489___24t(Vvar__0__R__90997,Vvar__1__rO__90998,Vvar__2__rI__90999,Vvar__3__radd__91000,Vvar__4__rmul__91005,Vvar__5__rsub__91010,Vvar__6__ropp__91015,Vvar__7__req__91018,Vvar__7__req__91018)
                   => ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(Vvar__0__R__90997,Vvar__1__rO__90998,Vvar__2__rI__90999,Vvar__3__radd__91000,Vvar__4__rmul__91005,Vvar__5__rsub__91010,Vvar__6__ropp__91015,Vvar__7__req__91018)
                     => ( ! [Vvar__var__var__var__var__var__8__x__91051__91052__91105__91106__91107__91108] :
                            ( t(Vvar__var__var__var__var__var__8__x__91051__91052__91105__91106__91107__91108,Vvar__0__R__90997)
                           => p(happ(happ(Vvar__7__req__91018,happ(happ(Vvar__3__radd__91000,Vvar__1__rO__90998),Vvar__var__var__var__var__var__8__x__91051__91052__91105__91106__91107__91108)),Vvar__var__var__var__var__var__8__x__91051__91052__91105__91106__91107__91108)) )
                        & ! [Vvar__var__var__var__var__9__x__91054__91056__91109__91111__91113] :
                            ( t(Vvar__var__var__var__var__9__x__91054__91056__91109__91111__91113,Vvar__0__R__90997)
                           => ! [Vvar__var__var__var__var__10__y__91055__91057__91110__91112__91114] :
                                ( t(Vvar__var__var__var__var__10__y__91055__91057__91110__91112__91114,Vvar__0__R__90997)
                               => p(happ(happ(Vvar__7__req__91018,happ(happ(Vvar__3__radd__91000,Vvar__var__var__var__var__9__x__91054__91056__91109__91111__91113),Vvar__var__var__var__var__10__y__91055__91057__91110__91112__91114)),happ(happ(Vvar__3__radd__91000,Vvar__var__var__var__var__10__y__91055__91057__91110__91112__91114),Vvar__var__var__var__var__9__x__91054__91056__91109__91111__91113))) ) )
                        & ! [Vvar__var__var__var__var__10__x__91059__91062__91115__91118__91121] :
                            ( t(Vvar__var__var__var__var__10__x__91059__91062__91115__91118__91121,Vvar__0__R__90997)
                           => ! [Vvar__var__var__var__var__11__y__91060__91063__91116__91119__91122] :
                                ( t(Vvar__var__var__var__var__11__y__91060__91063__91116__91119__91122,Vvar__0__R__90997)
                               => ! [Vvar__var__var__var__var__12__z__91061__91064__91117__91120__91123] :
                                    ( t(Vvar__var__var__var__var__12__z__91061__91064__91117__91120__91123,Vvar__0__R__90997)
                                   => p(happ(happ(Vvar__7__req__91018,happ(happ(Vvar__3__radd__91000,Vvar__var__var__var__var__10__x__91059__91062__91115__91118__91121),happ(happ(Vvar__3__radd__91000,Vvar__var__var__var__var__11__y__91060__91063__91116__91119__91122),Vvar__var__var__var__var__12__z__91061__91064__91117__91120__91123))),happ(happ(Vvar__3__radd__91000,happ(happ(Vvar__3__radd__91000,Vvar__var__var__var__var__10__x__91059__91062__91115__91118__91121),Vvar__var__var__var__var__11__y__91060__91063__91116__91119__91122)),Vvar__var__var__var__var__12__z__91061__91064__91117__91120__91123))) ) ) )
                        & ! [Vvar__var__var__var__var__var__11__x__91066__91067__91124__91125__91126__91127] :
                            ( t(Vvar__var__var__var__var__var__11__x__91066__91067__91124__91125__91126__91127,Vvar__0__R__90997)
                           => p(happ(happ(Vvar__7__req__91018,happ(happ(Vvar__4__rmul__91005,Vvar__2__rI__90999),Vvar__var__var__var__var__var__11__x__91066__91067__91124__91125__91126__91127)),Vvar__var__var__var__var__var__11__x__91066__91067__91124__91125__91126__91127)) )
                        & ! [Vvar__var__var__var__var__var__12__x__91069__91070__91128__91129__91130__91131] :
                            ( t(Vvar__var__var__var__var__var__12__x__91069__91070__91128__91129__91130__91131,Vvar__0__R__90997)
                           => p(happ(happ(Vvar__7__req__91018,happ(happ(Vvar__4__rmul__91005,Vvar__1__rO__90998),Vvar__var__var__var__var__var__12__x__91069__91070__91128__91129__91130__91131)),Vvar__1__rO__90998)) )
                        & ! [Vvar__var__var__var__var__13__x__91072__91074__91132__91134__91136] :
                            ( t(Vvar__var__var__var__var__13__x__91072__91074__91132__91134__91136,Vvar__0__R__90997)
                           => ! [Vvar__var__var__var__var__14__y__91073__91075__91133__91135__91137] :
                                ( t(Vvar__var__var__var__var__14__y__91073__91075__91133__91135__91137,Vvar__0__R__90997)
                               => p(happ(happ(Vvar__7__req__91018,happ(happ(Vvar__4__rmul__91005,Vvar__var__var__var__var__13__x__91072__91074__91132__91134__91136),Vvar__var__var__var__var__14__y__91073__91075__91133__91135__91137)),happ(happ(Vvar__4__rmul__91005,Vvar__var__var__var__var__14__y__91073__91075__91133__91135__91137),Vvar__var__var__var__var__13__x__91072__91074__91132__91134__91136))) ) )
                        & ! [Vvar__var__var__var__var__14__x__91077__91080__91138__91141__91144] :
                            ( t(Vvar__var__var__var__var__14__x__91077__91080__91138__91141__91144,Vvar__0__R__90997)
                           => ! [Vvar__var__var__var__var__15__y__91078__91081__91139__91142__91145] :
                                ( t(Vvar__var__var__var__var__15__y__91078__91081__91139__91142__91145,Vvar__0__R__90997)
                               => ! [Vvar__var__var__var__var__16__z__91079__91082__91140__91143__91146] :
                                    ( t(Vvar__var__var__var__var__16__z__91079__91082__91140__91143__91146,Vvar__0__R__90997)
                                   => p(happ(happ(Vvar__7__req__91018,happ(happ(Vvar__4__rmul__91005,Vvar__var__var__var__var__14__x__91077__91080__91138__91141__91144),happ(happ(Vvar__4__rmul__91005,Vvar__var__var__var__var__15__y__91078__91081__91139__91142__91145),Vvar__var__var__var__var__16__z__91079__91082__91140__91143__91146))),happ(happ(Vvar__4__rmul__91005,happ(happ(Vvar__4__rmul__91005,Vvar__var__var__var__var__14__x__91077__91080__91138__91141__91144),Vvar__var__var__var__var__15__y__91078__91081__91139__91142__91145)),Vvar__var__var__var__var__16__z__91079__91082__91140__91143__91146))) ) ) )
                        & ! [Vvar__var__var__var__var__var__15__x__91084__91087__91147__91150__91153__91156] :
                            ( t(Vvar__var__var__var__var__var__15__x__91084__91087__91147__91150__91153__91156,Vvar__0__R__90997)
                           => ! [Vvar__var__var__var__var__var__16__y__91085__91088__91148__91151__91154__91157] :
                                ( t(Vvar__var__var__var__var__var__16__y__91085__91088__91148__91151__91154__91157,Vvar__0__R__90997)
                               => ! [Vvar__var__var__var__var__var__17__z__91086__91089__91149__91152__91155__91158] :
                                    ( t(Vvar__var__var__var__var__var__17__z__91086__91089__91149__91152__91155__91158,Vvar__0__R__90997)
                                   => p(happ(happ(Vvar__7__req__91018,happ(happ(Vvar__4__rmul__91005,happ(happ(Vvar__3__radd__91000,Vvar__var__var__var__var__var__15__x__91084__91087__91147__91150__91153__91156),Vvar__var__var__var__var__var__16__y__91085__91088__91148__91151__91154__91157)),Vvar__var__var__var__var__var__17__z__91086__91089__91149__91152__91155__91158)),happ(happ(Vvar__3__radd__91000,happ(happ(Vvar__4__rmul__91005,Vvar__var__var__var__var__var__15__x__91084__91087__91147__91150__91153__91156),Vvar__var__var__var__var__var__17__z__91086__91089__91149__91152__91155__91158)),happ(happ(Vvar__4__rmul__91005,Vvar__var__var__var__var__var__16__y__91085__91088__91148__91151__91154__91157),Vvar__var__var__var__var__var__17__z__91086__91089__91149__91152__91155__91158)))) ) ) )
                        & ! [Vvar__var__var__var__var__var__16__x__91091__91093__91159__91161__91163__91165] :
                            ( t(Vvar__var__var__var__var__var__16__x__91091__91093__91159__91161__91163__91165,Vvar__0__R__90997)
                           => ! [Vvar__var__var__var__var__var__17__y__91092__91094__91160__91162__91164__91166] :
                                ( t(Vvar__var__var__var__var__var__17__y__91092__91094__91160__91162__91164__91166,Vvar__0__R__90997)
                               => p(happ(happ(Vvar__7__req__91018,happ(Vvar__6__ropp__91015,happ(happ(Vvar__4__rmul__91005,Vvar__var__var__var__var__var__16__x__91091__91093__91159__91161__91163__91165),Vvar__var__var__var__var__var__17__y__91092__91094__91160__91162__91164__91166))),happ(happ(Vvar__4__rmul__91005,happ(Vvar__6__ropp__91015,Vvar__var__var__var__var__var__16__x__91091__91093__91159__91161__91163__91165)),Vvar__var__var__var__var__var__17__y__91092__91094__91160__91162__91164__91166))) ) )
                        & ! [Vvar__var__var__var__var__var__17__x__91096__91098__91167__91169__91171__91173] :
                            ( t(Vvar__var__var__var__var__var__17__x__91096__91098__91167__91169__91171__91173,Vvar__0__R__90997)
                           => ! [Vvar__var__var__var__var__var__18__y__91097__91099__91168__91170__91172__91174] :
                                ( t(Vvar__var__var__var__var__var__18__y__91097__91099__91168__91170__91172__91174,Vvar__0__R__90997)
                               => p(happ(happ(Vvar__7__req__91018,happ(Vvar__6__ropp__91015,happ(happ(Vvar__3__radd__91000,Vvar__var__var__var__var__var__17__x__91096__91098__91167__91169__91171__91173),Vvar__var__var__var__var__var__18__y__91097__91099__91168__91170__91172__91174))),happ(happ(Vvar__3__radd__91000,happ(Vvar__6__ropp__91015,Vvar__var__var__var__var__var__17__x__91096__91098__91167__91169__91171__91173)),happ(Vvar__6__ropp__91015,Vvar__var__var__var__var__var__18__y__91097__91099__91168__91170__91172__91174)))) ) )
                        & ! [Vvar__var__var__var__var__var__var__18__x__91101__91103__91175__91177__91179__91181__91183] :
                            ( t(Vvar__var__var__var__var__var__var__18__x__91101__91103__91175__91177__91179__91181__91183,Vvar__0__R__90997)
                           => ! [Vvar__var__var__var__var__var__var__19__y__91102__91104__91176__91178__91180__91182__91184] :
                                ( t(Vvar__var__var__var__var__var__var__19__y__91102__91104__91176__91178__91180__91182__91184,Vvar__0__R__90997)
                               => p(happ(happ(Vvar__7__req__91018,happ(happ(Vvar__5__rsub__91010,Vvar__var__var__var__var__var__var__18__x__91101__91103__91175__91177__91179__91181__91183),Vvar__var__var__var__var__var__var__19__y__91102__91104__91176__91178__91180__91182__91184)),happ(happ(Vvar__3__radd__91000,Vvar__var__var__var__var__var__var__18__x__91101__91103__91175__91177__91179__91181__91183),happ(Vvar__6__ropp__91015,Vvar__var__var__var__var__var__var__19__y__91102__91104__91176__91178__91180__91182__91184)))) ) )
                        & p(c_24True) ) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Ring_theory.power_theory',axiom,
    ! [Vvar__0__R__106753,Vvar__1__rI__106754,Vvar__2__rmul__106755,Vvar__3__req__106760,Vvar__4__Cpow__106765,Vvar__5__Cp__phi__106766,Vvar__6__rpow__106769] :
      ( cType___24t(Vvar__0__R__106753)
     => ( t(Vvar__1__rI__106754,Vvar__0__R__106753)
       => ( c_24__type__106855___24t(Vvar__0__R__106753,Vvar__1__rI__106754,Vvar__2__rmul__106755,Vvar__3__req__106760,Vvar__4__Cpow__106765,Vvar__5__Cp__phi__106766,Vvar__6__rpow__106769,Vvar__2__rmul__106755)
         => ( c_24__type__106899___24t(Vvar__0__R__106753,Vvar__1__rI__106754,Vvar__2__rmul__106755,Vvar__3__req__106760,Vvar__4__Cpow__106765,Vvar__5__Cp__phi__106766,Vvar__6__rpow__106769,Vvar__3__req__106760)
           => ( cType___24t(Vvar__4__Cpow__106765)
             => ( c_24__type__106935___24t(Vvar__0__R__106753,Vvar__1__rI__106754,Vvar__2__rmul__106755,Vvar__3__req__106760,Vvar__4__Cpow__106765,Vvar__5__Cp__phi__106766,Vvar__6__rpow__106769,Vvar__5__Cp__phi__106766)
               => ( c_24__type__106979___24t(Vvar__0__R__106753,Vvar__1__rI__106754,Vvar__2__rmul__106755,Vvar__3__req__106760,Vvar__4__Cpow__106765,Vvar__5__Cp__phi__106766,Vvar__6__rpow__106769,Vvar__6__rpow__106769)
                 => ( cCoq_2esetoid__ring_2eRing__theory_2epower__theory___24a7(Vvar__0__R__106753,Vvar__1__rI__106754,Vvar__2__rmul__106755,Vvar__3__req__106760,Vvar__4__Cpow__106765,Vvar__5__Cp__phi__106766,Vvar__6__rpow__106769)
                   => ( ! [Vvar__var__var__var__var__var__var__var__7__r__106797__106799__106801__106803__106805__106807__106809__106811] :
                          ( t(Vvar__var__var__var__var__var__var__var__7__r__106797__106799__106801__106803__106805__106807__106809__106811,Vvar__0__R__106753)
                         => ! [Vvar__var__var__var__var__var__var__var__8__n__106798__106800__106802__106804__106806__106808__106810__106812] :
                              ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__var__var__var__var__var__var__var__8__n__106798__106800__106802__106804__106806__106808__106810__106812)
                             => p(happ(happ(Vvar__3__req__106760,happ(happ(Vvar__6__rpow__106769,Vvar__var__var__var__var__var__var__var__7__r__106797__106799__106801__106803__106805__106807__106809__106811),happ(Vvar__5__Cp__phi__106766,Vvar__var__var__var__var__var__var__var__8__n__106798__106800__106802__106804__106806__106808__106810__106812))),cCoq_2esetoid__ring_2eRing__theory_2epow__N___24a5(Vvar__0__R__106753,Vvar__1__rI__106754,Vvar__2__rmul__106755,Vvar__var__var__var__var__var__var__var__7__r__106797__106799__106801__106803__106805__106807__106809__106811,Vvar__var__var__var__var__var__var__var__8__n__106798__106800__106802__106804__106806__106808__106810__106812))) ) )
                      & p(c_24True) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Ring_theory.ring_eq_ext',axiom,
    ! [Vvar__0__R__88458,Vvar__1__radd__88459,Vvar__2__rmul__88464,Vvar__3__ropp__88469,Vvar__4__req__88472] :
      ( cType___24t(Vvar__0__R__88458)
     => ( c_24__type__88563___24t(Vvar__0__R__88458,Vvar__1__radd__88459,Vvar__2__rmul__88464,Vvar__3__ropp__88469,Vvar__4__req__88472,Vvar__1__radd__88459)
       => ( c_24__type__88593___24t(Vvar__0__R__88458,Vvar__1__radd__88459,Vvar__2__rmul__88464,Vvar__3__ropp__88469,Vvar__4__req__88472,Vvar__2__rmul__88464)
         => ( c_24__type__88617___24t(Vvar__0__R__88458,Vvar__1__radd__88459,Vvar__2__rmul__88464,Vvar__3__ropp__88469,Vvar__4__req__88472,Vvar__3__ropp__88469)
           => ( c_24__type__88647___24t(Vvar__0__R__88458,Vvar__1__radd__88459,Vvar__2__rmul__88464,Vvar__3__ropp__88469,Vvar__4__req__88472,Vvar__4__req__88472)
             => ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(Vvar__0__R__88458,Vvar__1__radd__88459,Vvar__2__rmul__88464,Vvar__3__ropp__88469,Vvar__4__req__88472)
               => ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__88677___24a5(Vvar__0__R__88458,Vvar__1__radd__88459,Vvar__2__rmul__88464,Vvar__3__ropp__88469,Vvar__4__req__88472),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__88458,c_24__type__88701___24a5(Vvar__0__R__88458,Vvar__1__radd__88459,Vvar__2__rmul__88464,Vvar__3__ropp__88469,Vvar__4__req__88472),Vvar__4__req__88472,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__88458,Vvar__0__R__88458,Vvar__4__req__88472,Vvar__4__req__88472)),Vvar__1__radd__88459)
                  & cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__88734___24a5(Vvar__0__R__88458,Vvar__1__radd__88459,Vvar__2__rmul__88464,Vvar__3__ropp__88469,Vvar__4__req__88472),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__88458,c_24__type__88758___24a5(Vvar__0__R__88458,Vvar__1__radd__88459,Vvar__2__rmul__88464,Vvar__3__ropp__88469,Vvar__4__req__88472),Vvar__4__req__88472,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__88458,Vvar__0__R__88458,Vvar__4__req__88472,Vvar__4__req__88472)),Vvar__2__rmul__88464)
                  & cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__88785___24a5(Vvar__0__R__88458,Vvar__1__radd__88459,Vvar__2__rmul__88464,Vvar__3__ropp__88469,Vvar__4__req__88472),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__88458,Vvar__0__R__88458,Vvar__4__req__88472,Vvar__4__req__88472),Vvar__3__ropp__88469)
                  & p(c_24True) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Ring_theory.ring_kind',axiom,
    ! [VX85696] :
      ( cCoq_2esetoid__ring_2eRing__theory_2ering__kind___24t(VX85696)
     => ( VX85696 = cCoq_2esetoid__ring_2eRing__theory_2eAbstract
        | ? [Vvar__0__R__85697] :
            ( cType___24t(Vvar__0__R__85697)
            & ? [Vvar__1__req__85698] :
                ( c_24__type__76843___24t(Vvar__0__R__85697,Vvar__1__req__85698)
                & ? [Vvar__2__reqb__85703] :
                    ( c_24__type__1372___24t(Vvar__0__R__85697,Vvar__2__reqb__85703)
                    & ! [Vvar__var__3__x__85709__85712] :
                        ( t(Vvar__var__3__x__85709__85712,Vvar__0__R__85697)
                       => ! [Vvar__var__4__y__85710__85713] :
                            ( t(Vvar__var__4__y__85710__85713,Vvar__0__R__85697)
                           => ( happ(happ(Vvar__2__reqb__85703,Vvar__var__3__x__85709__85712),Vvar__var__4__y__85710__85713) = cCoq_2eInit_2eDatatypes_2etrue
                             => p(happ(happ(Vvar__1__req__85698,Vvar__var__3__x__85709__85712),Vvar__var__4__y__85710__85713)) ) ) )
                    & VX85696 = cCoq_2esetoid__ring_2eRing__theory_2eComputational___24a3(Vvar__0__R__85697,Vvar__1__req__85698,Vvar__2__reqb__85703) ) ) )
        | ? [Vvar__0__R__85715] :
            ( cType___24t(Vvar__0__R__85715)
            & ? [Vvar__1__rO__85716] :
                ( t(Vvar__1__rO__85716,Vvar__0__R__85715)
                & ? [Vvar__2__rI__85717] :
                    ( t(Vvar__2__rI__85717,Vvar__0__R__85715)
                    & ? [Vvar__3__radd__85718] :
                        ( c_24__type__1859___24t(Vvar__0__R__85715,Vvar__3__radd__85718)
                        & ? [Vvar__4__rmul__85723] :
                            ( c_24__type__1859___24t(Vvar__0__R__85715,Vvar__4__rmul__85723)
                            & ? [Vvar__5__rsub__85728] :
                                ( c_24__type__1859___24t(Vvar__0__R__85715,Vvar__5__rsub__85728)
                                & ? [Vvar__6__ropp__85733] :
                                    ( c_24__type__1868___24t(Vvar__0__R__85715,Vvar__6__ropp__85733)
                                    & ? [Vvar__7__req__85736] :
                                        ( c_24__type__76843___24t(Vvar__0__R__85715,Vvar__7__req__85736)
                                        & ? [Vvar__8__C__85741] :
                                            ( cType___24t(Vvar__8__C__85741)
                                            & ? [Vvar__9__cO__85742] :
                                                ( t(Vvar__9__cO__85742,Vvar__8__C__85741)
                                                & ? [Vvar__10__cI__85743] :
                                                    ( t(Vvar__10__cI__85743,Vvar__8__C__85741)
                                                    & ? [Vvar__11__cadd__85744] :
                                                        ( c_24__type__82503___24t(Vvar__0__R__85715,Vvar__8__C__85741,Vvar__11__cadd__85744)
                                                        & ? [Vvar__12__cmul__85749] :
                                                            ( c_24__type__82503___24t(Vvar__0__R__85715,Vvar__8__C__85741,Vvar__12__cmul__85749)
                                                            & ? [Vvar__13__csub__85754] :
                                                                ( c_24__type__82503___24t(Vvar__0__R__85715,Vvar__8__C__85741,Vvar__13__csub__85754)
                                                                & ? [Vvar__14__copp__85759] :
                                                                    ( c_24__type__76882___24t(Vvar__0__R__85715,Vvar__8__C__85741,Vvar__14__copp__85759)
                                                                    & ? [Vvar__15__ceqb__85762] :
                                                                        ( c_24__type__82515___24t(Vvar__0__R__85715,Vvar__8__C__85741,Vvar__15__ceqb__85762)
                                                                        & ? [Vvar__16__phi__85767] :
                                                                            ( c_24__type__80902___24t(Vvar__0__R__85715,Vvar__8__C__85741,Vvar__16__phi__85767)
                                                                            & cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(Vvar__0__R__85715,Vvar__1__rO__85716,Vvar__2__rI__85717,Vvar__3__radd__85718,Vvar__4__rmul__85723,Vvar__5__rsub__85728,Vvar__6__ropp__85733,Vvar__7__req__85736,Vvar__8__C__85741,Vvar__9__cO__85742,Vvar__10__cI__85743,Vvar__11__cadd__85744,Vvar__12__cmul__85749,Vvar__13__csub__85754,Vvar__14__copp__85759,Vvar__15__ceqb__85762,Vvar__16__phi__85767)
                                                                            & VX85696 = cCoq_2esetoid__ring_2eRing__theory_2eMorphism___24a17(Vvar__0__R__85715,Vvar__1__rO__85716,Vvar__2__rI__85717,Vvar__3__radd__85718,Vvar__4__rmul__85723,Vvar__5__rsub__85728,Vvar__6__ropp__85733,Vvar__7__req__85736,Vvar__8__C__85741,Vvar__9__cO__85742,Vvar__10__cI__85743,Vvar__11__cadd__85744,Vvar__12__cmul__85749,Vvar__13__csub__85754,Vvar__14__copp__85759,Vvar__15__ceqb__85762,Vvar__16__phi__85767) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Ring_theory.ring_morph',axiom,
    ! [Vvar__0__R__103639,Vvar__1__rO__103640,Vvar__2__rI__103641,Vvar__3__radd__103642,Vvar__4__rmul__103647,Vvar__5__rsub__103652,Vvar__6__ropp__103657,Vvar__7__req__103660,Vvar__8__C__103665,Vvar__9__cO__103666,Vvar__10__cI__103667,Vvar__11__cadd__103668,Vvar__12__cmul__103673,Vvar__13__csub__103678,Vvar__14__copp__103683,Vvar__15__ceqb__103686,Vvar__16__phi__103691] :
      ( cType___24t(Vvar__0__R__103639)
     => ( t(Vvar__1__rO__103640,Vvar__0__R__103639)
       => ( t(Vvar__2__rI__103641,Vvar__0__R__103639)
         => ( c_24__type__104035___24t(Vvar__0__R__103639,Vvar__1__rO__103640,Vvar__2__rI__103641,Vvar__3__radd__103642,Vvar__4__rmul__103647,Vvar__5__rsub__103652,Vvar__6__ropp__103657,Vvar__7__req__103660,Vvar__8__C__103665,Vvar__9__cO__103666,Vvar__10__cI__103667,Vvar__11__cadd__103668,Vvar__12__cmul__103673,Vvar__13__csub__103678,Vvar__14__copp__103683,Vvar__15__ceqb__103686,Vvar__16__phi__103691,Vvar__3__radd__103642)
           => ( c_24__type__104248___24t(Vvar__0__R__103639,Vvar__1__rO__103640,Vvar__2__rI__103641,Vvar__3__radd__103642,Vvar__4__rmul__103647,Vvar__5__rsub__103652,Vvar__6__ropp__103657,Vvar__7__req__103660,Vvar__8__C__103665,Vvar__9__cO__103666,Vvar__10__cI__103667,Vvar__11__cadd__103668,Vvar__12__cmul__103673,Vvar__13__csub__103678,Vvar__14__copp__103683,Vvar__15__ceqb__103686,Vvar__16__phi__103691,Vvar__4__rmul__103647)
             => ( c_24__type__104461___24t(Vvar__0__R__103639,Vvar__1__rO__103640,Vvar__2__rI__103641,Vvar__3__radd__103642,Vvar__4__rmul__103647,Vvar__5__rsub__103652,Vvar__6__ropp__103657,Vvar__7__req__103660,Vvar__8__C__103665,Vvar__9__cO__103666,Vvar__10__cI__103667,Vvar__11__cadd__103668,Vvar__12__cmul__103673,Vvar__13__csub__103678,Vvar__14__copp__103683,Vvar__15__ceqb__103686,Vvar__16__phi__103691,Vvar__5__rsub__103652)
               => ( c_24__type__104656___24t(Vvar__0__R__103639,Vvar__1__rO__103640,Vvar__2__rI__103641,Vvar__3__radd__103642,Vvar__4__rmul__103647,Vvar__5__rsub__103652,Vvar__6__ropp__103657,Vvar__7__req__103660,Vvar__8__C__103665,Vvar__9__cO__103666,Vvar__10__cI__103667,Vvar__11__cadd__103668,Vvar__12__cmul__103673,Vvar__13__csub__103678,Vvar__14__copp__103683,Vvar__15__ceqb__103686,Vvar__16__phi__103691,Vvar__6__ropp__103657)
                 => ( c_24__type__104869___24t(Vvar__0__R__103639,Vvar__1__rO__103640,Vvar__2__rI__103641,Vvar__3__radd__103642,Vvar__4__rmul__103647,Vvar__5__rsub__103652,Vvar__6__ropp__103657,Vvar__7__req__103660,Vvar__8__C__103665,Vvar__9__cO__103666,Vvar__10__cI__103667,Vvar__11__cadd__103668,Vvar__12__cmul__103673,Vvar__13__csub__103678,Vvar__14__copp__103683,Vvar__15__ceqb__103686,Vvar__16__phi__103691,Vvar__7__req__103660)
                   => ( cType___24t(Vvar__8__C__103665)
                     => ( t(Vvar__9__cO__103666,Vvar__8__C__103665)
                       => ( t(Vvar__10__cI__103667,Vvar__8__C__103665)
                         => ( c_24__type__105082___24t(Vvar__0__R__103639,Vvar__1__rO__103640,Vvar__2__rI__103641,Vvar__3__radd__103642,Vvar__4__rmul__103647,Vvar__5__rsub__103652,Vvar__6__ropp__103657,Vvar__7__req__103660,Vvar__8__C__103665,Vvar__9__cO__103666,Vvar__10__cI__103667,Vvar__11__cadd__103668,Vvar__12__cmul__103673,Vvar__13__csub__103678,Vvar__14__copp__103683,Vvar__15__ceqb__103686,Vvar__16__phi__103691,Vvar__11__cadd__103668)
                           => ( c_24__type__105295___24t(Vvar__0__R__103639,Vvar__1__rO__103640,Vvar__2__rI__103641,Vvar__3__radd__103642,Vvar__4__rmul__103647,Vvar__5__rsub__103652,Vvar__6__ropp__103657,Vvar__7__req__103660,Vvar__8__C__103665,Vvar__9__cO__103666,Vvar__10__cI__103667,Vvar__11__cadd__103668,Vvar__12__cmul__103673,Vvar__13__csub__103678,Vvar__14__copp__103683,Vvar__15__ceqb__103686,Vvar__16__phi__103691,Vvar__12__cmul__103673)
                             => ( c_24__type__105508___24t(Vvar__0__R__103639,Vvar__1__rO__103640,Vvar__2__rI__103641,Vvar__3__radd__103642,Vvar__4__rmul__103647,Vvar__5__rsub__103652,Vvar__6__ropp__103657,Vvar__7__req__103660,Vvar__8__C__103665,Vvar__9__cO__103666,Vvar__10__cI__103667,Vvar__11__cadd__103668,Vvar__12__cmul__103673,Vvar__13__csub__103678,Vvar__14__copp__103683,Vvar__15__ceqb__103686,Vvar__16__phi__103691,Vvar__13__csub__103678)
                               => ( c_24__type__105703___24t(Vvar__0__R__103639,Vvar__1__rO__103640,Vvar__2__rI__103641,Vvar__3__radd__103642,Vvar__4__rmul__103647,Vvar__5__rsub__103652,Vvar__6__ropp__103657,Vvar__7__req__103660,Vvar__8__C__103665,Vvar__9__cO__103666,Vvar__10__cI__103667,Vvar__11__cadd__103668,Vvar__12__cmul__103673,Vvar__13__csub__103678,Vvar__14__copp__103683,Vvar__15__ceqb__103686,Vvar__16__phi__103691,Vvar__14__copp__103683)
                                 => ( c_24__type__105916___24t(Vvar__0__R__103639,Vvar__1__rO__103640,Vvar__2__rI__103641,Vvar__3__radd__103642,Vvar__4__rmul__103647,Vvar__5__rsub__103652,Vvar__6__ropp__103657,Vvar__7__req__103660,Vvar__8__C__103665,Vvar__9__cO__103666,Vvar__10__cI__103667,Vvar__11__cadd__103668,Vvar__12__cmul__103673,Vvar__13__csub__103678,Vvar__14__copp__103683,Vvar__15__ceqb__103686,Vvar__16__phi__103691,Vvar__15__ceqb__103686)
                                   => ( c_24__type__106111___24t(Vvar__0__R__103639,Vvar__1__rO__103640,Vvar__2__rI__103641,Vvar__3__radd__103642,Vvar__4__rmul__103647,Vvar__5__rsub__103652,Vvar__6__ropp__103657,Vvar__7__req__103660,Vvar__8__C__103665,Vvar__9__cO__103666,Vvar__10__cI__103667,Vvar__11__cadd__103668,Vvar__12__cmul__103673,Vvar__13__csub__103678,Vvar__14__copp__103683,Vvar__15__ceqb__103686,Vvar__16__phi__103691,Vvar__16__phi__103691)
                                     => ( cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(Vvar__0__R__103639,Vvar__1__rO__103640,Vvar__2__rI__103641,Vvar__3__radd__103642,Vvar__4__rmul__103647,Vvar__5__rsub__103652,Vvar__6__ropp__103657,Vvar__7__req__103660,Vvar__8__C__103665,Vvar__9__cO__103666,Vvar__10__cI__103667,Vvar__11__cadd__103668,Vvar__12__cmul__103673,Vvar__13__csub__103678,Vvar__14__copp__103683,Vvar__15__ceqb__103686,Vvar__16__phi__103691)
                                       => ( p(happ(happ(Vvar__7__req__103660,happ(Vvar__16__phi__103691,Vvar__9__cO__103666)),Vvar__1__rO__103640))
                                          & p(happ(happ(Vvar__7__req__103660,happ(Vvar__16__phi__103691,Vvar__10__cI__103667)),Vvar__2__rI__103641))
                                          & ! [Vvar__var__var__var__var__var__var__19__x__103753__103755__103777__103779__103781__103783__103785] :
                                              ( t(Vvar__var__var__var__var__var__var__19__x__103753__103755__103777__103779__103781__103783__103785,Vvar__8__C__103665)
                                             => ! [Vvar__var__var__var__var__var__var__20__y__103754__103756__103778__103780__103782__103784__103786] :
                                                  ( t(Vvar__var__var__var__var__var__var__20__y__103754__103756__103778__103780__103782__103784__103786,Vvar__8__C__103665)
                                                 => p(happ(happ(Vvar__7__req__103660,happ(Vvar__16__phi__103691,happ(happ(Vvar__11__cadd__103668,Vvar__var__var__var__var__var__var__19__x__103753__103755__103777__103779__103781__103783__103785),Vvar__var__var__var__var__var__var__20__y__103754__103756__103778__103780__103782__103784__103786))),happ(happ(Vvar__3__radd__103642,happ(Vvar__16__phi__103691,Vvar__var__var__var__var__var__var__19__x__103753__103755__103777__103779__103781__103783__103785)),happ(Vvar__16__phi__103691,Vvar__var__var__var__var__var__var__20__y__103754__103756__103778__103780__103782__103784__103786)))) ) )
                                          & ! [Vvar__var__var__var__var__var__var__20__x__103758__103760__103787__103789__103791__103793__103795] :
                                              ( t(Vvar__var__var__var__var__var__var__20__x__103758__103760__103787__103789__103791__103793__103795,Vvar__8__C__103665)
                                             => ! [Vvar__var__var__var__var__var__var__21__y__103759__103761__103788__103790__103792__103794__103796] :
                                                  ( t(Vvar__var__var__var__var__var__var__21__y__103759__103761__103788__103790__103792__103794__103796,Vvar__8__C__103665)
                                                 => p(happ(happ(Vvar__7__req__103660,happ(Vvar__16__phi__103691,happ(happ(Vvar__13__csub__103678,Vvar__var__var__var__var__var__var__20__x__103758__103760__103787__103789__103791__103793__103795),Vvar__var__var__var__var__var__var__21__y__103759__103761__103788__103790__103792__103794__103796))),happ(happ(Vvar__5__rsub__103652,happ(Vvar__16__phi__103691,Vvar__var__var__var__var__var__var__20__x__103758__103760__103787__103789__103791__103793__103795)),happ(Vvar__16__phi__103691,Vvar__var__var__var__var__var__var__21__y__103759__103761__103788__103790__103792__103794__103796)))) ) )
                                          & ! [Vvar__var__var__var__var__var__var__21__x__103763__103765__103797__103799__103801__103803__103805] :
                                              ( t(Vvar__var__var__var__var__var__var__21__x__103763__103765__103797__103799__103801__103803__103805,Vvar__8__C__103665)
                                             => ! [Vvar__var__var__var__var__var__var__22__y__103764__103766__103798__103800__103802__103804__103806] :
                                                  ( t(Vvar__var__var__var__var__var__var__22__y__103764__103766__103798__103800__103802__103804__103806,Vvar__8__C__103665)
                                                 => p(happ(happ(Vvar__7__req__103660,happ(Vvar__16__phi__103691,happ(happ(Vvar__12__cmul__103673,Vvar__var__var__var__var__var__var__21__x__103763__103765__103797__103799__103801__103803__103805),Vvar__var__var__var__var__var__var__22__y__103764__103766__103798__103800__103802__103804__103806))),happ(happ(Vvar__4__rmul__103647,happ(Vvar__16__phi__103691,Vvar__var__var__var__var__var__var__21__x__103763__103765__103797__103799__103801__103803__103805)),happ(Vvar__16__phi__103691,Vvar__var__var__var__var__var__var__22__y__103764__103766__103798__103800__103802__103804__103806)))) ) )
                                          & ! [Vvar__var__var__var__var__var__var__22__x__103768__103769__103807__103808__103809__103810__103811] :
                                              ( t(Vvar__var__var__var__var__var__var__22__x__103768__103769__103807__103808__103809__103810__103811,Vvar__8__C__103665)
                                             => p(happ(happ(Vvar__7__req__103660,happ(Vvar__16__phi__103691,happ(Vvar__14__copp__103683,Vvar__var__var__var__var__var__var__22__x__103768__103769__103807__103808__103809__103810__103811))),happ(Vvar__6__ropp__103657,happ(Vvar__16__phi__103691,Vvar__var__var__var__var__var__var__22__x__103768__103769__103807__103808__103809__103810__103811)))) )
                                          & ! [Vvar__var__var__var__var__var__23__x__103771__103774__103812__103815__103818__103821] :
                                              ( t(Vvar__var__var__var__var__var__23__x__103771__103774__103812__103815__103818__103821,Vvar__8__C__103665)
                                             => ! [Vvar__var__var__var__var__var__24__y__103772__103775__103813__103816__103819__103822] :
                                                  ( t(Vvar__var__var__var__var__var__24__y__103772__103775__103813__103816__103819__103822,Vvar__8__C__103665)
                                                 => ( happ(happ(Vvar__15__ceqb__103686,Vvar__var__var__var__var__var__23__x__103771__103774__103812__103815__103818__103821),Vvar__var__var__var__var__var__24__y__103772__103775__103813__103816__103819__103822) = cCoq_2eInit_2eDatatypes_2etrue
                                                   => p(happ(happ(Vvar__7__req__103660,happ(Vvar__16__phi__103691,Vvar__var__var__var__var__var__23__x__103771__103774__103812__103815__103818__103821)),happ(Vvar__16__phi__103691,Vvar__var__var__var__var__var__24__y__103772__103775__103813__103816__103819__103822))) ) ) )
                                          & p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Ring_theory.ring_theory',axiom,
    ! [Vvar__0__R__87971,Vvar__1__rO__87972,Vvar__2__rI__87973,Vvar__3__radd__87974,Vvar__4__rmul__87979,Vvar__5__rsub__87984,Vvar__6__ropp__87989,Vvar__7__req__87992] :
      ( cType___24t(Vvar__0__R__87971)
     => ( t(Vvar__1__rO__87972,Vvar__0__R__87971)
       => ( t(Vvar__2__rI__87973,Vvar__0__R__87971)
         => ( c_24__type__88195___24t(Vvar__0__R__87971,Vvar__1__rO__87972,Vvar__2__rI__87973,Vvar__3__radd__87974,Vvar__4__rmul__87979,Vvar__5__rsub__87984,Vvar__6__ropp__87989,Vvar__7__req__87992,Vvar__3__radd__87974)
           => ( c_24__type__88258___24t(Vvar__0__R__87971,Vvar__1__rO__87972,Vvar__2__rI__87973,Vvar__3__radd__87974,Vvar__4__rmul__87979,Vvar__5__rsub__87984,Vvar__6__ropp__87989,Vvar__7__req__87992,Vvar__4__rmul__87979)
             => ( c_24__type__88321___24t(Vvar__0__R__87971,Vvar__1__rO__87972,Vvar__2__rI__87973,Vvar__3__radd__87974,Vvar__4__rmul__87979,Vvar__5__rsub__87984,Vvar__6__ropp__87989,Vvar__7__req__87992,Vvar__5__rsub__87984)
               => ( c_24__type__88375___24t(Vvar__0__R__87971,Vvar__1__rO__87972,Vvar__2__rI__87973,Vvar__3__radd__87974,Vvar__4__rmul__87979,Vvar__5__rsub__87984,Vvar__6__ropp__87989,Vvar__7__req__87992,Vvar__6__ropp__87989)
                 => ( c_24__type__88438___24t(Vvar__0__R__87971,Vvar__1__rO__87972,Vvar__2__rI__87973,Vvar__3__radd__87974,Vvar__4__rmul__87979,Vvar__5__rsub__87984,Vvar__6__ropp__87989,Vvar__7__req__87992,Vvar__7__req__87992)
                   => ( cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(Vvar__0__R__87971,Vvar__1__rO__87972,Vvar__2__rI__87973,Vvar__3__radd__87974,Vvar__4__rmul__87979,Vvar__5__rsub__87984,Vvar__6__ropp__87989,Vvar__7__req__87992)
                     => ( ! [Vvar__var__var__var__var__var__8__x__88025__88026__88069__88070__88071__88072] :
                            ( t(Vvar__var__var__var__var__var__8__x__88025__88026__88069__88070__88071__88072,Vvar__0__R__87971)
                           => p(happ(happ(Vvar__7__req__87992,happ(happ(Vvar__3__radd__87974,Vvar__1__rO__87972),Vvar__var__var__var__var__var__8__x__88025__88026__88069__88070__88071__88072)),Vvar__var__var__var__var__var__8__x__88025__88026__88069__88070__88071__88072)) )
                        & ! [Vvar__var__var__var__var__9__x__88028__88030__88073__88075__88077] :
                            ( t(Vvar__var__var__var__var__9__x__88028__88030__88073__88075__88077,Vvar__0__R__87971)
                           => ! [Vvar__var__var__var__var__10__y__88029__88031__88074__88076__88078] :
                                ( t(Vvar__var__var__var__var__10__y__88029__88031__88074__88076__88078,Vvar__0__R__87971)
                               => p(happ(happ(Vvar__7__req__87992,happ(happ(Vvar__3__radd__87974,Vvar__var__var__var__var__9__x__88028__88030__88073__88075__88077),Vvar__var__var__var__var__10__y__88029__88031__88074__88076__88078)),happ(happ(Vvar__3__radd__87974,Vvar__var__var__var__var__10__y__88029__88031__88074__88076__88078),Vvar__var__var__var__var__9__x__88028__88030__88073__88075__88077))) ) )
                        & ! [Vvar__var__var__var__var__10__x__88033__88036__88079__88082__88085] :
                            ( t(Vvar__var__var__var__var__10__x__88033__88036__88079__88082__88085,Vvar__0__R__87971)
                           => ! [Vvar__var__var__var__var__11__y__88034__88037__88080__88083__88086] :
                                ( t(Vvar__var__var__var__var__11__y__88034__88037__88080__88083__88086,Vvar__0__R__87971)
                               => ! [Vvar__var__var__var__var__12__z__88035__88038__88081__88084__88087] :
                                    ( t(Vvar__var__var__var__var__12__z__88035__88038__88081__88084__88087,Vvar__0__R__87971)
                                   => p(happ(happ(Vvar__7__req__87992,happ(happ(Vvar__3__radd__87974,Vvar__var__var__var__var__10__x__88033__88036__88079__88082__88085),happ(happ(Vvar__3__radd__87974,Vvar__var__var__var__var__11__y__88034__88037__88080__88083__88086),Vvar__var__var__var__var__12__z__88035__88038__88081__88084__88087))),happ(happ(Vvar__3__radd__87974,happ(happ(Vvar__3__radd__87974,Vvar__var__var__var__var__10__x__88033__88036__88079__88082__88085),Vvar__var__var__var__var__11__y__88034__88037__88080__88083__88086)),Vvar__var__var__var__var__12__z__88035__88038__88081__88084__88087))) ) ) )
                        & ! [Vvar__var__var__var__var__var__11__x__88040__88041__88088__88089__88090__88091] :
                            ( t(Vvar__var__var__var__var__var__11__x__88040__88041__88088__88089__88090__88091,Vvar__0__R__87971)
                           => p(happ(happ(Vvar__7__req__87992,happ(happ(Vvar__4__rmul__87979,Vvar__2__rI__87973),Vvar__var__var__var__var__var__11__x__88040__88041__88088__88089__88090__88091)),Vvar__var__var__var__var__var__11__x__88040__88041__88088__88089__88090__88091)) )
                        & ! [Vvar__var__var__var__var__12__x__88043__88045__88092__88094__88096] :
                            ( t(Vvar__var__var__var__var__12__x__88043__88045__88092__88094__88096,Vvar__0__R__87971)
                           => ! [Vvar__var__var__var__var__13__y__88044__88046__88093__88095__88097] :
                                ( t(Vvar__var__var__var__var__13__y__88044__88046__88093__88095__88097,Vvar__0__R__87971)
                               => p(happ(happ(Vvar__7__req__87992,happ(happ(Vvar__4__rmul__87979,Vvar__var__var__var__var__12__x__88043__88045__88092__88094__88096),Vvar__var__var__var__var__13__y__88044__88046__88093__88095__88097)),happ(happ(Vvar__4__rmul__87979,Vvar__var__var__var__var__13__y__88044__88046__88093__88095__88097),Vvar__var__var__var__var__12__x__88043__88045__88092__88094__88096))) ) )
                        & ! [Vvar__var__var__var__var__13__x__88048__88051__88098__88101__88104] :
                            ( t(Vvar__var__var__var__var__13__x__88048__88051__88098__88101__88104,Vvar__0__R__87971)
                           => ! [Vvar__var__var__var__var__14__y__88049__88052__88099__88102__88105] :
                                ( t(Vvar__var__var__var__var__14__y__88049__88052__88099__88102__88105,Vvar__0__R__87971)
                               => ! [Vvar__var__var__var__var__15__z__88050__88053__88100__88103__88106] :
                                    ( t(Vvar__var__var__var__var__15__z__88050__88053__88100__88103__88106,Vvar__0__R__87971)
                                   => p(happ(happ(Vvar__7__req__87992,happ(happ(Vvar__4__rmul__87979,Vvar__var__var__var__var__13__x__88048__88051__88098__88101__88104),happ(happ(Vvar__4__rmul__87979,Vvar__var__var__var__var__14__y__88049__88052__88099__88102__88105),Vvar__var__var__var__var__15__z__88050__88053__88100__88103__88106))),happ(happ(Vvar__4__rmul__87979,happ(happ(Vvar__4__rmul__87979,Vvar__var__var__var__var__13__x__88048__88051__88098__88101__88104),Vvar__var__var__var__var__14__y__88049__88052__88099__88102__88105)),Vvar__var__var__var__var__15__z__88050__88053__88100__88103__88106))) ) ) )
                        & ! [Vvar__var__var__var__var__var__14__x__88055__88058__88107__88110__88113__88116] :
                            ( t(Vvar__var__var__var__var__var__14__x__88055__88058__88107__88110__88113__88116,Vvar__0__R__87971)
                           => ! [Vvar__var__var__var__var__var__15__y__88056__88059__88108__88111__88114__88117] :
                                ( t(Vvar__var__var__var__var__var__15__y__88056__88059__88108__88111__88114__88117,Vvar__0__R__87971)
                               => ! [Vvar__var__var__var__var__var__16__z__88057__88060__88109__88112__88115__88118] :
                                    ( t(Vvar__var__var__var__var__var__16__z__88057__88060__88109__88112__88115__88118,Vvar__0__R__87971)
                                   => p(happ(happ(Vvar__7__req__87992,happ(happ(Vvar__4__rmul__87979,happ(happ(Vvar__3__radd__87974,Vvar__var__var__var__var__var__14__x__88055__88058__88107__88110__88113__88116),Vvar__var__var__var__var__var__15__y__88056__88059__88108__88111__88114__88117)),Vvar__var__var__var__var__var__16__z__88057__88060__88109__88112__88115__88118)),happ(happ(Vvar__3__radd__87974,happ(happ(Vvar__4__rmul__87979,Vvar__var__var__var__var__var__14__x__88055__88058__88107__88110__88113__88116),Vvar__var__var__var__var__var__16__z__88057__88060__88109__88112__88115__88118)),happ(happ(Vvar__4__rmul__87979,Vvar__var__var__var__var__var__15__y__88056__88059__88108__88111__88114__88117),Vvar__var__var__var__var__var__16__z__88057__88060__88109__88112__88115__88118)))) ) ) )
                        & ! [Vvar__var__var__var__var__var__var__15__x__88062__88064__88119__88121__88123__88125__88127] :
                            ( t(Vvar__var__var__var__var__var__var__15__x__88062__88064__88119__88121__88123__88125__88127,Vvar__0__R__87971)
                           => ! [Vvar__var__var__var__var__var__var__16__y__88063__88065__88120__88122__88124__88126__88128] :
                                ( t(Vvar__var__var__var__var__var__var__16__y__88063__88065__88120__88122__88124__88126__88128,Vvar__0__R__87971)
                               => p(happ(happ(Vvar__7__req__87992,happ(happ(Vvar__5__rsub__87984,Vvar__var__var__var__var__var__var__15__x__88062__88064__88119__88121__88123__88125__88127),Vvar__var__var__var__var__var__var__16__y__88063__88065__88120__88122__88124__88126__88128)),happ(happ(Vvar__3__radd__87974,Vvar__var__var__var__var__var__var__15__x__88062__88064__88119__88121__88123__88125__88127),happ(Vvar__6__ropp__87989,Vvar__var__var__var__var__var__var__16__y__88063__88065__88120__88122__88124__88126__88128)))) ) )
                        & ! [Vvar__var__var__var__var__var__var__16__x__88067__88068__88129__88130__88131__88132__88133] :
                            ( t(Vvar__var__var__var__var__var__var__16__x__88067__88068__88129__88130__88131__88132__88133,Vvar__0__R__87971)
                           => p(happ(happ(Vvar__7__req__87992,happ(happ(Vvar__3__radd__87974,Vvar__var__var__var__var__var__var__16__x__88067__88068__88129__88130__88131__88132__88133),happ(Vvar__6__ropp__87989,Vvar__var__var__var__var__var__var__16__x__88067__88068__88129__88130__88131__88132__88133))),Vvar__1__rO__87972)) )
                        & p(c_24True) ) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Ring_theory.semi_morph',axiom,
    ! [Vvar__0__R__81491,Vvar__1__rO__81492,Vvar__2__rI__81493,Vvar__3__radd__81494,Vvar__4__rmul__81499,Vvar__5__req__81504,Vvar__6__C__81509,Vvar__7__cO__81510,Vvar__8__cI__81511,Vvar__9__cadd__81512,Vvar__10__cmul__81517,Vvar__11__ceqb__81522,Vvar__12__phi__81527] :
      ( cType___24t(Vvar__0__R__81491)
     => ( t(Vvar__1__rO__81492,Vvar__0__R__81491)
       => ( t(Vvar__2__rI__81493,Vvar__0__R__81491)
         => ( c_24__type__81744___24t(Vvar__0__R__81491,Vvar__1__rO__81492,Vvar__2__rI__81493,Vvar__3__radd__81494,Vvar__4__rmul__81499,Vvar__5__req__81504,Vvar__6__C__81509,Vvar__7__cO__81510,Vvar__8__cI__81511,Vvar__9__cadd__81512,Vvar__10__cmul__81517,Vvar__11__ceqb__81522,Vvar__12__phi__81527,Vvar__3__radd__81494)
           => ( c_24__type__81869___24t(Vvar__0__R__81491,Vvar__1__rO__81492,Vvar__2__rI__81493,Vvar__3__radd__81494,Vvar__4__rmul__81499,Vvar__5__req__81504,Vvar__6__C__81509,Vvar__7__cO__81510,Vvar__8__cI__81511,Vvar__9__cadd__81512,Vvar__10__cmul__81517,Vvar__11__ceqb__81522,Vvar__12__phi__81527,Vvar__4__rmul__81499)
             => ( c_24__type__81994___24t(Vvar__0__R__81491,Vvar__1__rO__81492,Vvar__2__rI__81493,Vvar__3__radd__81494,Vvar__4__rmul__81499,Vvar__5__req__81504,Vvar__6__C__81509,Vvar__7__cO__81510,Vvar__8__cI__81511,Vvar__9__cadd__81512,Vvar__10__cmul__81517,Vvar__11__ceqb__81522,Vvar__12__phi__81527,Vvar__5__req__81504)
               => ( cType___24t(Vvar__6__C__81509)
                 => ( t(Vvar__7__cO__81510,Vvar__6__C__81509)
                   => ( t(Vvar__8__cI__81511,Vvar__6__C__81509)
                     => ( c_24__type__82119___24t(Vvar__0__R__81491,Vvar__1__rO__81492,Vvar__2__rI__81493,Vvar__3__radd__81494,Vvar__4__rmul__81499,Vvar__5__req__81504,Vvar__6__C__81509,Vvar__7__cO__81510,Vvar__8__cI__81511,Vvar__9__cadd__81512,Vvar__10__cmul__81517,Vvar__11__ceqb__81522,Vvar__12__phi__81527,Vvar__9__cadd__81512)
                       => ( c_24__type__82244___24t(Vvar__0__R__81491,Vvar__1__rO__81492,Vvar__2__rI__81493,Vvar__3__radd__81494,Vvar__4__rmul__81499,Vvar__5__req__81504,Vvar__6__C__81509,Vvar__7__cO__81510,Vvar__8__cI__81511,Vvar__9__cadd__81512,Vvar__10__cmul__81517,Vvar__11__ceqb__81522,Vvar__12__phi__81527,Vvar__10__cmul__81517)
                         => ( c_24__type__82369___24t(Vvar__0__R__81491,Vvar__1__rO__81492,Vvar__2__rI__81493,Vvar__3__radd__81494,Vvar__4__rmul__81499,Vvar__5__req__81504,Vvar__6__C__81509,Vvar__7__cO__81510,Vvar__8__cI__81511,Vvar__9__cadd__81512,Vvar__10__cmul__81517,Vvar__11__ceqb__81522,Vvar__12__phi__81527,Vvar__11__ceqb__81522)
                           => ( c_24__type__82480___24t(Vvar__0__R__81491,Vvar__1__rO__81492,Vvar__2__rI__81493,Vvar__3__radd__81494,Vvar__4__rmul__81499,Vvar__5__req__81504,Vvar__6__C__81509,Vvar__7__cO__81510,Vvar__8__cI__81511,Vvar__9__cadd__81512,Vvar__10__cmul__81517,Vvar__11__ceqb__81522,Vvar__12__phi__81527,Vvar__12__phi__81527)
                             => ( cCoq_2esetoid__ring_2eRing__theory_2esemi__morph___24a13(Vvar__0__R__81491,Vvar__1__rO__81492,Vvar__2__rI__81493,Vvar__3__radd__81494,Vvar__4__rmul__81499,Vvar__5__req__81504,Vvar__6__C__81509,Vvar__7__cO__81510,Vvar__8__cI__81511,Vvar__9__cadd__81512,Vvar__10__cmul__81517,Vvar__11__ceqb__81522,Vvar__12__phi__81527)
                               => ( p(happ(happ(Vvar__5__req__81504,happ(Vvar__12__phi__81527,Vvar__7__cO__81510)),Vvar__1__rO__81492))
                                  & p(happ(happ(Vvar__5__req__81504,happ(Vvar__12__phi__81527,Vvar__8__cI__81511)),Vvar__2__rI__81493))
                                  & ! [Vvar__var__var__var__var__var__var__15__x__81573__81575__81589__81591__81593__81595__81597] :
                                      ( t(Vvar__var__var__var__var__var__var__15__x__81573__81575__81589__81591__81593__81595__81597,Vvar__6__C__81509)
                                     => ! [Vvar__var__var__var__var__var__var__16__y__81574__81576__81590__81592__81594__81596__81598] :
                                          ( t(Vvar__var__var__var__var__var__var__16__y__81574__81576__81590__81592__81594__81596__81598,Vvar__6__C__81509)
                                         => p(happ(happ(Vvar__5__req__81504,happ(Vvar__12__phi__81527,happ(happ(Vvar__9__cadd__81512,Vvar__var__var__var__var__var__var__15__x__81573__81575__81589__81591__81593__81595__81597),Vvar__var__var__var__var__var__var__16__y__81574__81576__81590__81592__81594__81596__81598))),happ(happ(Vvar__3__radd__81494,happ(Vvar__12__phi__81527,Vvar__var__var__var__var__var__var__15__x__81573__81575__81589__81591__81593__81595__81597)),happ(Vvar__12__phi__81527,Vvar__var__var__var__var__var__var__16__y__81574__81576__81590__81592__81594__81596__81598)))) ) )
                                  & ! [Vvar__var__var__var__var__var__var__16__x__81578__81580__81599__81601__81603__81605__81607] :
                                      ( t(Vvar__var__var__var__var__var__var__16__x__81578__81580__81599__81601__81603__81605__81607,Vvar__6__C__81509)
                                     => ! [Vvar__var__var__var__var__var__var__17__y__81579__81581__81600__81602__81604__81606__81608] :
                                          ( t(Vvar__var__var__var__var__var__var__17__y__81579__81581__81600__81602__81604__81606__81608,Vvar__6__C__81509)
                                         => p(happ(happ(Vvar__5__req__81504,happ(Vvar__12__phi__81527,happ(happ(Vvar__10__cmul__81517,Vvar__var__var__var__var__var__var__16__x__81578__81580__81599__81601__81603__81605__81607),Vvar__var__var__var__var__var__var__17__y__81579__81581__81600__81602__81604__81606__81608))),happ(happ(Vvar__4__rmul__81499,happ(Vvar__12__phi__81527,Vvar__var__var__var__var__var__var__16__x__81578__81580__81599__81601__81603__81605__81607)),happ(Vvar__12__phi__81527,Vvar__var__var__var__var__var__var__17__y__81579__81581__81600__81602__81604__81606__81608)))) ) )
                                  & ! [Vvar__var__var__var__var__var__17__x__81583__81586__81609__81612__81615__81618] :
                                      ( t(Vvar__var__var__var__var__var__17__x__81583__81586__81609__81612__81615__81618,Vvar__6__C__81509)
                                     => ! [Vvar__var__var__var__var__var__18__y__81584__81587__81610__81613__81616__81619] :
                                          ( t(Vvar__var__var__var__var__var__18__y__81584__81587__81610__81613__81616__81619,Vvar__6__C__81509)
                                         => ( happ(happ(Vvar__11__ceqb__81522,Vvar__var__var__var__var__var__17__x__81583__81586__81609__81612__81615__81618),Vvar__var__var__var__var__var__18__y__81584__81587__81610__81613__81616__81619) = cCoq_2eInit_2eDatatypes_2etrue
                                           => p(happ(happ(Vvar__5__req__81504,happ(Vvar__12__phi__81527,Vvar__var__var__var__var__var__17__x__81583__81586__81609__81612__81615__81618)),happ(Vvar__12__phi__81527,Vvar__var__var__var__var__var__18__y__81584__81587__81610__81613__81616__81619))) ) ) )
                                  & p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Ring_theory.semi_ring_theory',axiom,
    ! [Vvar__0__R__81202,Vvar__1__rO__81203,Vvar__2__rI__81204,Vvar__3__radd__81205,Vvar__4__rmul__81210,Vvar__5__req__81215] :
      ( cType___24t(Vvar__0__R__81202)
     => ( t(Vvar__1__rO__81203,Vvar__0__R__81202)
       => ( t(Vvar__2__rI__81204,Vvar__0__R__81202)
         => ( c_24__type__81370___24t(Vvar__0__R__81202,Vvar__1__rO__81203,Vvar__2__rI__81204,Vvar__3__radd__81205,Vvar__4__rmul__81210,Vvar__5__req__81215,Vvar__3__radd__81205)
           => ( c_24__type__81409___24t(Vvar__0__R__81202,Vvar__1__rO__81203,Vvar__2__rI__81204,Vvar__3__radd__81205,Vvar__4__rmul__81210,Vvar__5__req__81215,Vvar__4__rmul__81210)
             => ( c_24__type__81448___24t(Vvar__0__R__81202,Vvar__1__rO__81203,Vvar__2__rI__81204,Vvar__3__radd__81205,Vvar__4__rmul__81210,Vvar__5__req__81215,Vvar__5__req__81215)
               => ( cCoq_2esetoid__ring_2eRing__theory_2esemi__ring__theory___24a6(Vvar__0__R__81202,Vvar__1__rO__81203,Vvar__2__rI__81204,Vvar__3__radd__81205,Vvar__4__rmul__81210,Vvar__5__req__81215)
                 => ( ! [Vvar__var__var__var__var__var__6__n__81240__81241__81279__81280__81281__81282] :
                        ( t(Vvar__var__var__var__var__var__6__n__81240__81241__81279__81280__81281__81282,Vvar__0__R__81202)
                       => p(happ(happ(Vvar__5__req__81215,happ(happ(Vvar__3__radd__81205,Vvar__1__rO__81203),Vvar__var__var__var__var__var__6__n__81240__81241__81279__81280__81281__81282)),Vvar__var__var__var__var__var__6__n__81240__81241__81279__81280__81281__81282)) )
                    & ! [Vvar__var__var__var__var__7__n__81243__81245__81283__81285__81287] :
                        ( t(Vvar__var__var__var__var__7__n__81243__81245__81283__81285__81287,Vvar__0__R__81202)
                       => ! [Vvar__var__var__var__var__8__m__81244__81246__81284__81286__81288] :
                            ( t(Vvar__var__var__var__var__8__m__81244__81246__81284__81286__81288,Vvar__0__R__81202)
                           => p(happ(happ(Vvar__5__req__81215,happ(happ(Vvar__3__radd__81205,Vvar__var__var__var__var__7__n__81243__81245__81283__81285__81287),Vvar__var__var__var__var__8__m__81244__81246__81284__81286__81288)),happ(happ(Vvar__3__radd__81205,Vvar__var__var__var__var__8__m__81244__81246__81284__81286__81288),Vvar__var__var__var__var__7__n__81243__81245__81283__81285__81287))) ) )
                    & ! [Vvar__var__var__var__var__8__n__81248__81251__81289__81292__81295] :
                        ( t(Vvar__var__var__var__var__8__n__81248__81251__81289__81292__81295,Vvar__0__R__81202)
                       => ! [Vvar__var__var__var__var__9__m__81249__81252__81290__81293__81296] :
                            ( t(Vvar__var__var__var__var__9__m__81249__81252__81290__81293__81296,Vvar__0__R__81202)
                           => ! [Vvar__var__var__var__var__10__p__81250__81253__81291__81294__81297] :
                                ( t(Vvar__var__var__var__var__10__p__81250__81253__81291__81294__81297,Vvar__0__R__81202)
                               => p(happ(happ(Vvar__5__req__81215,happ(happ(Vvar__3__radd__81205,Vvar__var__var__var__var__8__n__81248__81251__81289__81292__81295),happ(happ(Vvar__3__radd__81205,Vvar__var__var__var__var__9__m__81249__81252__81290__81293__81296),Vvar__var__var__var__var__10__p__81250__81253__81291__81294__81297))),happ(happ(Vvar__3__radd__81205,happ(happ(Vvar__3__radd__81205,Vvar__var__var__var__var__8__n__81248__81251__81289__81292__81295),Vvar__var__var__var__var__9__m__81249__81252__81290__81293__81296)),Vvar__var__var__var__var__10__p__81250__81253__81291__81294__81297))) ) ) )
                    & ! [Vvar__var__var__var__var__var__9__n__81255__81256__81298__81299__81300__81301] :
                        ( t(Vvar__var__var__var__var__var__9__n__81255__81256__81298__81299__81300__81301,Vvar__0__R__81202)
                       => p(happ(happ(Vvar__5__req__81215,happ(happ(Vvar__4__rmul__81210,Vvar__2__rI__81204),Vvar__var__var__var__var__var__9__n__81255__81256__81298__81299__81300__81301)),Vvar__var__var__var__var__var__9__n__81255__81256__81298__81299__81300__81301)) )
                    & ! [Vvar__var__var__var__var__var__10__n__81258__81259__81302__81303__81304__81305] :
                        ( t(Vvar__var__var__var__var__var__10__n__81258__81259__81302__81303__81304__81305,Vvar__0__R__81202)
                       => p(happ(happ(Vvar__5__req__81215,happ(happ(Vvar__4__rmul__81210,Vvar__1__rO__81203),Vvar__var__var__var__var__var__10__n__81258__81259__81302__81303__81304__81305)),Vvar__1__rO__81203)) )
                    & ! [Vvar__var__var__var__var__11__n__81261__81263__81306__81308__81310] :
                        ( t(Vvar__var__var__var__var__11__n__81261__81263__81306__81308__81310,Vvar__0__R__81202)
                       => ! [Vvar__var__var__var__var__12__m__81262__81264__81307__81309__81311] :
                            ( t(Vvar__var__var__var__var__12__m__81262__81264__81307__81309__81311,Vvar__0__R__81202)
                           => p(happ(happ(Vvar__5__req__81215,happ(happ(Vvar__4__rmul__81210,Vvar__var__var__var__var__11__n__81261__81263__81306__81308__81310),Vvar__var__var__var__var__12__m__81262__81264__81307__81309__81311)),happ(happ(Vvar__4__rmul__81210,Vvar__var__var__var__var__12__m__81262__81264__81307__81309__81311),Vvar__var__var__var__var__11__n__81261__81263__81306__81308__81310))) ) )
                    & ! [Vvar__var__var__var__var__12__n__81266__81269__81312__81315__81318] :
                        ( t(Vvar__var__var__var__var__12__n__81266__81269__81312__81315__81318,Vvar__0__R__81202)
                       => ! [Vvar__var__var__var__var__13__m__81267__81270__81313__81316__81319] :
                            ( t(Vvar__var__var__var__var__13__m__81267__81270__81313__81316__81319,Vvar__0__R__81202)
                           => ! [Vvar__var__var__var__var__14__p__81268__81271__81314__81317__81320] :
                                ( t(Vvar__var__var__var__var__14__p__81268__81271__81314__81317__81320,Vvar__0__R__81202)
                               => p(happ(happ(Vvar__5__req__81215,happ(happ(Vvar__4__rmul__81210,Vvar__var__var__var__var__12__n__81266__81269__81312__81315__81318),happ(happ(Vvar__4__rmul__81210,Vvar__var__var__var__var__13__m__81267__81270__81313__81316__81319),Vvar__var__var__var__var__14__p__81268__81271__81314__81317__81320))),happ(happ(Vvar__4__rmul__81210,happ(happ(Vvar__4__rmul__81210,Vvar__var__var__var__var__12__n__81266__81269__81312__81315__81318),Vvar__var__var__var__var__13__m__81267__81270__81313__81316__81319)),Vvar__var__var__var__var__14__p__81268__81271__81314__81317__81320))) ) ) )
                    & ! [Vvar__var__var__var__var__var__13__n__81273__81276__81321__81324__81327__81330] :
                        ( t(Vvar__var__var__var__var__var__13__n__81273__81276__81321__81324__81327__81330,Vvar__0__R__81202)
                       => ! [Vvar__var__var__var__var__var__14__m__81274__81277__81322__81325__81328__81331] :
                            ( t(Vvar__var__var__var__var__var__14__m__81274__81277__81322__81325__81328__81331,Vvar__0__R__81202)
                           => ! [Vvar__var__var__var__var__var__15__p__81275__81278__81323__81326__81329__81332] :
                                ( t(Vvar__var__var__var__var__var__15__p__81275__81278__81323__81326__81329__81332,Vvar__0__R__81202)
                               => p(happ(happ(Vvar__5__req__81215,happ(happ(Vvar__4__rmul__81210,happ(happ(Vvar__3__radd__81205,Vvar__var__var__var__var__var__13__n__81273__81276__81321__81324__81327__81330),Vvar__var__var__var__var__var__14__m__81274__81277__81322__81325__81328__81331)),Vvar__var__var__var__var__var__15__p__81275__81278__81323__81326__81329__81332)),happ(happ(Vvar__3__radd__81205,happ(happ(Vvar__4__rmul__81210,Vvar__var__var__var__var__var__13__n__81273__81276__81321__81324__81327__81330),Vvar__var__var__var__var__var__15__p__81275__81278__81323__81326__81329__81332)),happ(happ(Vvar__4__rmul__81210,Vvar__var__var__var__var__var__14__m__81274__81277__81322__81325__81328__81331),Vvar__var__var__var__var__var__15__p__81275__81278__81323__81326__81329__81332)))) ) ) )
                    & p(c_24True) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Ring_theory.sring_eq_ext',axiom,
    ! [Vvar__0__R__91513,Vvar__1__radd__91514,Vvar__2__rmul__91519,Vvar__3__req__91524] :
      ( cType___24t(Vvar__0__R__91513)
     => ( c_24__type__91599___24t(Vvar__0__R__91513,Vvar__1__radd__91514,Vvar__2__rmul__91519,Vvar__3__req__91524,Vvar__1__radd__91514)
       => ( c_24__type__91622___24t(Vvar__0__R__91513,Vvar__1__radd__91514,Vvar__2__rmul__91519,Vvar__3__req__91524,Vvar__2__rmul__91519)
         => ( c_24__type__91645___24t(Vvar__0__R__91513,Vvar__1__radd__91514,Vvar__2__rmul__91519,Vvar__3__req__91524,Vvar__3__req__91524)
           => ( cCoq_2esetoid__ring_2eRing__theory_2esring__eq__ext___24a4(Vvar__0__R__91513,Vvar__1__radd__91514,Vvar__2__rmul__91519,Vvar__3__req__91524)
             => ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__91668___24a4(Vvar__0__R__91513,Vvar__1__radd__91514,Vvar__2__rmul__91519,Vvar__3__req__91524),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__91513,c_24__type__91686___24a4(Vvar__0__R__91513,Vvar__1__radd__91514,Vvar__2__rmul__91519,Vvar__3__req__91524),Vvar__3__req__91524,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__91513,Vvar__0__R__91513,Vvar__3__req__91524,Vvar__3__req__91524)),Vvar__1__radd__91514)
                & cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__91712___24a4(Vvar__0__R__91513,Vvar__1__radd__91514,Vvar__2__rmul__91519,Vvar__3__req__91524),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__91513,c_24__type__91730___24a4(Vvar__0__R__91513,Vvar__1__radd__91514,Vvar__2__rmul__91519,Vvar__3__req__91524),Vvar__3__req__91524,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__91513,Vvar__0__R__91513,Vvar__3__req__91524,Vvar__3__req__91524)),Vvar__2__rmul__91519)
                & p(c_24True) ) ) ) ) ) ) ).

fof('$_inversion_Hammer.Tactics.Reconstr.ReconstrT',axiom,
    ! [VX85547] :
      ( cHammer_2eTactics_2eReconstr_2eReconstrT___24t(VX85547)
     => ( VX85547 = cHammer_2eTactics_2eReconstr_2eEmpty
        | VX85547 = cHammer_2eTactics_2eReconstr_2eAllHyps ) ) ).

fof('$_inversion_PLF.Imp.AExp.aexp',axiom,
    ! [VX79368] :
      ( cPLF_2eImp_2eAExp_2eaexp___24t(VX79368)
     => ( ? [Vvar__0__n__79369] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__79369)
            & VX79368 = cPLF_2eImp_2eAExp_2eANum___24a1(Vvar__0__n__79369) )
        | ? [Vvar__0__a1__79370] :
            ( cPLF_2eImp_2eAExp_2eaexp___24t(Vvar__0__a1__79370)
            & ? [Vvar__1__a2__79371] :
                ( cPLF_2eImp_2eAExp_2eaexp___24t(Vvar__1__a2__79371)
                & VX79368 = cPLF_2eImp_2eAExp_2eAPlus___24a2(Vvar__0__a1__79370,Vvar__1__a2__79371) ) )
        | ? [Vvar__0__a1__79372] :
            ( cPLF_2eImp_2eAExp_2eaexp___24t(Vvar__0__a1__79372)
            & ? [Vvar__1__a2__79373] :
                ( cPLF_2eImp_2eAExp_2eaexp___24t(Vvar__1__a2__79373)
                & VX79368 = cPLF_2eImp_2eAExp_2eAMinus___24a2(Vvar__0__a1__79372,Vvar__1__a2__79373) ) )
        | ? [Vvar__0__a1__79374] :
            ( cPLF_2eImp_2eAExp_2eaexp___24t(Vvar__0__a1__79374)
            & ? [Vvar__1__a2__79375] :
                ( cPLF_2eImp_2eAExp_2eaexp___24t(Vvar__1__a2__79375)
                & VX79368 = cPLF_2eImp_2eAExp_2eAMult___24a2(Vvar__0__a1__79374,Vvar__1__a2__79375) ) ) ) ) ).

fof('$_inversion_PLF.Imp.AExp.bexp',axiom,
    ! [VX91896] :
      ( cPLF_2eImp_2eAExp_2ebexp___24t(VX91896)
     => ( VX91896 = cPLF_2eImp_2eAExp_2eBTrue
        | VX91896 = cPLF_2eImp_2eAExp_2eBFalse
        | ? [Vvar__0__a1__91897] :
            ( cPLF_2eImp_2eAExp_2eaexp___24t(Vvar__0__a1__91897)
            & ? [Vvar__1__a2__91898] :
                ( cPLF_2eImp_2eAExp_2eaexp___24t(Vvar__1__a2__91898)
                & VX91896 = cPLF_2eImp_2eAExp_2eBEq___24a2(Vvar__0__a1__91897,Vvar__1__a2__91898) ) )
        | ? [Vvar__0__a1__91899] :
            ( cPLF_2eImp_2eAExp_2eaexp___24t(Vvar__0__a1__91899)
            & ? [Vvar__1__a2__91900] :
                ( cPLF_2eImp_2eAExp_2eaexp___24t(Vvar__1__a2__91900)
                & VX91896 = cPLF_2eImp_2eAExp_2eBLe___24a2(Vvar__0__a1__91899,Vvar__1__a2__91900) ) )
        | ? [Vvar__0__b__91901] :
            ( cPLF_2eImp_2eAExp_2ebexp___24t(Vvar__0__b__91901)
            & VX91896 = cPLF_2eImp_2eAExp_2eBNot___24a1(Vvar__0__b__91901) )
        | ? [Vvar__0__b1__91902] :
            ( cPLF_2eImp_2eAExp_2ebexp___24t(Vvar__0__b1__91902)
            & ? [Vvar__1__b2__91903] :
                ( cPLF_2eImp_2eAExp_2ebexp___24t(Vvar__1__b2__91903)
                & VX91896 = cPLF_2eImp_2eAExp_2eBAnd___24a2(Vvar__0__b1__91902,Vvar__1__b2__91903) ) ) ) ) ).

fof('$_inversion_PLF.Imp.BreakImp.com',axiom,
    ! [VX91953] :
      ( cPLF_2eImp_2eBreakImp_2ecom___24t(VX91953)
     => ( VX91953 = cPLF_2eImp_2eBreakImp_2eCSkip
        | VX91953 = cPLF_2eImp_2eBreakImp_2eCBreak
        | ? [Vvar__0__x__91954] :
            ( cCoq_2eStrings_2eString_2estring___24t(Vvar__0__x__91954)
            & ? [Vvar__1__a__91955] :
                ( cPLF_2eImp_2eaexp___24t(Vvar__1__a__91955)
                & VX91953 = cPLF_2eImp_2eBreakImp_2eCAss___24a2(Vvar__0__x__91954,Vvar__1__a__91955) ) )
        | ? [Vvar__0__c1__91956] :
            ( cPLF_2eImp_2eBreakImp_2ecom___24t(Vvar__0__c1__91956)
            & ? [Vvar__1__c2__91957] :
                ( cPLF_2eImp_2eBreakImp_2ecom___24t(Vvar__1__c2__91957)
                & VX91953 = cPLF_2eImp_2eBreakImp_2eCSeq___24a2(Vvar__0__c1__91956,Vvar__1__c2__91957) ) )
        | ? [Vvar__0__b__91958] :
            ( cPLF_2eImp_2ebexp___24t(Vvar__0__b__91958)
            & ? [Vvar__1__c1__91959] :
                ( cPLF_2eImp_2eBreakImp_2ecom___24t(Vvar__1__c1__91959)
                & ? [Vvar__2__c2__91960] :
                    ( cPLF_2eImp_2eBreakImp_2ecom___24t(Vvar__2__c2__91960)
                    & VX91953 = cPLF_2eImp_2eBreakImp_2eCIf___24a3(Vvar__0__b__91958,Vvar__1__c1__91959,Vvar__2__c2__91960) ) ) )
        | ? [Vvar__0__b__91961] :
            ( cPLF_2eImp_2ebexp___24t(Vvar__0__b__91961)
            & ? [Vvar__1__c__91962] :
                ( cPLF_2eImp_2eBreakImp_2ecom___24t(Vvar__1__c__91962)
                & VX91953 = cPLF_2eImp_2eBreakImp_2eCWhile___24a2(Vvar__0__b__91961,Vvar__1__c__91962) ) ) ) ) ).

fof('$_inversion_PLF.Imp.BreakImp.result',axiom,
    ! [VX92026] :
      ( cPLF_2eImp_2eBreakImp_2eresult___24t(VX92026)
     => ( VX92026 = cPLF_2eImp_2eBreakImp_2eSContinue
        | VX92026 = cPLF_2eImp_2eBreakImp_2eSBreak ) ) ).

fof('$_inversion_PLF.Imp.aevalR_division.aexp',axiom,
    ! [VX83887] :
      ( cPLF_2eImp_2eaevalR__division_2eaexp___24t(VX83887)
     => ( ? [Vvar__0__n__83888] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__83888)
            & VX83887 = cPLF_2eImp_2eaevalR__division_2eANum___24a1(Vvar__0__n__83888) )
        | ? [Vvar__0__a1__83889] :
            ( cPLF_2eImp_2eaevalR__division_2eaexp___24t(Vvar__0__a1__83889)
            & ? [Vvar__1__a2__83890] :
                ( cPLF_2eImp_2eaevalR__division_2eaexp___24t(Vvar__1__a2__83890)
                & VX83887 = cPLF_2eImp_2eaevalR__division_2eAPlus___24a2(Vvar__0__a1__83889,Vvar__1__a2__83890) ) )
        | ? [Vvar__0__a1__83891] :
            ( cPLF_2eImp_2eaevalR__division_2eaexp___24t(Vvar__0__a1__83891)
            & ? [Vvar__1__a2__83892] :
                ( cPLF_2eImp_2eaevalR__division_2eaexp___24t(Vvar__1__a2__83892)
                & VX83887 = cPLF_2eImp_2eaevalR__division_2eAMinus___24a2(Vvar__0__a1__83891,Vvar__1__a2__83892) ) )
        | ? [Vvar__0__a1__83893] :
            ( cPLF_2eImp_2eaevalR__division_2eaexp___24t(Vvar__0__a1__83893)
            & ? [Vvar__1__a2__83894] :
                ( cPLF_2eImp_2eaevalR__division_2eaexp___24t(Vvar__1__a2__83894)
                & VX83887 = cPLF_2eImp_2eaevalR__division_2eAMult___24a2(Vvar__0__a1__83893,Vvar__1__a2__83894) ) )
        | ? [Vvar__0__a1__83895] :
            ( cPLF_2eImp_2eaevalR__division_2eaexp___24t(Vvar__0__a1__83895)
            & ? [Vvar__1__a2__83896] :
                ( cPLF_2eImp_2eaevalR__division_2eaexp___24t(Vvar__1__a2__83896)
                & VX83887 = cPLF_2eImp_2eaevalR__division_2eADiv___24a2(Vvar__0__a1__83895,Vvar__1__a2__83896) ) ) ) ) ).

fof('$_inversion_PLF.Imp.aevalR_extended.aexp',axiom,
    ! [VX92199] :
      ( cPLF_2eImp_2eaevalR__extended_2eaexp___24t(VX92199)
     => ( VX92199 = cPLF_2eImp_2eaevalR__extended_2eAAny
        | ? [Vvar__0__n__92200] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__92200)
            & VX92199 = cPLF_2eImp_2eaevalR__extended_2eANum___24a1(Vvar__0__n__92200) )
        | ? [Vvar__0__a1__92201] :
            ( cPLF_2eImp_2eaevalR__extended_2eaexp___24t(Vvar__0__a1__92201)
            & ? [Vvar__1__a2__92202] :
                ( cPLF_2eImp_2eaevalR__extended_2eaexp___24t(Vvar__1__a2__92202)
                & VX92199 = cPLF_2eImp_2eaevalR__extended_2eAPlus___24a2(Vvar__0__a1__92201,Vvar__1__a2__92202) ) )
        | ? [Vvar__0__a1__92203] :
            ( cPLF_2eImp_2eaevalR__extended_2eaexp___24t(Vvar__0__a1__92203)
            & ? [Vvar__1__a2__92204] :
                ( cPLF_2eImp_2eaevalR__extended_2eaexp___24t(Vvar__1__a2__92204)
                & VX92199 = cPLF_2eImp_2eaevalR__extended_2eAMinus___24a2(Vvar__0__a1__92203,Vvar__1__a2__92204) ) )
        | ? [Vvar__0__a1__92205] :
            ( cPLF_2eImp_2eaevalR__extended_2eaexp___24t(Vvar__0__a1__92205)
            & ? [Vvar__1__a2__92206] :
                ( cPLF_2eImp_2eaevalR__extended_2eaexp___24t(Vvar__1__a2__92206)
                & VX92199 = cPLF_2eImp_2eaevalR__extended_2eAMult___24a2(Vvar__0__a1__92205,Vvar__1__a2__92206) ) ) ) ) ).

fof('$_inversion_PLF.Imp.aexp',axiom,
    ! [VX334] :
      ( cPLF_2eImp_2eaexp___24t(VX334)
     => ( ? [Vvar__0__n__335] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__335)
            & VX334 = cPLF_2eImp_2eANum___24a1(Vvar__0__n__335) )
        | ? [Vvar__0__x__336] :
            ( cCoq_2eStrings_2eString_2estring___24t(Vvar__0__x__336)
            & VX334 = cPLF_2eImp_2eAId___24a1(Vvar__0__x__336) )
        | ? [Vvar__0__a1__337] :
            ( cPLF_2eImp_2eaexp___24t(Vvar__0__a1__337)
            & ? [Vvar__1__a2__338] :
                ( cPLF_2eImp_2eaexp___24t(Vvar__1__a2__338)
                & VX334 = cPLF_2eImp_2eAPlus___24a2(Vvar__0__a1__337,Vvar__1__a2__338) ) )
        | ? [Vvar__0__a1__339] :
            ( cPLF_2eImp_2eaexp___24t(Vvar__0__a1__339)
            & ? [Vvar__1__a2__340] :
                ( cPLF_2eImp_2eaexp___24t(Vvar__1__a2__340)
                & VX334 = cPLF_2eImp_2eAMinus___24a2(Vvar__0__a1__339,Vvar__1__a2__340) ) )
        | ? [Vvar__0__a1__341] :
            ( cPLF_2eImp_2eaexp___24t(Vvar__0__a1__341)
            & ? [Vvar__1__a2__342] :
                ( cPLF_2eImp_2eaexp___24t(Vvar__1__a2__342)
                & VX334 = cPLF_2eImp_2eAMult___24a2(Vvar__0__a1__341,Vvar__1__a2__342) ) ) ) ) ).

fof('$_inversion_PLF.Imp.bexp',axiom,
    ! [VX398] :
      ( cPLF_2eImp_2ebexp___24t(VX398)
     => ( VX398 = cPLF_2eImp_2eBTrue
        | VX398 = cPLF_2eImp_2eBFalse
        | ? [Vvar__0__a1__399] :
            ( cPLF_2eImp_2eaexp___24t(Vvar__0__a1__399)
            & ? [Vvar__1__a2__400] :
                ( cPLF_2eImp_2eaexp___24t(Vvar__1__a2__400)
                & VX398 = cPLF_2eImp_2eBEq___24a2(Vvar__0__a1__399,Vvar__1__a2__400) ) )
        | ? [Vvar__0__a1__401] :
            ( cPLF_2eImp_2eaexp___24t(Vvar__0__a1__401)
            & ? [Vvar__1__a2__402] :
                ( cPLF_2eImp_2eaexp___24t(Vvar__1__a2__402)
                & VX398 = cPLF_2eImp_2eBLe___24a2(Vvar__0__a1__401,Vvar__1__a2__402) ) )
        | ? [Vvar__0__b__403] :
            ( cPLF_2eImp_2ebexp___24t(Vvar__0__b__403)
            & VX398 = cPLF_2eImp_2eBNot___24a1(Vvar__0__b__403) )
        | ? [Vvar__0__b1__404] :
            ( cPLF_2eImp_2ebexp___24t(Vvar__0__b1__404)
            & ? [Vvar__1__b2__405] :
                ( cPLF_2eImp_2ebexp___24t(Vvar__1__b2__405)
                & VX398 = cPLF_2eImp_2eBAnd___24a2(Vvar__0__b1__404,Vvar__1__b2__405) ) ) ) ) ).

fof('$_inversion_PLF.Imp.com',axiom,
    ! [VX484] :
      ( cPLF_2eImp_2ecom___24t(VX484)
     => ( VX484 = cPLF_2eImp_2eCSkip
        | ? [Vvar__0__x__485] :
            ( cCoq_2eStrings_2eString_2estring___24t(Vvar__0__x__485)
            & ? [Vvar__1__a__486] :
                ( cPLF_2eImp_2eaexp___24t(Vvar__1__a__486)
                & VX484 = cPLF_2eImp_2eCAss___24a2(Vvar__0__x__485,Vvar__1__a__486) ) )
        | ? [Vvar__0__c1__487] :
            ( cPLF_2eImp_2ecom___24t(Vvar__0__c1__487)
            & ? [Vvar__1__c2__488] :
                ( cPLF_2eImp_2ecom___24t(Vvar__1__c2__488)
                & VX484 = cPLF_2eImp_2eCSeq___24a2(Vvar__0__c1__487,Vvar__1__c2__488) ) )
        | ? [Vvar__0__b__489] :
            ( cPLF_2eImp_2ebexp___24t(Vvar__0__b__489)
            & ? [Vvar__1__c1__490] :
                ( cPLF_2eImp_2ecom___24t(Vvar__1__c1__490)
                & ? [Vvar__2__c2__491] :
                    ( cPLF_2eImp_2ecom___24t(Vvar__2__c2__491)
                    & VX484 = cPLF_2eImp_2eCIf___24a3(Vvar__0__b__489,Vvar__1__c1__490,Vvar__2__c2__491) ) ) )
        | ? [Vvar__0__b__492] :
            ( cPLF_2eImp_2ebexp___24t(Vvar__0__b__492)
            & ? [Vvar__1__c__493] :
                ( cPLF_2eImp_2ecom___24t(Vvar__1__c__493)
                & VX484 = cPLF_2eImp_2eCWhile___24a2(Vvar__0__b__492,Vvar__1__c__493) ) ) ) ) ).

fof('$_inversion_PLF.Imp.sinstr',axiom,
    ! [VX76429] :
      ( cPLF_2eImp_2esinstr___24t(VX76429)
     => ( ? [Vvar__0__n__76430] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__76430)
            & VX76429 = cPLF_2eImp_2eSPush___24a1(Vvar__0__n__76430) )
        | ? [Vvar__0__x__76431] :
            ( cCoq_2eStrings_2eString_2estring___24t(Vvar__0__x__76431)
            & VX76429 = cPLF_2eImp_2eSLoad___24a1(Vvar__0__x__76431) )
        | VX76429 = cPLF_2eImp_2eSPlus
        | VX76429 = cPLF_2eImp_2eSMinus
        | VX76429 = cPLF_2eImp_2eSMult ) ) ).

fof('$_inversion_PLF.LibTactics.Boxer',axiom,
    ! [VX87801] :
      ( cPLF_2eLibTactics_2eBoxer___24t(VX87801)
     => ? [Vvar__0__A__87802] :
          ( cType___24t(Vvar__0__A__87802)
          & ? [Vvar__1___24Anonymous__87803] :
              ( t(Vvar__1___24Anonymous__87803,Vvar__0__A__87802)
              & VX87801 = cPLF_2eLibTactics_2eboxer___24a2(Vvar__0__A__87802,Vvar__1___24Anonymous__87803) ) ) ) ).

fof('$_inversion_PLF.LibTactics.Ltac_database_token',axiom,
    ( p(cPLF_2eLibTactics_2eLtac__database__token)
   => p(c_24True) ) ).

fof('$_inversion_PLF.LibTactics.ltac_Mark',axiom,
    ( p(cPLF_2eLibTactics_2eltac__Mark)
   => p(c_24True) ) ).

fof('$_inversion_PLF.LibTactics.ltac_No_arg',axiom,
    ! [VX87808] :
      ( cPLF_2eLibTactics_2eltac__No__arg___24t(VX87808)
     => VX87808 = cPLF_2eLibTactics_2eltac__no__arg ) ).

fof('$_inversion_PLF.LibTactics.ltac_Wild',axiom,
    ! [VX89685] :
      ( cPLF_2eLibTactics_2eltac__Wild___24t(VX89685)
     => VX89685 = cPLF_2eLibTactics_2eltac__wild ) ).

fof('$_inversion_PLF.LibTactics.ltac_Wilds',axiom,
    ! [VX85528] :
      ( cPLF_2eLibTactics_2eltac__Wilds___24t(VX85528)
     => VX85528 = cPLF_2eLibTactics_2eltac__wilds ) ).

fof('$_inversion_PLF.LibTactics.ltac_goal_to_discard',axiom,
    ( p(cPLF_2eLibTactics_2eltac__goal__to__discard)
   => p(c_24True) ) ).

fof('$_inversion_PLF.References.STLCRef.RefsAndNontermination.step_closure',axiom,
    ! [Vvar__0__X__212327,Vvar__1__R__212328,Vvar__2___24Anonymous__212329,Vvar__3___24Anonymous__212330] :
      ( cType___24t(Vvar__0__X__212327)
     => ( cPLF_2eSmallstep_2erelation___24t(Vvar__0__X__212327,Vvar__1__R__212328)
       => ( t(Vvar__2___24Anonymous__212329,Vvar__0__X__212327)
         => ( t(Vvar__3___24Anonymous__212330,Vvar__0__X__212327)
           => ( cPLF_2eReferences_2eSTLCRef_2eRefsAndNontermination_2estep__closure___24a4(Vvar__0__X__212327,Vvar__1__R__212328,Vvar__2___24Anonymous__212329,Vvar__3___24Anonymous__212330)
             => ( ? [Vvar__2__x__212334] :
                    ( t(Vvar__2__x__212334,Vvar__0__X__212327)
                    & ? [Vvar__3__y__212335] :
                        ( t(Vvar__3__y__212335,Vvar__0__X__212327)
                        & p(happ(happ(Vvar__1__R__212328,Vvar__2__x__212334),Vvar__3__y__212335))
                        & Vvar__3___24Anonymous__212330 = Vvar__3__y__212335
                        & Vvar__2___24Anonymous__212329 = Vvar__2__x__212334 ) )
                | ? [Vvar__2__x__212339] :
                    ( t(Vvar__2__x__212339,Vvar__0__X__212327)
                    & ? [Vvar__3__y__212340] :
                        ( t(Vvar__3__y__212340,Vvar__0__X__212327)
                        & ? [Vvar__4__z__212341] :
                            ( t(Vvar__4__z__212341,Vvar__0__X__212327)
                            & p(happ(happ(Vvar__1__R__212328,Vvar__2__x__212339),Vvar__3__y__212340))
                            & cPLF_2eReferences_2eSTLCRef_2eRefsAndNontermination_2estep__closure___24a4(Vvar__0__X__212327,Vvar__1__R__212328,Vvar__3__y__212340,Vvar__4__z__212341)
                            & Vvar__3___24Anonymous__212330 = Vvar__4__z__212341
                            & Vvar__2___24Anonymous__212329 = Vvar__2__x__212339 ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_PLF.References.STLCRef.appears_free_in',axiom,
    ! [Vvar__0___24Anonymous__212501,Vvar__1___24Anonymous__212502] :
      ( cCoq_2eStrings_2eString_2estring___24t(Vvar__0___24Anonymous__212501)
     => ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__1___24Anonymous__212502)
       => ( cPLF_2eReferences_2eSTLCRef_2eappears__free__in___24a2(Vvar__0___24Anonymous__212501,Vvar__1___24Anonymous__212502)
         => ( ? [Vvar__0__x__212504] :
                ( cCoq_2eStrings_2eString_2estring___24t(Vvar__0__x__212504)
                & Vvar__1___24Anonymous__212502 = cPLF_2eReferences_2eSTLCRef_2evar___24a1(Vvar__0__x__212504)
                & Vvar__0___24Anonymous__212501 = Vvar__0__x__212504 )
            | ? [Vvar__0__x__212505] :
                ( cCoq_2eStrings_2eString_2estring___24t(Vvar__0__x__212505)
                & ? [Vvar__1__t1__212506] :
                    ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__1__t1__212506)
                    & ? [Vvar__2__t2__212507] :
                        ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__2__t2__212507)
                        & cPLF_2eReferences_2eSTLCRef_2eappears__free__in___24a2(Vvar__0__x__212505,Vvar__1__t1__212506)
                        & Vvar__1___24Anonymous__212502 = cPLF_2eReferences_2eSTLCRef_2eapp___24a2(Vvar__1__t1__212506,Vvar__2__t2__212507)
                        & Vvar__0___24Anonymous__212501 = Vvar__0__x__212505 ) ) )
            | ? [Vvar__0__x__212509] :
                ( cCoq_2eStrings_2eString_2estring___24t(Vvar__0__x__212509)
                & ? [Vvar__1__t1__212510] :
                    ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__1__t1__212510)
                    & ? [Vvar__2__t2__212511] :
                        ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__2__t2__212511)
                        & cPLF_2eReferences_2eSTLCRef_2eappears__free__in___24a2(Vvar__0__x__212509,Vvar__2__t2__212511)
                        & Vvar__1___24Anonymous__212502 = cPLF_2eReferences_2eSTLCRef_2eapp___24a2(Vvar__1__t1__212510,Vvar__2__t2__212511)
                        & Vvar__0___24Anonymous__212501 = Vvar__0__x__212509 ) ) )
            | ? [Vvar__0__x__212513] :
                ( cCoq_2eStrings_2eString_2estring___24t(Vvar__0__x__212513)
                & ? [Vvar__1__y__212514] :
                    ( cCoq_2eStrings_2eString_2estring___24t(Vvar__1__y__212514)
                    & ? [Vvar__2__T11__212515] :
                        ( cPLF_2eReferences_2eSTLCRef_2ety___24t(Vvar__2__T11__212515)
                        & ? [Vvar__3__t12__212516] :
                            ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__3__t12__212516)
                            & Vvar__1__y__212514 != Vvar__0__x__212513
                            & cPLF_2eReferences_2eSTLCRef_2eappears__free__in___24a2(Vvar__0__x__212513,Vvar__3__t12__212516)
                            & Vvar__1___24Anonymous__212502 = cPLF_2eReferences_2eSTLCRef_2eabs___24a3(Vvar__1__y__212514,Vvar__2__T11__212515,Vvar__3__t12__212516)
                            & Vvar__0___24Anonymous__212501 = Vvar__0__x__212513 ) ) ) )
            | ? [Vvar__0__x__212519] :
                ( cCoq_2eStrings_2eString_2estring___24t(Vvar__0__x__212519)
                & ? [Vvar__1__t1__212520] :
                    ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__1__t1__212520)
                    & cPLF_2eReferences_2eSTLCRef_2eappears__free__in___24a2(Vvar__0__x__212519,Vvar__1__t1__212520)
                    & Vvar__1___24Anonymous__212502 = cPLF_2eReferences_2eSTLCRef_2escc___24a1(Vvar__1__t1__212520)
                    & Vvar__0___24Anonymous__212501 = Vvar__0__x__212519 ) )
            | ? [Vvar__0__x__212522] :
                ( cCoq_2eStrings_2eString_2estring___24t(Vvar__0__x__212522)
                & ? [Vvar__1__t1__212523] :
                    ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__1__t1__212523)
                    & cPLF_2eReferences_2eSTLCRef_2eappears__free__in___24a2(Vvar__0__x__212522,Vvar__1__t1__212523)
                    & Vvar__1___24Anonymous__212502 = cPLF_2eReferences_2eSTLCRef_2eprd___24a1(Vvar__1__t1__212523)
                    & Vvar__0___24Anonymous__212501 = Vvar__0__x__212522 ) )
            | ? [Vvar__0__x__212525] :
                ( cCoq_2eStrings_2eString_2estring___24t(Vvar__0__x__212525)
                & ? [Vvar__1__t1__212526] :
                    ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__1__t1__212526)
                    & ? [Vvar__2__t2__212527] :
                        ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__2__t2__212527)
                        & cPLF_2eReferences_2eSTLCRef_2eappears__free__in___24a2(Vvar__0__x__212525,Vvar__1__t1__212526)
                        & Vvar__1___24Anonymous__212502 = cPLF_2eReferences_2eSTLCRef_2emlt___24a2(Vvar__1__t1__212526,Vvar__2__t2__212527)
                        & Vvar__0___24Anonymous__212501 = Vvar__0__x__212525 ) ) )
            | ? [Vvar__0__x__212529] :
                ( cCoq_2eStrings_2eString_2estring___24t(Vvar__0__x__212529)
                & ? [Vvar__1__t1__212530] :
                    ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__1__t1__212530)
                    & ? [Vvar__2__t2__212531] :
                        ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__2__t2__212531)
                        & cPLF_2eReferences_2eSTLCRef_2eappears__free__in___24a2(Vvar__0__x__212529,Vvar__2__t2__212531)
                        & Vvar__1___24Anonymous__212502 = cPLF_2eReferences_2eSTLCRef_2emlt___24a2(Vvar__1__t1__212530,Vvar__2__t2__212531)
                        & Vvar__0___24Anonymous__212501 = Vvar__0__x__212529 ) ) )
            | ? [Vvar__0__x__212533] :
                ( cCoq_2eStrings_2eString_2estring___24t(Vvar__0__x__212533)
                & ? [Vvar__1__t1__212534] :
                    ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__1__t1__212534)
                    & ? [Vvar__2__t2__212535] :
                        ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__2__t2__212535)
                        & ? [Vvar__3__t3__212536] :
                            ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__3__t3__212536)
                            & cPLF_2eReferences_2eSTLCRef_2eappears__free__in___24a2(Vvar__0__x__212533,Vvar__1__t1__212534)
                            & Vvar__1___24Anonymous__212502 = cPLF_2eReferences_2eSTLCRef_2etest0___24a3(Vvar__1__t1__212534,Vvar__2__t2__212535,Vvar__3__t3__212536)
                            & Vvar__0___24Anonymous__212501 = Vvar__0__x__212533 ) ) ) )
            | ? [Vvar__0__x__212538] :
                ( cCoq_2eStrings_2eString_2estring___24t(Vvar__0__x__212538)
                & ? [Vvar__1__t1__212539] :
                    ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__1__t1__212539)
                    & ? [Vvar__2__t2__212540] :
                        ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__2__t2__212540)
                        & ? [Vvar__3__t3__212541] :
                            ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__3__t3__212541)
                            & cPLF_2eReferences_2eSTLCRef_2eappears__free__in___24a2(Vvar__0__x__212538,Vvar__2__t2__212540)
                            & Vvar__1___24Anonymous__212502 = cPLF_2eReferences_2eSTLCRef_2etest0___24a3(Vvar__1__t1__212539,Vvar__2__t2__212540,Vvar__3__t3__212541)
                            & Vvar__0___24Anonymous__212501 = Vvar__0__x__212538 ) ) ) )
            | ? [Vvar__0__x__212543] :
                ( cCoq_2eStrings_2eString_2estring___24t(Vvar__0__x__212543)
                & ? [Vvar__1__t1__212544] :
                    ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__1__t1__212544)
                    & ? [Vvar__2__t2__212545] :
                        ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__2__t2__212545)
                        & ? [Vvar__3__t3__212546] :
                            ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__3__t3__212546)
                            & cPLF_2eReferences_2eSTLCRef_2eappears__free__in___24a2(Vvar__0__x__212543,Vvar__3__t3__212546)
                            & Vvar__1___24Anonymous__212502 = cPLF_2eReferences_2eSTLCRef_2etest0___24a3(Vvar__1__t1__212544,Vvar__2__t2__212545,Vvar__3__t3__212546)
                            & Vvar__0___24Anonymous__212501 = Vvar__0__x__212543 ) ) ) )
            | ? [Vvar__0__x__212548] :
                ( cCoq_2eStrings_2eString_2estring___24t(Vvar__0__x__212548)
                & ? [Vvar__1__t1__212549] :
                    ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__1__t1__212549)
                    & cPLF_2eReferences_2eSTLCRef_2eappears__free__in___24a2(Vvar__0__x__212548,Vvar__1__t1__212549)
                    & Vvar__1___24Anonymous__212502 = cPLF_2eReferences_2eSTLCRef_2eref___24a1(Vvar__1__t1__212549)
                    & Vvar__0___24Anonymous__212501 = Vvar__0__x__212548 ) )
            | ? [Vvar__0__x__212551] :
                ( cCoq_2eStrings_2eString_2estring___24t(Vvar__0__x__212551)
                & ? [Vvar__1__t1__212552] :
                    ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__1__t1__212552)
                    & cPLF_2eReferences_2eSTLCRef_2eappears__free__in___24a2(Vvar__0__x__212551,Vvar__1__t1__212552)
                    & Vvar__1___24Anonymous__212502 = cPLF_2eReferences_2eSTLCRef_2ederef___24a1(Vvar__1__t1__212552)
                    & Vvar__0___24Anonymous__212501 = Vvar__0__x__212551 ) )
            | ? [Vvar__0__x__212554] :
                ( cCoq_2eStrings_2eString_2estring___24t(Vvar__0__x__212554)
                & ? [Vvar__1__t1__212555] :
                    ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__1__t1__212555)
                    & ? [Vvar__2__t2__212556] :
                        ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__2__t2__212556)
                        & cPLF_2eReferences_2eSTLCRef_2eappears__free__in___24a2(Vvar__0__x__212554,Vvar__1__t1__212555)
                        & Vvar__1___24Anonymous__212502 = cPLF_2eReferences_2eSTLCRef_2eassign___24a2(Vvar__1__t1__212555,Vvar__2__t2__212556)
                        & Vvar__0___24Anonymous__212501 = Vvar__0__x__212554 ) ) )
            | ? [Vvar__0__x__212558] :
                ( cCoq_2eStrings_2eString_2estring___24t(Vvar__0__x__212558)
                & ? [Vvar__1__t1__212559] :
                    ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__1__t1__212559)
                    & ? [Vvar__2__t2__212560] :
                        ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__2__t2__212560)
                        & cPLF_2eReferences_2eSTLCRef_2eappears__free__in___24a2(Vvar__0__x__212558,Vvar__2__t2__212560)
                        & Vvar__1___24Anonymous__212502 = cPLF_2eReferences_2eSTLCRef_2eassign___24a2(Vvar__1__t1__212559,Vvar__2__t2__212560)
                        & Vvar__0___24Anonymous__212501 = Vvar__0__x__212558 ) ) ) ) ) ) ) ).

fof('$_inversion_PLF.References.STLCRef.extends',axiom,
    ! [Vvar__0___24Anonymous__212319,Vvar__1___24Anonymous__212320] :
      ( cPLF_2eReferences_2eSTLCRef_2estore__ty___24t(Vvar__0___24Anonymous__212319)
     => ( cPLF_2eReferences_2eSTLCRef_2estore__ty___24t(Vvar__1___24Anonymous__212320)
       => ( cPLF_2eReferences_2eSTLCRef_2eextends___24a2(Vvar__0___24Anonymous__212319,Vvar__1___24Anonymous__212320)
         => ( ? [Vvar__0__ST_27__212322] :
                ( cPLF_2eReferences_2eSTLCRef_2estore__ty___24t(Vvar__0__ST_27__212322)
                & Vvar__1___24Anonymous__212320 = cCoq_2eInit_2eDatatypes_2enil___24a1(cPLF_2eReferences_2eSTLCRef_2ety)
                & Vvar__0___24Anonymous__212319 = Vvar__0__ST_27__212322 )
            | ? [Vvar__0__x__212323] :
                ( cPLF_2eReferences_2eSTLCRef_2ety___24t(Vvar__0__x__212323)
                & ? [Vvar__1__ST_27__212324] :
                    ( cPLF_2eReferences_2eSTLCRef_2estore__ty___24t(Vvar__1__ST_27__212324)
                    & ? [Vvar__2__ST__212325] :
                        ( cPLF_2eReferences_2eSTLCRef_2estore__ty___24t(Vvar__2__ST__212325)
                        & cPLF_2eReferences_2eSTLCRef_2eextends___24a2(Vvar__1__ST_27__212324,Vvar__2__ST__212325)
                        & Vvar__1___24Anonymous__212320 = cCoq_2eInit_2eDatatypes_2econs___24a3(cPLF_2eReferences_2eSTLCRef_2ety,Vvar__0__x__212323,Vvar__2__ST__212325)
                        & Vvar__0___24Anonymous__212319 = cCoq_2eInit_2eDatatypes_2econs___24a3(cPLF_2eReferences_2eSTLCRef_2ety,Vvar__0__x__212323,Vvar__1__ST_27__212324) ) ) ) ) ) ) ) ).

fof('$_inversion_PLF.References.STLCRef.has_type',axiom,
    ! [Vvar__0___24Anonymous__211759,Vvar__1___24Anonymous__211760,Vvar__2___24Anonymous__211761,Vvar__3___24Anonymous__211762] :
      ( cPLF_2eReferences_2eSTLCRef_2econtext___24t(Vvar__0___24Anonymous__211759)
     => ( cPLF_2eReferences_2eSTLCRef_2estore__ty___24t(Vvar__1___24Anonymous__211760)
       => ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__2___24Anonymous__211761)
         => ( cPLF_2eReferences_2eSTLCRef_2ety___24t(Vvar__3___24Anonymous__211762)
           => ( cPLF_2eReferences_2eSTLCRef_2ehas__type___24a4(Vvar__0___24Anonymous__211759,Vvar__1___24Anonymous__211760,Vvar__2___24Anonymous__211761,Vvar__3___24Anonymous__211762)
             => ( ? [Vvar__0__Gamma__211764] :
                    ( c_24__type__211861___24t(Vvar__0___24Anonymous__211759,Vvar__1___24Anonymous__211760,Vvar__2___24Anonymous__211761,Vvar__3___24Anonymous__211762,Vvar__0__Gamma__211764)
                    & ? [Vvar__1__ST__211766] :
                        ( cPLF_2eReferences_2eSTLCRef_2estore__ty___24t(Vvar__1__ST__211766)
                        & ? [Vvar__2__x__211767] :
                            ( cCoq_2eStrings_2eString_2estring___24t(Vvar__2__x__211767)
                            & ? [Vvar__3__T__211768] :
                                ( cPLF_2eReferences_2eSTLCRef_2ety___24t(Vvar__3__T__211768)
                                & happ(Vvar__0__Gamma__211764,Vvar__2__x__211767) = cCoq_2eInit_2eDatatypes_2eSome___24a2(cPLF_2eReferences_2eSTLCRef_2ety,Vvar__3__T__211768)
                                & Vvar__3___24Anonymous__211762 = Vvar__3__T__211768
                                & Vvar__2___24Anonymous__211761 = cPLF_2eReferences_2eSTLCRef_2evar___24a1(Vvar__2__x__211767)
                                & Vvar__1___24Anonymous__211760 = Vvar__1__ST__211766
                                & Vvar__0___24Anonymous__211759 = Vvar__0__Gamma__211764 ) ) ) )
                | ? [Vvar__0__Gamma__211770] :
                    ( cPLF_2eMaps_2epartial__map___24t(cPLF_2eReferences_2eSTLCRef_2ety,Vvar__0__Gamma__211770)
                    & ? [Vvar__1__ST__211771] :
                        ( cPLF_2eReferences_2eSTLCRef_2estore__ty___24t(Vvar__1__ST__211771)
                        & ? [Vvar__2__x__211772] :
                            ( cCoq_2eStrings_2eString_2estring___24t(Vvar__2__x__211772)
                            & ? [Vvar__3__T11__211773] :
                                ( cPLF_2eReferences_2eSTLCRef_2ety___24t(Vvar__3__T11__211773)
                                & ? [Vvar__4__T12__211774] :
                                    ( cPLF_2eReferences_2eSTLCRef_2ety___24t(Vvar__4__T12__211774)
                                    & ? [Vvar__5__t12__211775] :
                                        ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__5__t12__211775)
                                        & cPLF_2eReferences_2eSTLCRef_2ehas__type___24a4(cPLF_2eMaps_2eupdate___24a4(cPLF_2eReferences_2eSTLCRef_2ety,Vvar__0__Gamma__211770,Vvar__2__x__211772,Vvar__3__T11__211773),Vvar__1__ST__211771,Vvar__5__t12__211775,Vvar__4__T12__211774)
                                        & Vvar__3___24Anonymous__211762 = cPLF_2eReferences_2eSTLCRef_2eArrow___24a2(Vvar__3__T11__211773,Vvar__4__T12__211774)
                                        & Vvar__2___24Anonymous__211761 = cPLF_2eReferences_2eSTLCRef_2eabs___24a3(Vvar__2__x__211772,Vvar__3__T11__211773,Vvar__5__t12__211775)
                                        & Vvar__1___24Anonymous__211760 = Vvar__1__ST__211771
                                        & Vvar__0___24Anonymous__211759 = Vvar__0__Gamma__211770 ) ) ) ) ) )
                | ? [Vvar__0__T1__211777] :
                    ( cPLF_2eReferences_2eSTLCRef_2ety___24t(Vvar__0__T1__211777)
                    & ? [Vvar__1__T2__211778] :
                        ( cPLF_2eReferences_2eSTLCRef_2ety___24t(Vvar__1__T2__211778)
                        & ? [Vvar__2__Gamma__211779] :
                            ( cPLF_2eReferences_2eSTLCRef_2econtext___24t(Vvar__2__Gamma__211779)
                            & ? [Vvar__3__ST__211780] :
                                ( cPLF_2eReferences_2eSTLCRef_2estore__ty___24t(Vvar__3__ST__211780)
                                & ? [Vvar__4__t1__211781] :
                                    ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__4__t1__211781)
                                    & ? [Vvar__5__t2__211782] :
                                        ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__5__t2__211782)
                                        & cPLF_2eReferences_2eSTLCRef_2ehas__type___24a4(Vvar__2__Gamma__211779,Vvar__3__ST__211780,Vvar__4__t1__211781,cPLF_2eReferences_2eSTLCRef_2eArrow___24a2(Vvar__0__T1__211777,Vvar__1__T2__211778))
                                        & cPLF_2eReferences_2eSTLCRef_2ehas__type___24a4(Vvar__2__Gamma__211779,Vvar__3__ST__211780,Vvar__5__t2__211782,Vvar__0__T1__211777)
                                        & Vvar__3___24Anonymous__211762 = Vvar__1__T2__211778
                                        & Vvar__2___24Anonymous__211761 = cPLF_2eReferences_2eSTLCRef_2eapp___24a2(Vvar__4__t1__211781,Vvar__5__t2__211782)
                                        & Vvar__1___24Anonymous__211760 = Vvar__3__ST__211780
                                        & Vvar__0___24Anonymous__211759 = Vvar__2__Gamma__211779 ) ) ) ) ) )
                | ? [Vvar__0__Gamma__211785] :
                    ( cPLF_2eReferences_2eSTLCRef_2econtext___24t(Vvar__0__Gamma__211785)
                    & ? [Vvar__1__ST__211786] :
                        ( cPLF_2eReferences_2eSTLCRef_2estore__ty___24t(Vvar__1__ST__211786)
                        & ? [Vvar__2__n__211787] :
                            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__211787)
                            & Vvar__3___24Anonymous__211762 = cPLF_2eReferences_2eSTLCRef_2eNat
                            & Vvar__2___24Anonymous__211761 = cPLF_2eReferences_2eSTLCRef_2econst___24a1(Vvar__2__n__211787)
                            & Vvar__1___24Anonymous__211760 = Vvar__1__ST__211786
                            & Vvar__0___24Anonymous__211759 = Vvar__0__Gamma__211785 ) ) )
                | ? [Vvar__0__Gamma__211788] :
                    ( cPLF_2eReferences_2eSTLCRef_2econtext___24t(Vvar__0__Gamma__211788)
                    & ? [Vvar__1__ST__211789] :
                        ( cPLF_2eReferences_2eSTLCRef_2estore__ty___24t(Vvar__1__ST__211789)
                        & ? [Vvar__2__t1__211790] :
                            ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__2__t1__211790)
                            & cPLF_2eReferences_2eSTLCRef_2ehas__type___24a4(Vvar__0__Gamma__211788,Vvar__1__ST__211789,Vvar__2__t1__211790,cPLF_2eReferences_2eSTLCRef_2eNat)
                            & Vvar__3___24Anonymous__211762 = cPLF_2eReferences_2eSTLCRef_2eNat
                            & Vvar__2___24Anonymous__211761 = cPLF_2eReferences_2eSTLCRef_2escc___24a1(Vvar__2__t1__211790)
                            & Vvar__1___24Anonymous__211760 = Vvar__1__ST__211789
                            & Vvar__0___24Anonymous__211759 = Vvar__0__Gamma__211788 ) ) )
                | ? [Vvar__0__Gamma__211792] :
                    ( cPLF_2eReferences_2eSTLCRef_2econtext___24t(Vvar__0__Gamma__211792)
                    & ? [Vvar__1__ST__211793] :
                        ( cPLF_2eReferences_2eSTLCRef_2estore__ty___24t(Vvar__1__ST__211793)
                        & ? [Vvar__2__t1__211794] :
                            ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__2__t1__211794)
                            & cPLF_2eReferences_2eSTLCRef_2ehas__type___24a4(Vvar__0__Gamma__211792,Vvar__1__ST__211793,Vvar__2__t1__211794,cPLF_2eReferences_2eSTLCRef_2eNat)
                            & Vvar__3___24Anonymous__211762 = cPLF_2eReferences_2eSTLCRef_2eNat
                            & Vvar__2___24Anonymous__211761 = cPLF_2eReferences_2eSTLCRef_2eprd___24a1(Vvar__2__t1__211794)
                            & Vvar__1___24Anonymous__211760 = Vvar__1__ST__211793
                            & Vvar__0___24Anonymous__211759 = Vvar__0__Gamma__211792 ) ) )
                | ? [Vvar__0__Gamma__211796] :
                    ( cPLF_2eReferences_2eSTLCRef_2econtext___24t(Vvar__0__Gamma__211796)
                    & ? [Vvar__1__ST__211797] :
                        ( cPLF_2eReferences_2eSTLCRef_2estore__ty___24t(Vvar__1__ST__211797)
                        & ? [Vvar__2__t1__211798] :
                            ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__2__t1__211798)
                            & ? [Vvar__3__t2__211799] :
                                ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__3__t2__211799)
                                & cPLF_2eReferences_2eSTLCRef_2ehas__type___24a4(Vvar__0__Gamma__211796,Vvar__1__ST__211797,Vvar__2__t1__211798,cPLF_2eReferences_2eSTLCRef_2eNat)
                                & cPLF_2eReferences_2eSTLCRef_2ehas__type___24a4(Vvar__0__Gamma__211796,Vvar__1__ST__211797,Vvar__3__t2__211799,cPLF_2eReferences_2eSTLCRef_2eNat)
                                & Vvar__3___24Anonymous__211762 = cPLF_2eReferences_2eSTLCRef_2eNat
                                & Vvar__2___24Anonymous__211761 = cPLF_2eReferences_2eSTLCRef_2emlt___24a2(Vvar__2__t1__211798,Vvar__3__t2__211799)
                                & Vvar__1___24Anonymous__211760 = Vvar__1__ST__211797
                                & Vvar__0___24Anonymous__211759 = Vvar__0__Gamma__211796 ) ) ) )
                | ? [Vvar__0__Gamma__211802] :
                    ( cPLF_2eReferences_2eSTLCRef_2econtext___24t(Vvar__0__Gamma__211802)
                    & ? [Vvar__1__ST__211803] :
                        ( cPLF_2eReferences_2eSTLCRef_2estore__ty___24t(Vvar__1__ST__211803)
                        & ? [Vvar__2__t1__211804] :
                            ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__2__t1__211804)
                            & ? [Vvar__3__t2__211805] :
                                ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__3__t2__211805)
                                & ? [Vvar__4__t3__211806] :
                                    ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__4__t3__211806)
                                    & ? [Vvar__5__T__211807] :
                                        ( cPLF_2eReferences_2eSTLCRef_2ety___24t(Vvar__5__T__211807)
                                        & cPLF_2eReferences_2eSTLCRef_2ehas__type___24a4(Vvar__0__Gamma__211802,Vvar__1__ST__211803,Vvar__2__t1__211804,cPLF_2eReferences_2eSTLCRef_2eNat)
                                        & cPLF_2eReferences_2eSTLCRef_2ehas__type___24a4(Vvar__0__Gamma__211802,Vvar__1__ST__211803,Vvar__3__t2__211805,Vvar__5__T__211807)
                                        & cPLF_2eReferences_2eSTLCRef_2ehas__type___24a4(Vvar__0__Gamma__211802,Vvar__1__ST__211803,Vvar__4__t3__211806,Vvar__5__T__211807)
                                        & Vvar__3___24Anonymous__211762 = Vvar__5__T__211807
                                        & Vvar__2___24Anonymous__211761 = cPLF_2eReferences_2eSTLCRef_2etest0___24a3(Vvar__2__t1__211804,Vvar__3__t2__211805,Vvar__4__t3__211806)
                                        & Vvar__1___24Anonymous__211760 = Vvar__1__ST__211803
                                        & Vvar__0___24Anonymous__211759 = Vvar__0__Gamma__211802 ) ) ) ) ) )
                | ? [Vvar__0__Gamma__211811] :
                    ( cPLF_2eReferences_2eSTLCRef_2econtext___24t(Vvar__0__Gamma__211811)
                    & ? [Vvar__1__ST__211812] :
                        ( cPLF_2eReferences_2eSTLCRef_2estore__ty___24t(Vvar__1__ST__211812)
                        & Vvar__3___24Anonymous__211762 = cPLF_2eReferences_2eSTLCRef_2eUnit
                        & Vvar__2___24Anonymous__211761 = cPLF_2eReferences_2eSTLCRef_2eunit
                        & Vvar__1___24Anonymous__211760 = Vvar__1__ST__211812
                        & Vvar__0___24Anonymous__211759 = Vvar__0__Gamma__211811 ) )
                | ? [Vvar__0__Gamma__211813] :
                    ( cPLF_2eReferences_2eSTLCRef_2econtext___24t(Vvar__0__Gamma__211813)
                    & ? [Vvar__1__ST__211814] :
                        ( cCoq_2eInit_2eDatatypes_2elist___24t(cPLF_2eReferences_2eSTLCRef_2ety,Vvar__1__ST__211814)
                        & ? [Vvar__2__l__211815] :
                            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__l__211815)
                            & p(cCoq_2eInit_2ePeano_2elt___24a2(Vvar__2__l__211815,cCoq_2eInit_2eDatatypes_2elength___24a2(cPLF_2eReferences_2eSTLCRef_2ety,Vvar__1__ST__211814)))
                            & Vvar__3___24Anonymous__211762 = cPLF_2eReferences_2eSTLCRef_2eRef___24a1(c_24__case__Coq_2eInit_2eDatatypes_2enat_24212097___24a6(Vvar__0___24Anonymous__211759,Vvar__1___24Anonymous__211760,Vvar__2___24Anonymous__211761,Vvar__3___24Anonymous__211762,Vvar__1__ST__211814,Vvar__2__l__211815))
                            & Vvar__2___24Anonymous__211761 = cPLF_2eReferences_2eSTLCRef_2eloc___24a1(Vvar__2__l__211815)
                            & Vvar__1___24Anonymous__211760 = Vvar__1__ST__211814
                            & Vvar__0___24Anonymous__211759 = Vvar__0__Gamma__211813 ) ) )
                | ? [Vvar__0__Gamma__211840] :
                    ( cPLF_2eReferences_2eSTLCRef_2econtext___24t(Vvar__0__Gamma__211840)
                    & ? [Vvar__1__ST__211841] :
                        ( cPLF_2eReferences_2eSTLCRef_2estore__ty___24t(Vvar__1__ST__211841)
                        & ? [Vvar__2__t1__211842] :
                            ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__2__t1__211842)
                            & ? [Vvar__3__T1__211843] :
                                ( cPLF_2eReferences_2eSTLCRef_2ety___24t(Vvar__3__T1__211843)
                                & cPLF_2eReferences_2eSTLCRef_2ehas__type___24a4(Vvar__0__Gamma__211840,Vvar__1__ST__211841,Vvar__2__t1__211842,Vvar__3__T1__211843)
                                & Vvar__3___24Anonymous__211762 = cPLF_2eReferences_2eSTLCRef_2eRef___24a1(Vvar__3__T1__211843)
                                & Vvar__2___24Anonymous__211761 = cPLF_2eReferences_2eSTLCRef_2eref___24a1(Vvar__2__t1__211842)
                                & Vvar__1___24Anonymous__211760 = Vvar__1__ST__211841
                                & Vvar__0___24Anonymous__211759 = Vvar__0__Gamma__211840 ) ) ) )
                | ? [Vvar__0__Gamma__211845] :
                    ( cPLF_2eReferences_2eSTLCRef_2econtext___24t(Vvar__0__Gamma__211845)
                    & ? [Vvar__1__ST__211846] :
                        ( cPLF_2eReferences_2eSTLCRef_2estore__ty___24t(Vvar__1__ST__211846)
                        & ? [Vvar__2__t1__211847] :
                            ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__2__t1__211847)
                            & ? [Vvar__3__T11__211848] :
                                ( cPLF_2eReferences_2eSTLCRef_2ety___24t(Vvar__3__T11__211848)
                                & cPLF_2eReferences_2eSTLCRef_2ehas__type___24a4(Vvar__0__Gamma__211845,Vvar__1__ST__211846,Vvar__2__t1__211847,cPLF_2eReferences_2eSTLCRef_2eRef___24a1(Vvar__3__T11__211848))
                                & Vvar__3___24Anonymous__211762 = Vvar__3__T11__211848
                                & Vvar__2___24Anonymous__211761 = cPLF_2eReferences_2eSTLCRef_2ederef___24a1(Vvar__2__t1__211847)
                                & Vvar__1___24Anonymous__211760 = Vvar__1__ST__211846
                                & Vvar__0___24Anonymous__211759 = Vvar__0__Gamma__211845 ) ) ) )
                | ? [Vvar__0__Gamma__211850] :
                    ( cPLF_2eReferences_2eSTLCRef_2econtext___24t(Vvar__0__Gamma__211850)
                    & ? [Vvar__1__ST__211851] :
                        ( cPLF_2eReferences_2eSTLCRef_2estore__ty___24t(Vvar__1__ST__211851)
                        & ? [Vvar__2__t1__211852] :
                            ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__2__t1__211852)
                            & ? [Vvar__3__t2__211853] :
                                ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__3__t2__211853)
                                & ? [Vvar__4__T11__211854] :
                                    ( cPLF_2eReferences_2eSTLCRef_2ety___24t(Vvar__4__T11__211854)
                                    & cPLF_2eReferences_2eSTLCRef_2ehas__type___24a4(Vvar__0__Gamma__211850,Vvar__1__ST__211851,Vvar__2__t1__211852,cPLF_2eReferences_2eSTLCRef_2eRef___24a1(Vvar__4__T11__211854))
                                    & cPLF_2eReferences_2eSTLCRef_2ehas__type___24a4(Vvar__0__Gamma__211850,Vvar__1__ST__211851,Vvar__3__t2__211853,Vvar__4__T11__211854)
                                    & Vvar__3___24Anonymous__211762 = cPLF_2eReferences_2eSTLCRef_2eUnit
                                    & Vvar__2___24Anonymous__211761 = cPLF_2eReferences_2eSTLCRef_2eassign___24a2(Vvar__2__t1__211852,Vvar__3__t2__211853)
                                    & Vvar__1___24Anonymous__211760 = Vvar__1__ST__211851
                                    & Vvar__0___24Anonymous__211759 = Vvar__0__Gamma__211850 ) ) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_PLF.References.STLCRef.step',axiom,
    ! [Vvar__0___24Anonymous__203763,Vvar__1___24Anonymous__203764] :
      ( cCoq_2eInit_2eDatatypes_2eprod___24t(cPLF_2eReferences_2eSTLCRef_2etm,cPLF_2eReferences_2eSTLCRef_2estore,Vvar__0___24Anonymous__203763)
     => ( cCoq_2eInit_2eDatatypes_2eprod___24t(cPLF_2eReferences_2eSTLCRef_2etm,cPLF_2eReferences_2eSTLCRef_2estore,Vvar__1___24Anonymous__203764)
       => ( cPLF_2eReferences_2eSTLCRef_2estep___24a2(Vvar__0___24Anonymous__203763,Vvar__1___24Anonymous__203764)
         => ( ? [Vvar__0__x__203766] :
                ( cCoq_2eStrings_2eString_2estring___24t(Vvar__0__x__203766)
                & ? [Vvar__1__T__203767] :
                    ( cPLF_2eReferences_2eSTLCRef_2ety___24t(Vvar__1__T__203767)
                    & ? [Vvar__2__t12__203768] :
                        ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__2__t12__203768)
                        & ? [Vvar__3__v2__203769] :
                            ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__3__v2__203769)
                            & ? [Vvar__4__st__203770] :
                                ( cPLF_2eReferences_2eSTLCRef_2estore___24t(Vvar__4__st__203770)
                                & cPLF_2eReferences_2eSTLCRef_2evalue___24a1(Vvar__3__v2__203769)
                                & Vvar__1___24Anonymous__203764 = cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cCoq_2eInit_2eDatatypes_2elist___24a1(cPLF_2eReferences_2eSTLCRef_2etm),c_24__case__PLF_2eReferences_2eSTLCRef_2etm_24208442___24a5(Vvar__0___24Anonymous__203763,Vvar__1___24Anonymous__203764,Vvar__0__x__203766,Vvar__2__t12__203768,Vvar__3__v2__203769),Vvar__4__st__203770)
                                & Vvar__0___24Anonymous__203763 = cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cCoq_2eInit_2eDatatypes_2elist___24a1(cPLF_2eReferences_2eSTLCRef_2etm),cPLF_2eReferences_2eSTLCRef_2eapp___24a2(cPLF_2eReferences_2eSTLCRef_2eabs___24a3(Vvar__0__x__203766,Vvar__1__T__203767,Vvar__2__t12__203768),Vvar__3__v2__203769),Vvar__4__st__203770) ) ) ) ) )
            | ? [Vvar__0__t1__203794] :
                ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__0__t1__203794)
                & ? [Vvar__1__t1_27__203795] :
                    ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__1__t1_27__203795)
                    & ? [Vvar__2__t2__203796] :
                        ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__2__t2__203796)
                        & ? [Vvar__3__st__203797] :
                            ( cPLF_2eReferences_2eSTLCRef_2estore___24t(Vvar__3__st__203797)
                            & ? [Vvar__4__st_27__203798] :
                                ( cPLF_2eReferences_2eSTLCRef_2estore___24t(Vvar__4__st_27__203798)
                                & cPLF_2eReferences_2eSTLCRef_2estep___24a2(cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cPLF_2eReferences_2eSTLCRef_2estore,Vvar__0__t1__203794,Vvar__3__st__203797),cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cPLF_2eReferences_2eSTLCRef_2estore,Vvar__1__t1_27__203795,Vvar__4__st_27__203798))
                                & Vvar__1___24Anonymous__203764 = cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cCoq_2eInit_2eDatatypes_2elist___24a1(cPLF_2eReferences_2eSTLCRef_2etm),cPLF_2eReferences_2eSTLCRef_2eapp___24a2(Vvar__1__t1_27__203795,Vvar__2__t2__203796),Vvar__4__st_27__203798)
                                & Vvar__0___24Anonymous__203763 = cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cCoq_2eInit_2eDatatypes_2elist___24a1(cPLF_2eReferences_2eSTLCRef_2etm),cPLF_2eReferences_2eSTLCRef_2eapp___24a2(Vvar__0__t1__203794,Vvar__2__t2__203796),Vvar__3__st__203797) ) ) ) ) )
            | ? [Vvar__0__v1__203800] :
                ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__0__v1__203800)
                & ? [Vvar__1__t2__203801] :
                    ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__1__t2__203801)
                    & ? [Vvar__2__t2_27__203802] :
                        ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__2__t2_27__203802)
                        & ? [Vvar__3__st__203803] :
                            ( cPLF_2eReferences_2eSTLCRef_2estore___24t(Vvar__3__st__203803)
                            & ? [Vvar__4__st_27__203804] :
                                ( cPLF_2eReferences_2eSTLCRef_2estore___24t(Vvar__4__st_27__203804)
                                & cPLF_2eReferences_2eSTLCRef_2evalue___24a1(Vvar__0__v1__203800)
                                & cPLF_2eReferences_2eSTLCRef_2estep___24a2(cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cPLF_2eReferences_2eSTLCRef_2estore,Vvar__1__t2__203801,Vvar__3__st__203803),cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cPLF_2eReferences_2eSTLCRef_2estore,Vvar__2__t2_27__203802,Vvar__4__st_27__203804))
                                & Vvar__1___24Anonymous__203764 = cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cCoq_2eInit_2eDatatypes_2elist___24a1(cPLF_2eReferences_2eSTLCRef_2etm),cPLF_2eReferences_2eSTLCRef_2eapp___24a2(Vvar__0__v1__203800,Vvar__2__t2_27__203802),Vvar__4__st_27__203804)
                                & Vvar__0___24Anonymous__203763 = cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cCoq_2eInit_2eDatatypes_2elist___24a1(cPLF_2eReferences_2eSTLCRef_2etm),cPLF_2eReferences_2eSTLCRef_2eapp___24a2(Vvar__0__v1__203800,Vvar__1__t2__203801),Vvar__3__st__203803) ) ) ) ) )
            | ? [Vvar__0__n__203807] :
                ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__203807)
                & ? [Vvar__1__st__203808] :
                    ( cPLF_2eReferences_2eSTLCRef_2estore___24t(Vvar__1__st__203808)
                    & Vvar__1___24Anonymous__203764 = cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cCoq_2eInit_2eDatatypes_2elist___24a1(cPLF_2eReferences_2eSTLCRef_2etm),cPLF_2eReferences_2eSTLCRef_2econst___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0__n__203807)),Vvar__1__st__203808)
                    & Vvar__0___24Anonymous__203763 = cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cCoq_2eInit_2eDatatypes_2elist___24a1(cPLF_2eReferences_2eSTLCRef_2etm),cPLF_2eReferences_2eSTLCRef_2escc___24a1(cPLF_2eReferences_2eSTLCRef_2econst___24a1(Vvar__0__n__203807)),Vvar__1__st__203808) ) )
            | ? [Vvar__0__t1__203809] :
                ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__0__t1__203809)
                & ? [Vvar__1__t1_27__203810] :
                    ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__1__t1_27__203810)
                    & ? [Vvar__2__st__203811] :
                        ( cPLF_2eReferences_2eSTLCRef_2estore___24t(Vvar__2__st__203811)
                        & ? [Vvar__3__st_27__203812] :
                            ( cPLF_2eReferences_2eSTLCRef_2estore___24t(Vvar__3__st_27__203812)
                            & cPLF_2eReferences_2eSTLCRef_2estep___24a2(cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cPLF_2eReferences_2eSTLCRef_2estore,Vvar__0__t1__203809,Vvar__2__st__203811),cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cPLF_2eReferences_2eSTLCRef_2estore,Vvar__1__t1_27__203810,Vvar__3__st_27__203812))
                            & Vvar__1___24Anonymous__203764 = cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cCoq_2eInit_2eDatatypes_2elist___24a1(cPLF_2eReferences_2eSTLCRef_2etm),cPLF_2eReferences_2eSTLCRef_2escc___24a1(Vvar__1__t1_27__203810),Vvar__3__st_27__203812)
                            & Vvar__0___24Anonymous__203763 = cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cCoq_2eInit_2eDatatypes_2elist___24a1(cPLF_2eReferences_2eSTLCRef_2etm),cPLF_2eReferences_2eSTLCRef_2escc___24a1(Vvar__0__t1__203809),Vvar__2__st__203811) ) ) ) )
            | ? [Vvar__0__n__203814] :
                ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__203814)
                & ? [Vvar__1__st__203815] :
                    ( cPLF_2eReferences_2eSTLCRef_2estore___24t(Vvar__1__st__203815)
                    & Vvar__1___24Anonymous__203764 = cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cCoq_2eInit_2eDatatypes_2elist___24a1(cPLF_2eReferences_2eSTLCRef_2etm),cPLF_2eReferences_2eSTLCRef_2econst___24a1(c_24__case__Coq_2eInit_2eDatatypes_2enat_24210866___24a3(Vvar__0___24Anonymous__203763,Vvar__1___24Anonymous__203764,Vvar__0__n__203814)),Vvar__1__st__203815)
                    & Vvar__0___24Anonymous__203763 = cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cCoq_2eInit_2eDatatypes_2elist___24a1(cPLF_2eReferences_2eSTLCRef_2etm),cPLF_2eReferences_2eSTLCRef_2eprd___24a1(cPLF_2eReferences_2eSTLCRef_2econst___24a1(Vvar__0__n__203814)),Vvar__1__st__203815) ) )
            | ? [Vvar__0__t1__203818] :
                ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__0__t1__203818)
                & ? [Vvar__1__t1_27__203819] :
                    ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__1__t1_27__203819)
                    & ? [Vvar__2__st__203820] :
                        ( cPLF_2eReferences_2eSTLCRef_2estore___24t(Vvar__2__st__203820)
                        & ? [Vvar__3__st_27__203821] :
                            ( cPLF_2eReferences_2eSTLCRef_2estore___24t(Vvar__3__st_27__203821)
                            & cPLF_2eReferences_2eSTLCRef_2estep___24a2(cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cPLF_2eReferences_2eSTLCRef_2estore,Vvar__0__t1__203818,Vvar__2__st__203820),cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cPLF_2eReferences_2eSTLCRef_2estore,Vvar__1__t1_27__203819,Vvar__3__st_27__203821))
                            & Vvar__1___24Anonymous__203764 = cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cCoq_2eInit_2eDatatypes_2elist___24a1(cPLF_2eReferences_2eSTLCRef_2etm),cPLF_2eReferences_2eSTLCRef_2eprd___24a1(Vvar__1__t1_27__203819),Vvar__3__st_27__203821)
                            & Vvar__0___24Anonymous__203763 = cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cCoq_2eInit_2eDatatypes_2elist___24a1(cPLF_2eReferences_2eSTLCRef_2etm),cPLF_2eReferences_2eSTLCRef_2eprd___24a1(Vvar__0__t1__203818),Vvar__2__st__203820) ) ) ) )
            | ? [Vvar__0__n1__203823] :
                ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n1__203823)
                & ? [Vvar__1__n2__203824] :
                    ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__n2__203824)
                    & ? [Vvar__2__st__203825] :
                        ( cPLF_2eReferences_2eSTLCRef_2estore___24t(Vvar__2__st__203825)
                        & Vvar__1___24Anonymous__203764 = cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cCoq_2eInit_2eDatatypes_2elist___24a1(cPLF_2eReferences_2eSTLCRef_2etm),cPLF_2eReferences_2eSTLCRef_2econst___24a1(c_24__case__Coq_2eInit_2eDatatypes_2enat_24210921___24a4(Vvar__0___24Anonymous__203763,Vvar__1___24Anonymous__203764,Vvar__0__n1__203823,Vvar__1__n2__203824)),Vvar__2__st__203825)
                        & Vvar__0___24Anonymous__203763 = cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cCoq_2eInit_2eDatatypes_2elist___24a1(cPLF_2eReferences_2eSTLCRef_2etm),cPLF_2eReferences_2eSTLCRef_2emlt___24a2(cPLF_2eReferences_2eSTLCRef_2econst___24a1(Vvar__0__n1__203823),cPLF_2eReferences_2eSTLCRef_2econst___24a1(Vvar__1__n2__203824)),Vvar__2__st__203825) ) ) )
            | ? [Vvar__0__t1__203828] :
                ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__0__t1__203828)
                & ? [Vvar__1__t2__203829] :
                    ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__1__t2__203829)
                    & ? [Vvar__2__t1_27__203830] :
                        ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__2__t1_27__203830)
                        & ? [Vvar__3__st__203831] :
                            ( cPLF_2eReferences_2eSTLCRef_2estore___24t(Vvar__3__st__203831)
                            & ? [Vvar__4__st_27__203832] :
                                ( cPLF_2eReferences_2eSTLCRef_2estore___24t(Vvar__4__st_27__203832)
                                & cPLF_2eReferences_2eSTLCRef_2estep___24a2(cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cPLF_2eReferences_2eSTLCRef_2estore,Vvar__0__t1__203828,Vvar__3__st__203831),cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cPLF_2eReferences_2eSTLCRef_2estore,Vvar__2__t1_27__203830,Vvar__4__st_27__203832))
                                & Vvar__1___24Anonymous__203764 = cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cCoq_2eInit_2eDatatypes_2elist___24a1(cPLF_2eReferences_2eSTLCRef_2etm),cPLF_2eReferences_2eSTLCRef_2emlt___24a2(Vvar__2__t1_27__203830,Vvar__1__t2__203829),Vvar__4__st_27__203832)
                                & Vvar__0___24Anonymous__203763 = cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cCoq_2eInit_2eDatatypes_2elist___24a1(cPLF_2eReferences_2eSTLCRef_2etm),cPLF_2eReferences_2eSTLCRef_2emlt___24a2(Vvar__0__t1__203828,Vvar__1__t2__203829),Vvar__3__st__203831) ) ) ) ) )
            | ? [Vvar__0__v1__203834] :
                ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__0__v1__203834)
                & ? [Vvar__1__t2__203835] :
                    ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__1__t2__203835)
                    & ? [Vvar__2__t2_27__203836] :
                        ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__2__t2_27__203836)
                        & ? [Vvar__3__st__203837] :
                            ( cPLF_2eReferences_2eSTLCRef_2estore___24t(Vvar__3__st__203837)
                            & ? [Vvar__4__st_27__203838] :
                                ( cPLF_2eReferences_2eSTLCRef_2estore___24t(Vvar__4__st_27__203838)
                                & cPLF_2eReferences_2eSTLCRef_2evalue___24a1(Vvar__0__v1__203834)
                                & cPLF_2eReferences_2eSTLCRef_2estep___24a2(cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cPLF_2eReferences_2eSTLCRef_2estore,Vvar__1__t2__203835,Vvar__3__st__203837),cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cPLF_2eReferences_2eSTLCRef_2estore,Vvar__2__t2_27__203836,Vvar__4__st_27__203838))
                                & Vvar__1___24Anonymous__203764 = cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cCoq_2eInit_2eDatatypes_2elist___24a1(cPLF_2eReferences_2eSTLCRef_2etm),cPLF_2eReferences_2eSTLCRef_2emlt___24a2(Vvar__0__v1__203834,Vvar__2__t2_27__203836),Vvar__4__st_27__203838)
                                & Vvar__0___24Anonymous__203763 = cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cCoq_2eInit_2eDatatypes_2elist___24a1(cPLF_2eReferences_2eSTLCRef_2etm),cPLF_2eReferences_2eSTLCRef_2emlt___24a2(Vvar__0__v1__203834,Vvar__1__t2__203835),Vvar__3__st__203837) ) ) ) ) )
            | ? [Vvar__0__t1__203841] :
                ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__0__t1__203841)
                & ? [Vvar__1__t1_27__203842] :
                    ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__1__t1_27__203842)
                    & ? [Vvar__2__t2__203843] :
                        ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__2__t2__203843)
                        & ? [Vvar__3__t3__203844] :
                            ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__3__t3__203844)
                            & ? [Vvar__4__st__203845] :
                                ( cPLF_2eReferences_2eSTLCRef_2estore___24t(Vvar__4__st__203845)
                                & ? [Vvar__5__st_27__203846] :
                                    ( cPLF_2eReferences_2eSTLCRef_2estore___24t(Vvar__5__st_27__203846)
                                    & cPLF_2eReferences_2eSTLCRef_2estep___24a2(cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cPLF_2eReferences_2eSTLCRef_2estore,Vvar__0__t1__203841,Vvar__4__st__203845),cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cPLF_2eReferences_2eSTLCRef_2estore,Vvar__1__t1_27__203842,Vvar__5__st_27__203846))
                                    & Vvar__1___24Anonymous__203764 = cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cCoq_2eInit_2eDatatypes_2elist___24a1(cPLF_2eReferences_2eSTLCRef_2etm),cPLF_2eReferences_2eSTLCRef_2etest0___24a3(Vvar__1__t1_27__203842,Vvar__2__t2__203843,Vvar__3__t3__203844),Vvar__5__st_27__203846)
                                    & Vvar__0___24Anonymous__203763 = cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cCoq_2eInit_2eDatatypes_2elist___24a1(cPLF_2eReferences_2eSTLCRef_2etm),cPLF_2eReferences_2eSTLCRef_2etest0___24a3(Vvar__0__t1__203841,Vvar__2__t2__203843,Vvar__3__t3__203844),Vvar__4__st__203845) ) ) ) ) ) )
            | ? [Vvar__0__t2__203848] :
                ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__0__t2__203848)
                & ? [Vvar__1__t3__203849] :
                    ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__1__t3__203849)
                    & ? [Vvar__2__st__203850] :
                        ( cPLF_2eReferences_2eSTLCRef_2estore___24t(Vvar__2__st__203850)
                        & Vvar__1___24Anonymous__203764 = cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cCoq_2eInit_2eDatatypes_2elist___24a1(cPLF_2eReferences_2eSTLCRef_2etm),Vvar__0__t2__203848,Vvar__2__st__203850)
                        & Vvar__0___24Anonymous__203763 = cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cCoq_2eInit_2eDatatypes_2elist___24a1(cPLF_2eReferences_2eSTLCRef_2etm),cPLF_2eReferences_2eSTLCRef_2etest0___24a3(cPLF_2eReferences_2eSTLCRef_2econst___24a1(cCoq_2eInit_2eDatatypes_2eO),Vvar__0__t2__203848,Vvar__1__t3__203849),Vvar__2__st__203850) ) ) )
            | ? [Vvar__0__n__203851] :
                ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__203851)
                & ? [Vvar__1__t2__203852] :
                    ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__1__t2__203852)
                    & ? [Vvar__2__t3__203853] :
                        ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__2__t3__203853)
                        & ? [Vvar__3__st__203854] :
                            ( cPLF_2eReferences_2eSTLCRef_2estore___24t(Vvar__3__st__203854)
                            & Vvar__1___24Anonymous__203764 = cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cCoq_2eInit_2eDatatypes_2elist___24a1(cPLF_2eReferences_2eSTLCRef_2etm),Vvar__2__t3__203853,Vvar__3__st__203854)
                            & Vvar__0___24Anonymous__203763 = cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cCoq_2eInit_2eDatatypes_2elist___24a1(cPLF_2eReferences_2eSTLCRef_2etm),cPLF_2eReferences_2eSTLCRef_2etest0___24a3(cPLF_2eReferences_2eSTLCRef_2econst___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0__n__203851)),Vvar__1__t2__203852,Vvar__2__t3__203853),Vvar__3__st__203854) ) ) ) )
            | ? [Vvar__0__v1__203855] :
                ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__0__v1__203855)
                & ? [Vvar__1__st__203856] :
                    ( cPLF_2eReferences_2eSTLCRef_2estore___24t(Vvar__1__st__203856)
                    & cPLF_2eReferences_2eSTLCRef_2evalue___24a1(Vvar__0__v1__203855)
                    & Vvar__1___24Anonymous__203764 = cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cCoq_2eInit_2eDatatypes_2elist___24a1(cPLF_2eReferences_2eSTLCRef_2etm),cPLF_2eReferences_2eSTLCRef_2eloc___24a1(c_24__case__Coq_2eInit_2eDatatypes_2elist_24210988___24a3(Vvar__0___24Anonymous__203763,Vvar__1___24Anonymous__203764,Vvar__1__st__203856)),c_24__case__Coq_2eInit_2eDatatypes_2elist_24211097___24a4(Vvar__0___24Anonymous__203763,Vvar__1___24Anonymous__203764,Vvar__0__v1__203855,Vvar__1__st__203856))
                    & Vvar__0___24Anonymous__203763 = cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cCoq_2eInit_2eDatatypes_2elist___24a1(cPLF_2eReferences_2eSTLCRef_2etm),cPLF_2eReferences_2eSTLCRef_2eref___24a1(Vvar__0__v1__203855),Vvar__1__st__203856) ) )
            | ? [Vvar__0__t1__203878] :
                ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__0__t1__203878)
                & ? [Vvar__1__t1_27__203879] :
                    ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__1__t1_27__203879)
                    & ? [Vvar__2__st__203880] :
                        ( cPLF_2eReferences_2eSTLCRef_2estore___24t(Vvar__2__st__203880)
                        & ? [Vvar__3__st_27__203881] :
                            ( cPLF_2eReferences_2eSTLCRef_2estore___24t(Vvar__3__st_27__203881)
                            & cPLF_2eReferences_2eSTLCRef_2estep___24a2(cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cPLF_2eReferences_2eSTLCRef_2estore,Vvar__0__t1__203878,Vvar__2__st__203880),cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cPLF_2eReferences_2eSTLCRef_2estore,Vvar__1__t1_27__203879,Vvar__3__st_27__203881))
                            & Vvar__1___24Anonymous__203764 = cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cCoq_2eInit_2eDatatypes_2elist___24a1(cPLF_2eReferences_2eSTLCRef_2etm),cPLF_2eReferences_2eSTLCRef_2eref___24a1(Vvar__1__t1_27__203879),Vvar__3__st_27__203881)
                            & Vvar__0___24Anonymous__203763 = cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cCoq_2eInit_2eDatatypes_2elist___24a1(cPLF_2eReferences_2eSTLCRef_2etm),cPLF_2eReferences_2eSTLCRef_2eref___24a1(Vvar__0__t1__203878),Vvar__2__st__203880) ) ) ) )
            | ? [Vvar__0__st__203883] :
                ( cCoq_2eInit_2eDatatypes_2elist___24t(cPLF_2eReferences_2eSTLCRef_2etm,Vvar__0__st__203883)
                & ? [Vvar__1__l__203884] :
                    ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__l__203884)
                    & p(cCoq_2eInit_2ePeano_2elt___24a2(Vvar__1__l__203884,cCoq_2eInit_2eDatatypes_2elength___24a2(cPLF_2eReferences_2eSTLCRef_2etm,Vvar__0__st__203883)))
                    & Vvar__1___24Anonymous__203764 = cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cCoq_2eInit_2eDatatypes_2elist___24a1(cPLF_2eReferences_2eSTLCRef_2etm),c_24__case__Coq_2eInit_2eDatatypes_2enat_24211329___24a4(Vvar__0___24Anonymous__203763,Vvar__1___24Anonymous__203764,Vvar__0__st__203883,Vvar__1__l__203884),Vvar__0__st__203883)
                    & Vvar__0___24Anonymous__203763 = cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cCoq_2eInit_2eDatatypes_2elist___24a1(cPLF_2eReferences_2eSTLCRef_2etm),cPLF_2eReferences_2eSTLCRef_2ederef___24a1(cPLF_2eReferences_2eSTLCRef_2eloc___24a1(Vvar__1__l__203884)),Vvar__0__st__203883) ) )
            | ? [Vvar__0__t1__203909] :
                ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__0__t1__203909)
                & ? [Vvar__1__t1_27__203910] :
                    ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__1__t1_27__203910)
                    & ? [Vvar__2__st__203911] :
                        ( cPLF_2eReferences_2eSTLCRef_2estore___24t(Vvar__2__st__203911)
                        & ? [Vvar__3__st_27__203912] :
                            ( cPLF_2eReferences_2eSTLCRef_2estore___24t(Vvar__3__st_27__203912)
                            & cPLF_2eReferences_2eSTLCRef_2estep___24a2(cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cPLF_2eReferences_2eSTLCRef_2estore,Vvar__0__t1__203909,Vvar__2__st__203911),cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cPLF_2eReferences_2eSTLCRef_2estore,Vvar__1__t1_27__203910,Vvar__3__st_27__203912))
                            & Vvar__1___24Anonymous__203764 = cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cCoq_2eInit_2eDatatypes_2elist___24a1(cPLF_2eReferences_2eSTLCRef_2etm),cPLF_2eReferences_2eSTLCRef_2ederef___24a1(Vvar__1__t1_27__203910),Vvar__3__st_27__203912)
                            & Vvar__0___24Anonymous__203763 = cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cCoq_2eInit_2eDatatypes_2elist___24a1(cPLF_2eReferences_2eSTLCRef_2etm),cPLF_2eReferences_2eSTLCRef_2ederef___24a1(Vvar__0__t1__203909),Vvar__2__st__203911) ) ) ) )
            | ? [Vvar__0__v2__203914] :
                ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__0__v2__203914)
                & ? [Vvar__1__l__203915] :
                    ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__l__203915)
                    & ? [Vvar__2__st__203916] :
                        ( cCoq_2eInit_2eDatatypes_2elist___24t(cPLF_2eReferences_2eSTLCRef_2etm,Vvar__2__st__203916)
                        & cPLF_2eReferences_2eSTLCRef_2evalue___24a1(Vvar__0__v2__203914)
                        & p(cCoq_2eInit_2ePeano_2elt___24a2(Vvar__1__l__203915,cCoq_2eInit_2eDatatypes_2elength___24a2(cPLF_2eReferences_2eSTLCRef_2etm,Vvar__2__st__203916)))
                        & Vvar__1___24Anonymous__203764 = cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cCoq_2eInit_2eDatatypes_2elist___24a1(cPLF_2eReferences_2eSTLCRef_2etm),cPLF_2eReferences_2eSTLCRef_2eunit,c_24__case__Coq_2eInit_2eDatatypes_2elist_24211642___24a5(Vvar__0___24Anonymous__203763,Vvar__1___24Anonymous__203764,Vvar__0__v2__203914,Vvar__1__l__203915,Vvar__2__st__203916))
                        & Vvar__0___24Anonymous__203763 = cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cCoq_2eInit_2eDatatypes_2elist___24a1(cPLF_2eReferences_2eSTLCRef_2etm),cPLF_2eReferences_2eSTLCRef_2eassign___24a2(cPLF_2eReferences_2eSTLCRef_2eloc___24a1(Vvar__1__l__203915),Vvar__0__v2__203914),Vvar__2__st__203916) ) ) )
            | ? [Vvar__0__t1__203924] :
                ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__0__t1__203924)
                & ? [Vvar__1__t1_27__203925] :
                    ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__1__t1_27__203925)
                    & ? [Vvar__2__t2__203926] :
                        ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__2__t2__203926)
                        & ? [Vvar__3__st__203927] :
                            ( cPLF_2eReferences_2eSTLCRef_2estore___24t(Vvar__3__st__203927)
                            & ? [Vvar__4__st_27__203928] :
                                ( cPLF_2eReferences_2eSTLCRef_2estore___24t(Vvar__4__st_27__203928)
                                & cPLF_2eReferences_2eSTLCRef_2estep___24a2(cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cPLF_2eReferences_2eSTLCRef_2estore,Vvar__0__t1__203924,Vvar__3__st__203927),cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cPLF_2eReferences_2eSTLCRef_2estore,Vvar__1__t1_27__203925,Vvar__4__st_27__203928))
                                & Vvar__1___24Anonymous__203764 = cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cCoq_2eInit_2eDatatypes_2elist___24a1(cPLF_2eReferences_2eSTLCRef_2etm),cPLF_2eReferences_2eSTLCRef_2eassign___24a2(Vvar__1__t1_27__203925,Vvar__2__t2__203926),Vvar__4__st_27__203928)
                                & Vvar__0___24Anonymous__203763 = cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cCoq_2eInit_2eDatatypes_2elist___24a1(cPLF_2eReferences_2eSTLCRef_2etm),cPLF_2eReferences_2eSTLCRef_2eassign___24a2(Vvar__0__t1__203924,Vvar__2__t2__203926),Vvar__3__st__203927) ) ) ) ) )
            | ? [Vvar__0__v1__203930] :
                ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__0__v1__203930)
                & ? [Vvar__1__t2__203931] :
                    ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__1__t2__203931)
                    & ? [Vvar__2__t2_27__203932] :
                        ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__2__t2_27__203932)
                        & ? [Vvar__3__st__203933] :
                            ( cPLF_2eReferences_2eSTLCRef_2estore___24t(Vvar__3__st__203933)
                            & ? [Vvar__4__st_27__203934] :
                                ( cPLF_2eReferences_2eSTLCRef_2estore___24t(Vvar__4__st_27__203934)
                                & cPLF_2eReferences_2eSTLCRef_2evalue___24a1(Vvar__0__v1__203930)
                                & cPLF_2eReferences_2eSTLCRef_2estep___24a2(cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cPLF_2eReferences_2eSTLCRef_2estore,Vvar__1__t2__203931,Vvar__3__st__203933),cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cPLF_2eReferences_2eSTLCRef_2estore,Vvar__2__t2_27__203932,Vvar__4__st_27__203934))
                                & Vvar__1___24Anonymous__203764 = cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cCoq_2eInit_2eDatatypes_2elist___24a1(cPLF_2eReferences_2eSTLCRef_2etm),cPLF_2eReferences_2eSTLCRef_2eassign___24a2(Vvar__0__v1__203930,Vvar__2__t2_27__203932),Vvar__4__st_27__203934)
                                & Vvar__0___24Anonymous__203763 = cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cCoq_2eInit_2eDatatypes_2elist___24a1(cPLF_2eReferences_2eSTLCRef_2etm),cPLF_2eReferences_2eSTLCRef_2eassign___24a2(Vvar__0__v1__203930,Vvar__1__t2__203931),Vvar__3__st__203933) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_PLF.References.STLCRef.tm',axiom,
    ! [VX203387] :
      ( cPLF_2eReferences_2eSTLCRef_2etm___24t(VX203387)
     => ( ? [Vvar__0___24Anonymous__203388] :
            ( cCoq_2eStrings_2eString_2estring___24t(Vvar__0___24Anonymous__203388)
            & VX203387 = cPLF_2eReferences_2eSTLCRef_2evar___24a1(Vvar__0___24Anonymous__203388) )
        | ? [Vvar__0___24Anonymous__203389] :
            ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__0___24Anonymous__203389)
            & ? [Vvar__1___24Anonymous__203390] :
                ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__1___24Anonymous__203390)
                & VX203387 = cPLF_2eReferences_2eSTLCRef_2eapp___24a2(Vvar__0___24Anonymous__203389,Vvar__1___24Anonymous__203390) ) )
        | ? [Vvar__0___24Anonymous__203391] :
            ( cCoq_2eStrings_2eString_2estring___24t(Vvar__0___24Anonymous__203391)
            & ? [Vvar__1___24Anonymous__203392] :
                ( cPLF_2eReferences_2eSTLCRef_2ety___24t(Vvar__1___24Anonymous__203392)
                & ? [Vvar__2___24Anonymous__203393] :
                    ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__2___24Anonymous__203393)
                    & VX203387 = cPLF_2eReferences_2eSTLCRef_2eabs___24a3(Vvar__0___24Anonymous__203391,Vvar__1___24Anonymous__203392,Vvar__2___24Anonymous__203393) ) ) )
        | ? [Vvar__0___24Anonymous__203394] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__203394)
            & VX203387 = cPLF_2eReferences_2eSTLCRef_2econst___24a1(Vvar__0___24Anonymous__203394) )
        | ? [Vvar__0___24Anonymous__203395] :
            ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__0___24Anonymous__203395)
            & VX203387 = cPLF_2eReferences_2eSTLCRef_2escc___24a1(Vvar__0___24Anonymous__203395) )
        | ? [Vvar__0___24Anonymous__203396] :
            ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__0___24Anonymous__203396)
            & VX203387 = cPLF_2eReferences_2eSTLCRef_2eprd___24a1(Vvar__0___24Anonymous__203396) )
        | ? [Vvar__0___24Anonymous__203397] :
            ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__0___24Anonymous__203397)
            & ? [Vvar__1___24Anonymous__203398] :
                ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__1___24Anonymous__203398)
                & VX203387 = cPLF_2eReferences_2eSTLCRef_2emlt___24a2(Vvar__0___24Anonymous__203397,Vvar__1___24Anonymous__203398) ) )
        | ? [Vvar__0___24Anonymous__203399] :
            ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__0___24Anonymous__203399)
            & ? [Vvar__1___24Anonymous__203400] :
                ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__1___24Anonymous__203400)
                & ? [Vvar__2___24Anonymous__203401] :
                    ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__2___24Anonymous__203401)
                    & VX203387 = cPLF_2eReferences_2eSTLCRef_2etest0___24a3(Vvar__0___24Anonymous__203399,Vvar__1___24Anonymous__203400,Vvar__2___24Anonymous__203401) ) ) )
        | VX203387 = cPLF_2eReferences_2eSTLCRef_2eunit
        | ? [Vvar__0___24Anonymous__203402] :
            ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__0___24Anonymous__203402)
            & VX203387 = cPLF_2eReferences_2eSTLCRef_2eref___24a1(Vvar__0___24Anonymous__203402) )
        | ? [Vvar__0___24Anonymous__203403] :
            ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__0___24Anonymous__203403)
            & VX203387 = cPLF_2eReferences_2eSTLCRef_2ederef___24a1(Vvar__0___24Anonymous__203403) )
        | ? [Vvar__0___24Anonymous__203404] :
            ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__0___24Anonymous__203404)
            & ? [Vvar__1___24Anonymous__203405] :
                ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__1___24Anonymous__203405)
                & VX203387 = cPLF_2eReferences_2eSTLCRef_2eassign___24a2(Vvar__0___24Anonymous__203404,Vvar__1___24Anonymous__203405) ) )
        | ? [Vvar__0___24Anonymous__203406] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__203406)
            & VX203387 = cPLF_2eReferences_2eSTLCRef_2eloc___24a1(Vvar__0___24Anonymous__203406) ) ) ) ).

fof('$_inversion_PLF.References.STLCRef.ty',axiom,
    ! [VX203363] :
      ( cPLF_2eReferences_2eSTLCRef_2ety___24t(VX203363)
     => ( VX203363 = cPLF_2eReferences_2eSTLCRef_2eNat
        | VX203363 = cPLF_2eReferences_2eSTLCRef_2eUnit
        | ? [Vvar__0___24Anonymous__203364] :
            ( cPLF_2eReferences_2eSTLCRef_2ety___24t(Vvar__0___24Anonymous__203364)
            & ? [Vvar__1___24Anonymous__203365] :
                ( cPLF_2eReferences_2eSTLCRef_2ety___24t(Vvar__1___24Anonymous__203365)
                & VX203363 = cPLF_2eReferences_2eSTLCRef_2eArrow___24a2(Vvar__0___24Anonymous__203364,Vvar__1___24Anonymous__203365) ) )
        | ? [Vvar__0___24Anonymous__203366] :
            ( cPLF_2eReferences_2eSTLCRef_2ety___24t(Vvar__0___24Anonymous__203366)
            & VX203363 = cPLF_2eReferences_2eSTLCRef_2eRef___24a1(Vvar__0___24Anonymous__203366) ) ) ) ).

fof('$_inversion_PLF.References.STLCRef.value',axiom,
    ! [Vvar__0___24Anonymous__203694] :
      ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__0___24Anonymous__203694)
     => ( cPLF_2eReferences_2eSTLCRef_2evalue___24a1(Vvar__0___24Anonymous__203694)
       => ( ? [Vvar__0__x__203696] :
              ( cCoq_2eStrings_2eString_2estring___24t(Vvar__0__x__203696)
              & ? [Vvar__1__T__203697] :
                  ( cPLF_2eReferences_2eSTLCRef_2ety___24t(Vvar__1__T__203697)
                  & ? [Vvar__2__t__203698] :
                      ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vvar__2__t__203698)
                      & Vvar__0___24Anonymous__203694 = cPLF_2eReferences_2eSTLCRef_2eabs___24a3(Vvar__0__x__203696,Vvar__1__T__203697,Vvar__2__t__203698) ) ) )
          | ? [Vvar__0__n__203699] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__203699)
              & Vvar__0___24Anonymous__203694 = cPLF_2eReferences_2eSTLCRef_2econst___24a1(Vvar__0__n__203699) )
          | Vvar__0___24Anonymous__203694 = cPLF_2eReferences_2eSTLCRef_2eunit
          | ? [Vvar__0__l__203700] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__l__203700)
              & Vvar__0___24Anonymous__203694 = cPLF_2eReferences_2eSTLCRef_2eloc___24a1(Vvar__0__l__203700) ) ) ) ) ).

fof('$_inversion_PLF.Smallstep.CImp.com',axiom,
    ! [VX79475] :
      ( cPLF_2eSmallstep_2eCImp_2ecom___24t(VX79475)
     => ( VX79475 = cPLF_2eSmallstep_2eCImp_2eCSkip
        | ? [Vvar__0___24Anonymous__79476] :
            ( cCoq_2eStrings_2eString_2estring___24t(Vvar__0___24Anonymous__79476)
            & ? [Vvar__1___24Anonymous__79477] :
                ( cPLF_2eImp_2eaexp___24t(Vvar__1___24Anonymous__79477)
                & VX79475 = cPLF_2eSmallstep_2eCImp_2eCAss___24a2(Vvar__0___24Anonymous__79476,Vvar__1___24Anonymous__79477) ) )
        | ? [Vvar__0___24Anonymous__79478] :
            ( cPLF_2eSmallstep_2eCImp_2ecom___24t(Vvar__0___24Anonymous__79478)
            & ? [Vvar__1___24Anonymous__79479] :
                ( cPLF_2eSmallstep_2eCImp_2ecom___24t(Vvar__1___24Anonymous__79479)
                & VX79475 = cPLF_2eSmallstep_2eCImp_2eCSeq___24a2(Vvar__0___24Anonymous__79478,Vvar__1___24Anonymous__79479) ) )
        | ? [Vvar__0___24Anonymous__79480] :
            ( cPLF_2eImp_2ebexp___24t(Vvar__0___24Anonymous__79480)
            & ? [Vvar__1___24Anonymous__79481] :
                ( cPLF_2eSmallstep_2eCImp_2ecom___24t(Vvar__1___24Anonymous__79481)
                & ? [Vvar__2___24Anonymous__79482] :
                    ( cPLF_2eSmallstep_2eCImp_2ecom___24t(Vvar__2___24Anonymous__79482)
                    & VX79475 = cPLF_2eSmallstep_2eCImp_2eCIf___24a3(Vvar__0___24Anonymous__79480,Vvar__1___24Anonymous__79481,Vvar__2___24Anonymous__79482) ) ) )
        | ? [Vvar__0___24Anonymous__79483] :
            ( cPLF_2eImp_2ebexp___24t(Vvar__0___24Anonymous__79483)
            & ? [Vvar__1___24Anonymous__79484] :
                ( cPLF_2eSmallstep_2eCImp_2ecom___24t(Vvar__1___24Anonymous__79484)
                & VX79475 = cPLF_2eSmallstep_2eCImp_2eCWhile___24a2(Vvar__0___24Anonymous__79483,Vvar__1___24Anonymous__79484) ) )
        | ? [Vvar__0___24Anonymous__79485] :
            ( cPLF_2eSmallstep_2eCImp_2ecom___24t(Vvar__0___24Anonymous__79485)
            & ? [Vvar__1___24Anonymous__79486] :
                ( cPLF_2eSmallstep_2eCImp_2ecom___24t(Vvar__1___24Anonymous__79486)
                & VX79475 = cPLF_2eSmallstep_2eCImp_2eCPar___24a2(Vvar__0___24Anonymous__79485,Vvar__1___24Anonymous__79486) ) ) ) ) ).

fof('$_inversion_PLF.Smallstep.CImp.cstep',axiom,
    ! [Vvar__0___24Anonymous__79579,Vvar__1___24Anonymous__79580] :
      ( cCoq_2eInit_2eDatatypes_2eprod___24t(cPLF_2eSmallstep_2eCImp_2ecom,cPLF_2eImp_2estate,Vvar__0___24Anonymous__79579)
     => ( cCoq_2eInit_2eDatatypes_2eprod___24t(cPLF_2eSmallstep_2eCImp_2ecom,cPLF_2eImp_2estate,Vvar__1___24Anonymous__79580)
       => ( cPLF_2eSmallstep_2eCImp_2ecstep___24a2(Vvar__0___24Anonymous__79579,Vvar__1___24Anonymous__79580)
         => ( ? [Vvar__0__st__79582] :
                ( cPLF_2eImp_2estate___24t(Vvar__0__st__79582)
                & ? [Vvar__1__i__79583] :
                    ( cCoq_2eStrings_2eString_2estring___24t(Vvar__1__i__79583)
                    & ? [Vvar__2__a__79584] :
                        ( cPLF_2eImp_2eaexp___24t(Vvar__2__a__79584)
                        & ? [Vvar__3__a_27__79585] :
                            ( cPLF_2eImp_2eaexp___24t(Vvar__3__a_27__79585)
                            & cPLF_2eSmallstep_2eastep___24a3(Vvar__0__st__79582,Vvar__2__a__79584,Vvar__3__a_27__79585)
                            & Vvar__1___24Anonymous__79580 = cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eSmallstep_2eCImp_2ecom,c_24__type__79652___24a2(Vvar__0___24Anonymous__79579,Vvar__1___24Anonymous__79580),cPLF_2eSmallstep_2eCImp_2eCAss___24a2(Vvar__1__i__79583,Vvar__3__a_27__79585),Vvar__0__st__79582)
                            & Vvar__0___24Anonymous__79579 = cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eSmallstep_2eCImp_2ecom,c_24__type__79652___24a2(Vvar__0___24Anonymous__79579,Vvar__1___24Anonymous__79580),cPLF_2eSmallstep_2eCImp_2eCAss___24a2(Vvar__1__i__79583,Vvar__2__a__79584),Vvar__0__st__79582) ) ) ) )
            | ? [Vvar__0__st__79589] :
                ( cPLF_2eImp_2estate___24t(Vvar__0__st__79589)
                & ? [Vvar__1__i__79590] :
                    ( cCoq_2eStrings_2eString_2estring___24t(Vvar__1__i__79590)
                    & ? [Vvar__2__n__79591] :
                        ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__79591)
                        & Vvar__1___24Anonymous__79580 = cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eSmallstep_2eCImp_2ecom,c_24__type__79652___24a2(Vvar__0___24Anonymous__79579,Vvar__1___24Anonymous__79580),cPLF_2eSmallstep_2eCImp_2eCSkip,c_24__lam__79669___24a5(Vvar__0___24Anonymous__79579,Vvar__1___24Anonymous__79580,Vvar__0__st__79589,Vvar__1__i__79590,Vvar__2__n__79591))
                        & Vvar__0___24Anonymous__79579 = cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eSmallstep_2eCImp_2ecom,c_24__type__79652___24a2(Vvar__0___24Anonymous__79579,Vvar__1___24Anonymous__79580),cPLF_2eSmallstep_2eCImp_2eCAss___24a2(Vvar__1__i__79590,cPLF_2eImp_2eANum___24a1(Vvar__2__n__79591)),Vvar__0__st__79589) ) ) )
            | ? [Vvar__0__st__79596] :
                ( cPLF_2eImp_2estate___24t(Vvar__0__st__79596)
                & ? [Vvar__1__c1__79597] :
                    ( cPLF_2eSmallstep_2eCImp_2ecom___24t(Vvar__1__c1__79597)
                    & ? [Vvar__2__c1_27__79598] :
                        ( cPLF_2eSmallstep_2eCImp_2ecom___24t(Vvar__2__c1_27__79598)
                        & ? [Vvar__3__st_27__79599] :
                            ( cPLF_2eImp_2estate___24t(Vvar__3__st_27__79599)
                            & ? [Vvar__4__c2__79600] :
                                ( cPLF_2eSmallstep_2eCImp_2ecom___24t(Vvar__4__c2__79600)
                                & cPLF_2eSmallstep_2eCImp_2ecstep___24a2(cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eSmallstep_2eCImp_2ecom,cPLF_2eImp_2estate,Vvar__1__c1__79597,Vvar__0__st__79596),cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eSmallstep_2eCImp_2ecom,cPLF_2eImp_2estate,Vvar__2__c1_27__79598,Vvar__3__st_27__79599))
                                & Vvar__1___24Anonymous__79580 = cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eSmallstep_2eCImp_2ecom,c_24__type__79652___24a2(Vvar__0___24Anonymous__79579,Vvar__1___24Anonymous__79580),cPLF_2eSmallstep_2eCImp_2eCSeq___24a2(Vvar__2__c1_27__79598,Vvar__4__c2__79600),Vvar__3__st_27__79599)
                                & Vvar__0___24Anonymous__79579 = cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eSmallstep_2eCImp_2ecom,c_24__type__79652___24a2(Vvar__0___24Anonymous__79579,Vvar__1___24Anonymous__79580),cPLF_2eSmallstep_2eCImp_2eCSeq___24a2(Vvar__1__c1__79597,Vvar__4__c2__79600),Vvar__0__st__79596) ) ) ) ) )
            | ? [Vvar__0__st__79604] :
                ( cPLF_2eImp_2estate___24t(Vvar__0__st__79604)
                & ? [Vvar__1__c2__79605] :
                    ( cPLF_2eSmallstep_2eCImp_2ecom___24t(Vvar__1__c2__79605)
                    & Vvar__1___24Anonymous__79580 = cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eSmallstep_2eCImp_2ecom,c_24__type__79652___24a2(Vvar__0___24Anonymous__79579,Vvar__1___24Anonymous__79580),Vvar__1__c2__79605,Vvar__0__st__79604)
                    & Vvar__0___24Anonymous__79579 = cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eSmallstep_2eCImp_2ecom,c_24__type__79652___24a2(Vvar__0___24Anonymous__79579,Vvar__1___24Anonymous__79580),cPLF_2eSmallstep_2eCImp_2eCSeq___24a2(cPLF_2eSmallstep_2eCImp_2eCSkip,Vvar__1__c2__79605),Vvar__0__st__79604) ) )
            | ? [Vvar__0__st__79608] :
                ( cPLF_2eImp_2estate___24t(Vvar__0__st__79608)
                & ? [Vvar__1__b__79609] :
                    ( cPLF_2eImp_2ebexp___24t(Vvar__1__b__79609)
                    & ? [Vvar__2__b_27__79610] :
                        ( cPLF_2eImp_2ebexp___24t(Vvar__2__b_27__79610)
                        & ? [Vvar__3__c1__79611] :
                            ( cPLF_2eSmallstep_2eCImp_2ecom___24t(Vvar__3__c1__79611)
                            & ? [Vvar__4__c2__79612] :
                                ( cPLF_2eSmallstep_2eCImp_2ecom___24t(Vvar__4__c2__79612)
                                & cPLF_2eSmallstep_2ebstep___24a3(Vvar__0__st__79608,Vvar__1__b__79609,Vvar__2__b_27__79610)
                                & Vvar__1___24Anonymous__79580 = cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eSmallstep_2eCImp_2ecom,c_24__type__79652___24a2(Vvar__0___24Anonymous__79579,Vvar__1___24Anonymous__79580),cPLF_2eSmallstep_2eCImp_2eCIf___24a3(Vvar__2__b_27__79610,Vvar__3__c1__79611,Vvar__4__c2__79612),Vvar__0__st__79608)
                                & Vvar__0___24Anonymous__79579 = cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eSmallstep_2eCImp_2ecom,c_24__type__79652___24a2(Vvar__0___24Anonymous__79579,Vvar__1___24Anonymous__79580),cPLF_2eSmallstep_2eCImp_2eCIf___24a3(Vvar__1__b__79609,Vvar__3__c1__79611,Vvar__4__c2__79612),Vvar__0__st__79608) ) ) ) ) )
            | ? [Vvar__0__st__79616] :
                ( cPLF_2eImp_2estate___24t(Vvar__0__st__79616)
                & ? [Vvar__1__c1__79617] :
                    ( cPLF_2eSmallstep_2eCImp_2ecom___24t(Vvar__1__c1__79617)
                    & ? [Vvar__2__c2__79618] :
                        ( cPLF_2eSmallstep_2eCImp_2ecom___24t(Vvar__2__c2__79618)
                        & Vvar__1___24Anonymous__79580 = cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eSmallstep_2eCImp_2ecom,c_24__type__79652___24a2(Vvar__0___24Anonymous__79579,Vvar__1___24Anonymous__79580),Vvar__1__c1__79617,Vvar__0__st__79616)
                        & Vvar__0___24Anonymous__79579 = cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eSmallstep_2eCImp_2ecom,c_24__type__79652___24a2(Vvar__0___24Anonymous__79579,Vvar__1___24Anonymous__79580),cPLF_2eSmallstep_2eCImp_2eCIf___24a3(cPLF_2eImp_2eBTrue,Vvar__1__c1__79617,Vvar__2__c2__79618),Vvar__0__st__79616) ) ) )
            | ? [Vvar__0__st__79621] :
                ( cPLF_2eImp_2estate___24t(Vvar__0__st__79621)
                & ? [Vvar__1__c1__79622] :
                    ( cPLF_2eSmallstep_2eCImp_2ecom___24t(Vvar__1__c1__79622)
                    & ? [Vvar__2__c2__79623] :
                        ( cPLF_2eSmallstep_2eCImp_2ecom___24t(Vvar__2__c2__79623)
                        & Vvar__1___24Anonymous__79580 = cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eSmallstep_2eCImp_2ecom,c_24__type__79652___24a2(Vvar__0___24Anonymous__79579,Vvar__1___24Anonymous__79580),Vvar__2__c2__79623,Vvar__0__st__79621)
                        & Vvar__0___24Anonymous__79579 = cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eSmallstep_2eCImp_2ecom,c_24__type__79652___24a2(Vvar__0___24Anonymous__79579,Vvar__1___24Anonymous__79580),cPLF_2eSmallstep_2eCImp_2eCIf___24a3(cPLF_2eImp_2eBFalse,Vvar__1__c1__79622,Vvar__2__c2__79623),Vvar__0__st__79621) ) ) )
            | ? [Vvar__0__st__79626] :
                ( cPLF_2eImp_2estate___24t(Vvar__0__st__79626)
                & ? [Vvar__1__b__79627] :
                    ( cPLF_2eImp_2ebexp___24t(Vvar__1__b__79627)
                    & ? [Vvar__2__c1__79628] :
                        ( cPLF_2eSmallstep_2eCImp_2ecom___24t(Vvar__2__c1__79628)
                        & Vvar__1___24Anonymous__79580 = cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eSmallstep_2eCImp_2ecom,c_24__type__79652___24a2(Vvar__0___24Anonymous__79579,Vvar__1___24Anonymous__79580),cPLF_2eSmallstep_2eCImp_2eCIf___24a3(Vvar__1__b__79627,cPLF_2eSmallstep_2eCImp_2eCSeq___24a2(Vvar__2__c1__79628,cPLF_2eSmallstep_2eCImp_2eCWhile___24a2(Vvar__1__b__79627,Vvar__2__c1__79628)),cPLF_2eSmallstep_2eCImp_2eCSkip),Vvar__0__st__79626)
                        & Vvar__0___24Anonymous__79579 = cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eSmallstep_2eCImp_2ecom,c_24__type__79652___24a2(Vvar__0___24Anonymous__79579,Vvar__1___24Anonymous__79580),cPLF_2eSmallstep_2eCImp_2eCWhile___24a2(Vvar__1__b__79627,Vvar__2__c1__79628),Vvar__0__st__79626) ) ) )
            | ? [Vvar__0__st__79631] :
                ( cPLF_2eImp_2estate___24t(Vvar__0__st__79631)
                & ? [Vvar__1__c1__79632] :
                    ( cPLF_2eSmallstep_2eCImp_2ecom___24t(Vvar__1__c1__79632)
                    & ? [Vvar__2__c1_27__79633] :
                        ( cPLF_2eSmallstep_2eCImp_2ecom___24t(Vvar__2__c1_27__79633)
                        & ? [Vvar__3__c2__79634] :
                            ( cPLF_2eSmallstep_2eCImp_2ecom___24t(Vvar__3__c2__79634)
                            & ? [Vvar__4__st_27__79635] :
                                ( cPLF_2eImp_2estate___24t(Vvar__4__st_27__79635)
                                & cPLF_2eSmallstep_2eCImp_2ecstep___24a2(cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eSmallstep_2eCImp_2ecom,cPLF_2eImp_2estate,Vvar__1__c1__79632,Vvar__0__st__79631),cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eSmallstep_2eCImp_2ecom,cPLF_2eImp_2estate,Vvar__2__c1_27__79633,Vvar__4__st_27__79635))
                                & Vvar__1___24Anonymous__79580 = cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eSmallstep_2eCImp_2ecom,c_24__type__79652___24a2(Vvar__0___24Anonymous__79579,Vvar__1___24Anonymous__79580),cPLF_2eSmallstep_2eCImp_2eCPar___24a2(Vvar__2__c1_27__79633,Vvar__3__c2__79634),Vvar__4__st_27__79635)
                                & Vvar__0___24Anonymous__79579 = cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eSmallstep_2eCImp_2ecom,c_24__type__79652___24a2(Vvar__0___24Anonymous__79579,Vvar__1___24Anonymous__79580),cPLF_2eSmallstep_2eCImp_2eCPar___24a2(Vvar__1__c1__79632,Vvar__3__c2__79634),Vvar__0__st__79631) ) ) ) ) )
            | ? [Vvar__0__st__79639] :
                ( cPLF_2eImp_2estate___24t(Vvar__0__st__79639)
                & ? [Vvar__1__c1__79640] :
                    ( cPLF_2eSmallstep_2eCImp_2ecom___24t(Vvar__1__c1__79640)
                    & ? [Vvar__2__c2__79641] :
                        ( cPLF_2eSmallstep_2eCImp_2ecom___24t(Vvar__2__c2__79641)
                        & ? [Vvar__3__c2_27__79642] :
                            ( cPLF_2eSmallstep_2eCImp_2ecom___24t(Vvar__3__c2_27__79642)
                            & ? [Vvar__4__st_27__79643] :
                                ( cPLF_2eImp_2estate___24t(Vvar__4__st_27__79643)
                                & cPLF_2eSmallstep_2eCImp_2ecstep___24a2(cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eSmallstep_2eCImp_2ecom,cPLF_2eImp_2estate,Vvar__2__c2__79641,Vvar__0__st__79639),cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eSmallstep_2eCImp_2ecom,cPLF_2eImp_2estate,Vvar__3__c2_27__79642,Vvar__4__st_27__79643))
                                & Vvar__1___24Anonymous__79580 = cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eSmallstep_2eCImp_2ecom,c_24__type__79652___24a2(Vvar__0___24Anonymous__79579,Vvar__1___24Anonymous__79580),cPLF_2eSmallstep_2eCImp_2eCPar___24a2(Vvar__1__c1__79640,Vvar__3__c2_27__79642),Vvar__4__st_27__79643)
                                & Vvar__0___24Anonymous__79579 = cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eSmallstep_2eCImp_2ecom,c_24__type__79652___24a2(Vvar__0___24Anonymous__79579,Vvar__1___24Anonymous__79580),cPLF_2eSmallstep_2eCImp_2eCPar___24a2(Vvar__1__c1__79640,Vvar__2__c2__79641),Vvar__0__st__79639) ) ) ) ) )
            | ? [Vvar__0__st__79647] :
                ( cPLF_2eImp_2estate___24t(Vvar__0__st__79647)
                & Vvar__1___24Anonymous__79580 = cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eSmallstep_2eCImp_2ecom,c_24__type__79652___24a2(Vvar__0___24Anonymous__79579,Vvar__1___24Anonymous__79580),cPLF_2eSmallstep_2eCImp_2eCSkip,Vvar__0__st__79647)
                & Vvar__0___24Anonymous__79579 = cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eSmallstep_2eCImp_2ecom,c_24__type__79652___24a2(Vvar__0___24Anonymous__79579,Vvar__1___24Anonymous__79580),cPLF_2eSmallstep_2eCImp_2eCPar___24a2(cPLF_2eSmallstep_2eCImp_2eCSkip,cPLF_2eSmallstep_2eCImp_2eCSkip),Vvar__0__st__79647) ) ) ) ) ) ).

fof('$_inversion_PLF.Smallstep.Combined.tm',axiom,
    ! [VX92027] :
      ( cPLF_2eSmallstep_2eCombined_2etm___24t(VX92027)
     => ( ? [Vvar__0___24Anonymous__92028] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__92028)
            & VX92027 = cPLF_2eSmallstep_2eCombined_2eC___24a1(Vvar__0___24Anonymous__92028) )
        | ? [Vvar__0___24Anonymous__92029] :
            ( cPLF_2eSmallstep_2eCombined_2etm___24t(Vvar__0___24Anonymous__92029)
            & ? [Vvar__1___24Anonymous__92030] :
                ( cPLF_2eSmallstep_2eCombined_2etm___24t(Vvar__1___24Anonymous__92030)
                & VX92027 = cPLF_2eSmallstep_2eCombined_2eP___24a2(Vvar__0___24Anonymous__92029,Vvar__1___24Anonymous__92030) ) )
        | VX92027 = cPLF_2eSmallstep_2eCombined_2etru
        | VX92027 = cPLF_2eSmallstep_2eCombined_2efls
        | ? [Vvar__0___24Anonymous__92031] :
            ( cPLF_2eSmallstep_2eCombined_2etm___24t(Vvar__0___24Anonymous__92031)
            & ? [Vvar__1___24Anonymous__92032] :
                ( cPLF_2eSmallstep_2eCombined_2etm___24t(Vvar__1___24Anonymous__92032)
                & ? [Vvar__2___24Anonymous__92033] :
                    ( cPLF_2eSmallstep_2eCombined_2etm___24t(Vvar__2___24Anonymous__92033)
                    & VX92027 = cPLF_2eSmallstep_2eCombined_2etest___24a3(Vvar__0___24Anonymous__92031,Vvar__1___24Anonymous__92032,Vvar__2___24Anonymous__92033) ) ) ) ) ) ).

fof('$_inversion_PLF.Smallstep.SimpleArith1.step',axiom,
    ! [Vvar__0___24Anonymous__2390,Vvar__1___24Anonymous__2391] :
      ( cPLF_2eSmallstep_2etm___24t(Vvar__0___24Anonymous__2390)
     => ( cPLF_2eSmallstep_2etm___24t(Vvar__1___24Anonymous__2391)
       => ( cPLF_2eSmallstep_2eSimpleArith1_2estep___24a2(Vvar__0___24Anonymous__2390,Vvar__1___24Anonymous__2391)
         => ( ? [Vvar__0__n1__2393] :
                ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n1__2393)
                & ? [Vvar__1__n2__2394] :
                    ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__n2__2394)
                    & Vvar__1___24Anonymous__2391 = cPLF_2eSmallstep_2eC___24a1(c_24__case__Coq_2eInit_2eDatatypes_2enat_241023___24a4(Vvar__0___24Anonymous__2390,Vvar__1___24Anonymous__2391,Vvar__0__n1__2393,Vvar__1__n2__2394))
                    & Vvar__0___24Anonymous__2390 = cPLF_2eSmallstep_2eP___24a2(cPLF_2eSmallstep_2eC___24a1(Vvar__0__n1__2393),cPLF_2eSmallstep_2eC___24a1(Vvar__1__n2__2394)) ) )
            | ? [Vvar__0__t1__2397] :
                ( cPLF_2eSmallstep_2etm___24t(Vvar__0__t1__2397)
                & ? [Vvar__1__t1_27__2398] :
                    ( cPLF_2eSmallstep_2etm___24t(Vvar__1__t1_27__2398)
                    & ? [Vvar__2__t2__2399] :
                        ( cPLF_2eSmallstep_2etm___24t(Vvar__2__t2__2399)
                        & cPLF_2eSmallstep_2eSimpleArith1_2estep___24a2(Vvar__0__t1__2397,Vvar__1__t1_27__2398)
                        & Vvar__1___24Anonymous__2391 = cPLF_2eSmallstep_2eP___24a2(Vvar__1__t1_27__2398,Vvar__2__t2__2399)
                        & Vvar__0___24Anonymous__2390 = cPLF_2eSmallstep_2eP___24a2(Vvar__0__t1__2397,Vvar__2__t2__2399) ) ) )
            | ? [Vvar__0__n1__2401] :
                ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n1__2401)
                & ? [Vvar__1__t2__2402] :
                    ( cPLF_2eSmallstep_2etm___24t(Vvar__1__t2__2402)
                    & ? [Vvar__2__t2_27__2403] :
                        ( cPLF_2eSmallstep_2etm___24t(Vvar__2__t2_27__2403)
                        & cPLF_2eSmallstep_2eSimpleArith1_2estep___24a2(Vvar__1__t2__2402,Vvar__2__t2_27__2403)
                        & Vvar__1___24Anonymous__2391 = cPLF_2eSmallstep_2eP___24a2(cPLF_2eSmallstep_2eC___24a1(Vvar__0__n1__2401),Vvar__2__t2_27__2403)
                        & Vvar__0___24Anonymous__2390 = cPLF_2eSmallstep_2eP___24a2(cPLF_2eSmallstep_2eC___24a1(Vvar__0__n1__2401),Vvar__1__t2__2402) ) ) ) ) ) ) ) ).

fof('$_inversion_PLF.Smallstep.Temp1.step',axiom,
    ! [Vvar__0___24Anonymous__111701,Vvar__1___24Anonymous__111702] :
      ( cPLF_2eSmallstep_2etm___24t(Vvar__0___24Anonymous__111701)
     => ( cPLF_2eSmallstep_2etm___24t(Vvar__1___24Anonymous__111702)
       => ( cPLF_2eSmallstep_2eTemp1_2estep___24a2(Vvar__0___24Anonymous__111701,Vvar__1___24Anonymous__111702)
         => ( ? [Vvar__0__n1__111704] :
                ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n1__111704)
                & ? [Vvar__1__n2__111705] :
                    ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__n2__111705)
                    & Vvar__1___24Anonymous__111702 = cPLF_2eSmallstep_2eC___24a1(c_24__case__Coq_2eInit_2eDatatypes_2enat_241023___24a4(Vvar__0___24Anonymous__111701,Vvar__1___24Anonymous__111702,Vvar__0__n1__111704,Vvar__1__n2__111705))
                    & Vvar__0___24Anonymous__111701 = cPLF_2eSmallstep_2eP___24a2(cPLF_2eSmallstep_2eC___24a1(Vvar__0__n1__111704),cPLF_2eSmallstep_2eC___24a1(Vvar__1__n2__111705)) ) )
            | ? [Vvar__0__t1__111708] :
                ( cPLF_2eSmallstep_2etm___24t(Vvar__0__t1__111708)
                & ? [Vvar__1__t1_27__111709] :
                    ( cPLF_2eSmallstep_2etm___24t(Vvar__1__t1_27__111709)
                    & ? [Vvar__2__t2__111710] :
                        ( cPLF_2eSmallstep_2etm___24t(Vvar__2__t2__111710)
                        & cPLF_2eSmallstep_2eTemp1_2estep___24a2(Vvar__0__t1__111708,Vvar__1__t1_27__111709)
                        & Vvar__1___24Anonymous__111702 = cPLF_2eSmallstep_2eP___24a2(Vvar__1__t1_27__111709,Vvar__2__t2__111710)
                        & Vvar__0___24Anonymous__111701 = cPLF_2eSmallstep_2eP___24a2(Vvar__0__t1__111708,Vvar__2__t2__111710) ) ) )
            | ? [Vvar__0__v1__111712] :
                ( cPLF_2eSmallstep_2etm___24t(Vvar__0__v1__111712)
                & ? [Vvar__1__t2__111713] :
                    ( cPLF_2eSmallstep_2etm___24t(Vvar__1__t2__111713)
                    & ? [Vvar__2__t2_27__111714] :
                        ( cPLF_2eSmallstep_2etm___24t(Vvar__2__t2_27__111714)
                        & cPLF_2eSmallstep_2eTemp1_2evalue___24a1(Vvar__0__v1__111712)
                        & cPLF_2eSmallstep_2eTemp1_2estep___24a2(Vvar__1__t2__111713,Vvar__2__t2_27__111714)
                        & Vvar__1___24Anonymous__111702 = cPLF_2eSmallstep_2eP___24a2(Vvar__0__v1__111712,Vvar__2__t2_27__111714)
                        & Vvar__0___24Anonymous__111701 = cPLF_2eSmallstep_2eP___24a2(Vvar__0__v1__111712,Vvar__1__t2__111713) ) ) ) ) ) ) ) ).

fof('$_inversion_PLF.Smallstep.Temp1.value',axiom,
    ! [Vvar__0___24Anonymous__116406] :
      ( cPLF_2eSmallstep_2etm___24t(Vvar__0___24Anonymous__116406)
     => ( cPLF_2eSmallstep_2eTemp1_2evalue___24a1(Vvar__0___24Anonymous__116406)
       => ( ? [Vvar__0__n__116408] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__116408)
              & Vvar__0___24Anonymous__116406 = cPLF_2eSmallstep_2eC___24a1(Vvar__0__n__116408) )
          | ? [Vvar__0__t1__116409] :
              ( cPLF_2eSmallstep_2etm___24t(Vvar__0__t1__116409)
              & ? [Vvar__1__n2__116410] :
                  ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__n2__116410)
                  & Vvar__0___24Anonymous__116406 = cPLF_2eSmallstep_2eP___24a2(Vvar__0__t1__116409,cPLF_2eSmallstep_2eC___24a1(Vvar__1__n2__116410)) ) ) ) ) ) ).

fof('$_inversion_PLF.Smallstep.Temp2.step',axiom,
    ! [Vvar__0___24Anonymous__116414,Vvar__1___24Anonymous__116415] :
      ( cPLF_2eSmallstep_2etm___24t(Vvar__0___24Anonymous__116414)
     => ( cPLF_2eSmallstep_2etm___24t(Vvar__1___24Anonymous__116415)
       => ( cPLF_2eSmallstep_2eTemp2_2estep___24a2(Vvar__0___24Anonymous__116414,Vvar__1___24Anonymous__116415)
         => ( ? [Vvar__0__n__116417] :
                ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__116417)
                & Vvar__1___24Anonymous__116415 = cPLF_2eSmallstep_2eP___24a2(cPLF_2eSmallstep_2eC___24a1(Vvar__0__n__116417),cPLF_2eSmallstep_2eC___24a1(cCoq_2eInit_2eDatatypes_2eO))
                & Vvar__0___24Anonymous__116414 = cPLF_2eSmallstep_2eC___24a1(Vvar__0__n__116417) )
            | ? [Vvar__0__n1__116418] :
                ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n1__116418)
                & ? [Vvar__1__n2__116419] :
                    ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__n2__116419)
                    & Vvar__1___24Anonymous__116415 = cPLF_2eSmallstep_2eC___24a1(c_24__case__Coq_2eInit_2eDatatypes_2enat_241023___24a4(Vvar__0___24Anonymous__116414,Vvar__1___24Anonymous__116415,Vvar__0__n1__116418,Vvar__1__n2__116419))
                    & Vvar__0___24Anonymous__116414 = cPLF_2eSmallstep_2eP___24a2(cPLF_2eSmallstep_2eC___24a1(Vvar__0__n1__116418),cPLF_2eSmallstep_2eC___24a1(Vvar__1__n2__116419)) ) )
            | ? [Vvar__0__t1__116422] :
                ( cPLF_2eSmallstep_2etm___24t(Vvar__0__t1__116422)
                & ? [Vvar__1__t1_27__116423] :
                    ( cPLF_2eSmallstep_2etm___24t(Vvar__1__t1_27__116423)
                    & ? [Vvar__2__t2__116424] :
                        ( cPLF_2eSmallstep_2etm___24t(Vvar__2__t2__116424)
                        & cPLF_2eSmallstep_2eTemp2_2estep___24a2(Vvar__0__t1__116422,Vvar__1__t1_27__116423)
                        & Vvar__1___24Anonymous__116415 = cPLF_2eSmallstep_2eP___24a2(Vvar__1__t1_27__116423,Vvar__2__t2__116424)
                        & Vvar__0___24Anonymous__116414 = cPLF_2eSmallstep_2eP___24a2(Vvar__0__t1__116422,Vvar__2__t2__116424) ) ) )
            | ? [Vvar__0__v1__116426] :
                ( cPLF_2eSmallstep_2etm___24t(Vvar__0__v1__116426)
                & ? [Vvar__1__t2__116427] :
                    ( cPLF_2eSmallstep_2etm___24t(Vvar__1__t2__116427)
                    & ? [Vvar__2__t2_27__116428] :
                        ( cPLF_2eSmallstep_2etm___24t(Vvar__2__t2_27__116428)
                        & cPLF_2eSmallstep_2eTemp2_2evalue___24a1(Vvar__0__v1__116426)
                        & cPLF_2eSmallstep_2eTemp2_2estep___24a2(Vvar__1__t2__116427,Vvar__2__t2_27__116428)
                        & Vvar__1___24Anonymous__116415 = cPLF_2eSmallstep_2eP___24a2(Vvar__0__v1__116426,Vvar__2__t2_27__116428)
                        & Vvar__0___24Anonymous__116414 = cPLF_2eSmallstep_2eP___24a2(Vvar__0__v1__116426,Vvar__1__t2__116427) ) ) ) ) ) ) ) ).

fof('$_inversion_PLF.Smallstep.Temp2.value',axiom,
    ! [Vvar__0___24Anonymous__116411] :
      ( cPLF_2eSmallstep_2etm___24t(Vvar__0___24Anonymous__116411)
     => ( cPLF_2eSmallstep_2eTemp2_2evalue___24a1(Vvar__0___24Anonymous__116411)
       => ? [Vvar__0__n__116413] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__116413)
            & Vvar__0___24Anonymous__116411 = cPLF_2eSmallstep_2eC___24a1(Vvar__0__n__116413) ) ) ) ).

fof('$_inversion_PLF.Smallstep.Temp3.step',axiom,
    ! [Vvar__0___24Anonymous__116487,Vvar__1___24Anonymous__116488] :
      ( cPLF_2eSmallstep_2etm___24t(Vvar__0___24Anonymous__116487)
     => ( cPLF_2eSmallstep_2etm___24t(Vvar__1___24Anonymous__116488)
       => ( cPLF_2eSmallstep_2eTemp3_2estep___24a2(Vvar__0___24Anonymous__116487,Vvar__1___24Anonymous__116488)
         => ( ? [Vvar__0__n1__116490] :
                ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n1__116490)
                & ? [Vvar__1__n2__116491] :
                    ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__n2__116491)
                    & Vvar__1___24Anonymous__116488 = cPLF_2eSmallstep_2eC___24a1(c_24__case__Coq_2eInit_2eDatatypes_2enat_241023___24a4(Vvar__0___24Anonymous__116487,Vvar__1___24Anonymous__116488,Vvar__0__n1__116490,Vvar__1__n2__116491))
                    & Vvar__0___24Anonymous__116487 = cPLF_2eSmallstep_2eP___24a2(cPLF_2eSmallstep_2eC___24a1(Vvar__0__n1__116490),cPLF_2eSmallstep_2eC___24a1(Vvar__1__n2__116491)) ) )
            | ? [Vvar__0__t1__116494] :
                ( cPLF_2eSmallstep_2etm___24t(Vvar__0__t1__116494)
                & ? [Vvar__1__t1_27__116495] :
                    ( cPLF_2eSmallstep_2etm___24t(Vvar__1__t1_27__116495)
                    & ? [Vvar__2__t2__116496] :
                        ( cPLF_2eSmallstep_2etm___24t(Vvar__2__t2__116496)
                        & cPLF_2eSmallstep_2eTemp3_2estep___24a2(Vvar__0__t1__116494,Vvar__1__t1_27__116495)
                        & Vvar__1___24Anonymous__116488 = cPLF_2eSmallstep_2eP___24a2(Vvar__1__t1_27__116495,Vvar__2__t2__116496)
                        & Vvar__0___24Anonymous__116487 = cPLF_2eSmallstep_2eP___24a2(Vvar__0__t1__116494,Vvar__2__t2__116496) ) ) ) ) ) ) ) ).

fof('$_inversion_PLF.Smallstep.Temp3.value',axiom,
    ! [Vvar__0___24Anonymous__116484] :
      ( cPLF_2eSmallstep_2etm___24t(Vvar__0___24Anonymous__116484)
     => ( cPLF_2eSmallstep_2eTemp3_2evalue___24a1(Vvar__0___24Anonymous__116484)
       => ? [Vvar__0__n__116486] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__116486)
            & Vvar__0___24Anonymous__116484 = cPLF_2eSmallstep_2eC___24a1(Vvar__0__n__116486) ) ) ) ).

fof('$_inversion_PLF.Smallstep.Temp4.tm',axiom,
    ! [VX88812] :
      ( cPLF_2eSmallstep_2eTemp4_2etm___24t(VX88812)
     => ( VX88812 = cPLF_2eSmallstep_2eTemp4_2etru
        | VX88812 = cPLF_2eSmallstep_2eTemp4_2efls
        | ? [Vvar__0___24Anonymous__88813] :
            ( cPLF_2eSmallstep_2eTemp4_2etm___24t(Vvar__0___24Anonymous__88813)
            & ? [Vvar__1___24Anonymous__88814] :
                ( cPLF_2eSmallstep_2eTemp4_2etm___24t(Vvar__1___24Anonymous__88814)
                & ? [Vvar__2___24Anonymous__88815] :
                    ( cPLF_2eSmallstep_2eTemp4_2etm___24t(Vvar__2___24Anonymous__88815)
                    & VX88812 = cPLF_2eSmallstep_2eTemp4_2etest___24a3(Vvar__0___24Anonymous__88813,Vvar__1___24Anonymous__88814,Vvar__2___24Anonymous__88815) ) ) ) ) ) ).

fof('$_inversion_PLF.Smallstep.astep',axiom,
    ! [Vvar__0___24Anonymous__76932,Vvar__1___24Anonymous__76933,Vvar__2___24Anonymous__76934] :
      ( cPLF_2eImp_2estate___24t(Vvar__0___24Anonymous__76932)
     => ( cPLF_2eImp_2eaexp___24t(Vvar__1___24Anonymous__76933)
       => ( cPLF_2eImp_2eaexp___24t(Vvar__2___24Anonymous__76934)
         => ( cPLF_2eSmallstep_2eastep___24a3(Vvar__0___24Anonymous__76932,Vvar__1___24Anonymous__76933,Vvar__2___24Anonymous__76934)
           => ( ? [Vvar__0__st__76936] :
                  ( cPLF_2eImp_2estate___24t(Vvar__0__st__76936)
                  & ? [Vvar__1__i__76937] :
                      ( cCoq_2eStrings_2eString_2estring___24t(Vvar__1__i__76937)
                      & Vvar__2___24Anonymous__76934 = cPLF_2eImp_2eANum___24a1(happ(Vvar__0__st__76936,Vvar__1__i__76937))
                      & Vvar__1___24Anonymous__76933 = cPLF_2eImp_2eAId___24a1(Vvar__1__i__76937)
                      & Vvar__0___24Anonymous__76932 = Vvar__0__st__76936 ) )
              | ? [Vvar__0__st__76938] :
                  ( cPLF_2eImp_2estate___24t(Vvar__0__st__76938)
                  & ? [Vvar__1__a1__76939] :
                      ( cPLF_2eImp_2eaexp___24t(Vvar__1__a1__76939)
                      & ? [Vvar__2__a1_27__76940] :
                          ( cPLF_2eImp_2eaexp___24t(Vvar__2__a1_27__76940)
                          & ? [Vvar__3__a2__76941] :
                              ( cPLF_2eImp_2eaexp___24t(Vvar__3__a2__76941)
                              & cPLF_2eSmallstep_2eastep___24a3(Vvar__0__st__76938,Vvar__1__a1__76939,Vvar__2__a1_27__76940)
                              & Vvar__2___24Anonymous__76934 = cPLF_2eImp_2eAPlus___24a2(Vvar__2__a1_27__76940,Vvar__3__a2__76941)
                              & Vvar__1___24Anonymous__76933 = cPLF_2eImp_2eAPlus___24a2(Vvar__1__a1__76939,Vvar__3__a2__76941)
                              & Vvar__0___24Anonymous__76932 = Vvar__0__st__76938 ) ) ) )
              | ? [Vvar__0__st__76943] :
                  ( cPLF_2eImp_2estate___24t(Vvar__0__st__76943)
                  & ? [Vvar__1__v1__76944] :
                      ( cPLF_2eImp_2eaexp___24t(Vvar__1__v1__76944)
                      & ? [Vvar__2__a2__76945] :
                          ( cPLF_2eImp_2eaexp___24t(Vvar__2__a2__76945)
                          & ? [Vvar__3__a2_27__76946] :
                              ( cPLF_2eImp_2eaexp___24t(Vvar__3__a2_27__76946)
                              & cPLF_2eSmallstep_2eaval___24a1(Vvar__1__v1__76944)
                              & cPLF_2eSmallstep_2eastep___24a3(Vvar__0__st__76943,Vvar__2__a2__76945,Vvar__3__a2_27__76946)
                              & Vvar__2___24Anonymous__76934 = cPLF_2eImp_2eAPlus___24a2(Vvar__1__v1__76944,Vvar__3__a2_27__76946)
                              & Vvar__1___24Anonymous__76933 = cPLF_2eImp_2eAPlus___24a2(Vvar__1__v1__76944,Vvar__2__a2__76945)
                              & Vvar__0___24Anonymous__76932 = Vvar__0__st__76943 ) ) ) )
              | ? [Vvar__0__st__76949] :
                  ( cPLF_2eImp_2estate___24t(Vvar__0__st__76949)
                  & ? [Vvar__1__n1__76950] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__n1__76950)
                      & ? [Vvar__2__n2__76951] :
                          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n2__76951)
                          & Vvar__2___24Anonymous__76934 = cPLF_2eImp_2eANum___24a1(c_24__case__Coq_2eInit_2eDatatypes_2enat_2477050___24a5(Vvar__0___24Anonymous__76932,Vvar__1___24Anonymous__76933,Vvar__2___24Anonymous__76934,Vvar__1__n1__76950,Vvar__2__n2__76951))
                          & Vvar__1___24Anonymous__76933 = cPLF_2eImp_2eAPlus___24a2(cPLF_2eImp_2eANum___24a1(Vvar__1__n1__76950),cPLF_2eImp_2eANum___24a1(Vvar__2__n2__76951))
                          & Vvar__0___24Anonymous__76932 = Vvar__0__st__76949 ) ) )
              | ? [Vvar__0__st__76954] :
                  ( cPLF_2eImp_2estate___24t(Vvar__0__st__76954)
                  & ? [Vvar__1__a1__76955] :
                      ( cPLF_2eImp_2eaexp___24t(Vvar__1__a1__76955)
                      & ? [Vvar__2__a1_27__76956] :
                          ( cPLF_2eImp_2eaexp___24t(Vvar__2__a1_27__76956)
                          & ? [Vvar__3__a2__76957] :
                              ( cPLF_2eImp_2eaexp___24t(Vvar__3__a2__76957)
                              & cPLF_2eSmallstep_2eastep___24a3(Vvar__0__st__76954,Vvar__1__a1__76955,Vvar__2__a1_27__76956)
                              & Vvar__2___24Anonymous__76934 = cPLF_2eImp_2eAMinus___24a2(Vvar__2__a1_27__76956,Vvar__3__a2__76957)
                              & Vvar__1___24Anonymous__76933 = cPLF_2eImp_2eAMinus___24a2(Vvar__1__a1__76955,Vvar__3__a2__76957)
                              & Vvar__0___24Anonymous__76932 = Vvar__0__st__76954 ) ) ) )
              | ? [Vvar__0__st__76959] :
                  ( cPLF_2eImp_2estate___24t(Vvar__0__st__76959)
                  & ? [Vvar__1__v1__76960] :
                      ( cPLF_2eImp_2eaexp___24t(Vvar__1__v1__76960)
                      & ? [Vvar__2__a2__76961] :
                          ( cPLF_2eImp_2eaexp___24t(Vvar__2__a2__76961)
                          & ? [Vvar__3__a2_27__76962] :
                              ( cPLF_2eImp_2eaexp___24t(Vvar__3__a2_27__76962)
                              & cPLF_2eSmallstep_2eaval___24a1(Vvar__1__v1__76960)
                              & cPLF_2eSmallstep_2eastep___24a3(Vvar__0__st__76959,Vvar__2__a2__76961,Vvar__3__a2_27__76962)
                              & Vvar__2___24Anonymous__76934 = cPLF_2eImp_2eAMinus___24a2(Vvar__1__v1__76960,Vvar__3__a2_27__76962)
                              & Vvar__1___24Anonymous__76933 = cPLF_2eImp_2eAMinus___24a2(Vvar__1__v1__76960,Vvar__2__a2__76961)
                              & Vvar__0___24Anonymous__76932 = Vvar__0__st__76959 ) ) ) )
              | ? [Vvar__0__st__76965] :
                  ( cPLF_2eImp_2estate___24t(Vvar__0__st__76965)
                  & ? [Vvar__1__n1__76966] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__n1__76966)
                      & ? [Vvar__2__n2__76967] :
                          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n2__76967)
                          & Vvar__2___24Anonymous__76934 = cPLF_2eImp_2eANum___24a1(c_24__case__Coq_2eInit_2eDatatypes_2enat_2477172___24a5(Vvar__0___24Anonymous__76932,Vvar__1___24Anonymous__76933,Vvar__2___24Anonymous__76934,Vvar__1__n1__76966,Vvar__2__n2__76967))
                          & Vvar__1___24Anonymous__76933 = cPLF_2eImp_2eAMinus___24a2(cPLF_2eImp_2eANum___24a1(Vvar__1__n1__76966),cPLF_2eImp_2eANum___24a1(Vvar__2__n2__76967))
                          & Vvar__0___24Anonymous__76932 = Vvar__0__st__76965 ) ) )
              | ? [Vvar__0__st__76972] :
                  ( cPLF_2eImp_2estate___24t(Vvar__0__st__76972)
                  & ? [Vvar__1__a1__76973] :
                      ( cPLF_2eImp_2eaexp___24t(Vvar__1__a1__76973)
                      & ? [Vvar__2__a1_27__76974] :
                          ( cPLF_2eImp_2eaexp___24t(Vvar__2__a1_27__76974)
                          & ? [Vvar__3__a2__76975] :
                              ( cPLF_2eImp_2eaexp___24t(Vvar__3__a2__76975)
                              & cPLF_2eSmallstep_2eastep___24a3(Vvar__0__st__76972,Vvar__1__a1__76973,Vvar__2__a1_27__76974)
                              & Vvar__2___24Anonymous__76934 = cPLF_2eImp_2eAMult___24a2(Vvar__2__a1_27__76974,Vvar__3__a2__76975)
                              & Vvar__1___24Anonymous__76933 = cPLF_2eImp_2eAMult___24a2(Vvar__1__a1__76973,Vvar__3__a2__76975)
                              & Vvar__0___24Anonymous__76932 = Vvar__0__st__76972 ) ) ) )
              | ? [Vvar__0__st__76977] :
                  ( cPLF_2eImp_2estate___24t(Vvar__0__st__76977)
                  & ? [Vvar__1__v1__76978] :
                      ( cPLF_2eImp_2eaexp___24t(Vvar__1__v1__76978)
                      & ? [Vvar__2__a2__76979] :
                          ( cPLF_2eImp_2eaexp___24t(Vvar__2__a2__76979)
                          & ? [Vvar__3__a2_27__76980] :
                              ( cPLF_2eImp_2eaexp___24t(Vvar__3__a2_27__76980)
                              & cPLF_2eSmallstep_2eaval___24a1(Vvar__1__v1__76978)
                              & cPLF_2eSmallstep_2eastep___24a3(Vvar__0__st__76977,Vvar__2__a2__76979,Vvar__3__a2_27__76980)
                              & Vvar__2___24Anonymous__76934 = cPLF_2eImp_2eAMult___24a2(Vvar__1__v1__76978,Vvar__3__a2_27__76980)
                              & Vvar__1___24Anonymous__76933 = cPLF_2eImp_2eAMult___24a2(Vvar__1__v1__76978,Vvar__2__a2__76979)
                              & Vvar__0___24Anonymous__76932 = Vvar__0__st__76977 ) ) ) )
              | ? [Vvar__0__st__76983] :
                  ( cPLF_2eImp_2estate___24t(Vvar__0__st__76983)
                  & ? [Vvar__1__n1__76984] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__n1__76984)
                      & ? [Vvar__2__n2__76985] :
                          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n2__76985)
                          & Vvar__2___24Anonymous__76934 = cPLF_2eImp_2eANum___24a1(c_24__case__Coq_2eInit_2eDatatypes_2enat_2477280___24a5(Vvar__0___24Anonymous__76932,Vvar__1___24Anonymous__76933,Vvar__2___24Anonymous__76934,Vvar__1__n1__76984,Vvar__2__n2__76985))
                          & Vvar__1___24Anonymous__76933 = cPLF_2eImp_2eAMult___24a2(cPLF_2eImp_2eANum___24a1(Vvar__1__n1__76984),cPLF_2eImp_2eANum___24a1(Vvar__2__n2__76985))
                          & Vvar__0___24Anonymous__76932 = Vvar__0__st__76983 ) ) ) ) ) ) ) ) ).

fof('$_inversion_PLF.Smallstep.aval',axiom,
    ! [Vvar__0___24Anonymous__115652] :
      ( cPLF_2eImp_2eaexp___24t(Vvar__0___24Anonymous__115652)
     => ( cPLF_2eSmallstep_2eaval___24a1(Vvar__0___24Anonymous__115652)
       => ? [Vvar__0__n__115654] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__115654)
            & Vvar__0___24Anonymous__115652 = cPLF_2eImp_2eANum___24a1(Vvar__0__n__115654) ) ) ) ).

fof('$_inversion_PLF.Smallstep.bstep',axiom,
    ! [Vvar__0___24Anonymous__77301,Vvar__1___24Anonymous__77302,Vvar__2___24Anonymous__77303] :
      ( cPLF_2eImp_2estate___24t(Vvar__0___24Anonymous__77301)
     => ( cPLF_2eImp_2ebexp___24t(Vvar__1___24Anonymous__77302)
       => ( cPLF_2eImp_2ebexp___24t(Vvar__2___24Anonymous__77303)
         => ( cPLF_2eSmallstep_2ebstep___24a3(Vvar__0___24Anonymous__77301,Vvar__1___24Anonymous__77302,Vvar__2___24Anonymous__77303)
           => ( ? [Vvar__0__st__77305] :
                  ( cPLF_2eImp_2estate___24t(Vvar__0__st__77305)
                  & ? [Vvar__1__a1__77306] :
                      ( cPLF_2eImp_2eaexp___24t(Vvar__1__a1__77306)
                      & ? [Vvar__2__a1_27__77307] :
                          ( cPLF_2eImp_2eaexp___24t(Vvar__2__a1_27__77307)
                          & ? [Vvar__3__a2__77308] :
                              ( cPLF_2eImp_2eaexp___24t(Vvar__3__a2__77308)
                              & cPLF_2eSmallstep_2eastep___24a3(Vvar__0__st__77305,Vvar__1__a1__77306,Vvar__2__a1_27__77307)
                              & Vvar__2___24Anonymous__77303 = cPLF_2eImp_2eBEq___24a2(Vvar__2__a1_27__77307,Vvar__3__a2__77308)
                              & Vvar__1___24Anonymous__77302 = cPLF_2eImp_2eBEq___24a2(Vvar__1__a1__77306,Vvar__3__a2__77308)
                              & Vvar__0___24Anonymous__77301 = Vvar__0__st__77305 ) ) ) )
              | ? [Vvar__0__st__77310] :
                  ( cPLF_2eImp_2estate___24t(Vvar__0__st__77310)
                  & ? [Vvar__1__v1__77311] :
                      ( cPLF_2eImp_2eaexp___24t(Vvar__1__v1__77311)
                      & ? [Vvar__2__a2__77312] :
                          ( cPLF_2eImp_2eaexp___24t(Vvar__2__a2__77312)
                          & ? [Vvar__3__a2_27__77313] :
                              ( cPLF_2eImp_2eaexp___24t(Vvar__3__a2_27__77313)
                              & cPLF_2eSmallstep_2eaval___24a1(Vvar__1__v1__77311)
                              & cPLF_2eSmallstep_2eastep___24a3(Vvar__0__st__77310,Vvar__2__a2__77312,Vvar__3__a2_27__77313)
                              & Vvar__2___24Anonymous__77303 = cPLF_2eImp_2eBEq___24a2(Vvar__1__v1__77311,Vvar__3__a2_27__77313)
                              & Vvar__1___24Anonymous__77302 = cPLF_2eImp_2eBEq___24a2(Vvar__1__v1__77311,Vvar__2__a2__77312)
                              & Vvar__0___24Anonymous__77301 = Vvar__0__st__77310 ) ) ) )
              | ? [Vvar__0__st__77316] :
                  ( cPLF_2eImp_2estate___24t(Vvar__0__st__77316)
                  & ? [Vvar__1__n1__77317] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__n1__77317)
                      & ? [Vvar__2__n2__77318] :
                          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n2__77318)
                          & Vvar__2___24Anonymous__77303 = c_24__case__Coq_2eInit_2eDatatypes_2ebool_2477532___24a5(Vvar__0___24Anonymous__77301,Vvar__1___24Anonymous__77302,Vvar__2___24Anonymous__77303,Vvar__1__n1__77317,Vvar__2__n2__77318)
                          & Vvar__1___24Anonymous__77302 = cPLF_2eImp_2eBEq___24a2(cPLF_2eImp_2eANum___24a1(Vvar__1__n1__77317),cPLF_2eImp_2eANum___24a1(Vvar__2__n2__77318))
                          & Vvar__0___24Anonymous__77301 = Vvar__0__st__77316 ) ) )
              | ? [Vvar__0__st__77343] :
                  ( cPLF_2eImp_2estate___24t(Vvar__0__st__77343)
                  & ? [Vvar__1__a1__77344] :
                      ( cPLF_2eImp_2eaexp___24t(Vvar__1__a1__77344)
                      & ? [Vvar__2__a1_27__77345] :
                          ( cPLF_2eImp_2eaexp___24t(Vvar__2__a1_27__77345)
                          & ? [Vvar__3__a2__77346] :
                              ( cPLF_2eImp_2eaexp___24t(Vvar__3__a2__77346)
                              & cPLF_2eSmallstep_2eastep___24a3(Vvar__0__st__77343,Vvar__1__a1__77344,Vvar__2__a1_27__77345)
                              & Vvar__2___24Anonymous__77303 = cPLF_2eImp_2eBLe___24a2(Vvar__2__a1_27__77345,Vvar__3__a2__77346)
                              & Vvar__1___24Anonymous__77302 = cPLF_2eImp_2eBLe___24a2(Vvar__1__a1__77344,Vvar__3__a2__77346)
                              & Vvar__0___24Anonymous__77301 = Vvar__0__st__77343 ) ) ) )
              | ? [Vvar__0__st__77348] :
                  ( cPLF_2eImp_2estate___24t(Vvar__0__st__77348)
                  & ? [Vvar__1__v1__77349] :
                      ( cPLF_2eImp_2eaexp___24t(Vvar__1__v1__77349)
                      & ? [Vvar__2__a2__77350] :
                          ( cPLF_2eImp_2eaexp___24t(Vvar__2__a2__77350)
                          & ? [Vvar__3__a2_27__77351] :
                              ( cPLF_2eImp_2eaexp___24t(Vvar__3__a2_27__77351)
                              & cPLF_2eSmallstep_2eaval___24a1(Vvar__1__v1__77349)
                              & cPLF_2eSmallstep_2eastep___24a3(Vvar__0__st__77348,Vvar__2__a2__77350,Vvar__3__a2_27__77351)
                              & Vvar__2___24Anonymous__77303 = cPLF_2eImp_2eBLe___24a2(Vvar__1__v1__77349,Vvar__3__a2_27__77351)
                              & Vvar__1___24Anonymous__77302 = cPLF_2eImp_2eBLe___24a2(Vvar__1__v1__77349,Vvar__2__a2__77350)
                              & Vvar__0___24Anonymous__77301 = Vvar__0__st__77348 ) ) ) )
              | ? [Vvar__0__st__77354] :
                  ( cPLF_2eImp_2estate___24t(Vvar__0__st__77354)
                  & ? [Vvar__1__n1__77355] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__n1__77355)
                      & ? [Vvar__2__n2__77356] :
                          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n2__77356)
                          & Vvar__2___24Anonymous__77303 = c_24__case__Coq_2eInit_2eDatatypes_2ebool_2477863___24a5(Vvar__0___24Anonymous__77301,Vvar__1___24Anonymous__77302,Vvar__2___24Anonymous__77303,Vvar__1__n1__77355,Vvar__2__n2__77356)
                          & Vvar__1___24Anonymous__77302 = cPLF_2eImp_2eBLe___24a2(cPLF_2eImp_2eANum___24a1(Vvar__1__n1__77355),cPLF_2eImp_2eANum___24a1(Vvar__2__n2__77356))
                          & Vvar__0___24Anonymous__77301 = Vvar__0__st__77354 ) ) )
              | ? [Vvar__0__st__77375] :
                  ( cPLF_2eImp_2estate___24t(Vvar__0__st__77375)
                  & ? [Vvar__1__b1__77376] :
                      ( cPLF_2eImp_2ebexp___24t(Vvar__1__b1__77376)
                      & ? [Vvar__2__b1_27__77377] :
                          ( cPLF_2eImp_2ebexp___24t(Vvar__2__b1_27__77377)
                          & cPLF_2eSmallstep_2ebstep___24a3(Vvar__0__st__77375,Vvar__1__b1__77376,Vvar__2__b1_27__77377)
                          & Vvar__2___24Anonymous__77303 = cPLF_2eImp_2eBNot___24a1(Vvar__2__b1_27__77377)
                          & Vvar__1___24Anonymous__77302 = cPLF_2eImp_2eBNot___24a1(Vvar__1__b1__77376)
                          & Vvar__0___24Anonymous__77301 = Vvar__0__st__77375 ) ) )
              | ? [Vvar__0__st__77379] :
                  ( cPLF_2eImp_2estate___24t(Vvar__0__st__77379)
                  & Vvar__2___24Anonymous__77303 = cPLF_2eImp_2eBFalse
                  & Vvar__1___24Anonymous__77302 = cPLF_2eImp_2eBNot___24a1(cPLF_2eImp_2eBTrue)
                  & Vvar__0___24Anonymous__77301 = Vvar__0__st__77379 )
              | ? [Vvar__0__st__77380] :
                  ( cPLF_2eImp_2estate___24t(Vvar__0__st__77380)
                  & Vvar__2___24Anonymous__77303 = cPLF_2eImp_2eBTrue
                  & Vvar__1___24Anonymous__77302 = cPLF_2eImp_2eBNot___24a1(cPLF_2eImp_2eBFalse)
                  & Vvar__0___24Anonymous__77301 = Vvar__0__st__77380 )
              | ? [Vvar__0__st__77381] :
                  ( cPLF_2eImp_2estate___24t(Vvar__0__st__77381)
                  & ? [Vvar__1__b2__77382] :
                      ( cPLF_2eImp_2ebexp___24t(Vvar__1__b2__77382)
                      & ? [Vvar__2__b2_27__77383] :
                          ( cPLF_2eImp_2ebexp___24t(Vvar__2__b2_27__77383)
                          & cPLF_2eSmallstep_2ebstep___24a3(Vvar__0__st__77381,Vvar__1__b2__77382,Vvar__2__b2_27__77383)
                          & Vvar__2___24Anonymous__77303 = cPLF_2eImp_2eBAnd___24a2(cPLF_2eImp_2eBTrue,Vvar__2__b2_27__77383)
                          & Vvar__1___24Anonymous__77302 = cPLF_2eImp_2eBAnd___24a2(cPLF_2eImp_2eBTrue,Vvar__1__b2__77382)
                          & Vvar__0___24Anonymous__77301 = Vvar__0__st__77381 ) ) )
              | ? [Vvar__0__st__77385] :
                  ( cPLF_2eImp_2estate___24t(Vvar__0__st__77385)
                  & ? [Vvar__1__b1__77386] :
                      ( cPLF_2eImp_2ebexp___24t(Vvar__1__b1__77386)
                      & ? [Vvar__2__b1_27__77387] :
                          ( cPLF_2eImp_2ebexp___24t(Vvar__2__b1_27__77387)
                          & ? [Vvar__3__b2__77388] :
                              ( cPLF_2eImp_2ebexp___24t(Vvar__3__b2__77388)
                              & cPLF_2eSmallstep_2ebstep___24a3(Vvar__0__st__77385,Vvar__1__b1__77386,Vvar__2__b1_27__77387)
                              & Vvar__2___24Anonymous__77303 = cPLF_2eImp_2eBAnd___24a2(Vvar__2__b1_27__77387,Vvar__3__b2__77388)
                              & Vvar__1___24Anonymous__77302 = cPLF_2eImp_2eBAnd___24a2(Vvar__1__b1__77386,Vvar__3__b2__77388)
                              & Vvar__0___24Anonymous__77301 = Vvar__0__st__77385 ) ) ) )
              | ? [Vvar__0__st__77390] :
                  ( cPLF_2eImp_2estate___24t(Vvar__0__st__77390)
                  & Vvar__2___24Anonymous__77303 = cPLF_2eImp_2eBTrue
                  & Vvar__1___24Anonymous__77302 = cPLF_2eImp_2eBAnd___24a2(cPLF_2eImp_2eBTrue,cPLF_2eImp_2eBTrue)
                  & Vvar__0___24Anonymous__77301 = Vvar__0__st__77390 )
              | ? [Vvar__0__st__77391] :
                  ( cPLF_2eImp_2estate___24t(Vvar__0__st__77391)
                  & Vvar__2___24Anonymous__77303 = cPLF_2eImp_2eBFalse
                  & Vvar__1___24Anonymous__77302 = cPLF_2eImp_2eBAnd___24a2(cPLF_2eImp_2eBTrue,cPLF_2eImp_2eBFalse)
                  & Vvar__0___24Anonymous__77301 = Vvar__0__st__77391 )
              | ? [Vvar__0__st__77392] :
                  ( cPLF_2eImp_2estate___24t(Vvar__0__st__77392)
                  & ? [Vvar__1__b2__77393] :
                      ( cPLF_2eImp_2ebexp___24t(Vvar__1__b2__77393)
                      & Vvar__2___24Anonymous__77303 = cPLF_2eImp_2eBFalse
                      & Vvar__1___24Anonymous__77302 = cPLF_2eImp_2eBAnd___24a2(cPLF_2eImp_2eBFalse,Vvar__1__b2__77393)
                      & Vvar__0___24Anonymous__77301 = Vvar__0__st__77392 ) ) ) ) ) ) ) ).

fof('$_inversion_PLF.Smallstep.cstep',axiom,
    ! [Vvar__0___24Anonymous__168693,Vvar__1___24Anonymous__168694] :
      ( cCoq_2eInit_2eDatatypes_2eprod___24t(cPLF_2eImp_2ecom,cPLF_2eImp_2estate,Vvar__0___24Anonymous__168693)
     => ( cCoq_2eInit_2eDatatypes_2eprod___24t(cPLF_2eImp_2ecom,cPLF_2eImp_2estate,Vvar__1___24Anonymous__168694)
       => ( cPLF_2eSmallstep_2ecstep___24a2(Vvar__0___24Anonymous__168693,Vvar__1___24Anonymous__168694)
         => ( ? [Vvar__0__st__168696] :
                ( cPLF_2eImp_2estate___24t(Vvar__0__st__168696)
                & ? [Vvar__1__i__168697] :
                    ( cCoq_2eStrings_2eString_2estring___24t(Vvar__1__i__168697)
                    & ? [Vvar__2__a__168698] :
                        ( cPLF_2eImp_2eaexp___24t(Vvar__2__a__168698)
                        & ? [Vvar__3__a_27__168699] :
                            ( cPLF_2eImp_2eaexp___24t(Vvar__3__a_27__168699)
                            & cPLF_2eSmallstep_2eastep___24a3(Vvar__0__st__168696,Vvar__2__a__168698,Vvar__3__a_27__168699)
                            & Vvar__1___24Anonymous__168694 = cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eImp_2ecom,c_24__type__168747___24a2(Vvar__0___24Anonymous__168693,Vvar__1___24Anonymous__168694),cPLF_2eImp_2eCAss___24a2(Vvar__1__i__168697,Vvar__3__a_27__168699),Vvar__0__st__168696)
                            & Vvar__0___24Anonymous__168693 = cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eImp_2ecom,c_24__type__168747___24a2(Vvar__0___24Anonymous__168693,Vvar__1___24Anonymous__168694),cPLF_2eImp_2eCAss___24a2(Vvar__1__i__168697,Vvar__2__a__168698),Vvar__0__st__168696) ) ) ) )
            | ? [Vvar__0__st__168703] :
                ( cPLF_2eImp_2estate___24t(Vvar__0__st__168703)
                & ? [Vvar__1__i__168704] :
                    ( cCoq_2eStrings_2eString_2estring___24t(Vvar__1__i__168704)
                    & ? [Vvar__2__n__168705] :
                        ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__168705)
                        & Vvar__1___24Anonymous__168694 = cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eImp_2ecom,c_24__type__168747___24a2(Vvar__0___24Anonymous__168693,Vvar__1___24Anonymous__168694),cPLF_2eImp_2eCSkip,c_24__lam__168764___24a5(Vvar__0___24Anonymous__168693,Vvar__1___24Anonymous__168694,Vvar__0__st__168703,Vvar__1__i__168704,Vvar__2__n__168705))
                        & Vvar__0___24Anonymous__168693 = cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eImp_2ecom,c_24__type__168747___24a2(Vvar__0___24Anonymous__168693,Vvar__1___24Anonymous__168694),cPLF_2eImp_2eCAss___24a2(Vvar__1__i__168704,cPLF_2eImp_2eANum___24a1(Vvar__2__n__168705)),Vvar__0__st__168703) ) ) )
            | ? [Vvar__0__st__168710] :
                ( cPLF_2eImp_2estate___24t(Vvar__0__st__168710)
                & ? [Vvar__1__c1__168711] :
                    ( cPLF_2eImp_2ecom___24t(Vvar__1__c1__168711)
                    & ? [Vvar__2__c1_27__168712] :
                        ( cPLF_2eImp_2ecom___24t(Vvar__2__c1_27__168712)
                        & ? [Vvar__3__st_27__168713] :
                            ( cPLF_2eImp_2estate___24t(Vvar__3__st_27__168713)
                            & ? [Vvar__4__c2__168714] :
                                ( cPLF_2eImp_2ecom___24t(Vvar__4__c2__168714)
                                & cPLF_2eSmallstep_2ecstep___24a2(cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eImp_2ecom,cPLF_2eImp_2estate,Vvar__1__c1__168711,Vvar__0__st__168710),cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eImp_2ecom,cPLF_2eImp_2estate,Vvar__2__c1_27__168712,Vvar__3__st_27__168713))
                                & Vvar__1___24Anonymous__168694 = cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eImp_2ecom,c_24__type__168747___24a2(Vvar__0___24Anonymous__168693,Vvar__1___24Anonymous__168694),cPLF_2eImp_2eCSeq___24a2(Vvar__2__c1_27__168712,Vvar__4__c2__168714),Vvar__3__st_27__168713)
                                & Vvar__0___24Anonymous__168693 = cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eImp_2ecom,c_24__type__168747___24a2(Vvar__0___24Anonymous__168693,Vvar__1___24Anonymous__168694),cPLF_2eImp_2eCSeq___24a2(Vvar__1__c1__168711,Vvar__4__c2__168714),Vvar__0__st__168710) ) ) ) ) )
            | ? [Vvar__0__st__168718] :
                ( cPLF_2eImp_2estate___24t(Vvar__0__st__168718)
                & ? [Vvar__1__c2__168719] :
                    ( cPLF_2eImp_2ecom___24t(Vvar__1__c2__168719)
                    & Vvar__1___24Anonymous__168694 = cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eImp_2ecom,c_24__type__168747___24a2(Vvar__0___24Anonymous__168693,Vvar__1___24Anonymous__168694),Vvar__1__c2__168719,Vvar__0__st__168718)
                    & Vvar__0___24Anonymous__168693 = cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eImp_2ecom,c_24__type__168747___24a2(Vvar__0___24Anonymous__168693,Vvar__1___24Anonymous__168694),cPLF_2eImp_2eCSeq___24a2(cPLF_2eImp_2eCSkip,Vvar__1__c2__168719),Vvar__0__st__168718) ) )
            | ? [Vvar__0__st__168722] :
                ( cPLF_2eImp_2estate___24t(Vvar__0__st__168722)
                & ? [Vvar__1__b__168723] :
                    ( cPLF_2eImp_2ebexp___24t(Vvar__1__b__168723)
                    & ? [Vvar__2__b_27__168724] :
                        ( cPLF_2eImp_2ebexp___24t(Vvar__2__b_27__168724)
                        & ? [Vvar__3__c1__168725] :
                            ( cPLF_2eImp_2ecom___24t(Vvar__3__c1__168725)
                            & ? [Vvar__4__c2__168726] :
                                ( cPLF_2eImp_2ecom___24t(Vvar__4__c2__168726)
                                & cPLF_2eSmallstep_2ebstep___24a3(Vvar__0__st__168722,Vvar__1__b__168723,Vvar__2__b_27__168724)
                                & Vvar__1___24Anonymous__168694 = cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eImp_2ecom,c_24__type__168747___24a2(Vvar__0___24Anonymous__168693,Vvar__1___24Anonymous__168694),cPLF_2eImp_2eCIf___24a3(Vvar__2__b_27__168724,Vvar__3__c1__168725,Vvar__4__c2__168726),Vvar__0__st__168722)
                                & Vvar__0___24Anonymous__168693 = cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eImp_2ecom,c_24__type__168747___24a2(Vvar__0___24Anonymous__168693,Vvar__1___24Anonymous__168694),cPLF_2eImp_2eCIf___24a3(Vvar__1__b__168723,Vvar__3__c1__168725,Vvar__4__c2__168726),Vvar__0__st__168722) ) ) ) ) )
            | ? [Vvar__0__st__168730] :
                ( cPLF_2eImp_2estate___24t(Vvar__0__st__168730)
                & ? [Vvar__1__c1__168731] :
                    ( cPLF_2eImp_2ecom___24t(Vvar__1__c1__168731)
                    & ? [Vvar__2__c2__168732] :
                        ( cPLF_2eImp_2ecom___24t(Vvar__2__c2__168732)
                        & Vvar__1___24Anonymous__168694 = cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eImp_2ecom,c_24__type__168747___24a2(Vvar__0___24Anonymous__168693,Vvar__1___24Anonymous__168694),Vvar__1__c1__168731,Vvar__0__st__168730)
                        & Vvar__0___24Anonymous__168693 = cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eImp_2ecom,c_24__type__168747___24a2(Vvar__0___24Anonymous__168693,Vvar__1___24Anonymous__168694),cPLF_2eImp_2eCIf___24a3(cPLF_2eImp_2eBTrue,Vvar__1__c1__168731,Vvar__2__c2__168732),Vvar__0__st__168730) ) ) )
            | ? [Vvar__0__st__168735] :
                ( cPLF_2eImp_2estate___24t(Vvar__0__st__168735)
                & ? [Vvar__1__c1__168736] :
                    ( cPLF_2eImp_2ecom___24t(Vvar__1__c1__168736)
                    & ? [Vvar__2__c2__168737] :
                        ( cPLF_2eImp_2ecom___24t(Vvar__2__c2__168737)
                        & Vvar__1___24Anonymous__168694 = cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eImp_2ecom,c_24__type__168747___24a2(Vvar__0___24Anonymous__168693,Vvar__1___24Anonymous__168694),Vvar__2__c2__168737,Vvar__0__st__168735)
                        & Vvar__0___24Anonymous__168693 = cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eImp_2ecom,c_24__type__168747___24a2(Vvar__0___24Anonymous__168693,Vvar__1___24Anonymous__168694),cPLF_2eImp_2eCIf___24a3(cPLF_2eImp_2eBFalse,Vvar__1__c1__168736,Vvar__2__c2__168737),Vvar__0__st__168735) ) ) )
            | ? [Vvar__0__st__168740] :
                ( cPLF_2eImp_2estate___24t(Vvar__0__st__168740)
                & ? [Vvar__1__b__168741] :
                    ( cPLF_2eImp_2ebexp___24t(Vvar__1__b__168741)
                    & ? [Vvar__2__c1__168742] :
                        ( cPLF_2eImp_2ecom___24t(Vvar__2__c1__168742)
                        & Vvar__1___24Anonymous__168694 = cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eImp_2ecom,c_24__type__168747___24a2(Vvar__0___24Anonymous__168693,Vvar__1___24Anonymous__168694),cPLF_2eImp_2eCIf___24a3(Vvar__1__b__168741,cPLF_2eImp_2eCSeq___24a2(Vvar__2__c1__168742,cPLF_2eImp_2eCWhile___24a2(Vvar__1__b__168741,Vvar__2__c1__168742)),cPLF_2eImp_2eCSkip),Vvar__0__st__168740)
                        & Vvar__0___24Anonymous__168693 = cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eImp_2ecom,c_24__type__168747___24a2(Vvar__0___24Anonymous__168693,Vvar__1___24Anonymous__168694),cPLF_2eImp_2eCWhile___24a2(Vvar__1__b__168741,Vvar__2__c1__168742),Vvar__0__st__168740) ) ) ) ) ) ) ) ).

fof('$_inversion_PLF.Smallstep.multi',axiom,
    ! [Vvar__0__X__1044,Vvar__1__R__1045,Vvar__1___24Anonymous__1046,Vvar__2___24Anonymous__1047] :
      ( cType___24t(Vvar__0__X__1044)
     => ( cPLF_2eSmallstep_2erelation___24t(Vvar__0__X__1044,Vvar__1__R__1045)
       => ( t(Vvar__1___24Anonymous__1046,Vvar__0__X__1044)
         => ( t(Vvar__2___24Anonymous__1047,Vvar__0__X__1044)
           => ( cPLF_2eSmallstep_2emulti___24a4(Vvar__0__X__1044,Vvar__1__R__1045,Vvar__1___24Anonymous__1046,Vvar__2___24Anonymous__1047)
             => ( ? [Vvar__2__x__1051] :
                    ( t(Vvar__2__x__1051,Vvar__0__X__1044)
                    & Vvar__2___24Anonymous__1047 = Vvar__2__x__1051
                    & Vvar__1___24Anonymous__1046 = Vvar__2__x__1051 )
                | ? [Vvar__2__x__1054] :
                    ( t(Vvar__2__x__1054,Vvar__0__X__1044)
                    & ? [Vvar__3__y__1055] :
                        ( t(Vvar__3__y__1055,Vvar__0__X__1044)
                        & ? [Vvar__4__z__1056] :
                            ( t(Vvar__4__z__1056,Vvar__0__X__1044)
                            & p(happ(happ(Vvar__1__R__1045,Vvar__2__x__1054),Vvar__3__y__1055))
                            & cPLF_2eSmallstep_2emulti___24a4(Vvar__0__X__1044,Vvar__1__R__1045,Vvar__3__y__1055,Vvar__4__z__1056)
                            & Vvar__2___24Anonymous__1047 = Vvar__4__z__1056
                            & Vvar__1___24Anonymous__1046 = Vvar__2__x__1054 ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_PLF.Smallstep.stack_step',axiom,
    ! [Vvar__0___24Anonymous__162816,Vvar__1___24Anonymous__162817,Vvar__2___24Anonymous__162818] :
      ( cPLF_2eImp_2estate___24t(Vvar__0___24Anonymous__162816)
     => ( cCoq_2eInit_2eDatatypes_2eprod___24t(cPLF_2eSmallstep_2eprog,cPLF_2eSmallstep_2estack,Vvar__1___24Anonymous__162817)
       => ( cCoq_2eInit_2eDatatypes_2eprod___24t(cPLF_2eSmallstep_2eprog,cPLF_2eSmallstep_2estack,Vvar__2___24Anonymous__162818)
         => ( cPLF_2eSmallstep_2estack__step___24a3(Vvar__0___24Anonymous__162816,Vvar__1___24Anonymous__162817,Vvar__2___24Anonymous__162818)
           => ( ? [Vvar__0__st__162820] :
                  ( cPLF_2eImp_2estate___24t(Vvar__0__st__162820)
                  & ? [Vvar__1__stk__162821] :
                      ( cPLF_2eSmallstep_2estack___24t(Vvar__1__stk__162821)
                      & ? [Vvar__2__n__162822] :
                          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__162822)
                          & ? [Vvar__3__p_27__162823] :
                              ( cCoq_2eInit_2eDatatypes_2elist___24t(cPLF_2eImp_2esinstr,Vvar__3__p_27__162823)
                              & Vvar__2___24Anonymous__162818 = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eInit_2eDatatypes_2elist___24a1(cPLF_2eImp_2esinstr),cCoq_2eInit_2eDatatypes_2elist___24a1(cCoq_2eInit_2eDatatypes_2enat),Vvar__3__p_27__162823,cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2enat,Vvar__2__n__162822,Vvar__1__stk__162821))
                              & Vvar__1___24Anonymous__162817 = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eInit_2eDatatypes_2elist___24a1(cPLF_2eImp_2esinstr),cCoq_2eInit_2eDatatypes_2elist___24a1(cCoq_2eInit_2eDatatypes_2enat),cCoq_2eInit_2eDatatypes_2econs___24a3(cPLF_2eImp_2esinstr,cPLF_2eImp_2eSPush___24a1(Vvar__2__n__162822),Vvar__3__p_27__162823),Vvar__1__stk__162821)
                              & Vvar__0___24Anonymous__162816 = Vvar__0__st__162820 ) ) ) )
              | ? [Vvar__0__st__162824] :
                  ( cPLF_2eImp_2estate___24t(Vvar__0__st__162824)
                  & ? [Vvar__1__stk__162825] :
                      ( cPLF_2eSmallstep_2estack___24t(Vvar__1__stk__162825)
                      & ? [Vvar__2__i__162826] :
                          ( cCoq_2eStrings_2eString_2estring___24t(Vvar__2__i__162826)
                          & ? [Vvar__3__p_27__162827] :
                              ( cCoq_2eInit_2eDatatypes_2elist___24t(cPLF_2eImp_2esinstr,Vvar__3__p_27__162827)
                              & Vvar__2___24Anonymous__162818 = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eInit_2eDatatypes_2elist___24a1(cPLF_2eImp_2esinstr),cCoq_2eInit_2eDatatypes_2elist___24a1(cCoq_2eInit_2eDatatypes_2enat),Vvar__3__p_27__162827,cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2enat,happ(Vvar__0__st__162824,Vvar__2__i__162826),Vvar__1__stk__162825))
                              & Vvar__1___24Anonymous__162817 = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eInit_2eDatatypes_2elist___24a1(cPLF_2eImp_2esinstr),cCoq_2eInit_2eDatatypes_2elist___24a1(cCoq_2eInit_2eDatatypes_2enat),cCoq_2eInit_2eDatatypes_2econs___24a3(cPLF_2eImp_2esinstr,cPLF_2eImp_2eSLoad___24a1(Vvar__2__i__162826),Vvar__3__p_27__162827),Vvar__1__stk__162825)
                              & Vvar__0___24Anonymous__162816 = Vvar__0__st__162824 ) ) ) )
              | ? [Vvar__0__st__162828] :
                  ( cPLF_2eImp_2estate___24t(Vvar__0__st__162828)
                  & ? [Vvar__1__stk__162829] :
                      ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2enat,Vvar__1__stk__162829)
                      & ? [Vvar__2__n__162830] :
                          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__162830)
                          & ? [Vvar__3__m__162831] :
                              ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__3__m__162831)
                              & ? [Vvar__4__p_27__162832] :
                                  ( cCoq_2eInit_2eDatatypes_2elist___24t(cPLF_2eImp_2esinstr,Vvar__4__p_27__162832)
                                  & Vvar__2___24Anonymous__162818 = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eInit_2eDatatypes_2elist___24a1(cPLF_2eImp_2esinstr),cCoq_2eInit_2eDatatypes_2elist___24a1(cCoq_2eInit_2eDatatypes_2enat),Vvar__4__p_27__162832,cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2enat,c_24__case__Coq_2eInit_2eDatatypes_2enat_24162913___24a5(Vvar__0___24Anonymous__162816,Vvar__1___24Anonymous__162817,Vvar__2___24Anonymous__162818,Vvar__2__n__162830,Vvar__3__m__162831),Vvar__1__stk__162829))
                                  & Vvar__1___24Anonymous__162817 = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eInit_2eDatatypes_2elist___24a1(cPLF_2eImp_2esinstr),cCoq_2eInit_2eDatatypes_2elist___24a1(cCoq_2eInit_2eDatatypes_2enat),cCoq_2eInit_2eDatatypes_2econs___24a3(cPLF_2eImp_2esinstr,cPLF_2eImp_2eSPlus,Vvar__4__p_27__162832),cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2enat,Vvar__2__n__162830,cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2enat,Vvar__3__m__162831,Vvar__1__stk__162829)))
                                  & Vvar__0___24Anonymous__162816 = Vvar__0__st__162828 ) ) ) ) )
              | ? [Vvar__0__st__162835] :
                  ( cPLF_2eImp_2estate___24t(Vvar__0__st__162835)
                  & ? [Vvar__1__stk__162836] :
                      ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2enat,Vvar__1__stk__162836)
                      & ? [Vvar__2__n__162837] :
                          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__162837)
                          & ? [Vvar__3__m__162838] :
                              ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__3__m__162838)
                              & ? [Vvar__4__p_27__162839] :
                                  ( cCoq_2eInit_2eDatatypes_2elist___24t(cPLF_2eImp_2esinstr,Vvar__4__p_27__162839)
                                  & Vvar__2___24Anonymous__162818 = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eInit_2eDatatypes_2elist___24a1(cPLF_2eImp_2esinstr),cCoq_2eInit_2eDatatypes_2elist___24a1(cCoq_2eInit_2eDatatypes_2enat),Vvar__4__p_27__162839,cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2enat,c_24__case__Coq_2eInit_2eDatatypes_2enat_24163035___24a5(Vvar__0___24Anonymous__162816,Vvar__1___24Anonymous__162817,Vvar__2___24Anonymous__162818,Vvar__2__n__162837,Vvar__3__m__162838),Vvar__1__stk__162836))
                                  & Vvar__1___24Anonymous__162817 = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eInit_2eDatatypes_2elist___24a1(cPLF_2eImp_2esinstr),cCoq_2eInit_2eDatatypes_2elist___24a1(cCoq_2eInit_2eDatatypes_2enat),cCoq_2eInit_2eDatatypes_2econs___24a3(cPLF_2eImp_2esinstr,cPLF_2eImp_2eSMinus,Vvar__4__p_27__162839),cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2enat,Vvar__2__n__162837,cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2enat,Vvar__3__m__162838,Vvar__1__stk__162836)))
                                  & Vvar__0___24Anonymous__162816 = Vvar__0__st__162835 ) ) ) ) )
              | ? [Vvar__0__st__162844] :
                  ( cPLF_2eImp_2estate___24t(Vvar__0__st__162844)
                  & ? [Vvar__1__stk__162845] :
                      ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2enat,Vvar__1__stk__162845)
                      & ? [Vvar__2__n__162846] :
                          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__162846)
                          & ? [Vvar__3__m__162847] :
                              ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__3__m__162847)
                              & ? [Vvar__4__p_27__162848] :
                                  ( cCoq_2eInit_2eDatatypes_2elist___24t(cPLF_2eImp_2esinstr,Vvar__4__p_27__162848)
                                  & Vvar__2___24Anonymous__162818 = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eInit_2eDatatypes_2elist___24a1(cPLF_2eImp_2esinstr),cCoq_2eInit_2eDatatypes_2elist___24a1(cCoq_2eInit_2eDatatypes_2enat),Vvar__4__p_27__162848,cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2enat,c_24__case__Coq_2eInit_2eDatatypes_2enat_24163138___24a5(Vvar__0___24Anonymous__162816,Vvar__1___24Anonymous__162817,Vvar__2___24Anonymous__162818,Vvar__2__n__162846,Vvar__3__m__162847),Vvar__1__stk__162845))
                                  & Vvar__1___24Anonymous__162817 = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eInit_2eDatatypes_2elist___24a1(cPLF_2eImp_2esinstr),cCoq_2eInit_2eDatatypes_2elist___24a1(cCoq_2eInit_2eDatatypes_2enat),cCoq_2eInit_2eDatatypes_2econs___24a3(cPLF_2eImp_2esinstr,cPLF_2eImp_2eSMult,Vvar__4__p_27__162848),cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2enat,Vvar__2__n__162846,cCoq_2eInit_2eDatatypes_2econs___24a3(cCoq_2eInit_2eDatatypes_2enat,Vvar__3__m__162847,Vvar__1__stk__162845)))
                                  & Vvar__0___24Anonymous__162816 = Vvar__0__st__162844 ) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_PLF.Smallstep.step',axiom,
    ! [Vvar__0___24Anonymous__954,Vvar__1___24Anonymous__955] :
      ( cPLF_2eSmallstep_2etm___24t(Vvar__0___24Anonymous__954)
     => ( cPLF_2eSmallstep_2etm___24t(Vvar__1___24Anonymous__955)
       => ( cPLF_2eSmallstep_2estep___24a2(Vvar__0___24Anonymous__954,Vvar__1___24Anonymous__955)
         => ( ? [Vvar__0__n1__957] :
                ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n1__957)
                & ? [Vvar__1__n2__958] :
                    ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__n2__958)
                    & Vvar__1___24Anonymous__955 = cPLF_2eSmallstep_2eC___24a1(c_24__case__Coq_2eInit_2eDatatypes_2enat_241023___24a4(Vvar__0___24Anonymous__954,Vvar__1___24Anonymous__955,Vvar__0__n1__957,Vvar__1__n2__958))
                    & Vvar__0___24Anonymous__954 = cPLF_2eSmallstep_2eP___24a2(cPLF_2eSmallstep_2eC___24a1(Vvar__0__n1__957),cPLF_2eSmallstep_2eC___24a1(Vvar__1__n2__958)) ) )
            | ? [Vvar__0__t1__961] :
                ( cPLF_2eSmallstep_2etm___24t(Vvar__0__t1__961)
                & ? [Vvar__1__t1_27__962] :
                    ( cPLF_2eSmallstep_2etm___24t(Vvar__1__t1_27__962)
                    & ? [Vvar__2__t2__963] :
                        ( cPLF_2eSmallstep_2etm___24t(Vvar__2__t2__963)
                        & cPLF_2eSmallstep_2estep___24a2(Vvar__0__t1__961,Vvar__1__t1_27__962)
                        & Vvar__1___24Anonymous__955 = cPLF_2eSmallstep_2eP___24a2(Vvar__1__t1_27__962,Vvar__2__t2__963)
                        & Vvar__0___24Anonymous__954 = cPLF_2eSmallstep_2eP___24a2(Vvar__0__t1__961,Vvar__2__t2__963) ) ) )
            | ? [Vvar__0__v1__965] :
                ( cPLF_2eSmallstep_2etm___24t(Vvar__0__v1__965)
                & ? [Vvar__1__t2__966] :
                    ( cPLF_2eSmallstep_2etm___24t(Vvar__1__t2__966)
                    & ? [Vvar__2__t2_27__967] :
                        ( cPLF_2eSmallstep_2etm___24t(Vvar__2__t2_27__967)
                        & cPLF_2eSmallstep_2evalue___24a1(Vvar__0__v1__965)
                        & cPLF_2eSmallstep_2estep___24a2(Vvar__1__t2__966,Vvar__2__t2_27__967)
                        & Vvar__1___24Anonymous__955 = cPLF_2eSmallstep_2eP___24a2(Vvar__0__v1__965,Vvar__2__t2_27__967)
                        & Vvar__0___24Anonymous__954 = cPLF_2eSmallstep_2eP___24a2(Vvar__0__v1__965,Vvar__1__t2__966) ) ) ) ) ) ) ) ).

fof('$_inversion_PLF.Smallstep.tm',axiom,
    ! [VX936] :
      ( cPLF_2eSmallstep_2etm___24t(VX936)
     => ( ? [Vvar__0___24Anonymous__937] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__937)
            & VX936 = cPLF_2eSmallstep_2eC___24a1(Vvar__0___24Anonymous__937) )
        | ? [Vvar__0___24Anonymous__938] :
            ( cPLF_2eSmallstep_2etm___24t(Vvar__0___24Anonymous__938)
            & ? [Vvar__1___24Anonymous__939] :
                ( cPLF_2eSmallstep_2etm___24t(Vvar__1___24Anonymous__939)
                & VX936 = cPLF_2eSmallstep_2eP___24a2(Vvar__0___24Anonymous__938,Vvar__1___24Anonymous__939) ) ) ) ) ).

fof('$_inversion_PLF.Smallstep.value',axiom,
    ! [Vvar__0___24Anonymous__2059] :
      ( cPLF_2eSmallstep_2etm___24t(Vvar__0___24Anonymous__2059)
     => ( cPLF_2eSmallstep_2evalue___24a1(Vvar__0___24Anonymous__2059)
       => ? [Vvar__0__n__2061] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__2061)
            & Vvar__0___24Anonymous__2059 = cPLF_2eSmallstep_2eC___24a1(Vvar__0__n__2061) ) ) ) ).

fof('$_inversion_PLF.Stlc.STLC.has_type',axiom,
    ! [Vvar__0___24Anonymous__161892,Vvar__1___24Anonymous__161893,Vvar__2___24Anonymous__161894] :
      ( cPLF_2eStlc_2eSTLC_2econtext___24t(Vvar__0___24Anonymous__161892)
     => ( cPLF_2eStlc_2eSTLC_2etm___24t(Vvar__1___24Anonymous__161893)
       => ( cPLF_2eStlc_2eSTLC_2ety___24t(Vvar__2___24Anonymous__161894)
         => ( cPLF_2eStlc_2eSTLC_2ehas__type___24a3(Vvar__0___24Anonymous__161892,Vvar__1___24Anonymous__161893,Vvar__2___24Anonymous__161894)
           => ( ? [Vvar__0__Gamma__161896] :
                  ( c_24__type__161927___24t(Vvar__0___24Anonymous__161892,Vvar__1___24Anonymous__161893,Vvar__2___24Anonymous__161894,Vvar__0__Gamma__161896)
                  & ? [Vvar__1__x__161898] :
                      ( cCoq_2eStrings_2eString_2estring___24t(Vvar__1__x__161898)
                      & ? [Vvar__2__T__161899] :
                          ( cPLF_2eStlc_2eSTLC_2ety___24t(Vvar__2__T__161899)
                          & happ(Vvar__0__Gamma__161896,Vvar__1__x__161898) = cCoq_2eInit_2eDatatypes_2eSome___24a2(cPLF_2eStlc_2eSTLC_2ety,Vvar__2__T__161899)
                          & Vvar__2___24Anonymous__161894 = Vvar__2__T__161899
                          & Vvar__1___24Anonymous__161893 = cPLF_2eStlc_2eSTLC_2evar___24a1(Vvar__1__x__161898)
                          & Vvar__0___24Anonymous__161892 = Vvar__0__Gamma__161896 ) ) )
              | ? [Vvar__0__Gamma__161901] :
                  ( cPLF_2eMaps_2epartial__map___24t(cPLF_2eStlc_2eSTLC_2ety,Vvar__0__Gamma__161901)
                  & ? [Vvar__1__x__161902] :
                      ( cCoq_2eStrings_2eString_2estring___24t(Vvar__1__x__161902)
                      & ? [Vvar__2__T11__161903] :
                          ( cPLF_2eStlc_2eSTLC_2ety___24t(Vvar__2__T11__161903)
                          & ? [Vvar__3__T12__161904] :
                              ( cPLF_2eStlc_2eSTLC_2ety___24t(Vvar__3__T12__161904)
                              & ? [Vvar__4__t12__161905] :
                                  ( cPLF_2eStlc_2eSTLC_2etm___24t(Vvar__4__t12__161905)
                                  & cPLF_2eStlc_2eSTLC_2ehas__type___24a3(cPLF_2eMaps_2eupdate___24a4(cPLF_2eStlc_2eSTLC_2ety,Vvar__0__Gamma__161901,Vvar__1__x__161902,Vvar__2__T11__161903),Vvar__4__t12__161905,Vvar__3__T12__161904)
                                  & Vvar__2___24Anonymous__161894 = cPLF_2eStlc_2eSTLC_2eArrow___24a2(Vvar__2__T11__161903,Vvar__3__T12__161904)
                                  & Vvar__1___24Anonymous__161893 = cPLF_2eStlc_2eSTLC_2eabs___24a3(Vvar__1__x__161902,Vvar__2__T11__161903,Vvar__4__t12__161905)
                                  & Vvar__0___24Anonymous__161892 = Vvar__0__Gamma__161901 ) ) ) ) )
              | ? [Vvar__0__T11__161907] :
                  ( cPLF_2eStlc_2eSTLC_2ety___24t(Vvar__0__T11__161907)
                  & ? [Vvar__1__T12__161908] :
                      ( cPLF_2eStlc_2eSTLC_2ety___24t(Vvar__1__T12__161908)
                      & ? [Vvar__2__Gamma__161909] :
                          ( cPLF_2eStlc_2eSTLC_2econtext___24t(Vvar__2__Gamma__161909)
                          & ? [Vvar__3__t1__161910] :
                              ( cPLF_2eStlc_2eSTLC_2etm___24t(Vvar__3__t1__161910)
                              & ? [Vvar__4__t2__161911] :
                                  ( cPLF_2eStlc_2eSTLC_2etm___24t(Vvar__4__t2__161911)
                                  & cPLF_2eStlc_2eSTLC_2ehas__type___24a3(Vvar__2__Gamma__161909,Vvar__3__t1__161910,cPLF_2eStlc_2eSTLC_2eArrow___24a2(Vvar__0__T11__161907,Vvar__1__T12__161908))
                                  & cPLF_2eStlc_2eSTLC_2ehas__type___24a3(Vvar__2__Gamma__161909,Vvar__4__t2__161911,Vvar__0__T11__161907)
                                  & Vvar__2___24Anonymous__161894 = Vvar__1__T12__161908
                                  & Vvar__1___24Anonymous__161893 = cPLF_2eStlc_2eSTLC_2eapp___24a2(Vvar__3__t1__161910,Vvar__4__t2__161911)
                                  & Vvar__0___24Anonymous__161892 = Vvar__2__Gamma__161909 ) ) ) ) )
              | ? [Vvar__0__Gamma__161914] :
                  ( cPLF_2eStlc_2eSTLC_2econtext___24t(Vvar__0__Gamma__161914)
                  & Vvar__2___24Anonymous__161894 = cPLF_2eStlc_2eSTLC_2eBool
                  & Vvar__1___24Anonymous__161893 = cPLF_2eStlc_2eSTLC_2etru
                  & Vvar__0___24Anonymous__161892 = Vvar__0__Gamma__161914 )
              | ? [Vvar__0__Gamma__161915] :
                  ( cPLF_2eStlc_2eSTLC_2econtext___24t(Vvar__0__Gamma__161915)
                  & Vvar__2___24Anonymous__161894 = cPLF_2eStlc_2eSTLC_2eBool
                  & Vvar__1___24Anonymous__161893 = cPLF_2eStlc_2eSTLC_2efls
                  & Vvar__0___24Anonymous__161892 = Vvar__0__Gamma__161915 )
              | ? [Vvar__0__t1__161916] :
                  ( cPLF_2eStlc_2eSTLC_2etm___24t(Vvar__0__t1__161916)
                  & ? [Vvar__1__t2__161917] :
                      ( cPLF_2eStlc_2eSTLC_2etm___24t(Vvar__1__t2__161917)
                      & ? [Vvar__2__t3__161918] :
                          ( cPLF_2eStlc_2eSTLC_2etm___24t(Vvar__2__t3__161918)
                          & ? [Vvar__3__T__161919] :
                              ( cPLF_2eStlc_2eSTLC_2ety___24t(Vvar__3__T__161919)
                              & ? [Vvar__4__Gamma__161920] :
                                  ( cPLF_2eStlc_2eSTLC_2econtext___24t(Vvar__4__Gamma__161920)
                                  & cPLF_2eStlc_2eSTLC_2ehas__type___24a3(Vvar__4__Gamma__161920,Vvar__0__t1__161916,cPLF_2eStlc_2eSTLC_2eBool)
                                  & cPLF_2eStlc_2eSTLC_2ehas__type___24a3(Vvar__4__Gamma__161920,Vvar__1__t2__161917,Vvar__3__T__161919)
                                  & cPLF_2eStlc_2eSTLC_2ehas__type___24a3(Vvar__4__Gamma__161920,Vvar__2__t3__161918,Vvar__3__T__161919)
                                  & Vvar__2___24Anonymous__161894 = Vvar__3__T__161919
                                  & Vvar__1___24Anonymous__161893 = cPLF_2eStlc_2eSTLC_2etest___24a3(Vvar__0__t1__161916,Vvar__1__t2__161917,Vvar__2__t3__161918)
                                  & Vvar__0___24Anonymous__161892 = Vvar__4__Gamma__161920 ) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_PLF.Stlc.STLC.step',axiom,
    ! [Vvar__0___24Anonymous__109402,Vvar__1___24Anonymous__109403] :
      ( cPLF_2eStlc_2eSTLC_2etm___24t(Vvar__0___24Anonymous__109402)
     => ( cPLF_2eStlc_2eSTLC_2etm___24t(Vvar__1___24Anonymous__109403)
       => ( cPLF_2eStlc_2eSTLC_2estep___24a2(Vvar__0___24Anonymous__109402,Vvar__1___24Anonymous__109403)
         => ( ? [Vvar__0__x__109405] :
                ( cCoq_2eStrings_2eString_2estring___24t(Vvar__0__x__109405)
                & ? [Vvar__1__T__109406] :
                    ( cPLF_2eStlc_2eSTLC_2ety___24t(Vvar__1__T__109406)
                    & ? [Vvar__2__t12__109407] :
                        ( cPLF_2eStlc_2eSTLC_2etm___24t(Vvar__2__t12__109407)
                        & ? [Vvar__3__v2__109408] :
                            ( cPLF_2eStlc_2eSTLC_2etm___24t(Vvar__3__v2__109408)
                            & cPLF_2eStlc_2eSTLC_2evalue___24a1(Vvar__3__v2__109408)
                            & Vvar__1___24Anonymous__109403 = c_24__case__PLF_2eStlc_2eSTLC_2etm_24110793___24a5(Vvar__0___24Anonymous__109402,Vvar__1___24Anonymous__109403,Vvar__0__x__109405,Vvar__2__t12__109407,Vvar__3__v2__109408)
                            & Vvar__0___24Anonymous__109402 = cPLF_2eStlc_2eSTLC_2eapp___24a2(cPLF_2eStlc_2eSTLC_2eabs___24a3(Vvar__0__x__109405,Vvar__1__T__109406,Vvar__2__t12__109407),Vvar__3__v2__109408) ) ) ) )
            | ? [Vvar__0__t1__109422] :
                ( cPLF_2eStlc_2eSTLC_2etm___24t(Vvar__0__t1__109422)
                & ? [Vvar__1__t1_27__109423] :
                    ( cPLF_2eStlc_2eSTLC_2etm___24t(Vvar__1__t1_27__109423)
                    & ? [Vvar__2__t2__109424] :
                        ( cPLF_2eStlc_2eSTLC_2etm___24t(Vvar__2__t2__109424)
                        & cPLF_2eStlc_2eSTLC_2estep___24a2(Vvar__0__t1__109422,Vvar__1__t1_27__109423)
                        & Vvar__1___24Anonymous__109403 = cPLF_2eStlc_2eSTLC_2eapp___24a2(Vvar__1__t1_27__109423,Vvar__2__t2__109424)
                        & Vvar__0___24Anonymous__109402 = cPLF_2eStlc_2eSTLC_2eapp___24a2(Vvar__0__t1__109422,Vvar__2__t2__109424) ) ) )
            | ? [Vvar__0__v1__109426] :
                ( cPLF_2eStlc_2eSTLC_2etm___24t(Vvar__0__v1__109426)
                & ? [Vvar__1__t2__109427] :
                    ( cPLF_2eStlc_2eSTLC_2etm___24t(Vvar__1__t2__109427)
                    & ? [Vvar__2__t2_27__109428] :
                        ( cPLF_2eStlc_2eSTLC_2etm___24t(Vvar__2__t2_27__109428)
                        & cPLF_2eStlc_2eSTLC_2evalue___24a1(Vvar__0__v1__109426)
                        & cPLF_2eStlc_2eSTLC_2estep___24a2(Vvar__1__t2__109427,Vvar__2__t2_27__109428)
                        & Vvar__1___24Anonymous__109403 = cPLF_2eStlc_2eSTLC_2eapp___24a2(Vvar__0__v1__109426,Vvar__2__t2_27__109428)
                        & Vvar__0___24Anonymous__109402 = cPLF_2eStlc_2eSTLC_2eapp___24a2(Vvar__0__v1__109426,Vvar__1__t2__109427) ) ) )
            | ? [Vvar__0__t1__109431] :
                ( cPLF_2eStlc_2eSTLC_2etm___24t(Vvar__0__t1__109431)
                & ? [Vvar__1__t2__109432] :
                    ( cPLF_2eStlc_2eSTLC_2etm___24t(Vvar__1__t2__109432)
                    & Vvar__1___24Anonymous__109403 = Vvar__0__t1__109431
                    & Vvar__0___24Anonymous__109402 = cPLF_2eStlc_2eSTLC_2etest___24a3(cPLF_2eStlc_2eSTLC_2etru,Vvar__0__t1__109431,Vvar__1__t2__109432) ) )
            | ? [Vvar__0__t1__109433] :
                ( cPLF_2eStlc_2eSTLC_2etm___24t(Vvar__0__t1__109433)
                & ? [Vvar__1__t2__109434] :
                    ( cPLF_2eStlc_2eSTLC_2etm___24t(Vvar__1__t2__109434)
                    & Vvar__1___24Anonymous__109403 = Vvar__1__t2__109434
                    & Vvar__0___24Anonymous__109402 = cPLF_2eStlc_2eSTLC_2etest___24a3(cPLF_2eStlc_2eSTLC_2efls,Vvar__0__t1__109433,Vvar__1__t2__109434) ) )
            | ? [Vvar__0__t1__109435] :
                ( cPLF_2eStlc_2eSTLC_2etm___24t(Vvar__0__t1__109435)
                & ? [Vvar__1__t1_27__109436] :
                    ( cPLF_2eStlc_2eSTLC_2etm___24t(Vvar__1__t1_27__109436)
                    & ? [Vvar__2__t2__109437] :
                        ( cPLF_2eStlc_2eSTLC_2etm___24t(Vvar__2__t2__109437)
                        & ? [Vvar__3__t3__109438] :
                            ( cPLF_2eStlc_2eSTLC_2etm___24t(Vvar__3__t3__109438)
                            & cPLF_2eStlc_2eSTLC_2estep___24a2(Vvar__0__t1__109435,Vvar__1__t1_27__109436)
                            & Vvar__1___24Anonymous__109403 = cPLF_2eStlc_2eSTLC_2etest___24a3(Vvar__1__t1_27__109436,Vvar__2__t2__109437,Vvar__3__t3__109438)
                            & Vvar__0___24Anonymous__109402 = cPLF_2eStlc_2eSTLC_2etest___24a3(Vvar__0__t1__109435,Vvar__2__t2__109437,Vvar__3__t3__109438) ) ) ) ) ) ) ) ) ).

fof('$_inversion_PLF.Stlc.STLC.tm',axiom,
    ! [VX92126] :
      ( cPLF_2eStlc_2eSTLC_2etm___24t(VX92126)
     => ( ? [Vvar__0___24Anonymous__92127] :
            ( cCoq_2eStrings_2eString_2estring___24t(Vvar__0___24Anonymous__92127)
            & VX92126 = cPLF_2eStlc_2eSTLC_2evar___24a1(Vvar__0___24Anonymous__92127) )
        | ? [Vvar__0___24Anonymous__92128] :
            ( cPLF_2eStlc_2eSTLC_2etm___24t(Vvar__0___24Anonymous__92128)
            & ? [Vvar__1___24Anonymous__92129] :
                ( cPLF_2eStlc_2eSTLC_2etm___24t(Vvar__1___24Anonymous__92129)
                & VX92126 = cPLF_2eStlc_2eSTLC_2eapp___24a2(Vvar__0___24Anonymous__92128,Vvar__1___24Anonymous__92129) ) )
        | ? [Vvar__0___24Anonymous__92130] :
            ( cCoq_2eStrings_2eString_2estring___24t(Vvar__0___24Anonymous__92130)
            & ? [Vvar__1___24Anonymous__92131] :
                ( cPLF_2eStlc_2eSTLC_2ety___24t(Vvar__1___24Anonymous__92131)
                & ? [Vvar__2___24Anonymous__92132] :
                    ( cPLF_2eStlc_2eSTLC_2etm___24t(Vvar__2___24Anonymous__92132)
                    & VX92126 = cPLF_2eStlc_2eSTLC_2eabs___24a3(Vvar__0___24Anonymous__92130,Vvar__1___24Anonymous__92131,Vvar__2___24Anonymous__92132) ) ) )
        | VX92126 = cPLF_2eStlc_2eSTLC_2etru
        | VX92126 = cPLF_2eStlc_2eSTLC_2efls
        | ? [Vvar__0___24Anonymous__92133] :
            ( cPLF_2eStlc_2eSTLC_2etm___24t(Vvar__0___24Anonymous__92133)
            & ? [Vvar__1___24Anonymous__92134] :
                ( cPLF_2eStlc_2eSTLC_2etm___24t(Vvar__1___24Anonymous__92134)
                & ? [Vvar__2___24Anonymous__92135] :
                    ( cPLF_2eStlc_2eSTLC_2etm___24t(Vvar__2___24Anonymous__92135)
                    & VX92126 = cPLF_2eStlc_2eSTLC_2etest___24a3(Vvar__0___24Anonymous__92133,Vvar__1___24Anonymous__92134,Vvar__2___24Anonymous__92135) ) ) ) ) ) ).

fof('$_inversion_PLF.Stlc.STLC.ty',axiom,
    ! [VX92117] :
      ( cPLF_2eStlc_2eSTLC_2ety___24t(VX92117)
     => ( VX92117 = cPLF_2eStlc_2eSTLC_2eBool
        | ? [Vvar__0___24Anonymous__92118] :
            ( cPLF_2eStlc_2eSTLC_2ety___24t(Vvar__0___24Anonymous__92118)
            & ? [Vvar__1___24Anonymous__92119] :
                ( cPLF_2eStlc_2eSTLC_2ety___24t(Vvar__1___24Anonymous__92119)
                & VX92117 = cPLF_2eStlc_2eSTLC_2eArrow___24a2(Vvar__0___24Anonymous__92118,Vvar__1___24Anonymous__92119) ) ) ) ) ).

fof('$_inversion_PLF.Stlc.STLC.value',axiom,
    ! [Vvar__0___24Anonymous__109366] :
      ( cPLF_2eStlc_2eSTLC_2etm___24t(Vvar__0___24Anonymous__109366)
     => ( cPLF_2eStlc_2eSTLC_2evalue___24a1(Vvar__0___24Anonymous__109366)
       => ( ? [Vvar__0__x__109368] :
              ( cCoq_2eStrings_2eString_2estring___24t(Vvar__0__x__109368)
              & ? [Vvar__1__T__109369] :
                  ( cPLF_2eStlc_2eSTLC_2ety___24t(Vvar__1__T__109369)
                  & ? [Vvar__2__t__109370] :
                      ( cPLF_2eStlc_2eSTLC_2etm___24t(Vvar__2__t__109370)
                      & Vvar__0___24Anonymous__109366 = cPLF_2eStlc_2eSTLC_2eabs___24a3(Vvar__0__x__109368,Vvar__1__T__109369,Vvar__2__t__109370) ) ) )
          | Vvar__0___24Anonymous__109366 = cPLF_2eStlc_2eSTLC_2etru
          | Vvar__0___24Anonymous__109366 = cPLF_2eStlc_2eSTLC_2efls ) ) ) ).

fof('$_inversion_PLF.StlcProp.STLCArith.tm',axiom,
    ! [VX200671] :
      ( cPLF_2eStlcProp_2eSTLCArith_2etm___24t(VX200671)
     => ( ? [Vvar__0___24Anonymous__200672] :
            ( cCoq_2eStrings_2eString_2estring___24t(Vvar__0___24Anonymous__200672)
            & VX200671 = cPLF_2eStlcProp_2eSTLCArith_2evar___24a1(Vvar__0___24Anonymous__200672) )
        | ? [Vvar__0___24Anonymous__200673] :
            ( cPLF_2eStlcProp_2eSTLCArith_2etm___24t(Vvar__0___24Anonymous__200673)
            & ? [Vvar__1___24Anonymous__200674] :
                ( cPLF_2eStlcProp_2eSTLCArith_2etm___24t(Vvar__1___24Anonymous__200674)
                & VX200671 = cPLF_2eStlcProp_2eSTLCArith_2eapp___24a2(Vvar__0___24Anonymous__200673,Vvar__1___24Anonymous__200674) ) )
        | ? [Vvar__0___24Anonymous__200675] :
            ( cCoq_2eStrings_2eString_2estring___24t(Vvar__0___24Anonymous__200675)
            & ? [Vvar__1___24Anonymous__200676] :
                ( cPLF_2eStlcProp_2eSTLCArith_2ety___24t(Vvar__1___24Anonymous__200676)
                & ? [Vvar__2___24Anonymous__200677] :
                    ( cPLF_2eStlcProp_2eSTLCArith_2etm___24t(Vvar__2___24Anonymous__200677)
                    & VX200671 = cPLF_2eStlcProp_2eSTLCArith_2eabs___24a3(Vvar__0___24Anonymous__200675,Vvar__1___24Anonymous__200676,Vvar__2___24Anonymous__200677) ) ) )
        | ? [Vvar__0___24Anonymous__200678] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__200678)
            & VX200671 = cPLF_2eStlcProp_2eSTLCArith_2econst___24a1(Vvar__0___24Anonymous__200678) )
        | ? [Vvar__0___24Anonymous__200679] :
            ( cPLF_2eStlcProp_2eSTLCArith_2etm___24t(Vvar__0___24Anonymous__200679)
            & VX200671 = cPLF_2eStlcProp_2eSTLCArith_2escc___24a1(Vvar__0___24Anonymous__200679) )
        | ? [Vvar__0___24Anonymous__200680] :
            ( cPLF_2eStlcProp_2eSTLCArith_2etm___24t(Vvar__0___24Anonymous__200680)
            & VX200671 = cPLF_2eStlcProp_2eSTLCArith_2eprd___24a1(Vvar__0___24Anonymous__200680) )
        | ? [Vvar__0___24Anonymous__200681] :
            ( cPLF_2eStlcProp_2eSTLCArith_2etm___24t(Vvar__0___24Anonymous__200681)
            & ? [Vvar__1___24Anonymous__200682] :
                ( cPLF_2eStlcProp_2eSTLCArith_2etm___24t(Vvar__1___24Anonymous__200682)
                & VX200671 = cPLF_2eStlcProp_2eSTLCArith_2emlt___24a2(Vvar__0___24Anonymous__200681,Vvar__1___24Anonymous__200682) ) )
        | ? [Vvar__0___24Anonymous__200683] :
            ( cPLF_2eStlcProp_2eSTLCArith_2etm___24t(Vvar__0___24Anonymous__200683)
            & ? [Vvar__1___24Anonymous__200684] :
                ( cPLF_2eStlcProp_2eSTLCArith_2etm___24t(Vvar__1___24Anonymous__200684)
                & ? [Vvar__2___24Anonymous__200685] :
                    ( cPLF_2eStlcProp_2eSTLCArith_2etm___24t(Vvar__2___24Anonymous__200685)
                    & VX200671 = cPLF_2eStlcProp_2eSTLCArith_2etest0___24a3(Vvar__0___24Anonymous__200683,Vvar__1___24Anonymous__200684,Vvar__2___24Anonymous__200685) ) ) ) ) ) ).

fof('$_inversion_PLF.StlcProp.STLCArith.ty',axiom,
    ! [VX200662] :
      ( cPLF_2eStlcProp_2eSTLCArith_2ety___24t(VX200662)
     => ( ? [Vvar__0___24Anonymous__200663] :
            ( cPLF_2eStlcProp_2eSTLCArith_2ety___24t(Vvar__0___24Anonymous__200663)
            & ? [Vvar__1___24Anonymous__200664] :
                ( cPLF_2eStlcProp_2eSTLCArith_2ety___24t(Vvar__1___24Anonymous__200664)
                & VX200662 = cPLF_2eStlcProp_2eSTLCArith_2eArrow___24a2(Vvar__0___24Anonymous__200663,Vvar__1___24Anonymous__200664) ) )
        | VX200662 = cPLF_2eStlcProp_2eSTLCArith_2eNat ) ) ).

fof('$_inversion_PLF.StlcProp.STLCProp.appears_free_in',axiom,
    ! [Vvar__0___24Anonymous__198736,Vvar__1___24Anonymous__198737] :
      ( cCoq_2eStrings_2eString_2estring___24t(Vvar__0___24Anonymous__198736)
     => ( cPLF_2eStlc_2eSTLC_2etm___24t(Vvar__1___24Anonymous__198737)
       => ( cPLF_2eStlcProp_2eSTLCProp_2eappears__free__in___24a2(Vvar__0___24Anonymous__198736,Vvar__1___24Anonymous__198737)
         => ( ? [Vvar__0__x__198739] :
                ( cCoq_2eStrings_2eString_2estring___24t(Vvar__0__x__198739)
                & Vvar__1___24Anonymous__198737 = cPLF_2eStlc_2eSTLC_2evar___24a1(Vvar__0__x__198739)
                & Vvar__0___24Anonymous__198736 = Vvar__0__x__198739 )
            | ? [Vvar__0__x__198740] :
                ( cCoq_2eStrings_2eString_2estring___24t(Vvar__0__x__198740)
                & ? [Vvar__1__t1__198741] :
                    ( cPLF_2eStlc_2eSTLC_2etm___24t(Vvar__1__t1__198741)
                    & ? [Vvar__2__t2__198742] :
                        ( cPLF_2eStlc_2eSTLC_2etm___24t(Vvar__2__t2__198742)
                        & cPLF_2eStlcProp_2eSTLCProp_2eappears__free__in___24a2(Vvar__0__x__198740,Vvar__1__t1__198741)
                        & Vvar__1___24Anonymous__198737 = cPLF_2eStlc_2eSTLC_2eapp___24a2(Vvar__1__t1__198741,Vvar__2__t2__198742)
                        & Vvar__0___24Anonymous__198736 = Vvar__0__x__198740 ) ) )
            | ? [Vvar__0__x__198744] :
                ( cCoq_2eStrings_2eString_2estring___24t(Vvar__0__x__198744)
                & ? [Vvar__1__t1__198745] :
                    ( cPLF_2eStlc_2eSTLC_2etm___24t(Vvar__1__t1__198745)
                    & ? [Vvar__2__t2__198746] :
                        ( cPLF_2eStlc_2eSTLC_2etm___24t(Vvar__2__t2__198746)
                        & cPLF_2eStlcProp_2eSTLCProp_2eappears__free__in___24a2(Vvar__0__x__198744,Vvar__2__t2__198746)
                        & Vvar__1___24Anonymous__198737 = cPLF_2eStlc_2eSTLC_2eapp___24a2(Vvar__1__t1__198745,Vvar__2__t2__198746)
                        & Vvar__0___24Anonymous__198736 = Vvar__0__x__198744 ) ) )
            | ? [Vvar__0__x__198748] :
                ( cCoq_2eStrings_2eString_2estring___24t(Vvar__0__x__198748)
                & ? [Vvar__1__y__198749] :
                    ( cCoq_2eStrings_2eString_2estring___24t(Vvar__1__y__198749)
                    & ? [Vvar__2__T11__198750] :
                        ( cPLF_2eStlc_2eSTLC_2ety___24t(Vvar__2__T11__198750)
                        & ? [Vvar__3__t12__198751] :
                            ( cPLF_2eStlc_2eSTLC_2etm___24t(Vvar__3__t12__198751)
                            & Vvar__1__y__198749 != Vvar__0__x__198748
                            & cPLF_2eStlcProp_2eSTLCProp_2eappears__free__in___24a2(Vvar__0__x__198748,Vvar__3__t12__198751)
                            & Vvar__1___24Anonymous__198737 = cPLF_2eStlc_2eSTLC_2eabs___24a3(Vvar__1__y__198749,Vvar__2__T11__198750,Vvar__3__t12__198751)
                            & Vvar__0___24Anonymous__198736 = Vvar__0__x__198748 ) ) ) )
            | ? [Vvar__0__x__198754] :
                ( cCoq_2eStrings_2eString_2estring___24t(Vvar__0__x__198754)
                & ? [Vvar__1__t1__198755] :
                    ( cPLF_2eStlc_2eSTLC_2etm___24t(Vvar__1__t1__198755)
                    & ? [Vvar__2__t2__198756] :
                        ( cPLF_2eStlc_2eSTLC_2etm___24t(Vvar__2__t2__198756)
                        & ? [Vvar__3__t3__198757] :
                            ( cPLF_2eStlc_2eSTLC_2etm___24t(Vvar__3__t3__198757)
                            & cPLF_2eStlcProp_2eSTLCProp_2eappears__free__in___24a2(Vvar__0__x__198754,Vvar__1__t1__198755)
                            & Vvar__1___24Anonymous__198737 = cPLF_2eStlc_2eSTLC_2etest___24a3(Vvar__1__t1__198755,Vvar__2__t2__198756,Vvar__3__t3__198757)
                            & Vvar__0___24Anonymous__198736 = Vvar__0__x__198754 ) ) ) )
            | ? [Vvar__0__x__198759] :
                ( cCoq_2eStrings_2eString_2estring___24t(Vvar__0__x__198759)
                & ? [Vvar__1__t1__198760] :
                    ( cPLF_2eStlc_2eSTLC_2etm___24t(Vvar__1__t1__198760)
                    & ? [Vvar__2__t2__198761] :
                        ( cPLF_2eStlc_2eSTLC_2etm___24t(Vvar__2__t2__198761)
                        & ? [Vvar__3__t3__198762] :
                            ( cPLF_2eStlc_2eSTLC_2etm___24t(Vvar__3__t3__198762)
                            & cPLF_2eStlcProp_2eSTLCProp_2eappears__free__in___24a2(Vvar__0__x__198759,Vvar__2__t2__198761)
                            & Vvar__1___24Anonymous__198737 = cPLF_2eStlc_2eSTLC_2etest___24a3(Vvar__1__t1__198760,Vvar__2__t2__198761,Vvar__3__t3__198762)
                            & Vvar__0___24Anonymous__198736 = Vvar__0__x__198759 ) ) ) )
            | ? [Vvar__0__x__198764] :
                ( cCoq_2eStrings_2eString_2estring___24t(Vvar__0__x__198764)
                & ? [Vvar__1__t1__198765] :
                    ( cPLF_2eStlc_2eSTLC_2etm___24t(Vvar__1__t1__198765)
                    & ? [Vvar__2__t2__198766] :
                        ( cPLF_2eStlc_2eSTLC_2etm___24t(Vvar__2__t2__198766)
                        & ? [Vvar__3__t3__198767] :
                            ( cPLF_2eStlc_2eSTLC_2etm___24t(Vvar__3__t3__198767)
                            & cPLF_2eStlcProp_2eSTLCProp_2eappears__free__in___24a2(Vvar__0__x__198764,Vvar__3__t3__198767)
                            & Vvar__1___24Anonymous__198737 = cPLF_2eStlc_2eSTLC_2etest___24a3(Vvar__1__t1__198765,Vvar__2__t2__198766,Vvar__3__t3__198767)
                            & Vvar__0___24Anonymous__198736 = Vvar__0__x__198764 ) ) ) ) ) ) ) ) ).

fof('$_inversion_PLF.Types.bvalue',axiom,
    ! [Vvar__0___24Anonymous__200821] :
      ( cPLF_2eTypes_2etm___24t(Vvar__0___24Anonymous__200821)
     => ( cPLF_2eTypes_2ebvalue___24a1(Vvar__0___24Anonymous__200821)
       => ( Vvar__0___24Anonymous__200821 = cPLF_2eTypes_2etru
          | Vvar__0___24Anonymous__200821 = cPLF_2eTypes_2efls ) ) ) ).

fof('$_inversion_PLF.Types.nvalue',axiom,
    ! [Vvar__0___24Anonymous__200823] :
      ( cPLF_2eTypes_2etm___24t(Vvar__0___24Anonymous__200823)
     => ( cPLF_2eTypes_2envalue___24a1(Vvar__0___24Anonymous__200823)
       => ( Vvar__0___24Anonymous__200823 = cPLF_2eTypes_2ezro
          | ? [Vvar__0__t__200825] :
              ( cPLF_2eTypes_2etm___24t(Vvar__0__t__200825)
              & cPLF_2eTypes_2envalue___24a1(Vvar__0__t__200825)
              & Vvar__0___24Anonymous__200823 = cPLF_2eTypes_2escc___24a1(Vvar__0__t__200825) ) ) ) ) ).

fof('$_inversion_PLF.Types.step',axiom,
    ! [Vvar__0___24Anonymous__200827,Vvar__1___24Anonymous__200828] :
      ( cPLF_2eTypes_2etm___24t(Vvar__0___24Anonymous__200827)
     => ( cPLF_2eTypes_2etm___24t(Vvar__1___24Anonymous__200828)
       => ( cPLF_2eTypes_2estep___24a2(Vvar__0___24Anonymous__200827,Vvar__1___24Anonymous__200828)
         => ( ? [Vvar__0__t1__200830] :
                ( cPLF_2eTypes_2etm___24t(Vvar__0__t1__200830)
                & ? [Vvar__1__t2__200831] :
                    ( cPLF_2eTypes_2etm___24t(Vvar__1__t2__200831)
                    & Vvar__1___24Anonymous__200828 = Vvar__0__t1__200830
                    & Vvar__0___24Anonymous__200827 = cPLF_2eTypes_2etest___24a3(cPLF_2eTypes_2etru,Vvar__0__t1__200830,Vvar__1__t2__200831) ) )
            | ? [Vvar__0__t1__200832] :
                ( cPLF_2eTypes_2etm___24t(Vvar__0__t1__200832)
                & ? [Vvar__1__t2__200833] :
                    ( cPLF_2eTypes_2etm___24t(Vvar__1__t2__200833)
                    & Vvar__1___24Anonymous__200828 = Vvar__1__t2__200833
                    & Vvar__0___24Anonymous__200827 = cPLF_2eTypes_2etest___24a3(cPLF_2eTypes_2efls,Vvar__0__t1__200832,Vvar__1__t2__200833) ) )
            | ? [Vvar__0__t1__200834] :
                ( cPLF_2eTypes_2etm___24t(Vvar__0__t1__200834)
                & ? [Vvar__1__t1_27__200835] :
                    ( cPLF_2eTypes_2etm___24t(Vvar__1__t1_27__200835)
                    & ? [Vvar__2__t2__200836] :
                        ( cPLF_2eTypes_2etm___24t(Vvar__2__t2__200836)
                        & ? [Vvar__3__t3__200837] :
                            ( cPLF_2eTypes_2etm___24t(Vvar__3__t3__200837)
                            & cPLF_2eTypes_2estep___24a2(Vvar__0__t1__200834,Vvar__1__t1_27__200835)
                            & Vvar__1___24Anonymous__200828 = cPLF_2eTypes_2etest___24a3(Vvar__1__t1_27__200835,Vvar__2__t2__200836,Vvar__3__t3__200837)
                            & Vvar__0___24Anonymous__200827 = cPLF_2eTypes_2etest___24a3(Vvar__0__t1__200834,Vvar__2__t2__200836,Vvar__3__t3__200837) ) ) ) )
            | ? [Vvar__0__t1__200839] :
                ( cPLF_2eTypes_2etm___24t(Vvar__0__t1__200839)
                & ? [Vvar__1__t1_27__200840] :
                    ( cPLF_2eTypes_2etm___24t(Vvar__1__t1_27__200840)
                    & cPLF_2eTypes_2estep___24a2(Vvar__0__t1__200839,Vvar__1__t1_27__200840)
                    & Vvar__1___24Anonymous__200828 = cPLF_2eTypes_2escc___24a1(Vvar__1__t1_27__200840)
                    & Vvar__0___24Anonymous__200827 = cPLF_2eTypes_2escc___24a1(Vvar__0__t1__200839) ) )
            | ( Vvar__1___24Anonymous__200828 = cPLF_2eTypes_2ezro
              & Vvar__0___24Anonymous__200827 = cPLF_2eTypes_2eprd___24a1(cPLF_2eTypes_2ezro) )
            | ? [Vvar__0__t1__200842] :
                ( cPLF_2eTypes_2etm___24t(Vvar__0__t1__200842)
                & cPLF_2eTypes_2envalue___24a1(Vvar__0__t1__200842)
                & Vvar__1___24Anonymous__200828 = Vvar__0__t1__200842
                & Vvar__0___24Anonymous__200827 = cPLF_2eTypes_2eprd___24a1(cPLF_2eTypes_2escc___24a1(Vvar__0__t1__200842)) )
            | ? [Vvar__0__t1__200844] :
                ( cPLF_2eTypes_2etm___24t(Vvar__0__t1__200844)
                & ? [Vvar__1__t1_27__200845] :
                    ( cPLF_2eTypes_2etm___24t(Vvar__1__t1_27__200845)
                    & cPLF_2eTypes_2estep___24a2(Vvar__0__t1__200844,Vvar__1__t1_27__200845)
                    & Vvar__1___24Anonymous__200828 = cPLF_2eTypes_2eprd___24a1(Vvar__1__t1_27__200845)
                    & Vvar__0___24Anonymous__200827 = cPLF_2eTypes_2eprd___24a1(Vvar__0__t1__200844) ) )
            | ( Vvar__1___24Anonymous__200828 = cPLF_2eTypes_2etru
              & Vvar__0___24Anonymous__200827 = cPLF_2eTypes_2eiszro___24a1(cPLF_2eTypes_2ezro) )
            | ? [Vvar__0__t1__200847] :
                ( cPLF_2eTypes_2etm___24t(Vvar__0__t1__200847)
                & cPLF_2eTypes_2envalue___24a1(Vvar__0__t1__200847)
                & Vvar__1___24Anonymous__200828 = cPLF_2eTypes_2efls
                & Vvar__0___24Anonymous__200827 = cPLF_2eTypes_2eiszro___24a1(cPLF_2eTypes_2escc___24a1(Vvar__0__t1__200847)) )
            | ? [Vvar__0__t1__200849] :
                ( cPLF_2eTypes_2etm___24t(Vvar__0__t1__200849)
                & ? [Vvar__1__t1_27__200850] :
                    ( cPLF_2eTypes_2etm___24t(Vvar__1__t1_27__200850)
                    & cPLF_2eTypes_2estep___24a2(Vvar__0__t1__200849,Vvar__1__t1_27__200850)
                    & Vvar__1___24Anonymous__200828 = cPLF_2eTypes_2eiszro___24a1(Vvar__1__t1_27__200850)
                    & Vvar__0___24Anonymous__200827 = cPLF_2eTypes_2eiszro___24a1(Vvar__0__t1__200849) ) ) ) ) ) ) ).

fof('$_inversion_PLF.Types.tm',axiom,
    ! [VX199770] :
      ( cPLF_2eTypes_2etm___24t(VX199770)
     => ( VX199770 = cPLF_2eTypes_2etru
        | VX199770 = cPLF_2eTypes_2efls
        | ? [Vvar__0___24Anonymous__199771] :
            ( cPLF_2eTypes_2etm___24t(Vvar__0___24Anonymous__199771)
            & ? [Vvar__1___24Anonymous__199772] :
                ( cPLF_2eTypes_2etm___24t(Vvar__1___24Anonymous__199772)
                & ? [Vvar__2___24Anonymous__199773] :
                    ( cPLF_2eTypes_2etm___24t(Vvar__2___24Anonymous__199773)
                    & VX199770 = cPLF_2eTypes_2etest___24a3(Vvar__0___24Anonymous__199771,Vvar__1___24Anonymous__199772,Vvar__2___24Anonymous__199773) ) ) )
        | VX199770 = cPLF_2eTypes_2ezro
        | ? [Vvar__0___24Anonymous__199774] :
            ( cPLF_2eTypes_2etm___24t(Vvar__0___24Anonymous__199774)
            & VX199770 = cPLF_2eTypes_2escc___24a1(Vvar__0___24Anonymous__199774) )
        | ? [Vvar__0___24Anonymous__199775] :
            ( cPLF_2eTypes_2etm___24t(Vvar__0___24Anonymous__199775)
            & VX199770 = cPLF_2eTypes_2eprd___24a1(Vvar__0___24Anonymous__199775) )
        | ? [Vvar__0___24Anonymous__199776] :
            ( cPLF_2eTypes_2etm___24t(Vvar__0___24Anonymous__199776)
            & VX199770 = cPLF_2eTypes_2eiszro___24a1(Vvar__0___24Anonymous__199776) ) ) ) ).

fof('$_inversion_PLF.Types.ty',axiom,
    ! [VX199825] :
      ( cPLF_2eTypes_2ety___24t(VX199825)
     => ( VX199825 = cPLF_2eTypes_2eBool
        | VX199825 = cPLF_2eTypes_2eNat ) ) ).

fof('$_lam_102430',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
      ( c_24__lam__102430___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_102438',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
      ( c_24__lam__102438___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_102446',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
      ( c_24__lam__102446___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_102454',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
      ( c_24__lam__102454___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_108016',axiom,
    ! [Vv__CANONICAL__0] : c_24__lam__108016___24a1(Vv__CANONICAL__0) = Vv__CANONICAL__0 ).

fof('$_lam_112898',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] : c_24__lam__112898___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = happ(Vv__CANONICAL__2,Vv__CANONICAL__3) ).

fof('$_lam_112906',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] : c_24__lam__112906___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = happ(Vv__CANONICAL__2,Vv__CANONICAL__3) ).

fof('$_lam_168764',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] :
      ( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__3)
     => ( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__5)
       => ( ( cPLF_2eMaps_2eeqb__string___24a2(Vv__CANONICAL__3,Vv__CANONICAL__5) = cCoq_2eInit_2eDatatypes_2etrue
            & c_24__lam__168764___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = Vv__CANONICAL__4 )
          | ( cPLF_2eMaps_2eeqb__string___24a2(Vv__CANONICAL__3,Vv__CANONICAL__5) = cCoq_2eInit_2eDatatypes_2efalse
            & c_24__lam__168764___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = happ(Vv__CANONICAL__2,Vv__CANONICAL__5) ) ) ) ) ).

fof('$_lam_1722',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11] : c_24__lam__1722___24a12(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,Vv__CANONICAL__11) = c_24__let__11__subst__l__1650___24a10(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__7,Vv__CANONICAL__8,Vv__CANONICAL__9,Vv__CANONICAL__10,cCoq_2esetoid__ring_2eRing__polynom_2enorm__aux___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__11)) ).

fof('$_lam_2102',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__2102___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = Vv__CANONICAL__0 ).

fof('$_lam_2109',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] : c_24__lam__2109___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vv__CANONICAL__1 ).

fof('$_lam_2119',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2] : c_24__lam__2119___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eVectors_2eVectorDef_2et___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) ).

fof('$_lam_2126',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] : c_24__lam__2126___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vv__CANONICAL__3 ).

fof('$_lam_218144',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8] : c_24__lam__218144___24a9(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8) = cCoq_2eInit_2eWf_2eFix__F__2___24a8(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__7,Vv__CANONICAL__8,cCoq_2eInit_2eWf_2eAcc__inv___24a4(cCoq_2eInit_2eDatatypes_2eprod___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),Vv__CANONICAL__2,cCoq_2eInit_2eDatatypes_2epair___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__5,Vv__CANONICAL__6),cCoq_2eInit_2eDatatypes_2epair___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__7,Vv__CANONICAL__8))) ).

fof('$_lam_79669',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5] :
      ( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__3)
     => ( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__5)
       => ( ( cPLF_2eMaps_2eeqb__string___24a2(Vv__CANONICAL__3,Vv__CANONICAL__5) = cCoq_2eInit_2eDatatypes_2etrue
            & c_24__lam__79669___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = Vv__CANONICAL__4 )
          | ( cPLF_2eMaps_2eeqb__string___24a2(Vv__CANONICAL__3,Vv__CANONICAL__5) = cCoq_2eInit_2eDatatypes_2efalse
            & c_24__lam__79669___24a6(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5) = happ(Vv__CANONICAL__2,Vv__CANONICAL__5) ) ) ) ) ).

fof('$_prop_112334',axiom,
    ! [V0__n,V1__m] :
      ( p(c_24__prop__112334___24a2(V0__n,V1__m))
    <=> V0__n = V1__m ) ).

fof('$_prop_154310',axiom,
    ! [V0__x,V1__y] :
      ( p(c_24__prop__154310___24a2(V0__x,V1__y))
    <=> V0__x = V1__y ) ).

fof('$_prop_154311',axiom,
    ! [V0__x,V1__y] :
      ( p(c_24__prop__154311___24a2(V0__x,V1__y))
    <=> V0__x != V1__y ) ).

fof('$_prop_154312',axiom,
    ! [V0__x,V1__y] :
      ( p(c_24__prop__154312___24a2(V0__x,V1__y))
    <=> V0__x = V1__y ) ).

fof('$_prop_154313',axiom,
    ! [V0__x,V1__y] :
      ( p(c_24__prop__154313___24a2(V0__x,V1__y))
    <=> V0__x != V1__y ) ).

fof('$_prop_168300',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
      ( p(c_24__prop__168300___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
    <=> Vv__CANONICAL__0 = Vv__CANONICAL__1 ) ).

fof('$_prop_168301',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
      ( p(c_24__prop__168301___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
    <=> Vv__CANONICAL__0 = Vv__CANONICAL__1 ) ).

fof('$_prop_168302',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
      ( p(c_24__prop__168302___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
    <=> Vv__CANONICAL__0 = Vv__CANONICAL__1 ) ).

fof('$_prop_168303',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
      ( p(c_24__prop__168303___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
    <=> Vv__CANONICAL__0 = Vv__CANONICAL__1 ) ).

fof('$_prop_168309',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
      ( p(c_24__prop__168309___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
    <=> Vv__CANONICAL__0 = Vv__CANONICAL__1 ) ).

fof('$_prop_198720',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
      ( p(c_24__prop__198720___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1))
    <=> Vv__CANONICAL__0 = Vv__CANONICAL__1 ) ).

fof('$_prop_92094',axiom,
    ! [Vvar__0___24Anonymous__92070,Vvar__0__S__92072,Vvar__1__x__92073,Vvar__2__y__92074] :
      ( p(c_24__prop__92094___24a4(Vvar__0___24Anonymous__92070,Vvar__0__S__92072,Vvar__1__x__92073,Vvar__2__y__92074))
    <=> Vvar__1__x__92073 = Vvar__2__y__92074 ) ).

fof('$_prop_92095',axiom,
    ! [Vvar__0___24Anonymous__92070,Vvar__0__x__92075,Vvar__1__y__92076] :
      ( p(c_24__prop__92095___24a3(Vvar__0___24Anonymous__92070,Vvar__0__x__92075,Vvar__1__y__92076))
    <=> Vvar__0__x__92075 = Vvar__1__y__92076 ) ).

fof('$_prop_92096',axiom,
    ! [Vvar__0___24Anonymous__92070,Vvar__0__x__92077,Vvar__1__s__92078] :
      ( p(c_24__prop__92096___24a3(Vvar__0___24Anonymous__92070,Vvar__0__x__92077,Vvar__1__s__92078))
    <=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(Vvar__0__x__92077,Vvar__1__s__92078) = cCoq_2eInit_2eDatatypes_2etrue ) ).

fof('$_prop_92097',axiom,
    ! [Vvar__0___24Anonymous__92070,Vvar__0__P__92079,Vvar__1__Q__92080] :
      ( p(c_24__prop__92097___24a3(Vvar__0___24Anonymous__92070,Vvar__0__P__92079,Vvar__1__Q__92080))
    <=> ( p(Vvar__0__P__92079)
        & p(Vvar__1__Q__92080) ) ) ).

fof('$_prop_92098',axiom,
    ! [Vvar__0___24Anonymous__92070,Vvar__0__P__92083,Vvar__1__Q__92084] :
      ( p(c_24__prop__92098___24a3(Vvar__0___24Anonymous__92070,Vvar__0__P__92083,Vvar__1__Q__92084))
    <=> ( p(Vvar__0__P__92083)
        | p(Vvar__1__Q__92084) ) ) ).

fof('$_prop_92099',axiom,
    ! [Vvar__0___24Anonymous__92070,Vvar__0__P__92087,Vvar__1__Q__92088] :
      ( p(c_24__prop__92099___24a3(Vvar__0___24Anonymous__92070,Vvar__0__P__92087,Vvar__1__Q__92088))
    <=> ( p(Vvar__0__P__92087)
       => p(Vvar__1__Q__92088) ) ) ).

fof('$_prop_92100',axiom,
    ! [Vvar__0___24Anonymous__92070,Vvar__0__P__92092] :
      ( p(c_24__prop__92100___24a2(Vvar__0___24Anonymous__92070,Vvar__0__P__92092))
    <=> ~ p(Vvar__0__P__92092) ) ).

fof('$_prop_92114',axiom,
    ! [Vvar__0___24Anonymous__92101,Vvar__0__s__92105] :
      ( p(c_24__prop__92114___24a2(Vvar__0___24Anonymous__92101,Vvar__0__s__92105))
    <=> ! [Vvar__1__a__92106] :
          ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vvar__1__a__92106)
         => ~ cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(Vvar__1__a__92106,Vvar__0__s__92105) ) ) ).

fof('$_prop_92115',axiom,
    ! [Vvar__0___24Anonymous__92101,Vvar__0__s1__92107,Vvar__1__s2__92108] :
      ( p(c_24__prop__92115___24a3(Vvar__0___24Anonymous__92101,Vvar__0__s1__92107,Vvar__1__s2__92108))
    <=> ! [Vvar__2__a__92109] :
          ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vvar__2__a__92109)
         => ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(Vvar__2__a__92109,Vvar__0__s1__92107)
           => cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(Vvar__2__a__92109,Vvar__1__s2__92108) ) ) ) ).

fof('$_prop_92116',axiom,
    ! [Vvar__0___24Anonymous__92101,Vvar__0__s1__92111,Vvar__1__s2__92112] :
      ( p(c_24__prop__92116___24a3(Vvar__0___24Anonymous__92101,Vvar__0__s1__92111,Vvar__1__s2__92112))
    <=> ! [Vvar__2__a__92113] :
          ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vvar__2__a__92113)
         => ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(Vvar__2__a__92113,Vvar__0__s1__92111)
          <=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(Vvar__2__a__92113,Vvar__1__s2__92112) ) ) ) ).

fof('$_prop_94743',axiom,
    ! [V0__A,V1__B] :
      ( p(c_24__prop__94743___24a2(V0__A,V1__B))
    <=> ( p(V0__A)
        & p(V1__B) ) ) ).

fof('$_type_100304',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__100305] :
      ( c_24__type__100304___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__100305)
    <=> ! [Vv__CANONICAL__22] :
          ( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
         => ! [Vv__CANONICAL__23] :
              ( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
             => t(happ(happ(Vvar__100305,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__9) ) ) ) ).

fof('$_type_100627',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__100628] :
      ( c_24__type__100627___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__100628)
    <=> ! [Vv__CANONICAL__22] :
          ( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
         => t(happ(Vvar__100628,Vv__CANONICAL__22),Vv__CANONICAL__9) ) ) ).

fof('$_type_100973',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__100974] :
      ( c_24__type__100973___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__100974)
    <=> ! [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__100974,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).

fof('$_type_101319',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__101320] :
      ( c_24__type__101319___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__101320)
    <=> ! [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__101320,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).

fof('$_type_101642',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__101643] :
      ( c_24__type__101642___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__101643)
    <=> ! [Vv__CANONICAL__22] :
          ( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
         => t(happ(Vvar__101643,Vv__CANONICAL__22),Vv__CANONICAL__0) ) ) ).

fof('$_type_101965',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__101966] :
      ( c_24__type__101965___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__101966)
    <=> ! [Vv__CANONICAL__22] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__22)
         => t(happ(Vvar__101966,Vv__CANONICAL__22),Vv__CANONICAL__19) ) ) ).

fof('$_type_102311',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__102312] :
      ( c_24__type__102311___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__102312)
    <=> ! [Vv__CANONICAL__22] :
          ( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__23] :
              ( t(Vv__CANONICAL__23,Vv__CANONICAL__19)
             => t(happ(happ(Vvar__102312,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_102413',axiom,
    ! [Vvar__102414] :
      ( c_24__type__102413___24t(Vvar__102414)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__1859___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__1859___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( cType___24t(Vv__CANONICAL__3)
                     => ! [Vv__CANONICAL__4] :
                          ( c_24__type__80902___24t(Vv__CANONICAL__0,Vv__CANONICAL__3,Vv__CANONICAL__4)
                         => ! [Vv__CANONICAL__5] :
                              ( cCoq_2emicromega_2eRingMicromega_2ePolEnv___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
                             => ! [Vv__CANONICAL__6] :
                                  ( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(Vv__CANONICAL__3,Vv__CANONICAL__6)
                                 => t(happ(happ(happ(happ(happ(happ(happ(Vvar__102414,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_102497',axiom,
    ! [Vvar__102498] :
      ( c_24__type__102497___24t(Vvar__102498)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__76843___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( c_24__type__76843___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
                     => ! [Vv__CANONICAL__4] :
                          ( c_24__type__76843___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__102498,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ) ) ) ) ) ).

fof('$_type_102623',axiom,
    ! [Vvar__102624] :
      ( c_24__type__102623___24t(Vvar__102624)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__1859___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( c_24__type__1859___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
                     => ! [Vv__CANONICAL__4] :
                          ( c_24__type__76843___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
                         => ! [Vv__CANONICAL__5] :
                              ( c_24__type__76843___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
                             => ! [Vv__CANONICAL__6] :
                                  ( c_24__type__76843___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
                                 => ! [Vv__CANONICAL__7] :
                                      ( cType___24t(Vv__CANONICAL__7)
                                     => ! [Vv__CANONICAL__8] :
                                          ( c_24__type__80902___24t(Vv__CANONICAL__0,Vv__CANONICAL__7,Vv__CANONICAL__8)
                                         => ! [Vv__CANONICAL__9] :
                                              ( cCoq_2emicromega_2eRingMicromega_2ePolEnv___24t(Vv__CANONICAL__0,Vv__CANONICAL__9)
                                             => ! [Vv__CANONICAL__10] :
                                                  ( cCoq_2emicromega_2eRingMicromega_2eNFormula___24t(Vv__CANONICAL__7,Vv__CANONICAL__10)
                                                 => cProp___24t(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__102624,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__10)) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('$_type_102887',axiom,
    ! [Vvar__102888] :
      ( c_24__type__102887___24t(Vvar__102888)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__1372___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( c_24__type__1372___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
                     => ! [Vv__CANONICAL__4] :
                          ( cCoq_2emicromega_2eRingMicromega_2eNFormula___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
                         => cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(happ(happ(happ(Vvar__102888,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).

fof('$_type_104035',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__104036] :
      ( c_24__type__104035___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__104036)
    <=> ! [Vv__CANONICAL__17] :
          ( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__18] :
              ( t(Vv__CANONICAL__18,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__104036,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_104248',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__104249] :
      ( c_24__type__104248___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__104249)
    <=> ! [Vv__CANONICAL__17] :
          ( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__18] :
              ( t(Vv__CANONICAL__18,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__104249,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_104461',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__104462] :
      ( c_24__type__104461___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__104462)
    <=> ! [Vv__CANONICAL__17] :
          ( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__18] :
              ( t(Vv__CANONICAL__18,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__104462,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_104656',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__104657] :
      ( c_24__type__104656___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__104657)
    <=> ! [Vv__CANONICAL__17] :
          ( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
         => t(happ(Vvar__104657,Vv__CANONICAL__17),Vv__CANONICAL__0) ) ) ).

fof('$_type_104869',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__104870] :
      ( c_24__type__104869___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__104870)
    <=> ! [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__104870,Vv__CANONICAL__17),Vv__CANONICAL__18)) ) ) ) ).

fof('$_type_105082',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__105083] :
      ( c_24__type__105082___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__105083)
    <=> ! [Vv__CANONICAL__17] :
          ( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
         => ! [Vv__CANONICAL__18] :
              ( t(Vv__CANONICAL__18,Vv__CANONICAL__8)
             => t(happ(happ(Vvar__105083,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__8) ) ) ) ).

fof('$_type_105295',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__105296] :
      ( c_24__type__105295___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__105296)
    <=> ! [Vv__CANONICAL__17] :
          ( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
         => ! [Vv__CANONICAL__18] :
              ( t(Vv__CANONICAL__18,Vv__CANONICAL__8)
             => t(happ(happ(Vvar__105296,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__8) ) ) ) ).

fof('$_type_105508',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__105509] :
      ( c_24__type__105508___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__105509)
    <=> ! [Vv__CANONICAL__17] :
          ( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
         => ! [Vv__CANONICAL__18] :
              ( t(Vv__CANONICAL__18,Vv__CANONICAL__8)
             => t(happ(happ(Vvar__105509,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__8) ) ) ) ).

fof('$_type_105703',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__105704] :
      ( c_24__type__105703___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__105704)
    <=> ! [Vv__CANONICAL__17] :
          ( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
         => t(happ(Vvar__105704,Vv__CANONICAL__17),Vv__CANONICAL__8) ) ) ).

fof('$_type_105916',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__105917] :
      ( c_24__type__105916___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__105917)
    <=> ! [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__105917,Vv__CANONICAL__17),Vv__CANONICAL__18)) ) ) ) ).

fof('$_type_106111',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__106112] :
      ( c_24__type__106111___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__106112)
    <=> ! [Vv__CANONICAL__17] :
          ( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
         => t(happ(Vvar__106112,Vv__CANONICAL__17),Vv__CANONICAL__0) ) ) ).

fof('$_type_106855',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__106856] :
      ( c_24__type__106855___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__106856)
    <=> ! [Vv__CANONICAL__7] :
          ( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__8] :
              ( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__106856,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_106899',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__106900] :
      ( c_24__type__106899___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__106900)
    <=> ! [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__106900,Vv__CANONICAL__7),Vv__CANONICAL__8)) ) ) ) ).

fof('$_type_106935',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__106936] :
      ( c_24__type__106935___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__106936)
    <=> ! [Vv__CANONICAL__7] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__7)
         => t(happ(Vvar__106936,Vv__CANONICAL__7),Vv__CANONICAL__4) ) ) ).

fof('$_type_106979',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__106980] :
      ( c_24__type__106979___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__106980)
    <=> ! [Vv__CANONICAL__7] :
          ( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__8] :
              ( t(Vv__CANONICAL__8,Vv__CANONICAL__4)
             => t(happ(happ(Vvar__106980,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_107073',axiom,
    ! [Vvar__107074] :
      ( c_24__type__107073___24t(Vvar__107074)
    <=> ! [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__107074,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_1074',axiom,
    ! [Vvar__1075] :
      ( c_24__type__1074___24t(Vvar__1075)
    <=> ! [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__1075,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_108018',axiom,
    ! [Vvar__108019] :
      ( c_24__type__108018___24t(Vvar__108019)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2emicromega_2eRingMicromega_2ePolEnv___24t(cCoq_2eNumbers_2eBinNums_2eZ,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2emicromega_2eRingMicromega_2eNFormula___24t(cCoq_2eNumbers_2eBinNums_2eZ,Vv__CANONICAL__1)
             => cProp___24t(happ(happ(Vvar__108019,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_108021',axiom,
    ! [Vvar__108022] :
      ( c_24__type__108021___24t(Vvar__108022)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2emicromega_2eEnvRing_2ePol___24t(cCoq_2eNumbers_2eBinNums_2eZ,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2emicromega_2eEnvRing_2ePol___24t(cCoq_2eNumbers_2eBinNums_2eZ,Vv__CANONICAL__1)
             => cCoq_2emicromega_2eEnvRing_2ePol___24t(cCoq_2eNumbers_2eBinNums_2eZ,happ(happ(Vvar__108022,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_108024',axiom,
    ! [Vvar__108025] :
      ( c_24__type__108024___24t(Vvar__108025)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2emicromega_2eRingMicromega_2ePolEnv___24t(cCoq_2eNumbers_2eBinNums_2eZ,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(cCoq_2eNumbers_2eBinNums_2eZ,Vv__CANONICAL__1)
             => cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(happ(Vvar__108025,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_108195',axiom,
    ! [Vvar__108196] :
      ( c_24__type__108195___24t(Vvar__108196)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2emicromega_2eRingMicromega_2eOp1___24t(Vv__CANONICAL__0)
         => cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__108196,Vv__CANONICAL__0)) ) ) ).

fof('$_type_1087',axiom,
    ! [Vvar__1088] :
      ( c_24__type__1087___24t(Vvar__1088)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
         => cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(Vvar__1088,Vv__CANONICAL__0)) ) ) ).

fof('$_type_109200',axiom,
    ! [Vvar__109201] :
      ( c_24__type__109200___24t(Vvar__109201)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
         => cType___24t(happ(Vvar__109201,Vv__CANONICAL__0)) ) ) ).

fof('$_type_109241',axiom,
    ! [Vvar__109242] :
      ( c_24__type__109241___24t(Vvar__109242)
    <=> ! [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__109242,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_109349',axiom,
    ! [Vvar__109350] :
      ( c_24__type__109349___24t(Vvar__109350)
    <=> ! [Vv__CANONICAL__0] :
          ( cPLF_2eStlc_2eSTLC_2ety___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cPLF_2eStlc_2eSTLC_2ety___24t(Vv__CANONICAL__1)
             => cPLF_2eStlc_2eSTLC_2ety___24t(happ(happ(Vvar__109350,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_109351',axiom,
    ! [Vvar__109352] :
      ( c_24__type__109351___24t(Vvar__109352)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__0)
         => cPLF_2eStlc_2eSTLC_2etm___24t(happ(Vvar__109352,Vv__CANONICAL__0)) ) ) ).

fof('$_type_109354',axiom,
    ! [Vvar__109355] :
      ( c_24__type__109354___24t(Vvar__109355)
    <=> ! [Vv__CANONICAL__0] :
          ( cPLF_2eStlc_2eSTLC_2etm___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cPLF_2eStlc_2eSTLC_2etm___24t(Vv__CANONICAL__1)
             => cPLF_2eStlc_2eSTLC_2etm___24t(happ(happ(Vvar__109355,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_109359',axiom,
    ! [Vvar__109360] :
      ( c_24__type__109359___24t(Vvar__109360)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cPLF_2eStlc_2eSTLC_2ety___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( cPLF_2eStlc_2eSTLC_2etm___24t(Vv__CANONICAL__2)
                 => cPLF_2eStlc_2eSTLC_2etm___24t(happ(happ(happ(Vvar__109360,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_109364',axiom,
    ! [Vvar__109365] :
      ( c_24__type__109364___24t(Vvar__109365)
    <=> ! [Vv__CANONICAL__0] :
          ( cPLF_2eStlc_2eSTLC_2etm___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cPLF_2eStlc_2eSTLC_2etm___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( cPLF_2eStlc_2eSTLC_2etm___24t(Vv__CANONICAL__2)
                 => cPLF_2eStlc_2eSTLC_2etm___24t(happ(happ(happ(Vvar__109365,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_1094',axiom,
    ! [Vvar__1095] :
      ( c_24__type__1094___24t(Vvar__1095)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
         => cCoq_2eNumbers_2eBinNums_2eN___24t(happ(Vvar__1095,Vv__CANONICAL__0)) ) ) ).

fof('$_type_109400',axiom,
    ! [Vvar__109401] :
      ( c_24__type__109400___24t(Vvar__109401)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cPLF_2eStlc_2eSTLC_2etm___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( cPLF_2eStlc_2eSTLC_2etm___24t(Vv__CANONICAL__2)
                 => cPLF_2eStlc_2eSTLC_2etm___24t(happ(happ(happ(Vvar__109401,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_1107',axiom,
    ! [Vvar__1108] :
      ( c_24__type__1107___24t(Vvar__1108)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
         => cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__1108,Vv__CANONICAL__0)) ) ) ).

fof('$_type_1117',axiom,
    ! [Vvar__1118] :
      ( c_24__type__1117___24t(Vvar__1118)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cType___24t(Vv__CANONICAL__1)
             => cType___24t(happ(happ(Vvar__1118,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_112801',axiom,
    ! [Vvar__112802] :
      ( c_24__type__112801___24t(Vvar__112802)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__112802,Vv__CANONICAL__0)) ) ) ).

fof('$_type_112806',axiom,
    ! [Vvar__112807] :
      ( c_24__type__112806___24t(Vvar__112807)
    <=> ! [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__112807,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_112833',axiom,
    ! [Vvar__112834] :
      ( c_24__type__112833___24t(Vvar__112834)
    <=> ! [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__112834,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_type_112884',axiom,
    ! [Vv__CANONICAL__0,Vvar__112885] :
      ( c_24__type__112884___24t(Vv__CANONICAL__0,Vvar__112885)
    <=> ! [Vv__CANONICAL__1] :
          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
         => t(happ(Vvar__112885,Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ).

fof('$_type_112890',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__112891] :
      ( c_24__type__112890___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__112891)
    <=> ! [Vv__CANONICAL__2] :
          ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
         => t(happ(Vvar__112891,Vv__CANONICAL__2),happ(Vv__CANONICAL__1,Vv__CANONICAL__2)) ) ) ).

fof('$_type_112932',axiom,
    ! [Vvar__112933] :
      ( c_24__type__112932___24t(Vvar__112933)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__1859___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( c_24__type__1859___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__112933,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).

fof('$_type_112996',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__112997] :
      ( c_24__type__112996___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__112997)
    <=> ! [Vv__CANONICAL__3] :
          ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__4] :
              ( t(Vv__CANONICAL__4,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__5] :
                  ( t(Vv__CANONICAL__5,happ(Vv__CANONICAL__2,Vv__CANONICAL__4))
                 => cProp___24t(happ(happ(happ(Vvar__112997,Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ) ).

fof('$_type_113',axiom,
    ! [Vvar__114] :
      ( c_24__type__113___24t(Vvar__114)
    <=> ! [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__114,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_113005',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__113006] :
      ( c_24__type__113005___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__113006)
    <=> ! [Vv__CANONICAL__2] :
          ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__3] :
              ( t(Vv__CANONICAL__3,happ(Vv__CANONICAL__1,Vv__CANONICAL__2))
             => cType___24t(happ(happ(Vvar__113006,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).

fof('$_type_113037',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__113038] :
      ( c_24__type__113037___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__113038)
    <=> ! [Vv__CANONICAL__4] :
          ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__5] :
              ( t(Vv__CANONICAL__5,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__6] :
                  ( t(Vv__CANONICAL__6,happ(Vv__CANONICAL__2,Vv__CANONICAL__5))
                 => ! [Vv__CANONICAL__7] :
                      ( t(Vv__CANONICAL__7,happ(happ(Vv__CANONICAL__3,Vv__CANONICAL__5),Vv__CANONICAL__6))
                     => cProp___24t(happ(happ(happ(happ(Vvar__113038,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7)) ) ) ) ) ) ).

fof('$_type_113046',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__113047] :
      ( c_24__type__113046___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__113047)
    <=> ! [Vv__CANONICAL__2] :
          ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__3] :
              ( t(Vv__CANONICAL__3,happ(Vv__CANONICAL__1,Vv__CANONICAL__2))
             => cType___24t(happ(happ(Vvar__113047,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).

fof('$_type_113065',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__113066] :
      ( c_24__type__113065___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__113066)
    <=> ! [Vv__CANONICAL__3] :
          ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__4] :
              ( t(Vv__CANONICAL__4,happ(Vv__CANONICAL__1,Vv__CANONICAL__3))
             => ! [Vv__CANONICAL__5] :
                  ( t(Vv__CANONICAL__5,happ(happ(Vv__CANONICAL__2,Vv__CANONICAL__3),Vv__CANONICAL__4))
                 => cType___24t(happ(happ(happ(Vvar__113066,Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ) ).

fof('$_type_113122',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__113123] :
      ( c_24__type__113122___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__113123)
    <=> ! [Vv__CANONICAL__5] :
          ( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__6] :
              ( t(Vv__CANONICAL__6,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__7] :
                  ( t(Vv__CANONICAL__7,happ(Vv__CANONICAL__2,Vv__CANONICAL__6))
                 => ! [Vv__CANONICAL__8] :
                      ( t(Vv__CANONICAL__8,happ(happ(Vv__CANONICAL__3,Vv__CANONICAL__6),Vv__CANONICAL__7))
                     => ! [Vv__CANONICAL__9] :
                          ( t(Vv__CANONICAL__9,happ(happ(happ(Vv__CANONICAL__4,Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__8))
                         => cProp___24t(happ(happ(happ(happ(happ(Vvar__113123,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__9)) ) ) ) ) ) ) ).

fof('$_type_113131',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__113132] :
      ( c_24__type__113131___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__113132)
    <=> ! [Vv__CANONICAL__2] :
          ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__3] :
              ( t(Vv__CANONICAL__3,happ(Vv__CANONICAL__1,Vv__CANONICAL__2))
             => cType___24t(happ(happ(Vvar__113132,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).

fof('$_type_113150',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__113151] :
      ( c_24__type__113150___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__113151)
    <=> ! [Vv__CANONICAL__3] :
          ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__4] :
              ( t(Vv__CANONICAL__4,happ(Vv__CANONICAL__1,Vv__CANONICAL__3))
             => ! [Vv__CANONICAL__5] :
                  ( t(Vv__CANONICAL__5,happ(happ(Vv__CANONICAL__2,Vv__CANONICAL__3),Vv__CANONICAL__4))
                 => cType___24t(happ(happ(happ(Vvar__113151,Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ) ).

fof('$_type_113188',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__113189] :
      ( c_24__type__113188___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__113189)
    <=> ! [Vv__CANONICAL__4] :
          ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__5] :
              ( t(Vv__CANONICAL__5,happ(Vv__CANONICAL__1,Vv__CANONICAL__4))
             => ! [Vv__CANONICAL__6] :
                  ( t(Vv__CANONICAL__6,happ(happ(Vv__CANONICAL__2,Vv__CANONICAL__4),Vv__CANONICAL__5))
                 => ! [Vv__CANONICAL__7] :
                      ( t(Vv__CANONICAL__7,happ(happ(happ(Vv__CANONICAL__3,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6))
                     => cType___24t(happ(happ(happ(happ(Vvar__113189,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7)) ) ) ) ) ) ).

fof('$_type_113281',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__113282] :
      ( c_24__type__113281___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__113282)
    <=> ! [Vv__CANONICAL__6] :
          ( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__7] :
              ( t(Vv__CANONICAL__7,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__8] :
                  ( t(Vv__CANONICAL__8,happ(Vv__CANONICAL__2,Vv__CANONICAL__7))
                 => ! [Vv__CANONICAL__9] :
                      ( t(Vv__CANONICAL__9,happ(happ(Vv__CANONICAL__3,Vv__CANONICAL__7),Vv__CANONICAL__8))
                     => ! [Vv__CANONICAL__10] :
                          ( t(Vv__CANONICAL__10,happ(happ(happ(Vv__CANONICAL__4,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__9))
                         => ! [Vv__CANONICAL__11] :
                              ( t(Vv__CANONICAL__11,happ(happ(happ(happ(Vv__CANONICAL__5,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__10))
                             => cProp___24t(happ(happ(happ(happ(happ(happ(Vvar__113282,Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ) ) ) ) ).

fof('$_type_113285',axiom,
    ! [Vvar__113286] :
      ( c_24__type__113285___24t(Vvar__113286)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
         => cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__113286,Vv__CANONICAL__0)) ) ) ).

fof('$_type_1133',axiom,
    ! [Vvar__1134] :
      ( c_24__type__1133___24t(Vvar__1134)
    <=> ! [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__1134,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_type_113342',axiom,
    ! [Vvar__113343] :
      ( c_24__type__113342___24t(Vvar__113343)
    <=> ! [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__113343,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_113392',axiom,
    ! [Vvar__113393] :
      ( c_24__type__113392___24t(Vvar__113393)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__1859___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__113393,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).

fof('$_type_113413',axiom,
    ! [Vvar__113414] :
      ( c_24__type__113413___24t(Vvar__113414)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__1859___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__113414,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).

fof('$_type_113458',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__113459] :
      ( c_24__type__113458___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__113459)
    <=> ! [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__113459,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).

fof('$_type_113560',axiom,
    ! [Vvar__113561] :
      ( c_24__type__113560___24t(Vvar__113561)
    <=> ! [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__113561,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_113614',axiom,
    ! [Vvar__113615] :
      ( c_24__type__113614___24t(Vvar__113615)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
         => cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(Vvar__113615,Vv__CANONICAL__0)) ) ) ).

fof('$_type_113630',axiom,
    ! [Vvar__113631] :
      ( c_24__type__113630___24t(Vvar__113631)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDecimal_2euint___24t(Vv__CANONICAL__0)
         => cCoq_2eInit_2eDecimal_2eint___24t(happ(Vvar__113631,Vv__CANONICAL__0)) ) ) ).

fof('$_type_113654',axiom,
    ! [Vvar__113655] :
      ( c_24__type__113654___24t(Vvar__113655)
    <=> ! [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__113655,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_113662',axiom,
    ! [Vvar__113663] :
      ( c_24__type__113662___24t(Vvar__113663)
    <=> ! [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__113663,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_type_113665',axiom,
    ! [Vvar__113666] :
      ( c_24__type__113665___24t(Vvar__113666)
    <=> ! [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__113666,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_113699',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__113700] :
      ( c_24__type__113699___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__113700)
    <=> ! [Vv__CANONICAL__2] :
          ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
         => t(happ(Vvar__113700,Vv__CANONICAL__2),happ(Vv__CANONICAL__1,Vv__CANONICAL__2)) ) ) ).

fof('$_type_113704',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__113705] :
      ( c_24__type__113704___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__113705)
    <=> ! [Vv__CANONICAL__2] :
          ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
         => t(happ(Vvar__113705,Vv__CANONICAL__2),happ(Vv__CANONICAL__1,Vv__CANONICAL__2)) ) ) ).

fof('$_type_113710',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__113711] :
      ( c_24__type__113710___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__113711)
    <=> ! [Vv__CANONICAL__2] :
          ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
         => t(happ(Vvar__113711,Vv__CANONICAL__2),happ(Vv__CANONICAL__1,Vv__CANONICAL__2)) ) ) ).

fof('$_type_113715',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__113716] :
      ( c_24__type__113715___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__113716)
    <=> ! [Vv__CANONICAL__2] :
          ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
         => t(happ(Vvar__113716,Vv__CANONICAL__2),happ(Vv__CANONICAL__1,Vv__CANONICAL__2)) ) ) ).

fof('$_type_113822',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__113823] :
      ( c_24__type__113822___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__113823)
    <=> ! [Vv__CANONICAL__3] :
          ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__113823,Vv__CANONICAL__3)) ) ) ).

fof('$_type_113869',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__113870] :
      ( c_24__type__113869___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__113870)
    <=> ! [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__113870,Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ).

fof('$_type_1141',axiom,
    ! [Vvar__1142] :
      ( c_24__type__1141___24t(Vvar__1142)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => cType___24t(happ(Vvar__1142,Vv__CANONICAL__0)) ) ) ).

fof('$_type_114440',axiom,
    ! [Vvar__114441] :
      ( c_24__type__114440___24t(Vvar__114441)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
         => cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__114441,Vv__CANONICAL__0)) ) ) ).

fof('$_type_114845',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__114846] :
      ( c_24__type__114845___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__114846)
    <=> ! [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__114846,Vv__CANONICAL__6),Vv__CANONICAL__7)) ) ) ) ).

fof('$_type_114870',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__114871] :
      ( c_24__type__114870___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__114871)
    <=> ! [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__114871,Vv__CANONICAL__6),Vv__CANONICAL__7)) ) ) ) ).

fof('$_type_114912',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__114913] :
      ( c_24__type__114912___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__114913)
    <=> ! [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__114913,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).

fof('$_type_115061',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__115062] :
      ( c_24__type__115061___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__115062)
    <=> ! [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__115062,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).

fof('$_type_115492',axiom,
    ! [Vvar__115493] :
      ( c_24__type__115492___24t(Vvar__115493)
    <=> ! [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__115493,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_115497',axiom,
    ! [Vvar__115498] :
      ( c_24__type__115497___24t(Vvar__115498)
    <=> ! [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__115498,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_1155',axiom,
    ! [Vvar__1156] :
      ( c_24__type__1155___24t(Vvar__1156)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(Vvar__1156,Vv__CANONICAL__0)) ) ) ).

fof('$_type_115508',axiom,
    ! [Vvar__115509] :
      ( c_24__type__115508___24t(Vvar__115509)
    <=> ! [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__115509,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_115610',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__115611] :
      ( c_24__type__115610___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__115611)
    <=> ! [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__115611,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).

fof('$_type_115650',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__115651] :
      ( c_24__type__115650___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__115651)
    <=> ! [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__115651,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).

fof('$_type_115697',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__115698] :
      ( c_24__type__115697___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__115698)
    <=> ! [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__115698,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).

fof('$_type_115736',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__115737] :
      ( c_24__type__115736___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__115737)
    <=> ! [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__115737,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).

fof('$_type_115771',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__115772] :
      ( c_24__type__115771___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__115772)
    <=> ! [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__115772,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).

fof('$_type_115784',axiom,
    ! [Vvar__115785] :
      ( c_24__type__115784___24t(Vvar__115785)
    <=> ! [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__115785,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_115942',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__115943] :
      ( c_24__type__115942___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__115943)
    <=> ! [Vv__CANONICAL__4] :
          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__4)
         => cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__115943,Vv__CANONICAL__4)) ) ) ).

fof('$_type_115951',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__115952] :
      ( c_24__type__115951___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__115952)
    <=> ! [Vv__CANONICAL__4] :
          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__4)
         => cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__115952,Vv__CANONICAL__4)) ) ) ).

fof('$_type_116',axiom,
    ! [Vvar__117] :
      ( c_24__type__116___24t(Vvar__117)
    <=> ! [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__117,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_1160',axiom,
    ! [Vvar__1161] :
      ( c_24__type__1160___24t(Vvar__1161)
    <=> ! [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__1161,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_1179',axiom,
    ! [Vvar__1180] :
      ( c_24__type__1179___24t(Vvar__1180)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__1180,Vv__CANONICAL__0)) ) ) ).

fof('$_type_1192',axiom,
    ! [Vvar__1193] :
      ( c_24__type__1192___24t(Vvar__1193)
    <=> ! [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__1193,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_120971',axiom,
    ! [Vvar__120972] :
      ( c_24__type__120971___24t(Vvar__120972)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cType___24t(Vv__CANONICAL__1)
             => cCoq_2emicromega_2eTauto_2ecnf___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(Vvar__120972,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_121019',axiom,
    ! [Vvar__121020] :
      ( c_24__type__121019___24t(Vvar__121020)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cType___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( cCoq_2emicromega_2eTauto_2ecnf___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( cCoq_2emicromega_2eTauto_2ecnf___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
                     => cCoq_2emicromega_2eTauto_2ecnf___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(happ(happ(Vvar__121020,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_type_13',axiom,
    ! [Vvar__14] :
      ( c_24__type__13___24t(Vvar__14)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
         => cType___24t(happ(Vvar__14,Vv__CANONICAL__0)) ) ) ).

fof('$_type_1372',axiom,
    ! [Vv__CANONICAL__0,Vvar__1373] :
      ( c_24__type__1372___24t(Vv__CANONICAL__0,Vvar__1373)
    <=> ! [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__1373,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).

fof('$_type_1383',axiom,
    ! [Vvar__1384] :
      ( c_24__type__1383___24t(Vvar__1384)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__1372___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__1384,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_type_151257',axiom,
    ! [Vvar__151258] :
      ( c_24__type__151257___24t(Vvar__151258)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( cCoq_2emicromega_2eEnv_2eEnv___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__3)
                     => t(happ(happ(happ(happ(Vvar__151258,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).

fof('$_type_151260',axiom,
    ! [Vvar__151261] :
      ( c_24__type__151260___24t(Vvar__151261)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2emicromega_2eEnv_2eEnv___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => t(happ(happ(Vvar__151261,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_151265',axiom,
    ! [Vvar__151266] :
      ( c_24__type__151265___24t(Vvar__151266)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2emicromega_2eEnv_2eEnv___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__2)
                 => t(happ(happ(happ(Vvar__151266,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).

fof('$_type_154315',axiom,
    ! [Vvar__154316] :
      ( c_24__type__154315___24t(Vvar__154316)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => cPLF_2eMaps_2epartial__map___24t(Vv__CANONICAL__0,happ(Vvar__154316,Vv__CANONICAL__0)) ) ) ).

fof('$_type_155065',axiom,
    ! [Vvar__155066] :
      ( c_24__type__155065___24t(Vvar__155066)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__1372___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__155066,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_type_155088',axiom,
    ! [Vvar__155089] :
      ( c_24__type__155088___24t(Vvar__155089)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__1372___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__1372___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)
                         => cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(happ(happ(happ(Vvar__155089,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).

fof('$_type_161927',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__161928] :
      ( c_24__type__161927___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__161928)
    <=> ! [Vv__CANONICAL__3] :
          ( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__3)
         => cCoq_2eInit_2eDatatypes_2eoption___24t(cPLF_2eStlc_2eSTLC_2ety,happ(Vvar__161928,Vv__CANONICAL__3)) ) ) ).

fof('$_type_1632',axiom,
    ! [Vvar__1633] :
      ( c_24__type__1632___24t(Vvar__1633)
    <=> ! [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__1633,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_1635',axiom,
    ! [Vvar__1636] :
      ( c_24__type__1635___24t(Vvar__1636)
    <=> ! [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__1636,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_1640',axiom,
    ! [Vvar__1641] :
      ( c_24__type__1640___24t(Vvar__1641)
    <=> ! [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__1641,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_166416',axiom,
    ! [Vvar__166417] :
      ( c_24__type__166416___24t(Vvar__166417)
    <=> ! [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_2enat___24t(Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
                     => ! [Vv__CANONICAL__4] :
                          ( cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__4)
                         => cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,cCoq_2eInit_2eNat_2eadd___24a2(Vv__CANONICAL__1,Vv__CANONICAL__2),happ(happ(happ(happ(happ(Vvar__166417,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).

fof('$_type_168307',axiom,
    ! [Vvar__168308] :
      ( c_24__type__168307___24t(Vvar__168308)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
             => ( cCoq_2eInit_2ePeano_2ele___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1)
               => cCoq_2eInit_2eSpecif_2esumbool___24t(cCoq_2eInit_2ePeano_2elt___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),c_24__prop__168309___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),happ(happ(Vvar__168308,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ).

fof('$_type_168747',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__168748] :
      ( c_24__type__168747___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__168748)
    <=> ! [Vv__CANONICAL__2] :
          ( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__2)
         => cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__168748,Vv__CANONICAL__2)) ) ) ).

fof('$_type_174032',axiom,
    ! [Vvar__174033] :
      ( c_24__type__174032___24t(Vvar__174033)
    <=> ! [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_2eprod___24t(cCoq_2eNumbers_2eBinNums_2epositive,cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eNumbers_2eBinNums_2epositive,cCoq_2eNumbers_2eBinNums_2epositive),happ(happ(Vvar__174033,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_177135',axiom,
    ! [Vvar__177136] :
      ( c_24__type__177135___24t(Vvar__177136)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cPLF_2eMaps_2epartial__map___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
                     => ! [Vv__CANONICAL__4] :
                          ( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__4)
                         => cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__0,happ(happ(happ(happ(happ(Vvar__177136,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).

fof('$_type_182',axiom,
    ! [Vvar__183] :
      ( c_24__type__182___24t(Vvar__183)
    <=> ! [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__183,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_185353',axiom,
    ! [Vvar__185354] :
      ( c_24__type__185353___24t(Vvar__185354)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__0)
         => cCoq_2eInit_2eDatatypes_2eoption___24t(cPLF_2eStlc_2eSTLC_2ety,happ(Vvar__185354,Vv__CANONICAL__0)) ) ) ).

fof('$_type_1854',axiom,
    ! [Vvar__1855] :
      ( c_24__type__1854___24t(Vvar__1855)
    <=> ! [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__1859___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
                     => ! [Vv__CANONICAL__4] :
                          ( c_24__type__1859___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
                         => ! [Vv__CANONICAL__5] :
                              ( c_24__type__1859___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
                             => ! [Vv__CANONICAL__6] :
                                  ( c_24__type__1868___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
                                 => ! [Vv__CANONICAL__7] :
                                      ( c_24__type__1372___24t(Vv__CANONICAL__0,Vv__CANONICAL__7)
                                     => ! [Vv__CANONICAL__8] :
                                          ( c_24__type__1876___24t(Vv__CANONICAL__0,Vv__CANONICAL__8)
                                         => ! [Vv__CANONICAL__9] :
                                              ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__9)
                                             => ! [Vv__CANONICAL__10] :
                                                  ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2eprod___24a2(Vv__CANONICAL__0,cCoq_2esetoid__ring_2eRing__polynom_2eMon),cCoq_2esetoid__ring_2eRing__polynom_2ePol___24a1(Vv__CANONICAL__0)),Vv__CANONICAL__10)
                                                 => ! [Vv__CANONICAL__11] :
                                                      ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__11)
                                                     => cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__1855,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('$_type_1859',axiom,
    ! [Vv__CANONICAL__0,Vvar__1860] :
      ( c_24__type__1859___24t(Vv__CANONICAL__0,Vvar__1860)
    <=> ! [Vv__CANONICAL__1] :
          ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__2] :
              ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__1860,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_1868',axiom,
    ! [Vv__CANONICAL__0,Vvar__1869] :
      ( c_24__type__1868___24t(Vv__CANONICAL__0,Vvar__1869)
    <=> ! [Vv__CANONICAL__1] :
          ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
         => t(happ(Vvar__1869,Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ).

fof('$_type_1876',axiom,
    ! [Vv__CANONICAL__0,Vvar__1877] :
      ( c_24__type__1876___24t(Vv__CANONICAL__0,Vvar__1877)
    <=> ! [Vv__CANONICAL__1] :
          ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__2] :
              ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
             => cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__0,Vv__CANONICAL__0,happ(happ(Vvar__1877,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).

fof('$_type_198715',axiom,
    ! [Vvar__198716] :
      ( c_24__type__198715___24t(Vvar__198716)
    <=> ! [Vv__CANONICAL__0] :
          ( cPLF_2eStlc_2eSTLC_2etm___24t(Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__198716,Vv__CANONICAL__0)) ) ) ).

fof('$_type_198718',axiom,
    ! [Vvar__198719] :
      ( c_24__type__198718___24t(Vvar__198719)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__1)
             => cCoq_2eBool_2eBool_2ereflect___24t(c_24__prop__198720___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),cPLF_2eMaps_2eeqb__string___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),happ(happ(Vvar__198719,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_198772',axiom,
    ! [Vvar__198773] :
      ( c_24__type__198772___24t(Vvar__198773)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
             => cPLF_2eMaps_2etotal__map___24t(Vv__CANONICAL__0,happ(happ(Vvar__198773,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_199306',axiom,
    ! [Vv__CANONICAL__0,Vvar__199307] :
      ( c_24__type__199306___24t(Vv__CANONICAL__0,Vvar__199307)
    <=> ! [Vv__CANONICAL__1] :
          ( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
         => cProp___24t(happ(Vvar__199307,Vv__CANONICAL__1)) ) ) ).

fof('$_type_199450',axiom,
    ! [Vvar__199451] :
      ( c_24__type__199450___24t(Vvar__199451)
    <=> ! [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__1372___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
                     => ! [Vv__CANONICAL__4] :
                          ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
                         => ! [Vv__CANONICAL__5] :
                              ( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
                             => cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__0,Vv__CANONICAL__0,happ(happ(happ(happ(happ(happ(Vvar__199451,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).

fof('$_type_200033',axiom,
    ! [Vvar__200034] :
      ( c_24__type__200033___24t(Vvar__200034)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(cCoq_2eNumbers_2eBinNums_2eZ,Vv__CANONICAL__0)
         => cCoq_2eInit_2eDatatypes_2eprod___24t(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,happ(Vvar__200034,Vv__CANONICAL__0)) ) ) ).

fof('$_type_203383',axiom,
    ! [Vvar__203384] :
      ( c_24__type__203383___24t(Vvar__203384)
    <=> ! [Vv__CANONICAL__0] :
          ( cPLF_2eReferences_2eSTLCRef_2ety___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cPLF_2eReferences_2eSTLCRef_2ety___24t(Vv__CANONICAL__1)
             => cPLF_2eReferences_2eSTLCRef_2ety___24t(happ(happ(Vvar__203384,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_203385',axiom,
    ! [Vvar__203386] :
      ( c_24__type__203385___24t(Vvar__203386)
    <=> ! [Vv__CANONICAL__0] :
          ( cPLF_2eReferences_2eSTLCRef_2ety___24t(Vv__CANONICAL__0)
         => cPLF_2eReferences_2eSTLCRef_2ety___24t(happ(Vvar__203386,Vv__CANONICAL__0)) ) ) ).

fof('$_type_2036',axiom,
    ! [Vvar__2037] :
      ( c_24__type__2036___24t(Vvar__2037)
    <=> ! [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__1859___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
                     => ! [Vv__CANONICAL__4] :
                          ( c_24__type__1859___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
                         => ! [Vv__CANONICAL__5] :
                              ( c_24__type__1859___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
                             => ! [Vv__CANONICAL__6] :
                                  ( c_24__type__1868___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
                                 => ! [Vv__CANONICAL__7] :
                                      ( c_24__type__1372___24t(Vv__CANONICAL__0,Vv__CANONICAL__7)
                                     => ! [Vv__CANONICAL__8] :
                                          ( c_24__type__1876___24t(Vv__CANONICAL__0,Vv__CANONICAL__8)
                                         => ! [Vv__CANONICAL__9] :
                                              ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0),cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vv__CANONICAL__0)),Vv__CANONICAL__9)
                                             => cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cCoq_2eInit_2eDatatypes_2eprod___24a2(Vv__CANONICAL__0,cCoq_2esetoid__ring_2eRing__polynom_2eMon),cCoq_2esetoid__ring_2eRing__polynom_2ePol___24a1(Vv__CANONICAL__0)),happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(Vvar__2037,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__9)) ) ) ) ) ) ) ) ) ) ) ) ).

fof('$_type_203673',axiom,
    ! [Vvar__203674] :
      ( c_24__type__203673___24t(Vvar__203674)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__0)
         => cPLF_2eReferences_2eSTLCRef_2etm___24t(happ(Vvar__203674,Vv__CANONICAL__0)) ) ) ).

fof('$_type_203676',axiom,
    ! [Vvar__203677] :
      ( c_24__type__203676___24t(Vvar__203677)
    <=> ! [Vv__CANONICAL__0] :
          ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vv__CANONICAL__1)
             => cPLF_2eReferences_2eSTLCRef_2etm___24t(happ(happ(Vvar__203677,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_203681',axiom,
    ! [Vvar__203682] :
      ( c_24__type__203681___24t(Vvar__203682)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cPLF_2eReferences_2eSTLCRef_2ety___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vv__CANONICAL__2)
                 => cPLF_2eReferences_2eSTLCRef_2etm___24t(happ(happ(happ(Vvar__203682,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_203683',axiom,
    ! [Vvar__203684] :
      ( c_24__type__203683___24t(Vvar__203684)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
         => cPLF_2eReferences_2eSTLCRef_2etm___24t(happ(Vvar__203684,Vv__CANONICAL__0)) ) ) ).

fof('$_type_203685',axiom,
    ! [Vvar__203686] :
      ( c_24__type__203685___24t(Vvar__203686)
    <=> ! [Vv__CANONICAL__0] :
          ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vv__CANONICAL__0)
         => cPLF_2eReferences_2eSTLCRef_2etm___24t(happ(Vvar__203686,Vv__CANONICAL__0)) ) ) ).

fof('$_type_203691',axiom,
    ! [Vvar__203692] :
      ( c_24__type__203691___24t(Vvar__203692)
    <=> ! [Vv__CANONICAL__0] :
          ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vv__CANONICAL__2)
                 => cPLF_2eReferences_2eSTLCRef_2etm___24t(happ(happ(happ(Vvar__203692,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_203737',axiom,
    ! [Vvar__203738] :
      ( c_24__type__203737___24t(Vvar__203738)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vv__CANONICAL__2)
                 => cPLF_2eReferences_2eSTLCRef_2etm___24t(happ(happ(happ(Vvar__203738,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_203741',axiom,
    ! [Vvar__203742] :
      ( c_24__type__203741___24t(Vvar__203742)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cPLF_2eReferences_2eSTLCRef_2estore___24t(Vv__CANONICAL__1)
             => cPLF_2eReferences_2eSTLCRef_2etm___24t(happ(happ(Vvar__203742,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_203761',axiom,
    ! [Vvar__203762] :
      ( c_24__type__203761___24t(Vvar__203762)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
                 => ! [Vv__CANONICAL__3] :
                      ( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
                     => cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(happ(happ(happ(Vvar__203762,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_type_2071',axiom,
    ! [Vvar__2072] :
      ( c_24__type__2071___24t(Vvar__2072)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
             => cType___24t(happ(happ(Vvar__2072,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_2088',axiom,
    ! [Vvar__2089] :
      ( c_24__type__2088___24t(Vvar__2089)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eO,happ(Vvar__2089,Vv__CANONICAL__0)) ) ) ).

fof('$_type_2096',axiom,
    ! [Vvar__2097] :
      ( c_24__type__2096___24t(Vvar__2097)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
             => ! [Vv__CANONICAL__2] :
                  ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3)
                     => cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__2),happ(happ(happ(happ(Vvar__2097,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_type_2113',axiom,
    ! [Vvar__2114] :
      ( c_24__type__2113___24t(Vvar__2114)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__1),Vv__CANONICAL__2)
                 => t(happ(happ(happ(Vvar__2114,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).

fof('$_type_211757',axiom,
    ! [Vvar__211758] :
      ( c_24__type__211757___24t(Vvar__211758)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cPLF_2eReferences_2eSTLCRef_2estore__ty___24t(Vv__CANONICAL__1)
             => cPLF_2eReferences_2eSTLCRef_2ety___24t(happ(happ(Vvar__211758,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_211861',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__211862] :
      ( c_24__type__211861___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__211862)
    <=> ! [Vv__CANONICAL__4] :
          ( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__4)
         => cCoq_2eInit_2eDatatypes_2eoption___24t(cPLF_2eReferences_2eSTLCRef_2ety,happ(Vvar__211862,Vv__CANONICAL__4)) ) ) ).

fof('$_type_212228',axiom,
    ! [Vvar__212229] :
      ( c_24__type__212228___24t(Vvar__212229)
    <=> ! [Vv__CANONICAL__0] :
          ( cPLF_2eReferences_2eSTLCRef_2econtext___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cPLF_2eReferences_2eSTLCRef_2estore__ty___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( cPLF_2eReferences_2eSTLCRef_2ety___24t(Vv__CANONICAL__3)
                     => cProp___24t(happ(happ(happ(happ(Vvar__212229,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_type_212230',axiom,
    ! [Vvar__212231] :
      ( c_24__type__212230___24t(Vvar__212231)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__0)
         => cCoq_2eInit_2eDatatypes_2eoption___24t(cPLF_2eReferences_2eSTLCRef_2ety,happ(Vvar__212231,Vv__CANONICAL__0)) ) ) ).

fof('$_type_212317',axiom,
    ! [Vvar__212318] :
      ( c_24__type__212317___24t(Vvar__212318)
    <=> ! [Vv__CANONICAL__0] :
          ( cPLF_2eReferences_2eSTLCRef_2estore__ty___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cPLF_2eReferences_2eSTLCRef_2estore___24t(Vv__CANONICAL__1)
             => cProp___24t(happ(happ(Vvar__212318,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_212345',axiom,
    ! [Vvar__212346] :
      ( c_24__type__212345___24t(Vvar__212346)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2eprod___24t(cPLF_2eReferences_2eSTLCRef_2etm,cPLF_2eReferences_2eSTLCRef_2estore,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eInit_2eDatatypes_2eprod___24t(cPLF_2eReferences_2eSTLCRef_2etm,cPLF_2eReferences_2eSTLCRef_2estore,Vv__CANONICAL__1)
             => cProp___24t(happ(happ(Vvar__212346,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_212347',axiom,
    ! [Vvar__212348] :
      ( c_24__type__212347___24t(Vvar__212348)
    <=> ! [Vv__CANONICAL__0] :
          ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__212348,Vv__CANONICAL__0)) ) ) ).

fof('$_type_212493',axiom,
    ! [Vvar__212494] :
      ( c_24__type__212493___24t(Vvar__212494)
    <=> ! [Vv__CANONICAL__0] :
          ( cPLF_2eReferences_2eSTLCRef_2estore__ty___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cPLF_2eReferences_2eSTLCRef_2estore__ty___24t(Vv__CANONICAL__1)
             => cProp___24t(happ(happ(Vvar__212494,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_212563',axiom,
    ! [Vvar__212564] :
      ( c_24__type__212563___24t(Vvar__212564)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cPLF_2eReferences_2eSTLCRef_2etm___24t(Vv__CANONICAL__1)
             => cProp___24t(happ(happ(Vvar__212564,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_212675',axiom,
    ! [Vvar__212676] :
      ( c_24__type__212675___24t(Vvar__212676)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eStrings_2eAscii_2eascii___24t(Vv__CANONICAL__0)
         => cCoq_2eInit_2eByte_2ebyte___24t(happ(Vvar__212676,Vv__CANONICAL__0)) ) ) ).

fof('$_type_212688',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__212689] :
      ( c_24__type__212688___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__212689)
    <=> ! [Vv__CANONICAL__3] :
          ( cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
         => cType___24t(happ(Vvar__212689,Vv__CANONICAL__3)) ) ) ).

fof('$_type_212709',axiom,
    ! [Vvar__212710] :
      ( c_24__type__212709___24t(Vvar__212710)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cType___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__212713___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( c_24__type__212724___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
                     => ! [Vv__CANONICAL__4] :
                          ( cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__4)
                         => t(happ(happ(happ(happ(happ(Vvar__212710,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),happ(Vv__CANONICAL__2,Vv__CANONICAL__4)) ) ) ) ) ) ) ).

fof('$_type_212713',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__212714] :
      ( c_24__type__212713___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__212714)
    <=> ! [Vv__CANONICAL__2] :
          ( cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
         => cType___24t(happ(Vvar__212714,Vv__CANONICAL__2)) ) ) ).

fof('$_type_212724',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__212725] :
      ( c_24__type__212724___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__212725)
    <=> ! [Vv__CANONICAL__3] :
          ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__4] :
              ( t(Vv__CANONICAL__4,Vv__CANONICAL__1)
             => t(happ(happ(Vvar__212725,Vv__CANONICAL__3),Vv__CANONICAL__4),happ(Vv__CANONICAL__2,cCoq_2eInit_2eDatatypes_2epair___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3,Vv__CANONICAL__4))) ) ) ) ).

fof('$_type_212728',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__212729] :
      ( c_24__type__212728___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__212729)
    <=> ! [Vv__CANONICAL__2] :
          ( cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
         => cProp___24t(happ(Vvar__212729,Vv__CANONICAL__2)) ) ) ).

fof('$_type_212773',axiom,
    ! [Vvar__212774] :
      ( c_24__type__212773___24t(Vvar__212774)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cType___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( cType___24t(Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( c_24__type__212778___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
                     => ! [Vv__CANONICAL__4] :
                          ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
                         => ! [Vv__CANONICAL__5] :
                              ( t(Vv__CANONICAL__5,Vv__CANONICAL__1)
                             => t(happ(happ(happ(happ(happ(happ(Vvar__212774,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__2) ) ) ) ) ) ) ) ).

fof('$_type_212778',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__212779] :
      ( c_24__type__212778___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__212779)
    <=> ! [Vv__CANONICAL__3] :
          ( cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
         => t(happ(Vvar__212779,Vv__CANONICAL__3),Vv__CANONICAL__2) ) ) ).

fof('$_type_212989',axiom,
    ! [Vvar__212990] :
      ( c_24__type__212989___24t(Vvar__212990)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__1859___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( c_24__type__1372___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
                     => ! [Vv__CANONICAL__4] :
                          ( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
                         => ! [Vv__CANONICAL__5] :
                              ( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
                             => cCoq_2emicromega_2eEnvRing_2ePol___24t(Vv__CANONICAL__0,happ(happ(happ(happ(happ(happ(Vvar__212990,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).

fof('$_type_2130',axiom,
    ! [Vvar__2131] :
      ( c_24__type__2130___24t(Vvar__2131)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__1),Vv__CANONICAL__2)
                 => cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(happ(Vvar__2131,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_214288',axiom,
    ! [Vvar__214289] :
      ( c_24__type__214288___24t(Vvar__214289)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cType___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__214292___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
                     => cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__1,happ(happ(happ(happ(Vvar__214289,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_type_214292',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__214293] :
      ( c_24__type__214292___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__214293)
    <=> ! [Vv__CANONICAL__2] :
          ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
         => cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__1,happ(Vvar__214293,Vv__CANONICAL__2)) ) ) ).

fof('$_type_214401',axiom,
    ! [Vvar__214402] :
      ( c_24__type__214401___24t(Vvar__214402)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cType___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__1,Vv__CANONICAL__3)
                     => cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),happ(happ(happ(happ(Vvar__214402,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_type_214554',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__214555] :
      ( c_24__type__214554___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__214555)
    <=> ! [Vv__CANONICAL__2] :
          ( cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
         => ! [Vv__CANONICAL__3] :
              ( cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
             => cProp___24t(happ(happ(Vvar__214555,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).

fof('$_type_214597',axiom,
    ! [Vv__CANONICAL__0,Vvar__214598] :
      ( c_24__type__214597___24t(Vv__CANONICAL__0,Vvar__214598)
    <=> ! [Vv__CANONICAL__1] :
          ( cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__0,Vv__CANONICAL__0,Vv__CANONICAL__1)
         => ! [Vv__CANONICAL__2] :
              ( cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__0,Vv__CANONICAL__0,Vv__CANONICAL__2)
             => cProp___24t(happ(happ(Vvar__214598,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).

fof('$_type_214637',axiom,
    ! [Vvar__214638] :
      ( c_24__type__214637___24t(Vvar__214638)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cType___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__214641___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
                     => cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__1,happ(happ(happ(happ(Vvar__214638,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_type_214641',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__214642] :
      ( c_24__type__214641___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__214642)
    <=> ! [Vv__CANONICAL__2] :
          ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
         => cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__1,happ(Vvar__214642,Vv__CANONICAL__2)) ) ) ).

fof('$_type_214675',axiom,
    ! [Vvar__214676] :
      ( c_24__type__214675___24t(Vvar__214676)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cType___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( cType___24t(Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( c_24__type__214684___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3)
                     => ! [Vv__CANONICAL__4] :
                          ( cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
                         => ! [Vv__CANONICAL__5] :
                              ( cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__1,Vv__CANONICAL__5)
                             => cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__2,happ(happ(happ(happ(happ(happ(Vvar__214676,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).

fof('$_type_214684',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__214685] :
      ( c_24__type__214684___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__214685)
    <=> ! [Vv__CANONICAL__3] :
          ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__4] :
              ( t(Vv__CANONICAL__4,Vv__CANONICAL__1)
             => cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__2,happ(happ(Vvar__214685,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).

fof('$_type_215129',axiom,
    ! [Vvar__215130] :
      ( c_24__type__215129___24t(Vvar__215130)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__1859___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( c_24__type__1859___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
                     => ! [Vv__CANONICAL__4] :
                          ( c_24__type__1868___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
                         => ! [Vv__CANONICAL__5] :
                              ( c_24__type__1372___24t(Vv__CANONICAL__0,Vv__CANONICAL__5)
                             => ! [Vv__CANONICAL__6] :
                                  ( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vv__CANONICAL__0,Vv__CANONICAL__6)
                                 => ! [Vv__CANONICAL__7] :
                                      ( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vv__CANONICAL__0,Vv__CANONICAL__7)
                                     => cCoq_2emicromega_2eEnvRing_2ePol___24t(Vv__CANONICAL__0,happ(happ(happ(happ(happ(happ(happ(happ(Vvar__215130,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_216915',axiom,
    ! [Vvar__216916] :
      ( c_24__type__216915___24t(Vvar__216916)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
             => ! [Vv__CANONICAL__2] :
                  ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(Vv__CANONICAL__0,cCoq_2eNumbers_2eBinNums_2epositive),Vv__CANONICAL__3)
                     => cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(Vv__CANONICAL__0,cCoq_2eNumbers_2eBinNums_2epositive),happ(happ(happ(happ(Vvar__216916,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_type_218221',axiom,
    ! [Vvar__218222] :
      ( c_24__type__218221___24t(Vvar__218222)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cType___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__214554___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( c_24__type__79936___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
                     => ! [Vv__CANONICAL__4] :
                          ( c_24__type__218279___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4)
                         => ! [Vv__CANONICAL__5] :
                              ( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
                             => ! [Vv__CANONICAL__6] :
                                  ( t(Vv__CANONICAL__6,Vv__CANONICAL__1)
                                 => ( cCoq_2eInit_2eWf_2eAcc___24a3(cCoq_2eInit_2eDatatypes_2eprod___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),Vv__CANONICAL__2,cCoq_2eInit_2eDatatypes_2epair___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__5,Vv__CANONICAL__6))
                                   => t(happ(happ(happ(happ(happ(happ(happ(Vvar__218222,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),happ(happ(Vv__CANONICAL__3,Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ) ) ) ) ) ) ).

fof('$_type_218279',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__218280] :
      ( c_24__type__218279___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__218280)
    <=> ! [Vv__CANONICAL__4] :
          ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__5] :
              ( t(Vv__CANONICAL__5,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__6] :
                  ( c_24__type__218312___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6)
                 => t(happ(happ(happ(Vvar__218280,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),happ(happ(Vv__CANONICAL__3,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ) ).

fof('$_type_218312',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__218313] :
      ( c_24__type__218312___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__218313)
    <=> ! [Vv__CANONICAL__6] :
          ( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__7] :
              ( t(Vv__CANONICAL__7,Vv__CANONICAL__1)
             => ( p(happ(happ(Vv__CANONICAL__2,cCoq_2eInit_2eDatatypes_2epair___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__6,Vv__CANONICAL__7)),cCoq_2eInit_2eDatatypes_2epair___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__4,Vv__CANONICAL__5)))
               => t(happ(happ(Vvar__218313,Vv__CANONICAL__6),Vv__CANONICAL__7),happ(happ(Vv__CANONICAL__3,Vv__CANONICAL__6),Vv__CANONICAL__7)) ) ) ) ) ).

fof('$_type_218396',axiom,
    ! [Vvar__218397] :
      ( c_24__type__218396___24t(Vvar__218397)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cType___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__214554___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( c_24__type__79936___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
                     => ( cCoq_2eInit_2eWf_2ewell__founded___24a2(cCoq_2eInit_2eDatatypes_2eprod___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1),Vv__CANONICAL__2)
                       => ! [Vv__CANONICAL__5] :
                            ( c_24__type__218454___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__5)
                           => ! [Vv__CANONICAL__6] :
                                ( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
                               => ! [Vv__CANONICAL__7] :
                                    ( t(Vv__CANONICAL__7,Vv__CANONICAL__1)
                                   => t(happ(happ(happ(happ(happ(happ(happ(Vvar__218397,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__7),happ(happ(Vv__CANONICAL__3,Vv__CANONICAL__6),Vv__CANONICAL__7)) ) ) ) ) ) ) ) ) ) ).

fof('$_type_218454',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__218455] :
      ( c_24__type__218454___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__218455)
    <=> ! [Vv__CANONICAL__4] :
          ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__5] :
              ( t(Vv__CANONICAL__5,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__6] :
                  ( c_24__type__218487___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6)
                 => t(happ(happ(happ(Vvar__218455,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6),happ(happ(Vv__CANONICAL__3,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ) ).

fof('$_type_218487',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__218488] :
      ( c_24__type__218487___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__218488)
    <=> ! [Vv__CANONICAL__6] :
          ( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__7] :
              ( t(Vv__CANONICAL__7,Vv__CANONICAL__1)
             => ( p(happ(happ(Vv__CANONICAL__2,cCoq_2eInit_2eDatatypes_2epair___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__6,Vv__CANONICAL__7)),cCoq_2eInit_2eDatatypes_2epair___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__4,Vv__CANONICAL__5)))
               => t(happ(happ(Vvar__218488,Vv__CANONICAL__6),Vv__CANONICAL__7),happ(happ(Vv__CANONICAL__3,Vv__CANONICAL__6),Vv__CANONICAL__7)) ) ) ) ) ).

fof('$_type_218526',axiom,
    ! [Vvar__218527] :
      ( c_24__type__218526___24t(Vvar__218527)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(cCoq_2eNumbers_2eBinNums_2eZ,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__1)
             => cCoq_2emicromega_2eRingMicromega_2ePolC___24t(cCoq_2eNumbers_2eBinNums_2eZ,happ(happ(Vvar__218527,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_219117',axiom,
    ! [Vv__CANONICAL__0,Vvar__219118] :
      ( c_24__type__219117___24t(Vv__CANONICAL__0,Vvar__219118)
    <=> ! [Vv__CANONICAL__1] :
          ( cPLF_2eReferences_2eSTLCRef_2ety___24t(Vv__CANONICAL__1)
         => cType___24t(happ(Vvar__219118,Vv__CANONICAL__1)) ) ) ).

fof('$_type_219161',axiom,
    ! [Vvar__219162] :
      ( c_24__type__219161___24t(Vvar__219162)
    <=> ! [Vv__CANONICAL__0] :
          ( c_24__type__219163___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( t(Vv__CANONICAL__1,happ(Vv__CANONICAL__0,cPLF_2eReferences_2eSTLCRef_2eNat))
             => ! [Vv__CANONICAL__2] :
                  ( t(Vv__CANONICAL__2,happ(Vv__CANONICAL__0,cPLF_2eReferences_2eSTLCRef_2eUnit))
                 => ! [Vv__CANONICAL__3] :
                      ( c_24__type__219175___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
                     => ! [Vv__CANONICAL__4] :
                          ( c_24__type__219180___24t(Vv__CANONICAL__0,Vv__CANONICAL__4)
                         => ! [Vv__CANONICAL__5] :
                              ( cPLF_2eReferences_2eSTLCRef_2ety___24t(Vv__CANONICAL__5)
                             => t(happ(happ(happ(happ(happ(happ(Vvar__219162,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),happ(Vv__CANONICAL__0,Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).

fof('$_type_219163',axiom,
    ! [Vvar__219164] :
      ( c_24__type__219163___24t(Vvar__219164)
    <=> ! [Vv__CANONICAL__0] :
          ( cPLF_2eReferences_2eSTLCRef_2ety___24t(Vv__CANONICAL__0)
         => cType___24t(happ(Vvar__219164,Vv__CANONICAL__0)) ) ) ).

fof('$_type_219175',axiom,
    ! [Vv__CANONICAL__0,Vvar__219176] :
      ( c_24__type__219175___24t(Vv__CANONICAL__0,Vvar__219176)
    <=> ! [Vv__CANONICAL__1] :
          ( cPLF_2eReferences_2eSTLCRef_2ety___24t(Vv__CANONICAL__1)
         => ! [Vv__CANONICAL__2] :
              ( t(Vv__CANONICAL__2,happ(Vv__CANONICAL__0,Vv__CANONICAL__1))
             => ! [Vv__CANONICAL__3] :
                  ( cPLF_2eReferences_2eSTLCRef_2ety___24t(Vv__CANONICAL__3)
                 => ! [Vv__CANONICAL__4] :
                      ( t(Vv__CANONICAL__4,happ(Vv__CANONICAL__0,Vv__CANONICAL__3))
                     => t(happ(happ(happ(happ(Vvar__219176,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),happ(Vv__CANONICAL__0,cPLF_2eReferences_2eSTLCRef_2eArrow___24a2(Vv__CANONICAL__1,Vv__CANONICAL__3))) ) ) ) ) ) ).

fof('$_type_219180',axiom,
    ! [Vv__CANONICAL__0,Vvar__219181] :
      ( c_24__type__219180___24t(Vv__CANONICAL__0,Vvar__219181)
    <=> ! [Vv__CANONICAL__1] :
          ( cPLF_2eReferences_2eSTLCRef_2ety___24t(Vv__CANONICAL__1)
         => ! [Vv__CANONICAL__2] :
              ( t(Vv__CANONICAL__2,happ(Vv__CANONICAL__0,Vv__CANONICAL__1))
             => t(happ(happ(Vvar__219181,Vv__CANONICAL__1),Vv__CANONICAL__2),happ(Vv__CANONICAL__0,cPLF_2eReferences_2eSTLCRef_2eRef___24a1(Vv__CANONICAL__1))) ) ) ) ).

fof('$_type_219182',axiom,
    ! [Vvar__219183] :
      ( c_24__type__219182___24t(Vvar__219183)
    <=> ! [Vv__CANONICAL__0] :
          ( cPLF_2eReferences_2eSTLCRef_2ety___24t(Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__219183,Vv__CANONICAL__0)) ) ) ).

fof('$_type_220585',axiom,
    ! [Vvar__220586] :
      ( c_24__type__220585___24t(Vvar__220586)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDecimal_2eint___24t(Vv__CANONICAL__0)
         => cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__220586,Vv__CANONICAL__0)) ) ) ).

fof('$_type_2356',axiom,
    ! [Vvar__2357] :
      ( c_24__type__2356___24t(Vvar__2357)
    <=> ! [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__2357,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_2363',axiom,
    ! [Vvar__2364] :
      ( c_24__type__2363___24t(Vvar__2364)
    <=> ! [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__2364,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_2377',axiom,
    ! [Vvar__2378] :
      ( c_24__type__2377___24t(Vvar__2378)
    <=> ! [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__2378,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_2384',axiom,
    ! [Vvar__2385] :
      ( c_24__type__2384___24t(Vvar__2385)
    <=> ! [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_2eprod___24t(cCoq_2eNumbers_2eBinNums_2eN,cCoq_2eNumbers_2eBinNums_2eN,happ(happ(Vvar__2385,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

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

fof('$_type_2475',axiom,
    ! [Vvar__2476] :
      ( c_24__type__2475___24t(Vvar__2476)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
         => cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__2476,Vv__CANONICAL__0)) ) ) ).

fof('$_type_2492',axiom,
    ! [Vvar__2493] :
      ( c_24__type__2492___24t(Vvar__2493)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
         => cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__2493,Vv__CANONICAL__0)) ) ) ).

fof('$_type_2559',axiom,
    ! [Vvar__2560] :
      ( c_24__type__2559___24t(Vvar__2560)
    <=> ! [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_2eprod___24t(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,happ(happ(Vvar__2560,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_261',axiom,
    ! [Vvar__262] :
      ( c_24__type__261___24t(Vvar__262)
    <=> ! [Vv__CANONICAL__0] :
          ( cProp___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cProp___24t(Vv__CANONICAL__1)
             => cType___24t(happ(happ(Vvar__262,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_2615',axiom,
    ! [Vvar__2616] :
      ( c_24__type__2615___24t(Vvar__2616)
    <=> ! [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__2616,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_301',axiom,
    ! [Vvar__302] :
      ( c_24__type__301___24t(Vvar__302)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cProp___24t(Vv__CANONICAL__1)
             => cType___24t(happ(happ(Vvar__302,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_391',axiom,
    ! [Vvar__392] :
      ( c_24__type__391___24t(Vvar__392)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
         => cPLF_2eImp_2eaexp___24t(happ(Vvar__392,Vv__CANONICAL__0)) ) ) ).

fof('$_type_393',axiom,
    ! [Vvar__394] :
      ( c_24__type__393___24t(Vvar__394)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__0)
         => cPLF_2eImp_2eaexp___24t(happ(Vvar__394,Vv__CANONICAL__0)) ) ) ).

fof('$_type_396',axiom,
    ! [Vvar__397] :
      ( c_24__type__396___24t(Vvar__397)
    <=> ! [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__397,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_549',axiom,
    ! [Vvar__550] :
      ( c_24__type__549___24t(Vvar__550)
    <=> ! [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__550,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_554',axiom,
    ! [Vvar__555] :
      ( c_24__type__554___24t(Vvar__555)
    <=> ! [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__555,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_566',axiom,
    ! [Vvar__567] :
      ( c_24__type__566___24t(Vvar__567)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cPLF_2eMaps_2etotal__map___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
                     => ! [Vv__CANONICAL__4] :
                          ( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__4)
                         => t(happ(happ(happ(happ(happ(Vvar__567,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).

fof('$_type_580',axiom,
    ! [Vvar__581] :
      ( c_24__type__580___24t(Vvar__581)
    <=> ! [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__581,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_592',axiom,
    ! [Vvar__593] :
      ( c_24__type__592___24t(Vvar__593)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__593,Vv__CANONICAL__0)) ) ) ).

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

fof('$_type_75607',axiom,
    ! [Vvar__75608] :
      ( c_24__type__75607___24t(Vvar__75608)
    <=> ! [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__75608,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_75611',axiom,
    ! [Vvar__75612] :
      ( c_24__type__75611___24t(Vvar__75612)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
         => cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__75612,Vv__CANONICAL__0)) ) ) ).

fof('$_type_75624',axiom,
    ! [Vvar__75625] :
      ( c_24__type__75624___24t(Vvar__75625)
    <=> ! [Vv__CANONICAL__0] :
          ( c_24__type__13___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__75629___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
                     => t(happ(happ(happ(happ(Vvar__75625,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),happ(Vv__CANONICAL__0,Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_type_75629',axiom,
    ! [Vv__CANONICAL__0,Vvar__75630] :
      ( c_24__type__75629___24t(Vv__CANONICAL__0,Vvar__75630)
    <=> ! [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__75630,Vv__CANONICAL__1),Vv__CANONICAL__2),happ(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__1))) ) ) ) ).

fof('$_type_75646',axiom,
    ! [Vvar__75647] :
      ( c_24__type__75646___24t(Vvar__75647)
    <=> ! [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__75647,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_75648',axiom,
    ! [Vvar__75649] :
      ( c_24__type__75648___24t(Vvar__75649)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__0,happ(Vvar__75649,Vv__CANONICAL__0)) ) ) ).

fof('$_type_75666',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__75667] :
      ( c_24__type__75666___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__75667)
    <=> ! [Vv__CANONICAL__2] :
          ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
         => t(happ(Vvar__75667,Vv__CANONICAL__2),Vv__CANONICAL__1) ) ) ).

fof('$_type_75678',axiom,
    ! [Vvar__75679] :
      ( c_24__type__75678___24t(Vvar__75679)
    <=> ! [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__75679,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).

fof('$_type_75690',axiom,
    ! [Vvar__75691] :
      ( c_24__type__75690___24t(Vvar__75691)
    <=> ! [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__75691,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__1) ) ) ) ) ).

fof('$_type_75693',axiom,
    ! [Vv__CANONICAL__0,Vvar__75694] :
      ( c_24__type__75693___24t(Vv__CANONICAL__0,Vvar__75694)
    <=> ! [Vv__CANONICAL__1] :
          ( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
         => cProp___24t(happ(Vvar__75694,Vv__CANONICAL__1)) ) ) ).

fof('$_type_75706',axiom,
    ! [Vvar__75707] :
      ( c_24__type__75706___24t(Vvar__75707)
    <=> ! [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__75707,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_75718',axiom,
    ! [Vvar__75719] :
      ( c_24__type__75718___24t(Vvar__75719)
    <=> ! [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__75719,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_75738',axiom,
    ! [Vvar__75739] :
      ( c_24__type__75738___24t(Vvar__75739)
    <=> ! [Vv__CANONICAL__0] :
          ( cProp___24t(Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__75739,Vv__CANONICAL__0)) ) ) ).

fof('$_type_76419',axiom,
    ! [Vvar__76420] :
      ( c_24__type__76419___24t(Vvar__76420)
    <=> ! [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__76420,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_76444',axiom,
    ! [Vvar__76445] :
      ( c_24__type__76444___24t(Vvar__76445)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
         => cPLF_2eImp_2esinstr___24t(happ(Vvar__76445,Vv__CANONICAL__0)) ) ) ).

fof('$_type_76446',axiom,
    ! [Vvar__76447] :
      ( c_24__type__76446___24t(Vvar__76447)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__0)
         => cPLF_2eImp_2esinstr___24t(happ(Vvar__76447,Vv__CANONICAL__0)) ) ) ).

fof('$_type_76465',axiom,
    ! [Vvar__76466] :
      ( c_24__type__76465___24t(Vvar__76466)
    <=> ! [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__76466,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_76490',axiom,
    ! [Vvar__76491] :
      ( c_24__type__76490___24t(Vvar__76491)
    <=> ! [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__76491,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).

fof('$_type_76596',axiom,
    ! [Vv__CANONICAL__0,Vvar__76597] :
      ( c_24__type__76596___24t(Vv__CANONICAL__0,Vvar__76597)
    <=> ! [Vv__CANONICAL__1] :
          ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
         => cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__76597,Vv__CANONICAL__1)) ) ) ).

fof('$_type_76603',axiom,
    ! [Vvar__76604] :
      ( c_24__type__76603___24t(Vvar__76604)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__76596___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
                 => cCoq_2eInit_2eDatatypes_2eprod___24t(cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0),cCoq_2eInit_2eDatatypes_2elist___24a1(Vv__CANONICAL__0),happ(happ(happ(Vvar__76604,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_76653',axiom,
    ! [Vv__CANONICAL__0,Vvar__76654] :
      ( c_24__type__76653___24t(Vv__CANONICAL__0,Vvar__76654)
    <=> ! [Vv__CANONICAL__1] :
          ( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__1)
         => t(happ(Vvar__76654,Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ).

fof('$_type_76741',axiom,
    ! [Vvar__76742] :
      ( c_24__type__76741___24t(Vvar__76742)
    <=> ! [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_2eprod___24t(cCoq_2eInit_2eDatatypes_2enat,cCoq_2eInit_2eDatatypes_2enat,happ(happ(happ(happ(Vvar__76742,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_type_76838',axiom,
    ! [Vvar__76839] :
      ( c_24__type__76838___24t(Vvar__76839)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
         => cCoq_2eReals_2eRdefinitions_2eR___24t(happ(Vvar__76839,Vv__CANONICAL__0)) ) ) ).

fof('$_type_76843',axiom,
    ! [Vv__CANONICAL__0,Vvar__76844] :
      ( c_24__type__76843___24t(Vv__CANONICAL__0,Vvar__76844)
    <=> ! [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__76844,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).

fof('$_type_76863',axiom,
    ! [Vvar__76864] :
      ( c_24__type__76863___24t(Vvar__76864)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cType___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__76843___24t(Vv__CANONICAL__1,Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( c_24__type__76873___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
                     => cProp___24t(happ(happ(happ(happ(Vvar__76864,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_type_76873',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__76874] :
      ( c_24__type__76873___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__76874)
    <=> ! [Vv__CANONICAL__2] :
          ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__3] :
              ( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
             => t(happ(happ(Vvar__76874,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__1) ) ) ) ).

fof('$_type_76882',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__76883] :
      ( c_24__type__76882___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__76883)
    <=> ! [Vv__CANONICAL__2] :
          ( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
         => t(happ(Vvar__76883,Vv__CANONICAL__2),Vv__CANONICAL__1) ) ) ).

fof('$_type_76925',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__76926] :
      ( c_24__type__76925___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__76926)
    <=> ! [Vv__CANONICAL__2] :
          ( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
         => ! [Vv__CANONICAL__3] :
              ( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
             => cProp___24t(happ(happ(Vvar__76926,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).

fof('$_type_78055',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__78056] :
      ( c_24__type__78055___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__78056)
    <=> ! [Vv__CANONICAL__2] :
          ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__78056,Vv__CANONICAL__2)) ) ) ).

fof('$_type_78059',axiom,
    ! [Vvar__78060] :
      ( c_24__type__78059___24t(Vvar__78060)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__78062___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => cType___24t(happ(happ(Vvar__78060,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_78062',axiom,
    ! [Vv__CANONICAL__0,Vvar__78063] :
      ( c_24__type__78062___24t(Vv__CANONICAL__0,Vvar__78063)
    <=> ! [Vv__CANONICAL__1] :
          ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__78063,Vv__CANONICAL__1)) ) ) ).

fof('$_type_79565',axiom,
    ! [Vvar__79566] :
      ( c_24__type__79565___24t(Vvar__79566)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cPLF_2eImp_2eaexp___24t(Vv__CANONICAL__1)
             => cPLF_2eSmallstep_2eCImp_2ecom___24t(happ(happ(Vvar__79566,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_79568',axiom,
    ! [Vvar__79569] :
      ( c_24__type__79568___24t(Vvar__79569)
    <=> ! [Vv__CANONICAL__0] :
          ( cPLF_2eSmallstep_2eCImp_2ecom___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cPLF_2eSmallstep_2eCImp_2ecom___24t(Vv__CANONICAL__1)
             => cPLF_2eSmallstep_2eCImp_2ecom___24t(happ(happ(Vvar__79569,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_79573',axiom,
    ! [Vvar__79574] :
      ( c_24__type__79573___24t(Vvar__79574)
    <=> ! [Vv__CANONICAL__0] :
          ( cPLF_2eImp_2ebexp___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cPLF_2eSmallstep_2eCImp_2ecom___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( cPLF_2eSmallstep_2eCImp_2ecom___24t(Vv__CANONICAL__2)
                 => cPLF_2eSmallstep_2eCImp_2ecom___24t(happ(happ(happ(Vvar__79574,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_79576',axiom,
    ! [Vvar__79577] :
      ( c_24__type__79576___24t(Vvar__79577)
    <=> ! [Vv__CANONICAL__0] :
          ( cPLF_2eImp_2ebexp___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cPLF_2eSmallstep_2eCImp_2ecom___24t(Vv__CANONICAL__1)
             => cPLF_2eSmallstep_2eCImp_2ecom___24t(happ(happ(Vvar__79577,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_79652',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__79653] :
      ( c_24__type__79652___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__79653)
    <=> ! [Vv__CANONICAL__2] :
          ( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__2)
         => cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__79653,Vv__CANONICAL__2)) ) ) ).

fof('$_type_79795',axiom,
    ! [Vvar__79796] :
      ( c_24__type__79795___24t(Vvar__79796)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
         => cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__79796,Vv__CANONICAL__0)) ) ) ).

fof('$_type_79936',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__79937] :
      ( c_24__type__79936___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__79937)
    <=> ! [Vv__CANONICAL__2] :
          ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__3] :
              ( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
             => cType___24t(happ(happ(Vvar__79937,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).

fof('$_type_80052',axiom,
    ! [Vvar__80053] :
      ( c_24__type__80052___24t(Vvar__80053)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
         => cCoq_2eNumbers_2eBinNums_2eN___24t(happ(Vvar__80053,Vv__CANONICAL__0)) ) ) ).

fof('$_type_80073',axiom,
    ! [Vvar__80074] :
      ( c_24__type__80073___24t(Vvar__80074)
    <=> ! [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__80074,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_80296',axiom,
    ! [Vvar__80297] :
      ( c_24__type__80296___24t(Vvar__80297)
    <=> ! [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__80297,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_80340',axiom,
    ! [Vvar__80341] :
      ( c_24__type__80340___24t(Vvar__80341)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__1859___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__80341,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).

fof('$_type_80354',axiom,
    ! [Vvar__80355] :
      ( c_24__type__80354___24t(Vvar__80355)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__80355,Vv__CANONICAL__0)) ) ) ).

fof('$_type_80586',axiom,
    ! [Vvar__80587] :
      ( c_24__type__80586___24t(Vvar__80587)
    <=> ! [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__80587,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_80621',axiom,
    ! [Vv__CANONICAL__0,Vvar__80622] :
      ( c_24__type__80621___24t(Vv__CANONICAL__0,Vvar__80622)
    <=> ! [Vv__CANONICAL__1] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
         => cType___24t(happ(Vvar__80622,Vv__CANONICAL__1)) ) ) ).

fof('$_type_80690',axiom,
    ! [Vvar__80691] :
      ( c_24__type__80690___24t(Vvar__80691)
    <=> ! [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__80691,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_80902',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__80903] :
      ( c_24__type__80902___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__80903)
    <=> ! [Vv__CANONICAL__2] :
          ( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
         => t(happ(Vvar__80903,Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ).

fof('$_type_80907',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__80908] :
      ( c_24__type__80907___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__80908)
    <=> ! [Vv__CANONICAL__3] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__3)
         => t(happ(Vvar__80908,Vv__CANONICAL__3),Vv__CANONICAL__2) ) ) ).

fof('$_type_80916',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__80917] :
      ( c_24__type__80916___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__80917)
    <=> ! [Vv__CANONICAL__3] :
          ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__4] :
              ( t(Vv__CANONICAL__4,Vv__CANONICAL__2)
             => t(happ(happ(Vvar__80917,Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_81197',axiom,
    ! [Vvar__81198] :
      ( c_24__type__81197___24t(Vvar__81198)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__1859___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__81198,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).

fof('$_type_81370',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__81371] :
      ( c_24__type__81370___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__81371)
    <=> ! [Vv__CANONICAL__6] :
          ( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__7] :
              ( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__81371,Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_81409',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__81410] :
      ( c_24__type__81409___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__81410)
    <=> ! [Vv__CANONICAL__6] :
          ( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__7] :
              ( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__81410,Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_81448',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__81449] :
      ( c_24__type__81448___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__81449)
    <=> ! [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__81449,Vv__CANONICAL__6),Vv__CANONICAL__7)) ) ) ) ).

fof('$_type_81744',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__81745] :
      ( c_24__type__81744___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__81745)
    <=> ! [Vv__CANONICAL__13] :
          ( t(Vv__CANONICAL__13,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__14] :
              ( t(Vv__CANONICAL__14,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__81745,Vv__CANONICAL__13),Vv__CANONICAL__14),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_81869',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__81870] :
      ( c_24__type__81869___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__81870)
    <=> ! [Vv__CANONICAL__13] :
          ( t(Vv__CANONICAL__13,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__14] :
              ( t(Vv__CANONICAL__14,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__81870,Vv__CANONICAL__13),Vv__CANONICAL__14),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_81994',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__81995] :
      ( c_24__type__81994___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__81995)
    <=> ! [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__81995,Vv__CANONICAL__13),Vv__CANONICAL__14)) ) ) ) ).

fof('$_type_82119',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__82120] :
      ( c_24__type__82119___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__82120)
    <=> ! [Vv__CANONICAL__13] :
          ( t(Vv__CANONICAL__13,Vv__CANONICAL__6)
         => ! [Vv__CANONICAL__14] :
              ( t(Vv__CANONICAL__14,Vv__CANONICAL__6)
             => t(happ(happ(Vvar__82120,Vv__CANONICAL__13),Vv__CANONICAL__14),Vv__CANONICAL__6) ) ) ) ).

fof('$_type_82244',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__82245] :
      ( c_24__type__82244___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__82245)
    <=> ! [Vv__CANONICAL__13] :
          ( t(Vv__CANONICAL__13,Vv__CANONICAL__6)
         => ! [Vv__CANONICAL__14] :
              ( t(Vv__CANONICAL__14,Vv__CANONICAL__6)
             => t(happ(happ(Vvar__82245,Vv__CANONICAL__13),Vv__CANONICAL__14),Vv__CANONICAL__6) ) ) ) ).

fof('$_type_82369',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__82370] :
      ( c_24__type__82369___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__82370)
    <=> ! [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__82370,Vv__CANONICAL__13),Vv__CANONICAL__14)) ) ) ) ).

fof('$_type_82480',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__82481] :
      ( c_24__type__82480___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__82481)
    <=> ! [Vv__CANONICAL__13] :
          ( t(Vv__CANONICAL__13,Vv__CANONICAL__6)
         => t(happ(Vvar__82481,Vv__CANONICAL__13),Vv__CANONICAL__0) ) ) ).

fof('$_type_82503',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__82504] :
      ( c_24__type__82503___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__82504)
    <=> ! [Vv__CANONICAL__2] :
          ( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
         => ! [Vv__CANONICAL__3] :
              ( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
             => t(happ(happ(Vvar__82504,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__1) ) ) ) ).

fof('$_type_82515',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__82516] :
      ( c_24__type__82515___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__82516)
    <=> ! [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__82516,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).

fof('$_type_82538',axiom,
    ! [Vvar__82539] :
      ( c_24__type__82538___24t(Vvar__82539)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__82539,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_82594',axiom,
    ! [Vv__CANONICAL__0,Vvar__82595] :
      ( c_24__type__82594___24t(Vv__CANONICAL__0,Vvar__82595)
    <=> ! [Vv__CANONICAL__1] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
         => ! [Vv__CANONICAL__2] :
              ( cCoq_2eVectors_2eVectorDef_2et___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
             => cProp___24t(happ(happ(Vvar__82595,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).

fof('$_type_82621',axiom,
    ! [Vvar__82622] :
      ( c_24__type__82621___24t(Vvar__82622)
    <=> ! [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__82622,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_82624',axiom,
    ! [Vvar__82625] :
      ( c_24__type__82624___24t(Vvar__82625)
    <=> ! [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__82625,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_82725',axiom,
    ! [Vvar__82726] :
      ( c_24__type__82725___24t(Vvar__82726)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDecimal_2euint___24t(Vv__CANONICAL__0)
         => cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__82726,Vv__CANONICAL__0)) ) ) ).

fof('$_type_82801',axiom,
    ! [Vvar__82802] :
      ( c_24__type__82801___24t(Vvar__82802)
    <=> ! [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)
                 => t(happ(happ(happ(Vvar__82802,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).

fof('$_type_83489',axiom,
    ! [Vvar__83490] :
      ( c_24__type__83489___24t(Vvar__83490)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vv__CANONICAL__0)
         => cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__83490,Vv__CANONICAL__0)) ) ) ).

fof('$_type_83500',axiom,
    ! [Vvar__83501] :
      ( c_24__type__83500___24t(Vvar__83501)
    <=> ! [Vv__CANONICAL__0] :
          ( c_24__type__83489___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__1)
             => cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(happ(happ(Vvar__83501,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_83534',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__83535] :
      ( c_24__type__83534___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__83535)
    <=> ! [Vv__CANONICAL__3] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
         => cProp___24t(happ(Vvar__83535,Vv__CANONICAL__3)) ) ) ).

fof('$_type_83555',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__83556] :
      ( c_24__type__83555___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__83556)
    <=> ! [Vv__CANONICAL__3] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
         => cProp___24t(happ(Vvar__83556,Vv__CANONICAL__3)) ) ) ).

fof('$_type_83593',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__83594] :
      ( c_24__type__83593___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__83594)
    <=> ! [Vv__CANONICAL__5] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__5)
         => cProp___24t(happ(Vvar__83594,Vv__CANONICAL__5)) ) ) ).

fof('$_type_83601',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__83602] :
      ( c_24__type__83601___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__83602)
    <=> ! [Vv__CANONICAL__5] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__5)
         => cProp___24t(happ(Vvar__83602,Vv__CANONICAL__5)) ) ) ).

fof('$_type_83648',axiom,
    ! [Vvar__83649] :
      ( c_24__type__83648___24t(Vvar__83649)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cType___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__83655___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__83649,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).

fof('$_type_83655',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__83656] :
      ( c_24__type__83655___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__83656)
    <=> ! [Vv__CANONICAL__2] :
          ( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
         => ! [Vv__CANONICAL__3] :
              ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__83656,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_83764',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__83765] :
      ( c_24__type__83764___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__83765)
    <=> ! [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__83765,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).

fof('$_type_83777',axiom,
    ! [Vvar__83778] :
      ( c_24__type__83777___24t(Vvar__83778)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__76843___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => cProp___24t(happ(happ(Vvar__83778,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_84590',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__84591] :
      ( c_24__type__84590___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__84591)
    <=> ! [Vv__CANONICAL__2] :
          ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__3] :
              ( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
             => cProp___24t(happ(happ(Vvar__84591,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).

fof('$_type_84765',axiom,
    ! [Vvar__84766] :
      ( c_24__type__84765___24t(Vvar__84766)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__1)
             => cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__84766,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_85086',axiom,
    ! [Vv__CANONICAL__0,Vvar__85087] :
      ( c_24__type__85086___24t(Vv__CANONICAL__0,Vvar__85087)
    <=> ! [Vv__CANONICAL__1] :
          ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
         => cType___24t(happ(Vvar__85087,Vv__CANONICAL__1)) ) ) ).

fof('$_type_85185',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__85186] :
      ( c_24__type__85185___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__85186)
    <=> ! [Vv__CANONICAL__6] :
          ( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
         => cType___24t(happ(Vvar__85186,Vv__CANONICAL__6)) ) ) ).

fof('$_type_85531',axiom,
    ! [Vvar__85532] :
      ( c_24__type__85531___24t(Vvar__85532)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__85532,Vv__CANONICAL__0)) ) ) ).

fof('$_type_85936',axiom,
    ! [Vvar__85937] :
      ( c_24__type__85936___24t(Vvar__85937)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cType___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__76843___24t(Vv__CANONICAL__1,Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( c_24__type__85946___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
                     => ! [Vv__CANONICAL__4] :
                          ( c_24__type__76873___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__4)
                         => cProp___24t(happ(happ(happ(happ(happ(Vvar__85937,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).

fof('$_type_85946',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__85947] :
      ( c_24__type__85946___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__85947)
    <=> ! [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__85947,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).

fof('$_type_85967',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__85968] :
      ( c_24__type__85967___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__85968)
    <=> ! [Vv__CANONICAL__2] :
          ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
         => cType___24t(happ(Vvar__85968,Vv__CANONICAL__2)) ) ) ).

fof('$_type_85971',axiom,
    ! [Vvar__85972] :
      ( c_24__type__85971___24t(Vvar__85972)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__85086___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => cType___24t(happ(happ(Vvar__85972,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_86036',axiom,
    ! [Vvar__86037] :
      ( c_24__type__86036___24t(Vvar__86037)
    <=> ! [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__86037,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_type_86652',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__86653] :
      ( c_24__type__86652___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__86653)
    <=> ! [Vv__CANONICAL__6] :
          ( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
         => cType___24t(happ(Vvar__86653,Vv__CANONICAL__6)) ) ) ).

fof('$_type_86862',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__86863] :
      ( c_24__type__86862___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__86863)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__11] :
              ( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__86863,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_86955',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__86956] :
      ( c_24__type__86955___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__86956)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__11] :
              ( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__86956,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_87048',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__87049] :
      ( c_24__type__87048___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__87049)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__11] :
              ( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__87049,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_87130',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__87131] :
      ( c_24__type__87130___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__87131)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => t(happ(Vvar__87131,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).

fof('$_type_87223',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__87224] :
      ( c_24__type__87223___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__87224)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__11] :
              ( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__87224,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_87305',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__87306] :
      ( c_24__type__87305___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__87306)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => t(happ(Vvar__87306,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).

fof('$_type_87398',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__87399] :
      ( c_24__type__87398___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__87399)
    <=> ! [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__87399,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).

fof('$_type_87552',axiom,
    ! [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__87553] :
      ( c_24__type__87552___24t(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__87553)
    <=> ! [Vv__CANONICAL__8] :
          ( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__9] :
              ( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__87553,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_87615',axiom,
    ! [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__87616] :
      ( c_24__type__87615___24t(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__87616)
    <=> ! [Vv__CANONICAL__8] :
          ( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__9] :
              ( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__87616,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_87678',axiom,
    ! [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__87679] :
      ( c_24__type__87678___24t(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__87679)
    <=> ! [Vv__CANONICAL__8] :
          ( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__9] :
              ( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__87679,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_87732',axiom,
    ! [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__87733] :
      ( c_24__type__87732___24t(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__87733)
    <=> ! [Vv__CANONICAL__8] :
          ( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
         => t(happ(Vvar__87733,Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ).

fof('$_type_87795',axiom,
    ! [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__87796] :
      ( c_24__type__87795___24t(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__87796)
    <=> ! [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__87796,Vv__CANONICAL__8),Vv__CANONICAL__9)) ) ) ) ).

fof('$_type_88195',axiom,
    ! [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__88196] :
      ( c_24__type__88195___24t(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__88196)
    <=> ! [Vv__CANONICAL__8] :
          ( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__9] :
              ( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__88196,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_88258',axiom,
    ! [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__88259] :
      ( c_24__type__88258___24t(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__88259)
    <=> ! [Vv__CANONICAL__8] :
          ( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__9] :
              ( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__88259,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_88321',axiom,
    ! [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__88322] :
      ( c_24__type__88321___24t(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__88322)
    <=> ! [Vv__CANONICAL__8] :
          ( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__9] :
              ( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__88322,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_88375',axiom,
    ! [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__88376] :
      ( c_24__type__88375___24t(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__88376)
    <=> ! [Vv__CANONICAL__8] :
          ( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
         => t(happ(Vvar__88376,Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ).

fof('$_type_88438',axiom,
    ! [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__88439] :
      ( c_24__type__88438___24t(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__88439)
    <=> ! [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__88439,Vv__CANONICAL__8),Vv__CANONICAL__9)) ) ) ) ).

fof('$_type_88563',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__88564] :
      ( c_24__type__88563___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__88564)
    <=> ! [Vv__CANONICAL__5] :
          ( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__6] :
              ( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__88564,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_88593',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__88594] :
      ( c_24__type__88593___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__88594)
    <=> ! [Vv__CANONICAL__5] :
          ( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__6] :
              ( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__88594,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_88617',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__88618] :
      ( c_24__type__88617___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__88618)
    <=> ! [Vv__CANONICAL__5] :
          ( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
         => t(happ(Vvar__88618,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).

fof('$_type_88647',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__88648] :
      ( c_24__type__88647___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__88648)
    <=> ! [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__88648,Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ).

fof('$_type_88677',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__88678] :
      ( c_24__type__88677___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__88678)
    <=> ! [Vv__CANONICAL__5] :
          ( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__6] :
              ( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__88678,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_88701',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__88702] :
      ( c_24__type__88701___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__88702)
    <=> ! [Vv__CANONICAL__5] :
          ( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
         => t(happ(Vvar__88702,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).

fof('$_type_88734',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__88735] :
      ( c_24__type__88734___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__88735)
    <=> ! [Vv__CANONICAL__5] :
          ( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__6] :
              ( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__88735,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_88758',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__88759] :
      ( c_24__type__88758___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__88759)
    <=> ! [Vv__CANONICAL__5] :
          ( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
         => t(happ(Vvar__88759,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).

fof('$_type_88785',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__88786] :
      ( c_24__type__88785___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__88786)
    <=> ! [Vv__CANONICAL__5] :
          ( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
         => t(happ(Vvar__88786,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).

fof('$_type_89129',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__89130] :
      ( c_24__type__89129___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__89130)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__11] :
              ( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__89130,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_89222',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__89223] :
      ( c_24__type__89222___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__89223)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__11] :
              ( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__89223,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_89315',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__89316] :
      ( c_24__type__89315___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__89316)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__11] :
              ( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__89316,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_89397',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__89398] :
      ( c_24__type__89397___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__89398)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => t(happ(Vvar__89398,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).

fof('$_type_89490',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__89491] :
      ( c_24__type__89490___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__89491)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__11] :
              ( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__89491,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_89572',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__89573] :
      ( c_24__type__89572___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__89573)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => t(happ(Vvar__89573,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).

fof('$_type_89665',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__89666] :
      ( c_24__type__89665___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__89666)
    <=> ! [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__89666,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).

fof('$_type_89690',axiom,
    ! [Vvar__89691] :
      ( c_24__type__89690___24t(Vvar__89691)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
             => ! [Vv__CANONICAL__2] :
                  ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
                 => cProp___24t(happ(happ(happ(Vvar__89691,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_90125',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__90126] :
      ( c_24__type__90125___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__90126)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__11] :
              ( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__90126,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_90226',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__90227] :
      ( c_24__type__90226___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__90227)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__11] :
              ( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__90227,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_90327',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__90328] :
      ( c_24__type__90327___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__90328)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__11] :
              ( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__90328,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_90417',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__90418] :
      ( c_24__type__90417___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__90418)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => t(happ(Vvar__90418,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).

fof('$_type_90518',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__90519] :
      ( c_24__type__90518___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__90519)
    <=> ! [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__90519,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).

fof('$_type_90619',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__90620] :
      ( c_24__type__90619___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__90620)
    <=> ! [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__90620,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).

fof('$_type_90720',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__90721] :
      ( c_24__type__90720___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__90721)
    <=> ! [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__90721,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).

fof('$_type_90844',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__90845] :
      ( c_24__type__90844___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__90845)
    <=> ! [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__90845,Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ).

fof('$_type_90863',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__90864] :
      ( c_24__type__90863___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__90864)
    <=> ! [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__90864,Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ).

fof('$_type_90883',axiom,
    ! [Vvar__90884] :
      ( c_24__type__90883___24t(Vvar__90884)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__76843___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__76843___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__90884,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).

fof('$_type_90978',axiom,
    ! [Vvar__90979] :
      ( c_24__type__90978___24t(Vvar__90979)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
             => cProp___24t(happ(happ(Vvar__90979,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_91246',axiom,
    ! [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__91247] :
      ( c_24__type__91246___24t(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__91247)
    <=> ! [Vv__CANONICAL__8] :
          ( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__9] :
              ( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__91247,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_91309',axiom,
    ! [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__91310] :
      ( c_24__type__91309___24t(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__91310)
    <=> ! [Vv__CANONICAL__8] :
          ( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__9] :
              ( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__91310,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_91372',axiom,
    ! [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__91373] :
      ( c_24__type__91372___24t(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__91373)
    <=> ! [Vv__CANONICAL__8] :
          ( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__9] :
              ( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__91373,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_91426',axiom,
    ! [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__91427] :
      ( c_24__type__91426___24t(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__91427)
    <=> ! [Vv__CANONICAL__8] :
          ( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
         => t(happ(Vvar__91427,Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ).

fof('$_type_91489',axiom,
    ! [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__91490] :
      ( c_24__type__91489___24t(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__91490)
    <=> ! [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__91490,Vv__CANONICAL__8),Vv__CANONICAL__9)) ) ) ) ).

fof('$_type_91599',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__91600] :
      ( c_24__type__91599___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__91600)
    <=> ! [Vv__CANONICAL__4] :
          ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__5] :
              ( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__91600,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_91622',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__91623] :
      ( c_24__type__91622___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__91623)
    <=> ! [Vv__CANONICAL__4] :
          ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__5] :
              ( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__91623,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_91645',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__91646] :
      ( c_24__type__91645___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__91646)
    <=> ! [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__91646,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).

fof('$_type_91668',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__91669] :
      ( c_24__type__91668___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__91669)
    <=> ! [Vv__CANONICAL__4] :
          ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__5] :
              ( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__91669,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_91686',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__91687] :
      ( c_24__type__91686___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__91687)
    <=> ! [Vv__CANONICAL__4] :
          ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
         => t(happ(Vvar__91687,Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ).

fof('$_type_91712',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__91713] :
      ( c_24__type__91712___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__91713)
    <=> ! [Vv__CANONICAL__4] :
          ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__5] :
              ( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__91713,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_91730',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__91731] :
      ( c_24__type__91730___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__91731)
    <=> ! [Vv__CANONICAL__4] :
          ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
         => t(happ(Vvar__91731,Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ).

fof('$_type_91804',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__91805] :
      ( c_24__type__91804___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__91805)
    <=> ! [Vv__CANONICAL__3] :
          ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__91805,Vv__CANONICAL__3)) ) ) ).

fof('$_type_91812',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__91813] :
      ( c_24__type__91812___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__91813)
    <=> ! [Vv__CANONICAL__3] :
          ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__91813,Vv__CANONICAL__3)) ) ) ).

fof('$_type_91820',axiom,
    ! [Vvar__91821] :
      ( c_24__type__91820___24t(Vvar__91821)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__78062___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__78062___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
                 => cType___24t(happ(happ(happ(Vvar__91821,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_91860',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__91861] :
      ( c_24__type__91860___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__91861)
    <=> ! [Vv__CANONICAL__3] :
          ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
         => cType___24t(happ(Vvar__91861,Vv__CANONICAL__3)) ) ) ).

fof('$_type_91868',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__91869] :
      ( c_24__type__91868___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__91869)
    <=> ! [Vv__CANONICAL__3] :
          ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
         => cType___24t(happ(Vvar__91869,Vv__CANONICAL__3)) ) ) ).

fof('$_type_91876',axiom,
    ! [Vvar__91877] :
      ( c_24__type__91876___24t(Vvar__91877)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__85086___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__85086___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
                 => cType___24t(happ(happ(happ(Vvar__91877,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_91893',axiom,
    ! [Vvar__91894] :
      ( c_24__type__91893___24t(Vvar__91894)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ( p(c_24False)
           => t(happ(Vvar__91894,Vv__CANONICAL__0),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_921',axiom,
    ! [Vvar__922] :
      ( c_24__type__921___24t(Vvar__922)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
         => cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__922,Vv__CANONICAL__0)) ) ) ).

fof('$_type_92261',axiom,
    ! [Vvar__92262] :
      ( c_24__type__92261___24t(Vvar__92262)
    <=> ! [Vv__CANONICAL__0] :
          ( cProp___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__1)
             => cType___24t(happ(happ(Vvar__92262,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_931',axiom,
    ! [Vvar__932] :
      ( c_24__type__931___24t(Vvar__932)
    <=> ! [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__932,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_934',axiom,
    ! [Vv__CANONICAL__0,Vvar__935] :
      ( c_24__type__934___24t(Vv__CANONICAL__0,Vvar__935)
    <=> ! [Vv__CANONICAL__1] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
         => t(happ(Vvar__935,Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ).

fof('$_type_93878',axiom,
    ! [Vvar__93879] :
      ( c_24__type__93878___24t(Vvar__93879)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
         => cCoq_2ePArith_2eBinPosDef_2ePos_2emask___24t(happ(Vvar__93879,Vv__CANONICAL__0)) ) ) ).

fof('$_type_93894',axiom,
    ! [Vvar__93895] :
      ( c_24__type__93894___24t(Vvar__93895)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__1868___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__93895,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).

fof('$_type_93898',axiom,
    ! [Vvar__93899] :
      ( c_24__type__93898___24t(Vvar__93899)
    <=> ! [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__93899,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_93977',axiom,
    ! [Vvar__93978] :
      ( c_24__type__93977___24t(Vvar__93978)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vv__CANONICAL__0)
         => cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(happ(Vvar__93978,Vv__CANONICAL__0)) ) ) ).

fof('$_type_94744',axiom,
    ! [Vvar__94745] :
      ( c_24__type__94744___24t(Vvar__94745)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDecimal_2euint___24t(Vv__CANONICAL__0)
         => cCoq_2eInit_2eDecimal_2euint___24t(happ(Vvar__94745,Vv__CANONICAL__0)) ) ) ).

fof('$_type_94747',axiom,
    ! [Vvar__94748] :
      ( c_24__type__94747___24t(Vvar__94748)
    <=> ! [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__94748,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_94773',axiom,
    ! [Vvar__94774] :
      ( c_24__type__94773___24t(Vvar__94774)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__1859___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
                     => cCoq_2emicromega_2eEnvRing_2ePol___24t(Vv__CANONICAL__0,happ(happ(happ(happ(Vvar__94774,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_type_949',axiom,
    ! [Vvar__950] :
      ( c_24__type__949___24t(Vvar__950)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
         => cPLF_2eSmallstep_2etm___24t(happ(Vvar__950,Vv__CANONICAL__0)) ) ) ).

fof('$_type_952',axiom,
    ! [Vvar__953] :
      ( c_24__type__952___24t(Vvar__953)
    <=> ! [Vv__CANONICAL__0] :
          ( cPLF_2eSmallstep_2etm___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cPLF_2eSmallstep_2etm___24t(Vv__CANONICAL__1)
             => cPLF_2eSmallstep_2etm___24t(happ(happ(Vvar__953,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_96796',axiom,
    ! [Vvar__96797] :
      ( c_24__type__96796___24t(Vvar__96797)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cType___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__75666___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
                     => cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__1,happ(happ(happ(happ(Vvar__96797,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_type_96822',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__96823] :
      ( c_24__type__96822___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__96823)
    <=> ! [Vv__CANONICAL__3] :
          ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__96823,Vv__CANONICAL__3)) ) ) ).

fof('$_type_96920',axiom,
    ! [Vvar__96921] :
      ( c_24__type__96920___24t(Vvar__96921)
    <=> ! [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__96921,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_96925',axiom,
    ! [Vvar__96926] :
      ( c_24__type__96925___24t(Vvar__96926)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vv__CANONICAL__0)
         => cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__96926,Vv__CANONICAL__0)) ) ) ).

fof('$_type_96930',axiom,
    ! [Vvar__96931] :
      ( c_24__type__96930___24t(Vvar__96931)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vv__CANONICAL__0)
         => cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(Vvar__96931,Vv__CANONICAL__0)) ) ) ).

fof('$_type_97559',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__97560] :
      ( c_24__type__97559___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__97560)
    <=> ! [Vv__CANONICAL__22] :
          ( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__23] :
              ( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__97560,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_97905',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__97906] :
      ( c_24__type__97905___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__97906)
    <=> ! [Vv__CANONICAL__22] :
          ( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__23] :
              ( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__97906,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_98251',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__98252] :
      ( c_24__type__98251___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__98252)
    <=> ! [Vv__CANONICAL__22] :
          ( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__23] :
              ( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__98252,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_98574',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__98575] :
      ( c_24__type__98574___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__98575)
    <=> ! [Vv__CANONICAL__22] :
          ( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
         => t(happ(Vvar__98575,Vv__CANONICAL__22),Vv__CANONICAL__0) ) ) ).

fof('$_type_98920',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__98921] :
      ( c_24__type__98920___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__98921)
    <=> ! [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__98921,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).

fof('$_type_99266',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__99267] :
      ( c_24__type__99266___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__99267)
    <=> ! [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__99267,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).

fof('$_type_99612',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__99613] :
      ( c_24__type__99612___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__99613)
    <=> ! [Vv__CANONICAL__22] :
          ( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
         => ! [Vv__CANONICAL__23] :
              ( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
             => t(happ(happ(Vvar__99613,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__9) ) ) ) ).

fof('$_type_99958',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__99959] :
      ( c_24__type__99958___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__99959)
    <=> ! [Vv__CANONICAL__22] :
          ( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
         => ! [Vv__CANONICAL__23] :
              ( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
             => t(happ(happ(Vvar__99959,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__9) ) ) ) ).

fof('$_typeof_Coq.Arith.Compare_dec.le_lt_eq_dec',axiom,
    c_24__type__168307___24t(cCoq_2eArith_2eCompare__dec_2ele__lt__eq__dec) ).

fof('$_typeof_Coq.Arith.EqNat.eq_nat',axiom,
    c_24__type__580___24t(cCoq_2eArith_2eEqNat_2eeq__nat) ).

fof('$_typeof_Coq.Arith.PeanoNat.Nat.divmod',axiom,
    c_24__type__76741___24t(cCoq_2eArith_2ePeanoNat_2eNat_2edivmod) ).

fof('$_typeof_Coq.Arith.PeanoNat.Nat.le',axiom,
    c_24__type__580___24t(cCoq_2eArith_2ePeanoNat_2eNat_2ele) ).

fof('$_typeof_Coq.Arith.PeanoNat.Nat.lt',axiom,
    c_24__type__580___24t(cCoq_2eArith_2ePeanoNat_2eNat_2elt) ).

fof('$_typeof_Coq.Arith.PeanoNat.Nat.pred',axiom,
    c_24__type__6___24t(cCoq_2eArith_2ePeanoNat_2eNat_2epred) ).

fof('$_typeof_Coq.Arith.PeanoNat.Nat.sub',axiom,
    c_24__type__182___24t(cCoq_2eArith_2ePeanoNat_2eNat_2esub) ).

fof('$_typeof_Coq.Arith.PeanoNat.Nat.succ',axiom,
    c_24__type__6___24t(cCoq_2eArith_2ePeanoNat_2eNat_2esucc) ).

fof('$_typeof_Coq.Arith.PeanoNat.Nat.t',axiom,
    cType___24t(cCoq_2eArith_2ePeanoNat_2eNat_2et) ).

fof('$_typeof_Coq.Arith.PeanoNat.Nat.zero',axiom,
    cCoq_2eInit_2eDatatypes_2enat___24t(cCoq_2eArith_2ePeanoNat_2eNat_2ezero) ).

fof('$_typeof_Coq.Bool.Bool.Is_true',axiom,
    c_24__type__112801___24t(cCoq_2eBool_2eBool_2eIs__true) ).

fof('$_typeof_Coq.Bool.Bool.eqb',axiom,
    c_24__type__75607___24t(cCoq_2eBool_2eBool_2eeqb) ).

fof('$_typeof_Coq.Bool.Bool.ifb',axiom,
    c_24__type__112806___24t(cCoq_2eBool_2eBool_2eifb) ).

fof('$_typeof_Coq.Bool.Bool.reflect',axiom,
    c_24__type__92261___24t(cCoq_2eBool_2eBool_2ereflect) ).

fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.E.bits_lt',axiom,
    c_24__type__82624___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eE_2ebits__lt) ).

fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.E.t',axiom,
    cType___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eE_2et) ).

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__109241___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode) ).

fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.elt',axiom,
    cType___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt) ).

fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.filter',axiom,
    c_24__type__83500___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2efilter) ).

fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.rev',axiom,
    c_24__type__93977___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2erev) ).

fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.t',axiom,
    cType___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et) ).

fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.tree',axiom,
    cType___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree) ).

fof('$_typeof_Coq.Init.Byte.byte',axiom,
    cType___24t(cCoq_2eInit_2eByte_2ebyte) ).

fof('$_typeof_Coq.Init.Byte.x00',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex00) ).

fof('$_typeof_Coq.Init.Byte.x01',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex01) ).

fof('$_typeof_Coq.Init.Byte.x02',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex02) ).

fof('$_typeof_Coq.Init.Byte.x03',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex03) ).

fof('$_typeof_Coq.Init.Byte.x04',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex04) ).

fof('$_typeof_Coq.Init.Byte.x05',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex05) ).

fof('$_typeof_Coq.Init.Byte.x06',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex06) ).

fof('$_typeof_Coq.Init.Byte.x07',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex07) ).

fof('$_typeof_Coq.Init.Byte.x08',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex08) ).

fof('$_typeof_Coq.Init.Byte.x09',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex09) ).

fof('$_typeof_Coq.Init.Byte.x0a',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex0a) ).

fof('$_typeof_Coq.Init.Byte.x0b',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex0b) ).

fof('$_typeof_Coq.Init.Byte.x0c',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex0c) ).

fof('$_typeof_Coq.Init.Byte.x0d',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex0d) ).

fof('$_typeof_Coq.Init.Byte.x0e',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex0e) ).

fof('$_typeof_Coq.Init.Byte.x0f',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex0f) ).

fof('$_typeof_Coq.Init.Byte.x10',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex10) ).

fof('$_typeof_Coq.Init.Byte.x11',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex11) ).

fof('$_typeof_Coq.Init.Byte.x12',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex12) ).

fof('$_typeof_Coq.Init.Byte.x13',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex13) ).

fof('$_typeof_Coq.Init.Byte.x14',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex14) ).

fof('$_typeof_Coq.Init.Byte.x15',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex15) ).

fof('$_typeof_Coq.Init.Byte.x16',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex16) ).

fof('$_typeof_Coq.Init.Byte.x17',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex17) ).

fof('$_typeof_Coq.Init.Byte.x18',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex18) ).

fof('$_typeof_Coq.Init.Byte.x19',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex19) ).

fof('$_typeof_Coq.Init.Byte.x1a',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex1a) ).

fof('$_typeof_Coq.Init.Byte.x1b',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex1b) ).

fof('$_typeof_Coq.Init.Byte.x1c',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex1c) ).

fof('$_typeof_Coq.Init.Byte.x1d',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex1d) ).

fof('$_typeof_Coq.Init.Byte.x1e',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex1e) ).

fof('$_typeof_Coq.Init.Byte.x1f',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex1f) ).

fof('$_typeof_Coq.Init.Byte.x20',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex20) ).

fof('$_typeof_Coq.Init.Byte.x21',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex21) ).

fof('$_typeof_Coq.Init.Byte.x22',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex22) ).

fof('$_typeof_Coq.Init.Byte.x23',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex23) ).

fof('$_typeof_Coq.Init.Byte.x24',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex24) ).

fof('$_typeof_Coq.Init.Byte.x25',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex25) ).

fof('$_typeof_Coq.Init.Byte.x26',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex26) ).

fof('$_typeof_Coq.Init.Byte.x27',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex27) ).

fof('$_typeof_Coq.Init.Byte.x28',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex28) ).

fof('$_typeof_Coq.Init.Byte.x29',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex29) ).

fof('$_typeof_Coq.Init.Byte.x2a',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex2a) ).

fof('$_typeof_Coq.Init.Byte.x2b',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex2b) ).

fof('$_typeof_Coq.Init.Byte.x2c',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex2c) ).

fof('$_typeof_Coq.Init.Byte.x2d',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex2d) ).

fof('$_typeof_Coq.Init.Byte.x2e',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex2e) ).

fof('$_typeof_Coq.Init.Byte.x2f',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex2f) ).

fof('$_typeof_Coq.Init.Byte.x30',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex30) ).

fof('$_typeof_Coq.Init.Byte.x31',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex31) ).

fof('$_typeof_Coq.Init.Byte.x32',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex32) ).

fof('$_typeof_Coq.Init.Byte.x33',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex33) ).

fof('$_typeof_Coq.Init.Byte.x34',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex34) ).

fof('$_typeof_Coq.Init.Byte.x35',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex35) ).

fof('$_typeof_Coq.Init.Byte.x36',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex36) ).

fof('$_typeof_Coq.Init.Byte.x37',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex37) ).

fof('$_typeof_Coq.Init.Byte.x38',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex38) ).

fof('$_typeof_Coq.Init.Byte.x39',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex39) ).

fof('$_typeof_Coq.Init.Byte.x3a',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex3a) ).

fof('$_typeof_Coq.Init.Byte.x3b',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex3b) ).

fof('$_typeof_Coq.Init.Byte.x3c',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex3c) ).

fof('$_typeof_Coq.Init.Byte.x3d',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex3d) ).

fof('$_typeof_Coq.Init.Byte.x3e',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex3e) ).

fof('$_typeof_Coq.Init.Byte.x3f',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex3f) ).

fof('$_typeof_Coq.Init.Byte.x40',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex40) ).

fof('$_typeof_Coq.Init.Byte.x41',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex41) ).

fof('$_typeof_Coq.Init.Byte.x42',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex42) ).

fof('$_typeof_Coq.Init.Byte.x43',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex43) ).

fof('$_typeof_Coq.Init.Byte.x44',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex44) ).

fof('$_typeof_Coq.Init.Byte.x45',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex45) ).

fof('$_typeof_Coq.Init.Byte.x46',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex46) ).

fof('$_typeof_Coq.Init.Byte.x47',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex47) ).

fof('$_typeof_Coq.Init.Byte.x48',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex48) ).

fof('$_typeof_Coq.Init.Byte.x49',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex49) ).

fof('$_typeof_Coq.Init.Byte.x4a',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex4a) ).

fof('$_typeof_Coq.Init.Byte.x4b',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex4b) ).

fof('$_typeof_Coq.Init.Byte.x4c',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex4c) ).

fof('$_typeof_Coq.Init.Byte.x4d',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex4d) ).

fof('$_typeof_Coq.Init.Byte.x4e',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex4e) ).

fof('$_typeof_Coq.Init.Byte.x4f',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex4f) ).

fof('$_typeof_Coq.Init.Byte.x50',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex50) ).

fof('$_typeof_Coq.Init.Byte.x51',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex51) ).

fof('$_typeof_Coq.Init.Byte.x52',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex52) ).

fof('$_typeof_Coq.Init.Byte.x53',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex53) ).

fof('$_typeof_Coq.Init.Byte.x54',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex54) ).

fof('$_typeof_Coq.Init.Byte.x55',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex55) ).

fof('$_typeof_Coq.Init.Byte.x56',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex56) ).

fof('$_typeof_Coq.Init.Byte.x57',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex57) ).

fof('$_typeof_Coq.Init.Byte.x58',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex58) ).

fof('$_typeof_Coq.Init.Byte.x59',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex59) ).

fof('$_typeof_Coq.Init.Byte.x5a',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex5a) ).

fof('$_typeof_Coq.Init.Byte.x5b',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex5b) ).

fof('$_typeof_Coq.Init.Byte.x5c',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex5c) ).

fof('$_typeof_Coq.Init.Byte.x5d',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex5d) ).

fof('$_typeof_Coq.Init.Byte.x5e',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex5e) ).

fof('$_typeof_Coq.Init.Byte.x5f',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex5f) ).

fof('$_typeof_Coq.Init.Byte.x60',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex60) ).

fof('$_typeof_Coq.Init.Byte.x61',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex61) ).

fof('$_typeof_Coq.Init.Byte.x62',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex62) ).

fof('$_typeof_Coq.Init.Byte.x63',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex63) ).

fof('$_typeof_Coq.Init.Byte.x64',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex64) ).

fof('$_typeof_Coq.Init.Byte.x65',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex65) ).

fof('$_typeof_Coq.Init.Byte.x66',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex66) ).

fof('$_typeof_Coq.Init.Byte.x67',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex67) ).

fof('$_typeof_Coq.Init.Byte.x68',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex68) ).

fof('$_typeof_Coq.Init.Byte.x69',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex69) ).

fof('$_typeof_Coq.Init.Byte.x6a',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex6a) ).

fof('$_typeof_Coq.Init.Byte.x6b',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex6b) ).

fof('$_typeof_Coq.Init.Byte.x6c',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex6c) ).

fof('$_typeof_Coq.Init.Byte.x6d',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex6d) ).

fof('$_typeof_Coq.Init.Byte.x6e',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex6e) ).

fof('$_typeof_Coq.Init.Byte.x6f',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex6f) ).

fof('$_typeof_Coq.Init.Byte.x70',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex70) ).

fof('$_typeof_Coq.Init.Byte.x71',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex71) ).

fof('$_typeof_Coq.Init.Byte.x72',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex72) ).

fof('$_typeof_Coq.Init.Byte.x73',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex73) ).

fof('$_typeof_Coq.Init.Byte.x74',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex74) ).

fof('$_typeof_Coq.Init.Byte.x75',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex75) ).

fof('$_typeof_Coq.Init.Byte.x76',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex76) ).

fof('$_typeof_Coq.Init.Byte.x77',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex77) ).

fof('$_typeof_Coq.Init.Byte.x78',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex78) ).

fof('$_typeof_Coq.Init.Byte.x79',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex79) ).

fof('$_typeof_Coq.Init.Byte.x7a',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex7a) ).

fof('$_typeof_Coq.Init.Byte.x7b',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex7b) ).

fof('$_typeof_Coq.Init.Byte.x7c',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex7c) ).

fof('$_typeof_Coq.Init.Byte.x7d',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex7d) ).

fof('$_typeof_Coq.Init.Byte.x7e',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex7e) ).

fof('$_typeof_Coq.Init.Byte.x7f',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex7f) ).

fof('$_typeof_Coq.Init.Byte.x80',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex80) ).

fof('$_typeof_Coq.Init.Byte.x81',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex81) ).

fof('$_typeof_Coq.Init.Byte.x82',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex82) ).

fof('$_typeof_Coq.Init.Byte.x83',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex83) ).

fof('$_typeof_Coq.Init.Byte.x84',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex84) ).

fof('$_typeof_Coq.Init.Byte.x85',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex85) ).

fof('$_typeof_Coq.Init.Byte.x86',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex86) ).

fof('$_typeof_Coq.Init.Byte.xcd',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2excd) ).

fof('$_typeof_Coq.Init.Byte.xce',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exce) ).

fof('$_typeof_Coq.Init.Byte.xcf',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2excf) ).

fof('$_typeof_Coq.Init.Byte.xd0',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exd0) ).

fof('$_typeof_Coq.Init.Byte.xd1',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exd1) ).

fof('$_typeof_Coq.Init.Byte.xd2',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exd2) ).

fof('$_typeof_Coq.Init.Byte.xd3',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exd3) ).

fof('$_typeof_Coq.Init.Byte.xd4',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exd4) ).

fof('$_typeof_Coq.Init.Byte.xd5',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exd5) ).

fof('$_typeof_Coq.Init.Byte.xd6',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exd6) ).

fof('$_typeof_Coq.Init.Byte.xd7',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exd7) ).

fof('$_typeof_Coq.Init.Byte.xd8',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exd8) ).

fof('$_typeof_Coq.Init.Byte.xd9',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exd9) ).

fof('$_typeof_Coq.Init.Byte.xda',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exda) ).

fof('$_typeof_Coq.Init.Byte.xdb',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exdb) ).

fof('$_typeof_Coq.Init.Byte.xdc',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exdc) ).

fof('$_typeof_Coq.Init.Byte.xdd',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exdd) ).

fof('$_typeof_Coq.Init.Byte.xde',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exde) ).

fof('$_typeof_Coq.Init.Byte.xdf',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exdf) ).

fof('$_typeof_Coq.Init.Byte.xe0',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exe0) ).

fof('$_typeof_Coq.Init.Byte.xe1',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exe1) ).

fof('$_typeof_Coq.Init.Byte.xe2',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exe2) ).

fof('$_typeof_Coq.Init.Byte.xe3',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exe3) ).

fof('$_typeof_Coq.Init.Byte.xe4',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exe4) ).

fof('$_typeof_Coq.Init.Byte.xe5',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exe5) ).

fof('$_typeof_Coq.Init.Byte.xe6',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exe6) ).

fof('$_typeof_Coq.Init.Byte.xe7',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exe7) ).

fof('$_typeof_Coq.Init.Byte.xe8',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exe8) ).

fof('$_typeof_Coq.Init.Byte.xe9',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exe9) ).

fof('$_typeof_Coq.Init.Byte.xea',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exea) ).

fof('$_typeof_Coq.Init.Byte.xeb',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exeb) ).

fof('$_typeof_Coq.Init.Byte.xec',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exec) ).

fof('$_typeof_Coq.Init.Byte.xed',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exed) ).

fof('$_typeof_Coq.Init.Byte.xee',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exee) ).

fof('$_typeof_Coq.Init.Byte.xef',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exef) ).

fof('$_typeof_Coq.Init.Byte.xf0',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exf0) ).

fof('$_typeof_Coq.Init.Byte.xf1',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exf1) ).

fof('$_typeof_Coq.Init.Byte.xf2',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exf2) ).

fof('$_typeof_Coq.Init.Byte.xf3',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exf3) ).

fof('$_typeof_Coq.Init.Byte.xf4',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exf4) ).

fof('$_typeof_Coq.Init.Byte.xf5',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exf5) ).

fof('$_typeof_Coq.Init.Byte.xf6',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exf6) ).

fof('$_typeof_Coq.Init.Byte.xf7',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exf7) ).

fof('$_typeof_Coq.Init.Byte.xf8',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exf8) ).

fof('$_typeof_Coq.Init.Byte.xf9',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exf9) ).

fof('$_typeof_Coq.Init.Byte.xfa',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exfa) ).

fof('$_typeof_Coq.Init.Byte.xfb',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exfb) ).

fof('$_typeof_Coq.Init.Byte.xfc',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exfc) ).

fof('$_typeof_Coq.Init.Byte.xfd',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exfd) ).

fof('$_typeof_Coq.Init.Byte.xfe',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exfe) ).

fof('$_typeof_Coq.Init.Byte.xff',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exff) ).

fof('$_typeof_Coq.Init.Datatypes.CompareSpecT',axiom,
    c_24__type__112833___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__75648___24t(cCoq_2eInit_2eDatatypes_2eNone) ).

fof('$_typeof_Coq.Init.Datatypes.O',axiom,
    cCoq_2eInit_2eDatatypes_2enat___24t(cCoq_2eInit_2eDatatypes_2eO) ).

fof('$_typeof_Coq.Init.Datatypes.S',axiom,
    c_24__type__6___24t(cCoq_2eInit_2eDatatypes_2eS) ).

fof('$_typeof_Coq.Init.Datatypes.Some',axiom,
    c_24__type__75646___24t(cCoq_2eInit_2eDatatypes_2eSome) ).

fof('$_typeof_Coq.Init.Datatypes.andb',axiom,
    c_24__type__75607___24t(cCoq_2eInit_2eDatatypes_2eandb) ).

fof('$_typeof_Coq.Init.Datatypes.app',axiom,
    c_24__type__75718___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__1160___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__75678___24t(cCoq_2eInit_2eDatatypes_2efst) ).

fof('$_typeof_Coq.Init.Datatypes.length',axiom,
    c_24__type__75706___24t(cCoq_2eInit_2eDatatypes_2elength) ).

fof('$_typeof_Coq.Init.Datatypes.list',axiom,
    c_24__type__1141___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__75624___24t(cCoq_2eInit_2eDatatypes_2enat__rect) ).

fof('$_typeof_Coq.Init.Datatypes.negb',axiom,
    c_24__type__75611___24t(cCoq_2eInit_2eDatatypes_2enegb) ).

fof('$_typeof_Coq.Init.Datatypes.nil',axiom,
    c_24__type__1155___24t(cCoq_2eInit_2eDatatypes_2enil) ).

fof('$_typeof_Coq.Init.Datatypes.option',axiom,
    c_24__type__1141___24t(cCoq_2eInit_2eDatatypes_2eoption) ).

fof('$_typeof_Coq.Init.Datatypes.orb',axiom,
    c_24__type__75607___24t(cCoq_2eInit_2eDatatypes_2eorb) ).

fof('$_typeof_Coq.Init.Datatypes.pair',axiom,
    c_24__type__1133___24t(cCoq_2eInit_2eDatatypes_2epair) ).

fof('$_typeof_Coq.Init.Datatypes.prod',axiom,
    c_24__type__1117___24t(cCoq_2eInit_2eDatatypes_2eprod) ).

fof('$_typeof_Coq.Init.Datatypes.prod_rec',axiom,
    c_24__type__212709___24t(cCoq_2eInit_2eDatatypes_2eprod__rec) ).

fof('$_typeof_Coq.Init.Datatypes.prod_rect',axiom,
    c_24__type__212709___24t(cCoq_2eInit_2eDatatypes_2eprod__rect) ).

fof('$_typeof_Coq.Init.Datatypes.prod_uncurry',axiom,
    c_24__type__212773___24t(cCoq_2eInit_2eDatatypes_2eprod__uncurry) ).

fof('$_typeof_Coq.Init.Datatypes.snd',axiom,
    c_24__type__75690___24t(cCoq_2eInit_2eDatatypes_2esnd) ).

fof('$_typeof_Coq.Init.Datatypes.sum',axiom,
    c_24__type__1117___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__75607___24t(cCoq_2eInit_2eDatatypes_2exorb) ).

fof('$_typeof_Coq.Init.Decimal.Neg',axiom,
    c_24__type__113630___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__113630___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.nb_digits',axiom,
    c_24__type__82725___24t(cCoq_2eInit_2eDecimal_2enb__digits) ).

fof('$_typeof_Coq.Init.Decimal.rev',axiom,
    c_24__type__94744___24t(cCoq_2eInit_2eDecimal_2erev) ).

fof('$_typeof_Coq.Init.Decimal.uint',axiom,
    cType___24t(cCoq_2eInit_2eDecimal_2euint) ).

fof('$_typeof_Coq.Init.Logic_Type.notT',axiom,
    c_24__type__85531___24t(cCoq_2eInit_2eLogic__Type_2enotT) ).

fof('$_typeof_Coq.Init.Nat.add',axiom,
    c_24__type__182___24t(cCoq_2eInit_2eNat_2eadd) ).

fof('$_typeof_Coq.Init.Nat.divmod',axiom,
    c_24__type__76741___24t(cCoq_2eInit_2eNat_2edivmod) ).

fof('$_typeof_Coq.Init.Nat.eqb',axiom,
    c_24__type__931___24t(cCoq_2eInit_2eNat_2eeqb) ).

fof('$_typeof_Coq.Init.Nat.even',axiom,
    c_24__type__921___24t(cCoq_2eInit_2eNat_2eeven) ).

fof('$_typeof_Coq.Init.Nat.max',axiom,
    c_24__type__182___24t(cCoq_2eInit_2eNat_2emax) ).

fof('$_typeof_Coq.Init.Nat.min',axiom,
    c_24__type__182___24t(cCoq_2eInit_2eNat_2emin) ).

fof('$_typeof_Coq.Init.Nat.mul',axiom,
    c_24__type__182___24t(cCoq_2eInit_2eNat_2emul) ).

fof('$_typeof_Coq.Init.Nat.pred',axiom,
    c_24__type__6___24t(cCoq_2eInit_2eNat_2epred) ).

fof('$_typeof_Coq.Init.Nat.sub',axiom,
    c_24__type__182___24t(cCoq_2eInit_2eNat_2esub) ).

fof('$_typeof_Coq.Init.Nat.succ',axiom,
    c_24__type__6___24t(cCoq_2eInit_2eNat_2esucc) ).

fof('$_typeof_Coq.Init.Nat.t',axiom,
    cType___24t(cCoq_2eInit_2eNat_2et) ).

fof('$_typeof_Coq.Init.Nat.zero',axiom,
    cCoq_2eInit_2eDatatypes_2enat___24t(cCoq_2eInit_2eNat_2ezero) ).

fof('$_typeof_Coq.Init.Peano.IsSucc',axiom,
    c_24__type__592___24t(cCoq_2eInit_2ePeano_2eIsSucc) ).

fof('$_typeof_Coq.Init.Peano.ge',axiom,
    c_24__type__580___24t(cCoq_2eInit_2ePeano_2ege) ).

fof('$_typeof_Coq.Init.Peano.gt',axiom,
    c_24__type__580___24t(cCoq_2eInit_2ePeano_2egt) ).

fof('$_typeof_Coq.Init.Peano.lt',axiom,
    c_24__type__580___24t(cCoq_2eInit_2ePeano_2elt) ).

fof('$_typeof_Coq.Init.Specif.except',axiom,
    c_24__type__91893___24t(cCoq_2eInit_2eSpecif_2eexcept) ).

fof('$_typeof_Coq.Init.Specif.sig',axiom,
    c_24__type__78059___24t(cCoq_2eInit_2eSpecif_2esig) ).

fof('$_typeof_Coq.Init.Specif.sig2',axiom,
    c_24__type__91820___24t(cCoq_2eInit_2eSpecif_2esig2) ).

fof('$_typeof_Coq.Init.Specif.sigT',axiom,
    c_24__type__85971___24t(cCoq_2eInit_2eSpecif_2esigT) ).

fof('$_typeof_Coq.Init.Specif.sigT2',axiom,
    c_24__type__91876___24t(cCoq_2eInit_2eSpecif_2esigT2) ).

fof('$_typeof_Coq.Init.Specif.sumbool',axiom,
    c_24__type__261___24t(cCoq_2eInit_2eSpecif_2esumbool) ).

fof('$_typeof_Coq.Init.Specif.sumor',axiom,
    c_24__type__301___24t(cCoq_2eInit_2eSpecif_2esumor) ).

fof('$_typeof_Coq.Init.Wf.Fix_F_2',axiom,
    c_24__type__218221___24t(cCoq_2eInit_2eWf_2eFix__F__2) ).

fof('$_typeof_Coq.Init.Wf.well_founded',axiom,
    c_24__type__83777___24t(cCoq_2eInit_2eWf_2ewell__founded) ).

fof('$_typeof_Coq.Init.Wf.well_founded_induction_type_2',axiom,
    c_24__type__218396___24t(cCoq_2eInit_2eWf_2ewell__founded__induction__type__2) ).

fof('$_typeof_Coq.Lists.List.In',axiom,
    c_24__type__76465___24t(cCoq_2eLists_2eList_2eIn) ).

fof('$_typeof_Coq.Lists.List.combine',axiom,
    c_24__type__214401___24t(cCoq_2eLists_2eList_2ecombine) ).

fof('$_typeof_Coq.Lists.List.flat_map',axiom,
    c_24__type__214288___24t(cCoq_2eLists_2eList_2eflat__map) ).

fof('$_typeof_Coq.Lists.List.fold_right',axiom,
    c_24__type__83648___24t(cCoq_2eLists_2eList_2efold__right) ).

fof('$_typeof_Coq.Lists.List.map',axiom,
    c_24__type__96796___24t(cCoq_2eLists_2eList_2emap) ).

fof('$_typeof_Coq.Lists.List.nth',axiom,
    c_24__type__76490___24t(cCoq_2eLists_2eList_2enth) ).

fof('$_typeof_Coq.Lists.List.partition',axiom,
    c_24__type__76603___24t(cCoq_2eLists_2eList_2epartition) ).

fof('$_typeof_Coq.Lists.SetoidList.transpose',axiom,
    c_24__type__76863___24t(cCoq_2eLists_2eSetoidList_2etranspose) ).

fof('$_typeof_Coq.Lists.SetoidList.transpose2',axiom,
    c_24__type__76863___24t(cCoq_2eLists_2eSetoidList_2etranspose2) ).

fof('$_typeof_Coq.Lists.SetoidList.transpose_restr',axiom,
    c_24__type__85936___24t(cCoq_2eLists_2eSetoidList_2etranspose__restr) ).

fof('$_typeof_Coq.Lists.SetoidList.transpose_restr2',axiom,
    c_24__type__85936___24t(cCoq_2eLists_2eSetoidList_2etranspose__restr2) ).

fof('$_typeof_Coq.Logic.Decidable.decidable',axiom,
    c_24__type__75738___24t(cCoq_2eLogic_2eDecidable_2edecidable) ).

fof('$_typeof_Coq.NArith.BinNat.N.div_eucl',axiom,
    c_24__type__2384___24t(cCoq_2eNArith_2eBinNat_2eN_2ediv__eucl) ).

fof('$_typeof_Coq.NArith.BinNat.N.le',axiom,
    c_24__type__80073___24t(cCoq_2eNArith_2eBinNat_2eN_2ele) ).

fof('$_typeof_Coq.NArith.BinNat.N.lt',axiom,
    c_24__type__80073___24t(cCoq_2eNArith_2eBinNat_2eN_2elt) ).

fof('$_typeof_Coq.NArith.BinNat.N.t',axiom,
    cType___24t(cCoq_2eNArith_2eBinNat_2eN_2et) ).

fof('$_typeof_Coq.NArith.BinNatDef.N.add',axiom,
    c_24__type__2363___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eadd) ).

fof('$_typeof_Coq.NArith.BinNatDef.N.div_eucl',axiom,
    c_24__type__2384___24t(cCoq_2eNArith_2eBinNatDef_2eN_2ediv__eucl) ).

fof('$_typeof_Coq.NArith.BinNatDef.N.double',axiom,
    c_24__type__80052___24t(cCoq_2eNArith_2eBinNatDef_2eN_2edouble) ).

fof('$_typeof_Coq.NArith.BinNatDef.N.leb',axiom,
    c_24__type__2377___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eleb) ).

fof('$_typeof_Coq.NArith.BinNatDef.N.sub',axiom,
    c_24__type__2363___24t(cCoq_2eNArith_2eBinNatDef_2eN_2esub) ).

fof('$_typeof_Coq.NArith.BinNatDef.N.succ_double',axiom,
    c_24__type__80052___24t(cCoq_2eNArith_2eBinNatDef_2eN_2esucc__double) ).

fof('$_typeof_Coq.NArith.BinNatDef.N.t',axiom,
    cType___24t(cCoq_2eNArith_2eBinNatDef_2eN_2et) ).

fof('$_typeof_Coq.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__1094___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__1107___24t(cCoq_2eNumbers_2eBinNums_2eZneg) ).

fof('$_typeof_Coq.Numbers.BinNums.Zpos',axiom,
    c_24__type__1107___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__1087___24t(cCoq_2eNumbers_2eBinNums_2exI) ).

fof('$_typeof_Coq.Numbers.BinNums.xO',axiom,
    c_24__type__1087___24t(cCoq_2eNumbers_2eBinNums_2exO) ).

fof('$_typeof_Coq.PArith.BinPos.Pos.PeanoView',axiom,
    c_24__type__109200___24t(cCoq_2ePArith_2eBinPos_2ePos_2ePeanoView) ).

fof('$_typeof_Coq.PArith.BinPos.Pos.iter',axiom,
    c_24__type__93894___24t(cCoq_2ePArith_2eBinPos_2ePos_2eiter) ).

fof('$_typeof_Coq.PArith.BinPos.Pos.iter_op',axiom,
    c_24__type__80340___24t(cCoq_2ePArith_2eBinPos_2ePos_2eiter__op) ).

fof('$_typeof_Coq.PArith.BinPos.Pos.le',axiom,
    c_24__type__82624___24t(cCoq_2ePArith_2eBinPos_2ePos_2ele) ).

fof('$_typeof_Coq.PArith.BinPos.Pos.mask',axiom,
    cType___24t(cCoq_2ePArith_2eBinPos_2ePos_2emask) ).

fof('$_typeof_Coq.PArith.BinPos.Pos.t',axiom,
    cType___24t(cCoq_2ePArith_2eBinPos_2ePos_2et) ).

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__93878___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos) ).

fof('$_typeof_Coq.PArith.BinPosDef.Pos.add',axiom,
    c_24__type__80296___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd) ).

fof('$_typeof_Coq.PArith.BinPosDef.Pos.compare',axiom,
    c_24__type__93898___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare) ).

fof('$_typeof_Coq.PArith.BinPosDef.Pos.div2',axiom,
    c_24__type__1087___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2ediv2) ).

fof('$_typeof_Coq.PArith.BinPosDef.Pos.ggcd',axiom,
    c_24__type__174032___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eggcd) ).

fof('$_typeof_Coq.PArith.BinPosDef.Pos.iter',axiom,
    c_24__type__93894___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eiter) ).

fof('$_typeof_Coq.PArith.BinPosDef.Pos.iter_op',axiom,
    c_24__type__80340___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eiter__op) ).

fof('$_typeof_Coq.PArith.BinPosDef.Pos.leb',axiom,
    c_24__type__82621___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eleb) ).

fof('$_typeof_Coq.PArith.BinPosDef.Pos.mask',axiom,
    cType___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2emask) ).

fof('$_typeof_Coq.PArith.BinPosDef.Pos.mul',axiom,
    c_24__type__80296___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2emul) ).

fof('$_typeof_Coq.PArith.BinPosDef.Pos.sub',axiom,
    c_24__type__80296___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2esub) ).

fof('$_typeof_Coq.PArith.BinPosDef.Pos.t',axiom,
    cType___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2et) ).

fof('$_typeof_Coq.PArith.BinPosDef.Pos.to_nat',axiom,
    c_24__type__79795___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eto__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__96930___24t(cCoq_2eQArith_2eQArith__base_2eQden) ).

fof('$_typeof_Coq.QArith.QArith_base.Qmake',axiom,
    c_24__type__96920___24t(cCoq_2eQArith_2eQArith__base_2eQmake) ).

fof('$_typeof_Coq.QArith.QArith_base.Qnum',axiom,
    c_24__type__96925___24t(cCoq_2eQArith_2eQArith__base_2eQnum) ).

fof('$_typeof_Coq.Reals.RIneq.negreal',axiom,
    cType___24t(cCoq_2eReals_2eRIneq_2enegreal) ).

fof('$_typeof_Coq.Reals.RIneq.nonnegreal',axiom,
    cType___24t(cCoq_2eReals_2eRIneq_2enonnegreal) ).

fof('$_typeof_Coq.Reals.RIneq.nonposreal',axiom,
    cType___24t(cCoq_2eReals_2eRIneq_2enonposreal) ).

fof('$_typeof_Coq.Reals.RIneq.nonzeroreal',axiom,
    cType___24t(cCoq_2eReals_2eRIneq_2enonzeroreal) ).

fof('$_typeof_Coq.Reals.RIneq.posreal',axiom,
    cType___24t(cCoq_2eReals_2eRIneq_2eposreal) ).

fof('$_typeof_Coq.Reals.Rdefinitions.R',axiom,
    cType___24t(cCoq_2eReals_2eRdefinitions_2eR) ).

fof('$_typeof_Coq.Reals.Rdefinitions.R0',axiom,
    cCoq_2eReals_2eRdefinitions_2eR___24t(cCoq_2eReals_2eRdefinitions_2eR0) ).

fof('$_typeof_Coq.Reals.Rdefinitions.R1',axiom,
    cCoq_2eReals_2eRdefinitions_2eR___24t(cCoq_2eReals_2eRdefinitions_2eR1) ).

fof('$_typeof_Coq.Reals.Rdefinitions.Rinv',axiom,
    c_24__type__76838___24t(cCoq_2eReals_2eRdefinitions_2eRinv) ).

fof('$_typeof_Coq.Reals.Rdefinitions.Rlt',axiom,
    c_24__type__80690___24t(cCoq_2eReals_2eRdefinitions_2eRlt) ).

fof('$_typeof_Coq.Reals.Rdefinitions.Rmult',axiom,
    c_24__type__1192___24t(cCoq_2eReals_2eRdefinitions_2eRmult) ).

fof('$_typeof_Coq.Reals.Rdefinitions.Ropp',axiom,
    c_24__type__76838___24t(cCoq_2eReals_2eRdefinitions_2eRopp) ).

fof('$_typeof_Coq.Reals.Rdefinitions.Rplus',axiom,
    c_24__type__1192___24t(cCoq_2eReals_2eRdefinitions_2eRplus) ).

fof('$_typeof_Coq.Reals.Rdefinitions.up',axiom,
    c_24__type__113285___24t(cCoq_2eReals_2eRdefinitions_2eup) ).

fof('$_typeof_Coq.Reals.Rfunctions.Z_spec',axiom,
    c_24__type__113342___24t(cCoq_2eReals_2eRfunctions_2eZ__spec) ).

fof('$_typeof_Coq.Relations.Relation_Definitions.relation',axiom,
    c_24__type__1141___24t(cCoq_2eRelations_2eRelation__Definitions_2erelation) ).

fof('$_typeof_Coq.Setoids.Setoid.Setoid_Theory',axiom,
    c_24__type__107073___24t(cCoq_2eSetoids_2eSetoid_2eSetoid__Theory) ).

fof('$_typeof_Coq.Sets.Relations_1.Relation',axiom,
    c_24__type__1141___24t(cCoq_2eSets_2eRelations__1_2eRelation) ).

fof('$_typeof_Coq.Strings.Ascii.Ascii',axiom,
    c_24__type__2615___24t(cCoq_2eStrings_2eAscii_2eAscii) ).

fof('$_typeof_Coq.Strings.Ascii.ascii',axiom,
    cType___24t(cCoq_2eStrings_2eAscii_2eascii) ).

fof('$_typeof_Coq.Strings.Ascii.byte_of_ascii',axiom,
    c_24__type__212675___24t(cCoq_2eStrings_2eAscii_2ebyte__of__ascii) ).

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__115784___24t(cCoq_2eStrings_2eString_2eString) ).

fof('$_typeof_Coq.Strings.String.string',axiom,
    cType___24t(cCoq_2eStrings_2eString_2estring) ).

fof('$_typeof_Coq.Structures.DecidableTypeEx.N_as_DT.t',axiom,
    cType___24t(cCoq_2eStructures_2eDecidableTypeEx_2eN__as__DT_2et) ).

fof('$_typeof_Coq.Structures.DecidableTypeEx.Nat_as_DT.lt',axiom,
    c_24__type__580___24t(cCoq_2eStructures_2eDecidableTypeEx_2eNat__as__DT_2elt) ).

fof('$_typeof_Coq.Structures.DecidableTypeEx.Nat_as_DT.t',axiom,
    cType___24t(cCoq_2eStructures_2eDecidableTypeEx_2eNat__as__DT_2et) ).

fof('$_typeof_Coq.Structures.DecidableTypeEx.Positive_as_DT.t',axiom,
    cType___24t(cCoq_2eStructures_2eDecidableTypeEx_2ePositive__as__DT_2et) ).

fof('$_typeof_Coq.Structures.DecidableTypeEx.Z_as_DT.t',axiom,
    cType___24t(cCoq_2eStructures_2eDecidableTypeEx_2eZ__as__DT_2et) ).

fof('$_typeof_Coq.Structures.OrderedType.Compare',axiom,
    c_24__type__90883___24t(cCoq_2eStructures_2eOrderedType_2eCompare) ).

fof('$_typeof_Coq.Structures.OrderedTypeEx.N_as_OT.lt',axiom,
    c_24__type__80073___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__580___24t(cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2eeq) ).

fof('$_typeof_Coq.Structures.OrderedTypeEx.Nat_as_OT.lt',axiom,
    c_24__type__580___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__82624___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt) ).

fof('$_typeof_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.eq',axiom,
    c_24__type__82624___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2eeq) ).

fof('$_typeof_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.lt',axiom,
    c_24__type__82624___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.t',axiom,
    cType___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositive__as__OT_2et) ).

fof('$_typeof_Coq.Structures.OrderedTypeEx.String_as_OT.t',axiom,
    cType___24t(cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2et) ).

fof('$_typeof_Coq.Structures.OrderedTypeEx.Z_as_OT.eq',axiom,
    c_24__type__1074___24t(cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2eeq) ).

fof('$_typeof_Coq.Structures.OrderedTypeEx.Z_as_OT.t',axiom,
    cType___24t(cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2et) ).

fof('$_typeof_Coq.Structures.OrdersTac.OEQ',axiom,
    cCoq_2eStructures_2eOrdersTac_2eord___24t(cCoq_2eStructures_2eOrdersTac_2eOEQ) ).

fof('$_typeof_Coq.Structures.OrdersTac.OLE',axiom,
    cCoq_2eStructures_2eOrdersTac_2eord___24t(cCoq_2eStructures_2eOrdersTac_2eOLE) ).

fof('$_typeof_Coq.Structures.OrdersTac.OLT',axiom,
    cCoq_2eStructures_2eOrdersTac_2eord___24t(cCoq_2eStructures_2eOrdersTac_2eOLT) ).

fof('$_typeof_Coq.Structures.OrdersTac.ord',axiom,
    cType___24t(cCoq_2eStructures_2eOrdersTac_2eord) ).

fof('$_typeof_Coq.Vectors.Fin.t',axiom,
    c_24__type__13___24t(cCoq_2eVectors_2eFin_2et) ).

fof('$_typeof_Coq.Vectors.Vector.t',axiom,
    c_24__type__2071___24t(cCoq_2eVectors_2eVector_2et) ).

fof('$_typeof_Coq.Vectors.VectorDef.append',axiom,
    c_24__type__166416___24t(cCoq_2eVectors_2eVectorDef_2eappend) ).

fof('$_typeof_Coq.Vectors.VectorDef.cons',axiom,
    c_24__type__2096___24t(cCoq_2eVectors_2eVectorDef_2econs) ).

fof('$_typeof_Coq.Vectors.VectorDef.hd',axiom,
    c_24__type__2113___24t(cCoq_2eVectors_2eVectorDef_2ehd) ).

fof('$_typeof_Coq.Vectors.VectorDef.nil',axiom,
    c_24__type__2088___24t(cCoq_2eVectors_2eVectorDef_2enil) ).

fof('$_typeof_Coq.Vectors.VectorDef.t',axiom,
    c_24__type__2071___24t(cCoq_2eVectors_2eVectorDef_2et) ).

fof('$_typeof_Coq.Vectors.VectorDef.tl',axiom,
    c_24__type__2130___24t(cCoq_2eVectors_2eVectorDef_2etl) ).

fof('$_typeof_Coq.ZArith.BinInt.Z.divide',axiom,
    c_24__type__1074___24t(cCoq_2eZArith_2eBinInt_2eZ_2edivide) ).

fof('$_typeof_Coq.ZArith.BinInt.Z.eq',axiom,
    c_24__type__1074___24t(cCoq_2eZArith_2eBinInt_2eZ_2eeq) ).

fof('$_typeof_Coq.ZArith.BinInt.Z.ge',axiom,
    c_24__type__1074___24t(cCoq_2eZArith_2eBinInt_2eZ_2ege) ).

fof('$_typeof_Coq.ZArith.BinInt.Z.gt',axiom,
    c_24__type__1074___24t(cCoq_2eZArith_2eBinInt_2eZ_2egt) ).

fof('$_typeof_Coq.ZArith.BinInt.Z.le',axiom,
    c_24__type__1074___24t(cCoq_2eZArith_2eBinInt_2eZ_2ele) ).

fof('$_typeof_Coq.ZArith.BinInt.Z.lt',axiom,
    c_24__type__1074___24t(cCoq_2eZArith_2eBinInt_2eZ_2elt) ).

fof('$_typeof_Coq.ZArith.BinInt.Z.t',axiom,
    cType___24t(cCoq_2eZArith_2eBinInt_2eZ_2et) ).

fof('$_typeof_Coq.ZArith.BinInt.Z.zero',axiom,
    cCoq_2eNumbers_2eBinNums_2eZ___24t(cCoq_2eZArith_2eBinInt_2eZ_2ezero) ).

fof('$_typeof_Coq.ZArith.BinInt.Zne',axiom,
    c_24__type__1074___24t(cCoq_2eZArith_2eBinInt_2eZne) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.abs',axiom,
    c_24__type__2475___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eabs) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.add',axiom,
    c_24__type__2471___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.compare',axiom,
    c_24__type__80586___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.gcd',axiom,
    c_24__type__2471___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2egcd) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.gtb',axiom,
    c_24__type__2356___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2egtb) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.leb',axiom,
    c_24__type__2356___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eleb) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.ltb',axiom,
    c_24__type__2356___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eltb) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.max',axiom,
    c_24__type__2471___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emax) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.mul',axiom,
    c_24__type__2471___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emul) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.of_N',axiom,
    c_24__type__114440___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.of_int',axiom,
    c_24__type__220585___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__int) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.of_nat',axiom,
    c_24__type__2492___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.opp',axiom,
    c_24__type__2475___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eopp) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.quotrem',axiom,
    c_24__type__2559___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.sgn',axiom,
    c_24__type__2475___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2esgn) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.sub',axiom,
    c_24__type__2471___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2esub) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.succ',axiom,
    c_24__type__2475___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2esucc) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.t',axiom,
    cType___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2et) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.to_pos',axiom,
    c_24__type__113614___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__2356___24t(cCoq_2eZArith_2eZbool_2eZeq__bool) ).

fof('$_typeof_Coq.ZArith.Zeven.Zeven',axiom,
    c_24__type__1179___24t(cCoq_2eZArith_2eZeven_2eZeven) ).

fof('$_typeof_Coq.ZArith.Zeven.Zodd',axiom,
    c_24__type__1179___24t(cCoq_2eZArith_2eZeven_2eZodd) ).

fof('$_typeof_Coq.ZArith.Zlogarithm.Is_power',axiom,
    c_24__type__80354___24t(cCoq_2eZArith_2eZlogarithm_2eIs__power) ).

fof('$_typeof_Coq.ZArith.Znumtheory.Euclid',axiom,
    c_24__type__113342___24t(cCoq_2eZArith_2eZnumtheory_2eEuclid) ).

fof('$_typeof_Coq.ZArith.Zpower.Zdiv_rest_proofs',axiom,
    c_24__type__113560___24t(cCoq_2eZArith_2eZpower_2eZdiv__rest__proofs) ).

fof('$_typeof_Coq.ZArith.Zpower.two_power_nat',axiom,
    c_24__type__2492___24t(cCoq_2eZArith_2eZpower_2etwo__power__nat) ).

fof('$_typeof_Coq.ZArith.Zpower.two_power_pos',axiom,
    c_24__type__1107___24t(cCoq_2eZArith_2eZpower_2etwo__power__pos) ).

fof('$_typeof_Coq.micromega.Env.Env',axiom,
    c_24__type__1141___24t(cCoq_2emicromega_2eEnv_2eEnv) ).

fof('$_typeof_Coq.micromega.Env.hd',axiom,
    c_24__type__151260___24t(cCoq_2emicromega_2eEnv_2ehd) ).

fof('$_typeof_Coq.micromega.Env.jump',axiom,
    c_24__type__151257___24t(cCoq_2emicromega_2eEnv_2ejump) ).

fof('$_typeof_Coq.micromega.Env.tail',axiom,
    c_24__type__151265___24t(cCoq_2emicromega_2eEnv_2etail) ).

fof('$_typeof_Coq.micromega.EnvRing.Mon',axiom,
    cType___24t(cCoq_2emicromega_2eEnvRing_2eMon) ).

fof('$_typeof_Coq.micromega.EnvRing.PExpr',axiom,
    c_24__type__1141___24t(cCoq_2emicromega_2eEnvRing_2ePExpr) ).

fof('$_typeof_Coq.micromega.EnvRing.PX',axiom,
    c_24__type__113662___24t(cCoq_2emicromega_2eEnvRing_2ePX) ).

fof('$_typeof_Coq.micromega.EnvRing.Pc',axiom,
    c_24__type__94747___24t(cCoq_2emicromega_2eEnvRing_2ePc) ).

fof('$_typeof_Coq.micromega.EnvRing.Pinj',axiom,
    c_24__type__113654___24t(cCoq_2emicromega_2eEnvRing_2ePinj) ).

fof('$_typeof_Coq.micromega.EnvRing.Pol',axiom,
    c_24__type__1141___24t(cCoq_2emicromega_2eEnvRing_2ePol) ).

fof('$_typeof_Coq.micromega.EnvRing.PsubC',axiom,
    c_24__type__94773___24t(cCoq_2emicromega_2eEnvRing_2ePsubC) ).

fof('$_typeof_Coq.micromega.EnvRing.mkPinj',axiom,
    c_24__type__113654___24t(cCoq_2emicromega_2eEnvRing_2emkPinj) ).

fof('$_typeof_Coq.micromega.EnvRing.mkZmon',axiom,
    c_24__type__113665___24t(cCoq_2emicromega_2eEnvRing_2emkZmon) ).

fof('$_typeof_Coq.micromega.EnvRing.vmon',axiom,
    c_24__type__113665___24t(cCoq_2emicromega_2eEnvRing_2evmon) ).

fof('$_typeof_Coq.micromega.EnvRing.zmon',axiom,
    c_24__type__113665___24t(cCoq_2emicromega_2eEnvRing_2ezmon) ).

fof('$_typeof_Coq.micromega.EnvRing.zmon_pred',axiom,
    c_24__type__113665___24t(cCoq_2emicromega_2eEnvRing_2ezmon__pred) ).

fof('$_typeof_Coq.micromega.RMicromega.Rcst',axiom,
    cType___24t(cCoq_2emicromega_2eRMicromega_2eRcst) ).

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__1141___24t(cCoq_2emicromega_2eRingMicromega_2eFormula) ).

fof('$_typeof_Coq.micromega.RingMicromega.NFormula',axiom,
    c_24__type__1141___24t(cCoq_2emicromega_2eRingMicromega_2eNFormula) ).

fof('$_typeof_Coq.micromega.RingMicromega.NonEqual',axiom,
    cCoq_2emicromega_2eRingMicromega_2eOp1___24t(cCoq_2emicromega_2eRingMicromega_2eNonEqual) ).

fof('$_typeof_Coq.micromega.RingMicromega.NonStrict',axiom,
    cCoq_2emicromega_2eRingMicromega_2eOp1___24t(cCoq_2emicromega_2eRingMicromega_2eNonStrict) ).

fof('$_typeof_Coq.micromega.RingMicromega.Op1',axiom,
    cType___24t(cCoq_2emicromega_2eRingMicromega_2eOp1) ).

fof('$_typeof_Coq.micromega.RingMicromega.Op2',axiom,
    cType___24t(cCoq_2emicromega_2eRingMicromega_2eOp2) ).

fof('$_typeof_Coq.micromega.RingMicromega.OpEq',axiom,
    cCoq_2emicromega_2eRingMicromega_2eOp2___24t(cCoq_2emicromega_2eRingMicromega_2eOpEq) ).

fof('$_typeof_Coq.micromega.RingMicromega.OpGe',axiom,
    cCoq_2emicromega_2eRingMicromega_2eOp2___24t(cCoq_2emicromega_2eRingMicromega_2eOpGe) ).

fof('$_typeof_Coq.micromega.RingMicromega.OpGt',axiom,
    cCoq_2emicromega_2eRingMicromega_2eOp2___24t(cCoq_2emicromega_2eRingMicromega_2eOpGt) ).

fof('$_typeof_Coq.micromega.RingMicromega.OpLe',axiom,
    cCoq_2emicromega_2eRingMicromega_2eOp2___24t(cCoq_2emicromega_2eRingMicromega_2eOpLe) ).

fof('$_typeof_Coq.micromega.RingMicromega.OpLt',axiom,
    cCoq_2emicromega_2eRingMicromega_2eOp2___24t(cCoq_2emicromega_2eRingMicromega_2eOpLt) ).

fof('$_typeof_Coq.micromega.RingMicromega.OpNEq',axiom,
    cCoq_2emicromega_2eRingMicromega_2eOp2___24t(cCoq_2emicromega_2eRingMicromega_2eOpNEq) ).

fof('$_typeof_Coq.micromega.RingMicromega.PolC',axiom,
    c_24__type__1141___24t(cCoq_2emicromega_2eRingMicromega_2ePolC) ).

fof('$_typeof_Coq.micromega.RingMicromega.PolEnv',axiom,
    c_24__type__1141___24t(cCoq_2emicromega_2eRingMicromega_2ePolEnv) ).

fof('$_typeof_Coq.micromega.RingMicromega.Psatz',axiom,
    c_24__type__1141___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.check_inconsistent',axiom,
    c_24__type__102887___24t(cCoq_2emicromega_2eRingMicromega_2echeck__inconsistent) ).

fof('$_typeof_Coq.micromega.RingMicromega.cltb',axiom,
    c_24__type__155088___24t(cCoq_2emicromega_2eRingMicromega_2ecltb) ).

fof('$_typeof_Coq.micromega.RingMicromega.cneqb',axiom,
    c_24__type__155065___24t(cCoq_2emicromega_2eRingMicromega_2ecneqb) ).

fof('$_typeof_Coq.micromega.RingMicromega.eval_nformula',axiom,
    c_24__type__102623___24t(cCoq_2emicromega_2eRingMicromega_2eeval__nformula) ).

fof('$_typeof_Coq.micromega.RingMicromega.eval_op1',axiom,
    c_24__type__102497___24t(cCoq_2emicromega_2eRingMicromega_2eeval__op1) ).

fof('$_typeof_Coq.micromega.RingMicromega.eval_pol',axiom,
    c_24__type__102413___24t(cCoq_2emicromega_2eRingMicromega_2eeval__pol) ).

fof('$_typeof_Coq.micromega.RingMicromega.map_option',axiom,
    c_24__type__214637___24t(cCoq_2emicromega_2eRingMicromega_2emap__option) ).

fof('$_typeof_Coq.micromega.RingMicromega.map_option2',axiom,
    c_24__type__214675___24t(cCoq_2emicromega_2eRingMicromega_2emap__option2) ).

fof('$_typeof_Coq.micromega.RingMicromega.padd',axiom,
    c_24__type__212989___24t(cCoq_2emicromega_2eRingMicromega_2epadd) ).

fof('$_typeof_Coq.micromega.RingMicromega.psub',axiom,
    c_24__type__215129___24t(cCoq_2emicromega_2eRingMicromega_2epsub) ).

fof('$_typeof_Coq.micromega.RingMicromega.psubC',axiom,
    c_24__type__94773___24t(cCoq_2emicromega_2eRingMicromega_2epsubC) ).

fof('$_typeof_Coq.micromega.Tauto.GFormula',axiom,
    c_24__type__86036___24t(cCoq_2emicromega_2eTauto_2eGFormula) ).

fof('$_typeof_Coq.micromega.Tauto.TFormula',axiom,
    c_24__type__86036___24t(cCoq_2emicromega_2eTauto_2eTFormula) ).

fof('$_typeof_Coq.micromega.Tauto.and_cnf',axiom,
    c_24__type__121019___24t(cCoq_2emicromega_2eTauto_2eand__cnf) ).

fof('$_typeof_Coq.micromega.Tauto.clause',axiom,
    c_24__type__1117___24t(cCoq_2emicromega_2eTauto_2eclause) ).

fof('$_typeof_Coq.micromega.Tauto.cnf',axiom,
    c_24__type__1117___24t(cCoq_2emicromega_2eTauto_2ecnf) ).

fof('$_typeof_Coq.micromega.Tauto.cnf_tt',axiom,
    c_24__type__120971___24t(cCoq_2emicromega_2eTauto_2ecnf__tt) ).

fof('$_typeof_Coq.micromega.VarMap.t',axiom,
    c_24__type__1141___24t(cCoq_2emicromega_2eVarMap_2et) ).

fof('$_typeof_Coq.micromega.ZMicromega.Vars.E.bits_lt',axiom,
    c_24__type__82624___24t(cCoq_2emicromega_2eZMicromega_2eVars_2eE_2ebits__lt) ).

fof('$_typeof_Coq.micromega.ZMicromega.Vars.E.t',axiom,
    cType___24t(cCoq_2emicromega_2eZMicromega_2eVars_2eE_2et) ).

fof('$_typeof_Coq.micromega.ZMicromega.Vars.elt',axiom,
    cType___24t(cCoq_2emicromega_2eZMicromega_2eVars_2eelt) ).

fof('$_typeof_Coq.micromega.ZMicromega.Vars.tree',axiom,
    cType___24t(cCoq_2emicromega_2eZMicromega_2eVars_2etree) ).

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.Zdiv_pol',axiom,
    c_24__type__218526___24t(cCoq_2emicromega_2eZMicromega_2eZdiv__pol) ).

fof('$_typeof_Coq.micromega.ZMicromega.ZgcdM',axiom,
    c_24__type__2471___24t(cCoq_2emicromega_2eZMicromega_2eZgcdM) ).

fof('$_typeof_Coq.micromega.ZMicromega.Zgcd_pol',axiom,
    c_24__type__200033___24t(cCoq_2emicromega_2eZMicromega_2eZgcd__pol) ).

fof('$_typeof_Coq.micromega.ZMicromega.ceiling',axiom,
    c_24__type__2471___24t(cCoq_2emicromega_2eZMicromega_2eceiling) ).

fof('$_typeof_Coq.micromega.ZMicromega.eval_nformula',axiom,
    c_24__type__108018___24t(cCoq_2emicromega_2eZMicromega_2eeval__nformula) ).

fof('$_typeof_Coq.micromega.ZMicromega.eval_pol',axiom,
    c_24__type__108024___24t(cCoq_2emicromega_2eZMicromega_2eeval__pol) ).

fof('$_typeof_Coq.micromega.ZMicromega.padd',axiom,
    c_24__type__108021___24t(cCoq_2emicromega_2eZMicromega_2epadd) ).

fof('$_typeof_Coq.micromega.ZMicromega.valid_cut_sign',axiom,
    c_24__type__108195___24t(cCoq_2emicromega_2eZMicromega_2evalid__cut__sign) ).

fof('$_typeof_Coq.setoid_ring.Field_theory.FExpr',axiom,
    c_24__type__1141___24t(cCoq_2esetoid__ring_2eField__theory_2eFExpr) ).

fof('$_typeof_Coq.setoid_ring.Field_theory.linear',axiom,
    c_24__type__1141___24t(cCoq_2esetoid__ring_2eField__theory_2elinear) ).

fof('$_typeof_Coq.setoid_ring.Field_theory.rsplit',axiom,
    c_24__type__1141___24t(cCoq_2esetoid__ring_2eField__theory_2ersplit) ).

fof('$_typeof_Coq.setoid_ring.InitialRing.gen_phiPOS',axiom,
    c_24__type__112932___24t(cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS) ).

fof('$_typeof_Coq.setoid_ring.InitialRing.gen_phiPOS1',axiom,
    c_24__type__112932___24t(cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1) ).

fof('$_typeof_Coq.setoid_ring.InitialRing.hypo',axiom,
    cType___24t(cCoq_2esetoid__ring_2eInitialRing_2ehypo) ).

fof('$_typeof_Coq.setoid_ring.InitialRing.triv_div',axiom,
    c_24__type__199450___24t(cCoq_2esetoid__ring_2eInitialRing_2etriv__div) ).

fof('$_typeof_Coq.setoid_ring.Ring_polynom.Mon',axiom,
    cType___24t(cCoq_2esetoid__ring_2eRing__polynom_2eMon) ).

fof('$_typeof_Coq.setoid_ring.Ring_polynom.P0',axiom,
    c_24__type__115492___24t(cCoq_2esetoid__ring_2eRing__polynom_2eP0) ).

fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEX',axiom,
    c_24__type__1635___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEX) ).

fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEadd',axiom,
    c_24__type__1640___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEadd) ).

fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEc',axiom,
    c_24__type__1632___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEc) ).

fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEmul',axiom,
    c_24__type__1640___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEmul) ).

fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEsub',axiom,
    c_24__type__1640___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEsub) ).

fof('$_typeof_Coq.setoid_ring.Ring_polynom.PExpr',axiom,
    c_24__type__1141___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr) ).

fof('$_typeof_Coq.setoid_ring.Ring_polynom.Pc',axiom,
    c_24__type__115492___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePc) ).

fof('$_typeof_Coq.setoid_ring.Ring_polynom.Peq',axiom,
    c_24__type__1383___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePeq) ).

fof('$_typeof_Coq.setoid_ring.Ring_polynom.Pol',axiom,
    c_24__type__1141___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePol) ).

fof('$_typeof_Coq.setoid_ring.Ring_polynom.add_pow_list',axiom,
    c_24__type__216915___24t(cCoq_2esetoid__ring_2eRing__polynom_2eadd__pow__list) ).

fof('$_typeof_Coq.setoid_ring.Ring_polynom.mkPinj',axiom,
    c_24__type__115497___24t(cCoq_2esetoid__ring_2eRing__polynom_2emkPinj) ).

fof('$_typeof_Coq.setoid_ring.Ring_polynom.mkZmon',axiom,
    c_24__type__115508___24t(cCoq_2esetoid__ring_2eRing__polynom_2emkZmon) ).

fof('$_typeof_Coq.setoid_ring.Ring_polynom.mk_monpol_list',axiom,
    c_24__type__2036___24t(cCoq_2esetoid__ring_2eRing__polynom_2emk__monpol__list) ).

fof('$_typeof_Coq.setoid_ring.Ring_polynom.mkmult_pow',axiom,
    c_24__type__113392___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.norm_subst',axiom,
    c_24__type__1854___24t(cCoq_2esetoid__ring_2eRing__polynom_2enorm__subst) ).

fof('$_typeof_Coq.setoid_ring.Ring_polynom.vmon',axiom,
    c_24__type__115508___24t(cCoq_2esetoid__ring_2eRing__polynom_2evmon) ).

fof('$_typeof_Coq.setoid_ring.Ring_polynom.zmon',axiom,
    c_24__type__115508___24t(cCoq_2esetoid__ring_2eRing__polynom_2ezmon) ).

fof('$_typeof_Coq.setoid_ring.Ring_polynom.zmon_pred',axiom,
    c_24__type__115508___24t(cCoq_2esetoid__ring_2eRing__polynom_2ezmon__pred) ).

fof('$_typeof_Coq.setoid_ring.Ring_tac.ring_subst_niter',axiom,
    cCoq_2eInit_2eDatatypes_2enat___24t(cCoq_2esetoid__ring_2eRing__tac_2ering__subst__niter) ).

fof('$_typeof_Coq.setoid_ring.Ring_theory.IDphi',axiom,
    c_24__type__82538___24t(cCoq_2esetoid__ring_2eRing__theory_2eIDphi) ).

fof('$_typeof_Coq.setoid_ring.Ring_theory.SRopp',axiom,
    c_24__type__82538___24t(cCoq_2esetoid__ring_2eRing__theory_2eSRopp) ).

fof('$_typeof_Coq.setoid_ring.Ring_theory.id_phi_N',axiom,
    c_24__type__80052___24t(cCoq_2esetoid__ring_2eRing__theory_2eid__phi__N) ).

fof('$_typeof_Coq.setoid_ring.Ring_theory.pow_N',axiom,
    c_24__type__81197___24t(cCoq_2esetoid__ring_2eRing__theory_2epow__N) ).

fof('$_typeof_Coq.setoid_ring.Ring_theory.pow_pos',axiom,
    c_24__type__113413___24t(cCoq_2esetoid__ring_2eRing__theory_2epow__pos) ).

fof('$_typeof_Coq.setoid_ring.Ring_theory.ring_kind',axiom,
    cType___24t(cCoq_2esetoid__ring_2eRing__theory_2ering__kind) ).

fof('$_typeof_Hammer.Tactics.Reconstr.ReconstrT',axiom,
    cType___24t(cHammer_2eTactics_2eReconstr_2eReconstrT) ).

fof('$_typeof_Hammer.Tactics.Reconstr.rdone',axiom,
    c_24__type__90978___24t(cHammer_2eTactics_2eReconstr_2erdone) ).

fof('$_typeof_Hammer.Tactics.Tactics.rdone',axiom,
    c_24__type__90978___24t(cHammer_2eTactics_2eTactics_2erdone) ).

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.AId',axiom,
    c_24__type__393___24t(cPLF_2eImp_2eAId) ).

fof('$_typeof_PLF.Imp.ANum',axiom,
    c_24__type__391___24t(cPLF_2eImp_2eANum) ).

fof('$_typeof_PLF.Imp.APlus',axiom,
    c_24__type__396___24t(cPLF_2eImp_2eAPlus) ).

fof('$_typeof_PLF.Imp.BEq',axiom,
    c_24__type__76419___24t(cPLF_2eImp_2eBEq) ).

fof('$_typeof_PLF.Imp.BFalse',axiom,
    cPLF_2eImp_2ebexp___24t(cPLF_2eImp_2eBFalse) ).

fof('$_typeof_PLF.Imp.BTrue',axiom,
    cPLF_2eImp_2ebexp___24t(cPLF_2eImp_2eBTrue) ).

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__549___24t(cPLF_2eImp_2eCAss) ).

fof('$_typeof_PLF.Imp.CIf',axiom,
    c_24__type__554___24t(cPLF_2eImp_2eCIf) ).

fof('$_typeof_PLF.Imp.CSeq',axiom,
    c_24__type__113___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__116___24t(cPLF_2eImp_2eCWhile) ).

fof('$_typeof_PLF.Imp.SLoad',axiom,
    c_24__type__76446___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__76444___24t(cPLF_2eImp_2eSPush) ).

fof('$_typeof_PLF.Imp.X',axiom,
    cCoq_2eStrings_2eString_2estring___24t(cPLF_2eImp_2eX) ).

fof('$_typeof_PLF.Imp.Y',axiom,
    cCoq_2eStrings_2eString_2estring___24t(cPLF_2eImp_2eY) ).

fof('$_typeof_PLF.Imp.aevalR_division.aexp',axiom,
    cType___24t(cPLF_2eImp_2eaevalR__division_2eaexp) ).

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.empty_st',axiom,
    cPLF_2eMaps_2etotal__map___24t(cCoq_2eInit_2eDatatypes_2enat,cPLF_2eImp_2eempty__st) ).

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.LibTactics.Boxer',axiom,
    cType___24t(cPLF_2eLibTactics_2eBoxer) ).

fof('$_typeof_PLF.LibTactics.COIND',axiom,
    c_24__type__75738___24t(cPLF_2eLibTactics_2eCOIND) ).

fof('$_typeof_PLF.LibTactics.dup_lemma',axiom,
    c_24__type__82801___24t(cPLF_2eLibTactics_2edup__lemma) ).

fof('$_typeof_PLF.LibTactics.eq\'',axiom,
    c_24__type__89690___24t(cPLF_2eLibTactics_2eeq_27) ).

fof('$_typeof_PLF.LibTactics.ltac_No_arg',axiom,
    cType___24t(cPLF_2eLibTactics_2eltac__No__arg) ).

fof('$_typeof_PLF.LibTactics.ltac_Wild',axiom,
    cType___24t(cPLF_2eLibTactics_2eltac__Wild) ).

fof('$_typeof_PLF.LibTactics.ltac_Wilds',axiom,
    cType___24t(cPLF_2eLibTactics_2eltac__Wilds) ).

fof('$_typeof_PLF.LibTactics.ltac_something',axiom,
    c_24__type__82538___24t(cPLF_2eLibTactics_2eltac__something) ).

fof('$_typeof_PLF.LibTactics.ltac_tag_subst',axiom,
    c_24__type__82538___24t(cPLF_2eLibTactics_2eltac__tag__subst) ).

fof('$_typeof_PLF.LibTactics.ltac_to_generalize',axiom,
    c_24__type__82538___24t(cPLF_2eLibTactics_2eltac__to__generalize) ).

fof('$_typeof_PLF.LibTactics.rm',axiom,
    c_24__type__82538___24t(cPLF_2eLibTactics_2erm) ).

fof('$_typeof_PLF.Maps.empty',axiom,
    c_24__type__154315___24t(cPLF_2eMaps_2eempty) ).

fof('$_typeof_PLF.Maps.eqb_string',axiom,
    c_24__type__84765___24t(cPLF_2eMaps_2eeqb__string) ).

fof('$_typeof_PLF.Maps.eqb_stringP',axiom,
    c_24__type__198718___24t(cPLF_2eMaps_2eeqb__stringP) ).

fof('$_typeof_PLF.Maps.partial_map',axiom,
    c_24__type__1141___24t(cPLF_2eMaps_2epartial__map) ).

fof('$_typeof_PLF.Maps.t_empty',axiom,
    c_24__type__198772___24t(cPLF_2eMaps_2et__empty) ).

fof('$_typeof_PLF.Maps.t_update',axiom,
    c_24__type__566___24t(cPLF_2eMaps_2et__update) ).

fof('$_typeof_PLF.Maps.total_map',axiom,
    c_24__type__1141___24t(cPLF_2eMaps_2etotal__map) ).

fof('$_typeof_PLF.Maps.update',axiom,
    c_24__type__177135___24t(cPLF_2eMaps_2eupdate) ).

fof('$_typeof_PLF.References.STLCRef.Arrow',axiom,
    c_24__type__203383___24t(cPLF_2eReferences_2eSTLCRef_2eArrow) ).

fof('$_typeof_PLF.References.STLCRef.ExampleVariables.r',axiom,
    cCoq_2eStrings_2eString_2estring___24t(cPLF_2eReferences_2eSTLCRef_2eExampleVariables_2er) ).

fof('$_typeof_PLF.References.STLCRef.ExampleVariables.x',axiom,
    cCoq_2eStrings_2eString_2estring___24t(cPLF_2eReferences_2eSTLCRef_2eExampleVariables_2ex) ).

fof('$_typeof_PLF.References.STLCRef.Nat',axiom,
    cPLF_2eReferences_2eSTLCRef_2ety___24t(cPLF_2eReferences_2eSTLCRef_2eNat) ).

fof('$_typeof_PLF.References.STLCRef.Ref',axiom,
    c_24__type__203385___24t(cPLF_2eReferences_2eSTLCRef_2eRef) ).

fof('$_typeof_PLF.References.STLCRef.RefsAndNontermination.factorial',axiom,
    cPLF_2eReferences_2eSTLCRef_2etm___24t(cPLF_2eReferences_2eSTLCRef_2eRefsAndNontermination_2efactorial) ).

fof('$_typeof_PLF.References.STLCRef.RefsAndNontermination.loop',axiom,
    cPLF_2eReferences_2eSTLCRef_2etm___24t(cPLF_2eReferences_2eSTLCRef_2eRefsAndNontermination_2eloop) ).

fof('$_typeof_PLF.References.STLCRef.RefsAndNontermination.loop_fun',axiom,
    cPLF_2eReferences_2eSTLCRef_2etm___24t(cPLF_2eReferences_2eSTLCRef_2eRefsAndNontermination_2eloop__fun) ).

fof('$_typeof_PLF.References.STLCRef.RefsAndNontermination.multistep1',axiom,
    c_24__type__212345___24t(cPLF_2eReferences_2eSTLCRef_2eRefsAndNontermination_2emultistep1) ).

fof('$_typeof_PLF.References.STLCRef.Unit',axiom,
    cPLF_2eReferences_2eSTLCRef_2ety___24t(cPLF_2eReferences_2eSTLCRef_2eUnit) ).

fof('$_typeof_PLF.References.STLCRef.abs',axiom,
    c_24__type__203681___24t(cPLF_2eReferences_2eSTLCRef_2eabs) ).

fof('$_typeof_PLF.References.STLCRef.app',axiom,
    c_24__type__203676___24t(cPLF_2eReferences_2eSTLCRef_2eapp) ).

fof('$_typeof_PLF.References.STLCRef.assign',axiom,
    c_24__type__203676___24t(cPLF_2eReferences_2eSTLCRef_2eassign) ).

fof('$_typeof_PLF.References.STLCRef.const',axiom,
    c_24__type__203683___24t(cPLF_2eReferences_2eSTLCRef_2econst) ).

fof('$_typeof_PLF.References.STLCRef.context',axiom,
    cType___24t(cPLF_2eReferences_2eSTLCRef_2econtext) ).

fof('$_typeof_PLF.References.STLCRef.deref',axiom,
    c_24__type__203685___24t(cPLF_2eReferences_2eSTLCRef_2ederef) ).

fof('$_typeof_PLF.References.STLCRef.loc',axiom,
    c_24__type__203683___24t(cPLF_2eReferences_2eSTLCRef_2eloc) ).

fof('$_typeof_PLF.References.STLCRef.mlt',axiom,
    c_24__type__203676___24t(cPLF_2eReferences_2eSTLCRef_2emlt) ).

fof('$_typeof_PLF.References.STLCRef.multistep',axiom,
    cPLF_2eSmallstep_2erelation___24t(cCoq_2eInit_2eDatatypes_2eprod___24a2(cPLF_2eReferences_2eSTLCRef_2etm,cPLF_2eReferences_2eSTLCRef_2estore),cPLF_2eReferences_2eSTLCRef_2emultistep) ).

fof('$_typeof_PLF.References.STLCRef.prd',axiom,
    c_24__type__203685___24t(cPLF_2eReferences_2eSTLCRef_2eprd) ).

fof('$_typeof_PLF.References.STLCRef.preservation_theorem',axiom,
    cProp___24t(cPLF_2eReferences_2eSTLCRef_2epreservation__theorem) ).

fof('$_typeof_PLF.References.STLCRef.ref',axiom,
    c_24__type__203685___24t(cPLF_2eReferences_2eSTLCRef_2eref) ).

fof('$_typeof_PLF.References.STLCRef.replace',axiom,
    c_24__type__203761___24t(cPLF_2eReferences_2eSTLCRef_2ereplace) ).

fof('$_typeof_PLF.References.STLCRef.scc',axiom,
    c_24__type__203685___24t(cPLF_2eReferences_2eSTLCRef_2escc) ).

fof('$_typeof_PLF.References.STLCRef.store',axiom,
    cType___24t(cPLF_2eReferences_2eSTLCRef_2estore) ).

fof('$_typeof_PLF.References.STLCRef.store_Tlookup',axiom,
    c_24__type__211757___24t(cPLF_2eReferences_2eSTLCRef_2estore__Tlookup) ).

fof('$_typeof_PLF.References.STLCRef.store_lookup',axiom,
    c_24__type__203741___24t(cPLF_2eReferences_2eSTLCRef_2estore__lookup) ).

fof('$_typeof_PLF.References.STLCRef.store_ty',axiom,
    cType___24t(cPLF_2eReferences_2eSTLCRef_2estore__ty) ).

fof('$_typeof_PLF.References.STLCRef.store_well_typed',axiom,
    c_24__type__212317___24t(cPLF_2eReferences_2eSTLCRef_2estore__well__typed) ).

fof('$_typeof_PLF.References.STLCRef.subst',axiom,
    c_24__type__203737___24t(cPLF_2eReferences_2eSTLCRef_2esubst) ).

fof('$_typeof_PLF.References.STLCRef.test0',axiom,
    c_24__type__203691___24t(cPLF_2eReferences_2eSTLCRef_2etest0) ).

fof('$_typeof_PLF.References.STLCRef.tm',axiom,
    cType___24t(cPLF_2eReferences_2eSTLCRef_2etm) ).

fof('$_typeof_PLF.References.STLCRef.tseq',axiom,
    c_24__type__203676___24t(cPLF_2eReferences_2eSTLCRef_2etseq) ).

fof('$_typeof_PLF.References.STLCRef.ty',axiom,
    cType___24t(cPLF_2eReferences_2eSTLCRef_2ety) ).

fof('$_typeof_PLF.References.STLCRef.ty_rec',axiom,
    c_24__type__219161___24t(cPLF_2eReferences_2eSTLCRef_2ety__rec) ).

fof('$_typeof_PLF.References.STLCRef.ty_rect',axiom,
    c_24__type__219161___24t(cPLF_2eReferences_2eSTLCRef_2ety__rect) ).

fof('$_typeof_PLF.References.STLCRef.unit',axiom,
    cPLF_2eReferences_2eSTLCRef_2etm___24t(cPLF_2eReferences_2eSTLCRef_2eunit) ).

fof('$_typeof_PLF.References.STLCRef.var',axiom,
    c_24__type__203673___24t(cPLF_2eReferences_2eSTLCRef_2evar) ).

fof('$_typeof_PLF.Smallstep.C',axiom,
    c_24__type__949___24t(cPLF_2eSmallstep_2eC) ).

fof('$_typeof_PLF.Smallstep.CImp.CAss',axiom,
    c_24__type__79565___24t(cPLF_2eSmallstep_2eCImp_2eCAss) ).

fof('$_typeof_PLF.Smallstep.CImp.CIf',axiom,
    c_24__type__79573___24t(cPLF_2eSmallstep_2eCImp_2eCIf) ).

fof('$_typeof_PLF.Smallstep.CImp.CPar',axiom,
    c_24__type__79568___24t(cPLF_2eSmallstep_2eCImp_2eCPar) ).

fof('$_typeof_PLF.Smallstep.CImp.CSeq',axiom,
    c_24__type__79568___24t(cPLF_2eSmallstep_2eCImp_2eCSeq) ).

fof('$_typeof_PLF.Smallstep.CImp.CSkip',axiom,
    cPLF_2eSmallstep_2eCImp_2ecom___24t(cPLF_2eSmallstep_2eCImp_2eCSkip) ).

fof('$_typeof_PLF.Smallstep.CImp.CWhile',axiom,
    c_24__type__79576___24t(cPLF_2eSmallstep_2eCImp_2eCWhile) ).

fof('$_typeof_PLF.Smallstep.CImp.com',axiom,
    cType___24t(cPLF_2eSmallstep_2eCImp_2ecom) ).

fof('$_typeof_PLF.Smallstep.Combined.tm',axiom,
    cType___24t(cPLF_2eSmallstep_2eCombined_2etm) ).

fof('$_typeof_PLF.Smallstep.P',axiom,
    c_24__type__952___24t(cPLF_2eSmallstep_2eP) ).

fof('$_typeof_PLF.Smallstep.Temp4.tm',axiom,
    cType___24t(cPLF_2eSmallstep_2eTemp4_2etm) ).

fof('$_typeof_PLF.Smallstep.compiler_is_correct_statement',axiom,
    cProp___24t(cPLF_2eSmallstep_2ecompiler__is__correct__statement) ).

fof('$_typeof_PLF.Smallstep.prog',axiom,
    cType___24t(cPLF_2eSmallstep_2eprog) ).

fof('$_typeof_PLF.Smallstep.relation',axiom,
    c_24__type__1141___24t(cPLF_2eSmallstep_2erelation) ).

fof('$_typeof_PLF.Smallstep.stack',axiom,
    cType___24t(cPLF_2eSmallstep_2estack) ).

fof('$_typeof_PLF.Smallstep.tm',axiom,
    cType___24t(cPLF_2eSmallstep_2etm) ).

fof('$_typeof_PLF.Stlc.STLC.Arrow',axiom,
    c_24__type__109349___24t(cPLF_2eStlc_2eSTLC_2eArrow) ).

fof('$_typeof_PLF.Stlc.STLC.Bool',axiom,
    cPLF_2eStlc_2eSTLC_2ety___24t(cPLF_2eStlc_2eSTLC_2eBool) ).

fof('$_typeof_PLF.Stlc.STLC.abs',axiom,
    c_24__type__109359___24t(cPLF_2eStlc_2eSTLC_2eabs) ).

fof('$_typeof_PLF.Stlc.STLC.app',axiom,
    c_24__type__109354___24t(cPLF_2eStlc_2eSTLC_2eapp) ).

fof('$_typeof_PLF.Stlc.STLC.context',axiom,
    cType___24t(cPLF_2eStlc_2eSTLC_2econtext) ).

fof('$_typeof_PLF.Stlc.STLC.fls',axiom,
    cPLF_2eStlc_2eSTLC_2etm___24t(cPLF_2eStlc_2eSTLC_2efls) ).

fof('$_typeof_PLF.Stlc.STLC.subst',axiom,
    c_24__type__109400___24t(cPLF_2eStlc_2eSTLC_2esubst) ).

fof('$_typeof_PLF.Stlc.STLC.test',axiom,
    c_24__type__109364___24t(cPLF_2eStlc_2eSTLC_2etest) ).

fof('$_typeof_PLF.Stlc.STLC.tm',axiom,
    cType___24t(cPLF_2eStlc_2eSTLC_2etm) ).

fof('$_typeof_PLF.Stlc.STLC.tru',axiom,
    cPLF_2eStlc_2eSTLC_2etm___24t(cPLF_2eStlc_2eSTLC_2etru) ).

fof('$_typeof_PLF.Stlc.STLC.ty',axiom,
    cType___24t(cPLF_2eStlc_2eSTLC_2ety) ).

fof('$_typeof_PLF.Stlc.STLC.var',axiom,
    c_24__type__109351___24t(cPLF_2eStlc_2eSTLC_2evar) ).

fof('$_typeof_PLF.Stlc.STLC.x',axiom,
    cCoq_2eStrings_2eString_2estring___24t(cPLF_2eStlc_2eSTLC_2ex) ).

fof('$_typeof_PLF.Stlc.STLC.y',axiom,
    cCoq_2eStrings_2eString_2estring___24t(cPLF_2eStlc_2eSTLC_2ey) ).

fof('$_typeof_PLF.Stlc.STLC.z',axiom,
    cCoq_2eStrings_2eString_2estring___24t(cPLF_2eStlc_2eSTLC_2ez) ).

fof('$_typeof_PLF.StlcProp.STLCArith.tm',axiom,
    cType___24t(cPLF_2eStlcProp_2eSTLCArith_2etm) ).

fof('$_typeof_PLF.StlcProp.STLCArith.ty',axiom,
    cType___24t(cPLF_2eStlcProp_2eSTLCArith_2ety) ).

fof('$_typeof_PLF.StlcProp.STLCProp.closed',axiom,
    c_24__type__198715___24t(cPLF_2eStlcProp_2eSTLCProp_2eclosed) ).

fof('$_typeof_PLF.Types.fls',axiom,
    cPLF_2eTypes_2etm___24t(cPLF_2eTypes_2efls) ).

fof('$_typeof_PLF.Types.tm',axiom,
    cType___24t(cPLF_2eTypes_2etm) ).

fof('$_typeof_PLF.Types.tru',axiom,
    cPLF_2eTypes_2etm___24t(cPLF_2eTypes_2etru) ).

fof('$_typeof_PLF.Types.ty',axiom,
    cType___24t(cPLF_2eTypes_2ety) ).

fof('$_typeof_PLF.Types.zro',axiom,
    cPLF_2eTypes_2etm___24t(cPLF_2eTypes_2ezro) ).

fof('Coq.Arith.Compare_dec.dec_ge',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
         => cCoq_2eLogic_2eDecidable_2edecidable___24a1(cCoq_2eInit_2ePeano_2ege___24a2(V0__n,V1__m)) ) ) ).

fof('Coq.Arith.Compare_dec.dec_lt',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
         => cCoq_2eLogic_2eDecidable_2edecidable___24a1(cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)) ) ) ).

fof('Coq.Arith.Compare_dec.not_ge',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
         => ( ~ p(cCoq_2eInit_2ePeano_2ege___24a2(V0__n,V1__m))
           => p(cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)) ) ) ) ).

fof('Coq.Arith.Compare_dec.not_lt',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
         => ( ~ p(cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m))
           => p(cCoq_2eInit_2ePeano_2ege___24a2(V0__n,V1__m)) ) ) ) ).

fof('Coq.Arith.Lt.lt_S_n',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
         => ( p(cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m)))
           => p(cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)) ) ) ) ).

fof('Coq.Arith.Lt.lt_n_S',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
         => ( p(cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m))
           => p(cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n),cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m))) ) ) ) ).

fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.eq_refl',axiom,
    ! [V0__x] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
     => V0__x = V0__x ) ).

fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.lt_irrefl',axiom,
    ! [V0__x] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
     => ~ p(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.eq_equiv',axiom,
    cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(cCoq_2eInit_2eDatatypes_2enat,c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat)) ).

fof('Coq.Arith.PeanoNat.Nat.eqb_eq',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
         => ( cCoq_2eInit_2eNat_2eeqb___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2etrue
          <=> V0__n = V1__m ) ) ) ).

fof('Coq.Arith.PeanoNat.Nat.eqb_neq',axiom,
    ! [V0__x] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
         => ( cCoq_2eInit_2eNat_2eeqb___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efalse
          <=> V0__x != V1__y ) ) ) ).

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.sub_diag',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => cCoq_2eInit_2eNat_2esub___24a2(V0__n,V0__n) = cCoq_2eInit_2eDatatypes_2eO ) ).

fof('Coq.Init.Datatypes.list_ind',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__P] :
          ( c_24__type__75693___24t(V0__A,V1__P)
         => ( p(happ(V1__P,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)))
           => ( ! [V3__a] :
                  ( t(V3__a,V0__A)
                 => ! [V4__l] :
                      ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
                     => ( p(happ(V1__P,V4__l))
                       => p(happ(V1__P,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__a,V4__l))) ) ) )
             => ! [V4__l] :
                  ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
                 => p(happ(V1__P,V4__l)) ) ) ) ) ) ).

fof('Coq.Init.Datatypes.nat_ind',axiom,
    ! [V0__P] :
      ( c_24__type__592___24t(V0__P)
     => ( p(happ(V0__P,cCoq_2eInit_2eDatatypes_2eO))
       => ( ! [V2__n] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
             => ( p(happ(V0__P,V2__n))
               => p(happ(V0__P,cCoq_2eInit_2eDatatypes_2eS___24a1(V2__n))) ) )
         => ! [V3__n] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(V3__n)
             => p(happ(V0__P,V3__n)) ) ) ) ) ).

fof('Coq.Init.Datatypes.pair_equal_spec',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__B] :
          ( cType___24t(V1__B)
         => ! [V2__a1] :
              ( t(V2__a1,V0__A)
             => ! [V3__a2] :
                  ( t(V3__a2,V0__A)
                 => ! [V4__b1] :
                      ( t(V4__b1,V1__B)
                     => ! [V5__b2] :
                          ( t(V5__b2,V1__B)
                         => ( cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V1__B,V2__a1,V4__b1) = cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V1__B,V3__a2,V5__b2)
                          <=> ( V2__a1 = V3__a2
                              & V4__b1 = V5__b2 ) ) ) ) ) ) ) ) ).

fof('Coq.Init.Datatypes.prod_ind',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__B] :
          ( cType___24t(V1__B)
         => ! [V2__P] :
              ( c_24__type__212728___24t(V0__A,V1__B,V2__P)
             => ( ! [V3__a] :
                    ( t(V3__a,V0__A)
                   => ! [V4__b] :
                        ( t(V4__b,V1__B)
                       => p(happ(V2__P,cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V1__B,V3__a,V4__b))) ) )
               => ! [V4__p] :
                    ( cCoq_2eInit_2eDatatypes_2eprod___24t(V0__A,V1__B,V4__p)
                   => p(happ(V2__P,V4__p)) ) ) ) ) ) ).

fof('Coq.Init.Datatypes.prod_sind',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__B] :
          ( cType___24t(V1__B)
         => ! [V2__P] :
              ( c_24__type__212728___24t(V0__A,V1__B,V2__P)
             => ( ! [V3__a] :
                    ( t(V3__a,V0__A)
                   => ! [V4__b] :
                        ( t(V4__b,V1__B)
                       => p(happ(V2__P,cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V1__B,V3__a,V4__b))) ) )
               => ! [V4__p] :
                    ( cCoq_2eInit_2eDatatypes_2eprod___24t(V0__A,V1__B,V4__p)
                   => p(happ(V2__P,V4__p)) ) ) ) ) ) ).

fof('Coq.Init.Peano.f_equal_nat',axiom,
    ! [V0__B] :
      ( cType___24t(V0__B)
     => ! [V1__f] :
          ( c_24__type__934___24t(V0__B,V1__f)
         => ! [V2__x] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__x)
             => ! [V3__y] :
                  ( cCoq_2eInit_2eDatatypes_2enat___24t(V3__y)
                 => ( V2__x = V3__y
                   => happ(V1__f,V2__x) = happ(V1__f,V3__y) ) ) ) ) ) ).

fof('Coq.Init.Peano.le_n',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V0__n) ) ).

fof('Coq.Init.Peano.plus_n_Sm',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
         => cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2eadd___24a2(V0__n,V1__m)) = cCoq_2eInit_2eNat_2eadd___24a2(V0__n,cCoq_2eInit_2eDatatypes_2eS___24a1(V1__m)) ) ) ).

fof('Coq.Init.Wf.Acc_inv',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__R] :
          ( c_24__type__76843___24t(V0__A,V1__R)
         => ! [V2__x] :
              ( t(V2__x,V0__A)
             => ( cCoq_2eInit_2eWf_2eAcc___24a3(V0__A,V1__R,V2__x)
               => ! [V4__y] :
                    ( t(V4__y,V0__A)
                   => ( p(happ(happ(V1__R,V4__y),V2__x))
                     => cCoq_2eInit_2eWf_2eAcc___24a3(V0__A,V1__R,V4__y) ) ) ) ) ) ) ).

fof('Coq.Lists.List.app_length',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__l] :
          ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
         => ! [V2__l_27] :
              ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l_27)
             => cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__l,V2__l_27)) = cCoq_2eInit_2eNat_2eadd___24a2(cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V1__l),cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__l_27)) ) ) ) ).

fof('Coq.Lists.List.app_nth1',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__l] :
          ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
         => ! [V2__l_27] :
              ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l_27)
             => ! [V3__d] :
                  ( t(V3__d,V0__A)
                 => ! [V4__n] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(V4__n)
                     => ( p(cCoq_2eInit_2ePeano_2elt___24a2(V4__n,cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V1__l)))
                       => cCoq_2eLists_2eList_2enth___24a4(V0__A,V4__n,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__l,V2__l_27),V3__d) = cCoq_2eLists_2eList_2enth___24a4(V0__A,V4__n,V1__l,V3__d) ) ) ) ) ) ) ).

fof('Coq.Lists.List.app_nth2',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__l] :
          ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
         => ! [V2__l_27] :
              ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l_27)
             => ! [V3__d] :
                  ( t(V3__d,V0__A)
                 => ! [V4__n] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(V4__n)
                     => ( p(cCoq_2eInit_2ePeano_2ege___24a2(V4__n,cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V1__l)))
                       => cCoq_2eLists_2eList_2enth___24a4(V0__A,V4__n,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__l,V2__l_27),V3__d) = cCoq_2eLists_2eList_2enth___24a4(V0__A,cCoq_2eInit_2eNat_2esub___24a2(V4__n,cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V1__l)),V2__l_27,V3__d) ) ) ) ) ) ) ).

fof('Coq.Lists.List.elements_in_partition',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__f] :
          ( c_24__type__76596___24t(V0__A,V1__f)
         => ! [V2__l] :
              ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
             => ! [V3__l1] :
                  ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l1)
                 => ! [V4__l2] :
                      ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l2)
                     => ( cCoq_2eLists_2eList_2epartition___24a3(V0__A,V1__f,V2__l) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),V3__l1,V4__l2)
                       => ! [V6__x] :
                            ( t(V6__x,V0__A)
                           => ( cCoq_2eLists_2eList_2eIn___24a3(V0__A,V6__x,V2__l)
                            <=> ( cCoq_2eLists_2eList_2eIn___24a3(V0__A,V6__x,V3__l1)
                                | cCoq_2eLists_2eList_2eIn___24a3(V0__A,V6__x,V4__l2) ) ) ) ) ) ) ) ) ) ).

fof('Coq.Lists.List.in_app_or',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__l] :
          ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
         => ! [V2__m] :
              ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__m)
             => ! [V3__a] :
                  ( t(V3__a,V0__A)
                 => ( cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__a,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__l,V2__m))
                   => ( cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__a,V1__l)
                      | cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__a,V2__m) ) ) ) ) ) ) ).

fof('Coq.Lists.List.in_combine_l',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__B] :
          ( cType___24t(V1__B)
         => ! [V2__l] :
              ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
             => ! [V3__l_27] :
                  ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,V3__l_27)
                 => ! [V4__x] :
                      ( t(V4__x,V0__A)
                     => ! [V5__y] :
                          ( t(V5__y,V1__B)
                         => ( cCoq_2eLists_2eList_2eIn___24a3(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__A,V1__B),cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V1__B,V4__x,V5__y),cCoq_2eLists_2eList_2ecombine___24a4(V0__A,V1__B,V2__l,V3__l_27))
                           => cCoq_2eLists_2eList_2eIn___24a3(V0__A,V4__x,V2__l) ) ) ) ) ) ) ) ).

fof('Coq.Lists.List.in_combine_r',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__B] :
          ( cType___24t(V1__B)
         => ! [V2__l] :
              ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
             => ! [V3__l_27] :
                  ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,V3__l_27)
                 => ! [V4__x] :
                      ( t(V4__x,V0__A)
                     => ! [V5__y] :
                          ( t(V5__y,V1__B)
                         => ( cCoq_2eLists_2eList_2eIn___24a3(cCoq_2eInit_2eDatatypes_2eprod___24a2(V0__A,V1__B),cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V1__B,V4__x,V5__y),cCoq_2eLists_2eList_2ecombine___24a4(V0__A,V1__B,V2__l,V3__l_27))
                           => cCoq_2eLists_2eList_2eIn___24a3(V1__B,V5__y,V3__l_27) ) ) ) ) ) ) ) ).

fof('Coq.Lists.List.in_or_app',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__l] :
          ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
         => ! [V2__m] :
              ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__m)
             => ! [V3__a] :
                  ( t(V3__a,V0__A)
                 => ( ( cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__a,V1__l)
                      | cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__a,V2__m) )
                   => cCoq_2eLists_2eList_2eIn___24a3(V0__A,V3__a,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__l,V2__m)) ) ) ) ) ) ).

fof('Coq.Lists.List.partition_cons1',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__f] :
          ( c_24__type__76596___24t(V0__A,V1__f)
         => ! [V2__a] :
              ( t(V2__a,V0__A)
             => ! [V3__l] :
                  ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
                 => ! [V4__l1] :
                      ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l1)
                     => ! [V5__l2] :
                          ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l2)
                         => ( cCoq_2eLists_2eList_2epartition___24a3(V0__A,V1__f,V3__l) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),V4__l1,V5__l2)
                           => ( happ(V1__f,V2__a) = cCoq_2eInit_2eDatatypes_2etrue
                             => cCoq_2eLists_2eList_2epartition___24a3(V0__A,V1__f,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__a,V3__l)) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__a,V4__l1),V5__l2) ) ) ) ) ) ) ) ) ).

fof('Coq.Lists.List.partition_cons2',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__f] :
          ( c_24__type__76596___24t(V0__A,V1__f)
         => ! [V2__a] :
              ( t(V2__a,V0__A)
             => ! [V3__l] :
                  ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
                 => ! [V4__l1] :
                      ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l1)
                     => ! [V5__l2] :
                          ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V5__l2)
                         => ( cCoq_2eLists_2eList_2epartition___24a3(V0__A,V1__f,V3__l) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),V4__l1,V5__l2)
                           => ( happ(V1__f,V2__a) = cCoq_2eInit_2eDatatypes_2efalse
                             => cCoq_2eLists_2eList_2epartition___24a3(V0__A,V1__f,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__a,V3__l)) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),V4__l1,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__a,V5__l2)) ) ) ) ) ) ) ) ) ).

fof('Coq.Lists.List.partition_length',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__f] :
          ( c_24__type__76596___24t(V0__A,V1__f)
         => ! [V2__l] :
              ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
             => ! [V3__l1] :
                  ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l1)
                 => ! [V4__l2] :
                      ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l2)
                     => ( cCoq_2eLists_2eList_2epartition___24a3(V0__A,V1__f,V2__l) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),cCoq_2eInit_2eDatatypes_2elist___24a1(V0__A),V3__l1,V4__l2)
                       => cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__l) = cCoq_2eInit_2eNat_2eadd___24a2(cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V3__l1),cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V4__l2)) ) ) ) ) ) ) ).

fof('Coq.Lists.SetoidList.InA_cons_hd',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__eqA] :
          ( c_24__type__76843___24t(V0__A,V1__eqA)
         => ! [V2__x] :
              ( t(V2__x,V0__A)
             => ! [V3__y] :
                  ( t(V3__y,V0__A)
                 => ! [V4__l] :
                      ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
                     => ( p(happ(happ(V1__eqA,V2__x),V3__y))
                       => cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V2__x,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__y,V4__l)) ) ) ) ) ) ) ).

fof('Coq.Lists.SetoidList.InA_cons_tl',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__eqA] :
          ( c_24__type__76843___24t(V0__A,V1__eqA)
         => ! [V2__x] :
              ( t(V2__x,V0__A)
             => ! [V3__y] :
                  ( t(V3__y,V0__A)
                 => ! [V4__l] :
                      ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V4__l)
                     => ( cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V2__x,V4__l)
                       => cCoq_2eLists_2eSetoidList_2eInA___24a4(V0__A,V1__eqA,V2__x,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V3__y,V4__l)) ) ) ) ) ) ) ).

fof('Coq.Logic.Decidable.dec_and',axiom,
    ! [V0__A] :
      ( cProp___24t(V0__A)
     => ! [V1__B] :
          ( cProp___24t(V1__B)
         => ( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V0__A)
           => ( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V1__B)
             => cCoq_2eLogic_2eDecidable_2edecidable___24a1(c_24__prop__94743___24a2(V0__A,V1__B)) ) ) ) ) ).

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.imp_simp',axiom,
    ! [V0__A] :
      ( cProp___24t(V0__A)
     => ! [V1__B] :
          ( cProp___24t(V1__B)
         => ( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V0__A)
           => ( ( p(V0__A)
               => p(V1__B) )
             => ( ~ p(V0__A)
                | p(V1__B) ) ) ) ) ) ).

fof('Coq.Logic.Decidable.not_and',axiom,
    ! [V0__A] :
      ( cProp___24t(V0__A)
     => ! [V1__B] :
          ( cProp___24t(V1__B)
         => ( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V0__A)
           => ( ~ ( p(V0__A)
                  & p(V1__B) )
             => ( ~ p(V0__A)
                | ~ p(V1__B) ) ) ) ) ) ).

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.FunctionalExtensionality.equal_f',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__B] :
          ( cType___24t(V1__B)
         => ! [V2__f] :
              ( c_24__type__75666___24t(V0__A,V1__B,V2__f)
             => ! [V3__g] :
                  ( c_24__type__75666___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__85086___24t(V0__A,V1__B)
         => ! [V2__f] :
              ( c_24__type__113699___24t(V0__A,V1__B,V2__f)
             => ! [V3__g] :
                  ( c_24__type__113704___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__75666___24t(V0__A,V1__B,V2__f)
             => V2__f = c_24__lam__112906___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__85086___24t(V0__A,V1__B)
         => ! [V2__f] :
              ( c_24__type__112890___24t(V0__A,V1__B,V2__f)
             => V2__f = c_24__lam__112898___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__75666___24t(V0__A,V1__B,V2__f)
             => ! [V3__g] :
                  ( c_24__type__75666___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__85086___24t(V0__A,V1__B)
         => ! [V2__f] :
              ( c_24__type__113710___24t(V0__A,V1__B,V2__f)
             => ! [V3__g] :
                  ( c_24__type__113715___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.ProofIrrelevance.proof_irrelevance',axiom,
    ! [V0__P] :
      ( cProp___24t(V0__P)
     => ( p(V0__P)
       => ( p(V0__P)
         => c_24Proof = c_24Proof ) ) ) ).

fof('Coq.PArith.BinPos.Pos.iter_invariant',axiom,
    ! [V0__p] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
     => ! [V1__A] :
          ( cType___24t(V1__A)
         => ! [V2__f] :
              ( c_24__type__1868___24t(V1__A,V2__f)
             => ! [V3__Inv] :
                  ( c_24__type__78062___24t(V1__A,V3__Inv)
                 => ( ! [V4__x] :
                        ( t(V4__x,V1__A)
                       => ( p(happ(V3__Inv,V4__x))
                         => p(happ(V3__Inv,happ(V2__f,V4__x))) ) )
                   => ! [V5__x] :
                        ( t(V5__x,V1__A)
                       => ( p(happ(V3__Inv,V5__x))
                         => p(happ(V3__Inv,cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V1__A,V2__f,V5__x,V0__p))) ) ) ) ) ) ) ) ).

fof('Coq.Relations.Relation_Operators.left_sym',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__B] :
          ( cType___24t(V1__B)
         => ! [V2__leA] :
              ( c_24__type__76843___24t(V0__A,V2__leA)
             => ! [V3__leB] :
                  ( c_24__type__76925___24t(V0__A,V1__B,V3__leB)
                 => ! [V4__x] :
                      ( t(V4__x,V0__A)
                     => ! [V5__x_27] :
                          ( t(V5__x_27,V0__A)
                         => ( p(happ(happ(V2__leA,V4__x),V5__x_27))
                           => ! [V7__y] :
                                ( t(V7__y,V1__B)
                               => cCoq_2eRelations_2eRelation__Operators_2esymprod___24a6(V0__A,V1__B,V2__leA,V3__leB,cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V1__B,V4__x,V7__y),cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V1__B,V5__x_27,V7__y)) ) ) ) ) ) ) ) ) ).

fof('Coq.Relations.Relation_Operators.right_sym',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__B] :
          ( cType___24t(V1__B)
         => ! [V2__leA] :
              ( c_24__type__76843___24t(V0__A,V2__leA)
             => ! [V3__leB] :
                  ( c_24__type__76925___24t(V0__A,V1__B,V3__leB)
                 => ! [V4__y] :
                      ( t(V4__y,V1__B)
                     => ! [V5__y_27] :
                          ( t(V5__y_27,V1__B)
                         => ( p(happ(happ(V3__leB,V4__y),V5__y_27))
                           => ! [V7__x] :
                                ( t(V7__x,V0__A)
                               => cCoq_2eRelations_2eRelation__Operators_2esymprod___24a6(V0__A,V1__B,V2__leA,V3__leB,cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V1__B,V7__x,V4__y),cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V1__B,V7__x,V5__y_27)) ) ) ) ) ) ) ) ) ).

fof('Coq.Relations.Relation_Operators.sp_noswap',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__R] :
          ( c_24__type__76843___24t(V0__A,V1__R)
         => ! [V2__x] :
              ( t(V2__x,V0__A)
             => ! [V3__y] :
                  ( t(V3__y,V0__A)
                 => ! [V4__p] :
                      ( cCoq_2eInit_2eDatatypes_2eprod___24t(V0__A,V0__A,V4__p)
                     => ( cCoq_2eRelations_2eRelation__Operators_2esymprod___24a6(V0__A,V0__A,V1__R,V1__R,cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V0__A,V2__x,V3__y),V4__p)
                       => cCoq_2eRelations_2eRelation__Operators_2eswapprod___24a4(V0__A,V1__R,cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V0__A,V2__x,V3__y),V4__p) ) ) ) ) ) ) ).

fof('Coq.Relations.Relation_Operators.sp_swap',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__R] :
          ( c_24__type__76843___24t(V0__A,V1__R)
         => ! [V2__x] :
              ( t(V2__x,V0__A)
             => ! [V3__y] :
                  ( t(V3__y,V0__A)
                 => ! [V4__p] :
                      ( cCoq_2eInit_2eDatatypes_2eprod___24t(V0__A,V0__A,V4__p)
                     => ( cCoq_2eRelations_2eRelation__Operators_2esymprod___24a6(V0__A,V0__A,V1__R,V1__R,cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V0__A,V2__x,V3__y),V4__p)
                       => cCoq_2eRelations_2eRelation__Operators_2eswapprod___24a4(V0__A,V1__R,cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V0__A,V3__y,V2__x),V4__p) ) ) ) ) ) ) ).

fof('Coq.Relations.Relation_Operators.swapprod_ind',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__R] :
          ( c_24__type__76843___24t(V0__A,V1__R)
         => ! [V2__P] :
              ( c_24__type__214597___24t(V0__A,V2__P)
             => ( ! [V3__x] :
                    ( t(V3__x,V0__A)
                   => ! [V4__y] :
                        ( t(V4__y,V0__A)
                       => ! [V5__p] :
                            ( cCoq_2eInit_2eDatatypes_2eprod___24t(V0__A,V0__A,V5__p)
                           => ( cCoq_2eRelations_2eRelation__Operators_2esymprod___24a6(V0__A,V0__A,V1__R,V1__R,cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V0__A,V3__x,V4__y),V5__p)
                             => p(happ(happ(V2__P,cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V0__A,V3__x,V4__y)),V5__p)) ) ) ) )
               => ( ! [V4__x] :
                      ( t(V4__x,V0__A)
                     => ! [V5__y] :
                          ( t(V5__y,V0__A)
                         => ! [V6__p] :
                              ( cCoq_2eInit_2eDatatypes_2eprod___24t(V0__A,V0__A,V6__p)
                             => ( cCoq_2eRelations_2eRelation__Operators_2esymprod___24a6(V0__A,V0__A,V1__R,V1__R,cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V0__A,V4__x,V5__y),V6__p)
                               => p(happ(happ(V2__P,cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V0__A,V5__y,V4__x)),V6__p)) ) ) ) )
                 => ! [V5__p] :
                      ( cCoq_2eInit_2eDatatypes_2eprod___24t(V0__A,V0__A,V5__p)
                     => ! [V6__p] :
                          ( cCoq_2eInit_2eDatatypes_2eprod___24t(V0__A,V0__A,V6__p)
                         => ( cCoq_2eRelations_2eRelation__Operators_2eswapprod___24a4(V0__A,V1__R,V5__p,V6__p)
                           => p(happ(happ(V2__P,V5__p),V6__p)) ) ) ) ) ) ) ) ) ).

fof('Coq.Relations.Relation_Operators.swapprod_sind',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__R] :
          ( c_24__type__76843___24t(V0__A,V1__R)
         => ! [V2__P] :
              ( c_24__type__214597___24t(V0__A,V2__P)
             => ( ! [V3__x] :
                    ( t(V3__x,V0__A)
                   => ! [V4__y] :
                        ( t(V4__y,V0__A)
                       => ! [V5__p] :
                            ( cCoq_2eInit_2eDatatypes_2eprod___24t(V0__A,V0__A,V5__p)
                           => ( cCoq_2eRelations_2eRelation__Operators_2esymprod___24a6(V0__A,V0__A,V1__R,V1__R,cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V0__A,V3__x,V4__y),V5__p)
                             => p(happ(happ(V2__P,cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V0__A,V3__x,V4__y)),V5__p)) ) ) ) )
               => ( ! [V4__x] :
                      ( t(V4__x,V0__A)
                     => ! [V5__y] :
                          ( t(V5__y,V0__A)
                         => ! [V6__p] :
                              ( cCoq_2eInit_2eDatatypes_2eprod___24t(V0__A,V0__A,V6__p)
                             => ( cCoq_2eRelations_2eRelation__Operators_2esymprod___24a6(V0__A,V0__A,V1__R,V1__R,cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V0__A,V4__x,V5__y),V6__p)
                               => p(happ(happ(V2__P,cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V0__A,V5__y,V4__x)),V6__p)) ) ) ) )
                 => ! [V5__p] :
                      ( cCoq_2eInit_2eDatatypes_2eprod___24t(V0__A,V0__A,V5__p)
                     => ! [V6__p] :
                          ( cCoq_2eInit_2eDatatypes_2eprod___24t(V0__A,V0__A,V6__p)
                         => ( cCoq_2eRelations_2eRelation__Operators_2eswapprod___24a4(V0__A,V1__R,V5__p,V6__p)
                           => p(happ(happ(V2__P,V5__p),V6__p)) ) ) ) ) ) ) ) ) ).

fof('Coq.Relations.Relation_Operators.symprod_ind',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__B] :
          ( cType___24t(V1__B)
         => ! [V2__leA] :
              ( c_24__type__76843___24t(V0__A,V2__leA)
             => ! [V3__leB] :
                  ( c_24__type__76925___24t(V0__A,V1__B,V3__leB)
                 => ! [V4__P] :
                      ( c_24__type__214554___24t(V0__A,V1__B,V4__P)
                     => ( ! [V5__x] :
                            ( t(V5__x,V0__A)
                           => ! [V6__x_27] :
                                ( t(V6__x_27,V0__A)
                               => ( p(happ(happ(V2__leA,V5__x),V6__x_27))
                                 => ! [V8__y] :
                                      ( t(V8__y,V1__B)
                                     => p(happ(happ(V4__P,cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V1__B,V5__x,V8__y)),cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V1__B,V6__x_27,V8__y))) ) ) ) )
                       => ( ! [V6__y] :
                              ( t(V6__y,V1__B)
                             => ! [V7__y_27] :
                                  ( t(V7__y_27,V1__B)
                                 => ( p(happ(happ(V3__leB,V6__y),V7__y_27))
                                   => ! [V9__x] :
                                        ( t(V9__x,V0__A)
                                       => p(happ(happ(V4__P,cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V1__B,V9__x,V6__y)),cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V1__B,V9__x,V7__y_27))) ) ) ) )
                         => ! [V7__p] :
                              ( cCoq_2eInit_2eDatatypes_2eprod___24t(V0__A,V1__B,V7__p)
                             => ! [V8__p] :
                                  ( cCoq_2eInit_2eDatatypes_2eprod___24t(V0__A,V1__B,V8__p)
                                 => ( cCoq_2eRelations_2eRelation__Operators_2esymprod___24a6(V0__A,V1__B,V2__leA,V3__leB,V7__p,V8__p)
                                   => p(happ(happ(V4__P,V7__p),V8__p)) ) ) ) ) ) ) ) ) ) ) ).

fof('Coq.Relations.Relation_Operators.symprod_sind',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__B] :
          ( cType___24t(V1__B)
         => ! [V2__leA] :
              ( c_24__type__76843___24t(V0__A,V2__leA)
             => ! [V3__leB] :
                  ( c_24__type__76925___24t(V0__A,V1__B,V3__leB)
                 => ! [V4__P] :
                      ( c_24__type__214554___24t(V0__A,V1__B,V4__P)
                     => ( ! [V5__x] :
                            ( t(V5__x,V0__A)
                           => ! [V6__x_27] :
                                ( t(V6__x_27,V0__A)
                               => ( p(happ(happ(V2__leA,V5__x),V6__x_27))
                                 => ! [V8__y] :
                                      ( t(V8__y,V1__B)
                                     => p(happ(happ(V4__P,cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V1__B,V5__x,V8__y)),cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V1__B,V6__x_27,V8__y))) ) ) ) )
                       => ( ! [V6__y] :
                              ( t(V6__y,V1__B)
                             => ! [V7__y_27] :
                                  ( t(V7__y_27,V1__B)
                                 => ( p(happ(happ(V3__leB,V6__y),V7__y_27))
                                   => ! [V9__x] :
                                        ( t(V9__x,V0__A)
                                       => p(happ(happ(V4__P,cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V1__B,V9__x,V6__y)),cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V1__B,V9__x,V7__y_27))) ) ) ) )
                         => ! [V7__p] :
                              ( cCoq_2eInit_2eDatatypes_2eprod___24t(V0__A,V1__B,V7__p)
                             => ! [V8__p] :
                                  ( cCoq_2eInit_2eDatatypes_2eprod___24t(V0__A,V1__B,V8__p)
                                 => ( cCoq_2eRelations_2eRelation__Operators_2esymprod___24a6(V0__A,V1__B,V2__leA,V3__leB,V7__p,V8__p)
                                   => p(happ(happ(V4__P,V7__p),V8__p)) ) ) ) ) ) ) ) ) ) ) ).

fof('Coq.Vectors.Vector.append_splitat',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__n] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
         => ! [V2__m] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
             => ! [V3__v] :
                  ( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V1__n,V3__v)
                 => ! [V4__w] :
                      ( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V2__m,V4__w)
                     => ! [V5__vw] :
                          ( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,cCoq_2eInit_2eNat_2eadd___24a2(V1__n,V2__m),V5__vw)
                         => ( cCoq_2eVectors_2eVectorDef_2esplitat___24a4(V0__A,V1__n,V2__m,V5__vw) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eVectors_2eVectorDef_2et___24a2(V0__A,V1__n),cCoq_2eVectors_2eVectorDef_2et___24a2(V0__A,V2__m),V3__v,V4__w)
                           => V5__vw = cCoq_2eVectors_2eVectorDef_2eappend___24a5(V0__A,V1__n,V2__m,V3__v,V4__w) ) ) ) ) ) ) ) ).

fof('Coq.Vectors.VectorDef.t_ind',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__P] :
          ( c_24__type__82594___24t(V0__A,V1__P)
         => ( p(happ(happ(V1__P,cCoq_2eInit_2eDatatypes_2eO),cCoq_2eVectors_2eVectorDef_2enil___24a1(V0__A)))
           => ( ! [V3__h] :
                  ( t(V3__h,V0__A)
                 => ! [V4__n] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(V4__n)
                     => ! [V5__t] :
                          ( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V4__n,V5__t)
                         => ( p(happ(happ(V1__P,V4__n),V5__t))
                           => p(happ(happ(V1__P,cCoq_2eInit_2eDatatypes_2eS___24a1(V4__n)),cCoq_2eVectors_2eVectorDef_2econs___24a4(V0__A,V3__h,V4__n,V5__t))) ) ) ) )
             => ! [V4__n] :
                  ( cCoq_2eInit_2eDatatypes_2enat___24t(V4__n)
                 => ! [V5__t] :
                      ( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V4__n,V5__t)
                     => p(happ(happ(V1__P,V4__n),V5__t)) ) ) ) ) ) ) ).

fof('Coq.Vectors.VectorSpec.append_splitat',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__n] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
         => ! [V2__m] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
             => ! [V3__v] :
                  ( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V1__n,V3__v)
                 => ! [V4__w] :
                      ( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,V2__m,V4__w)
                     => ! [V5__vw] :
                          ( cCoq_2eVectors_2eVectorDef_2et___24t(V0__A,cCoq_2eInit_2eNat_2eadd___24a2(V1__n,V2__m),V5__vw)
                         => ( cCoq_2eVectors_2eVectorDef_2esplitat___24a4(V0__A,V1__n,V2__m,V5__vw) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eVectors_2eVectorDef_2et___24a2(V0__A,V1__n),cCoq_2eVectors_2eVectorDef_2et___24a2(V0__A,V2__m),V3__v,V4__w)
                           => V5__vw = cCoq_2eVectors_2eVectorDef_2eappend___24a5(V0__A,V1__n,V2__m,V3__v,V4__w) ) ) ) ) ) ) ) ).

fof('Coq.ZArith.BinInt.Pos2Z.inj_xO',axiom,
    ! [V0__p] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
     => cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(V0__p)) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eNumbers_2eBinNums_2eZpos___24a1(V0__p)) ) ).

fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.eq_refl',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
     => V0__x = V0__x ) ).

fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.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.add_nonneg_nonneg',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
         => ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__n))
           => ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__m))
             => p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,V1__m))) ) ) ) ) ).

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__112334___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.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_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.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.mul_add_distr_r',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
         => ! [V2__p] :
              ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
             => cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,V1__m),V2__p) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V2__p),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m,V2__p)) ) ) ) ).

fof('Coq.ZArith.BinInt.Z.mul_assoc',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
         => ! [V2__p] :
              ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
             => cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m,V2__p)) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m),V2__p) ) ) ) ).

fof('Coq.ZArith.BinInt.Z.mul_shuffle3',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
         => ! [V2__p] :
              ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
             => cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m,V2__p)) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V2__p)) ) ) ) ).

fof('Coq.ZArith.BinInt.Z.mul_sub_distr_r',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
         => ! [V2__p] :
              ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
             => cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(V0__n,V1__m),V2__p) = cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V2__p),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m,V2__p)) ) ) ) ).

fof('Coq.ZArith.Zbool.Zgt_cases',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
         => c_24__case__Coq_2eInit_2eDatatypes_2ebool_24108704___24a2(V0__n,V1__m) ) ) ).

fof('Coq.ZArith.Zmax.Zmax_spec',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
         => ( ( p(cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(V0__x,V1__y))
              & cCoq_2eZArith_2eBinIntDef_2eZ_2emax___24a2(V0__x,V1__y) = V0__x )
            | ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V1__y))
              & cCoq_2eZArith_2eBinIntDef_2eZ_2emax___24a2(V0__x,V1__y) = V1__y ) ) ) ) ).

fof('Coq.ZArith.Znat.Nat2Z.inj_add',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
         => cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(cCoq_2eInit_2eNat_2eadd___24a2(V0__n,V1__m)) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V1__m)) ) ) ).

fof('Coq.ZArith.Znat.Nat2Z.inj_succ',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n)) = cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V0__n)) ) ).

fof('Coq.ZArith.Znat.inj_eq',axiom,
    ! [V0__x] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
         => ( V0__x = V1__y
           => cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V0__x) = cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V1__y) ) ) ) ).

fof('Coq.ZArith.Znat.inj_ge',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
         => ( p(cCoq_2eInit_2ePeano_2ege___24a2(V0__n,V1__m))
           => p(cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V1__m))) ) ) ) ).

fof('Coq.ZArith.Znat.inj_lt',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
         => ( p(cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m))
           => p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V0__n),cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V1__m))) ) ) ) ).

fof('Coq.ZArith.Znumtheory.Zgcd_is_gcd',axiom,
    ! [V0__a] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
     => ! [V1__b] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
         => cCoq_2eZArith_2eZnumtheory_2eZis__gcd___24a3(V0__a,V1__b,cCoq_2eZArith_2eBinIntDef_2eZ_2egcd___24a2(V0__a,V1__b)) ) ) ).

fof('Coq.ZArith.Zorder.Znot_ge_lt',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
         => ( ~ p(cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(V0__n,V1__m))
           => p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m)) ) ) ) ).

fof('Coq.ZArith.Zorder.Znot_le_gt',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
         => ( ~ p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
           => cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V0__n,V1__m) ) ) ) ).

fof('Coq.ZArith.Zorder.Znot_lt_ge',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_2ege___24a2(V0__n,V1__m)) ) ) ) ).

fof('Coq.ZArith.Zorder.dec_Zge',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_2ege___24a2(V0__n,V1__m)) ) ) ).

fof('Coq.ZArith.auxiliary.Zegal_left',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
         => ( V0__n = V1__m
           => cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__m)) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ).

fof('Coq.ZArith.auxiliary.Zge_left',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
         => ( p(cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(V0__n,V1__m))
           => p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__m)))) ) ) ) ).

fof('Coq.ZArith.auxiliary.Zgt_left',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
         => ( cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V0__n,V1__m)
           => p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__m)))) ) ) ) ).

fof('Coq.ZArith.auxiliary.Zle_left',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(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__m,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__n)))) ) ) ) ).

fof('Coq.ZArith.auxiliary.Zlt_left',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(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__m,cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__n)))) ) ) ) ).

fof('Coq.ZArith.auxiliary.Zne_left',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
         => ( cCoq_2eZArith_2eBinInt_2eZne___24a2(V0__n,V1__m)
           => cCoq_2eZArith_2eBinInt_2eZne___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__m)),cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ) ).

fof('Coq.micromega.EnvRing.Pol_ind',axiom,
    ! [V0__C] :
      ( cType___24t(V0__C)
     => ! [V1__P] :
          ( c_24__type__199306___24t(V0__C,V1__P)
         => ( ! [V2__c] :
                ( t(V2__c,V0__C)
               => p(happ(V1__P,cCoq_2emicromega_2eEnvRing_2ePc___24a2(V0__C,V2__c))) )
           => ( ! [V3__p] :
                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__p)
                 => ! [V4__p] :
                      ( cCoq_2emicromega_2eEnvRing_2ePol___24t(V0__C,V4__p)
                     => ( p(happ(V1__P,V4__p))
                       => p(happ(V1__P,cCoq_2emicromega_2eEnvRing_2ePinj___24a3(V0__C,V3__p,V4__p))) ) ) )
             => ( ! [V4__p] :
                    ( cCoq_2emicromega_2eEnvRing_2ePol___24t(V0__C,V4__p)
                   => ( p(happ(V1__P,V4__p))
                     => ! [V6__p] :
                          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V6__p)
                         => ! [V7__p] :
                              ( cCoq_2emicromega_2eEnvRing_2ePol___24t(V0__C,V7__p)
                             => ( p(happ(V1__P,V7__p))
                               => p(happ(V1__P,cCoq_2emicromega_2eEnvRing_2ePX___24a4(V0__C,V4__p,V6__p,V7__p))) ) ) ) ) )
               => ! [V5__p] :
                    ( cCoq_2emicromega_2eEnvRing_2ePol___24t(V0__C,V5__p)
                   => p(happ(V1__P,V5__p)) ) ) ) ) ) ) ).

fof('Coq.micromega.OrderedRing.Rle_ngt',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__1859___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__1859___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__1859___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__1868___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__76843___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__76843___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__76843___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.Rlt_nge',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__1859___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__1859___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__1859___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__1868___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__76843___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__76843___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__76843___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(V8__rle,V12__m),V11__n)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('Coq.micromega.RingMicromega.SORrm',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__1859___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__1859___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__1859___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__1868___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__76843___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__76843___24t(V0__R,V8__rle)
                                     => ! [V9__C] :
                                          ( cType___24t(V9__C)
                                         => ! [V10__cO] :
                                              ( t(V10__cO,V9__C)
                                             => ! [V11__cI] :
                                                  ( t(V11__cI,V9__C)
                                                 => ! [V12__cplus] :
                                                      ( c_24__type__82503___24t(V0__R,V9__C,V12__cplus)
                                                     => ! [V13__ctimes] :
                                                          ( c_24__type__82503___24t(V0__R,V9__C,V13__ctimes)
                                                         => ! [V14__cminus] :
                                                              ( c_24__type__82503___24t(V0__R,V9__C,V14__cminus)
                                                             => ! [V15__copp] :
                                                                  ( c_24__type__76882___24t(V0__R,V9__C,V15__copp)
                                                                 => ! [V16__ceqb] :
                                                                      ( c_24__type__82515___24t(V0__R,V9__C,V16__ceqb)
                                                                     => ! [V17__cleb] :
                                                                          ( c_24__type__82515___24t(V0__R,V9__C,V17__cleb)
                                                                         => ! [V18__phi] :
                                                                              ( c_24__type__80902___24t(V0__R,V9__C,V18__phi)
                                                                             => ! [V19__E] :
                                                                                  ( cType___24t(V19__E)
                                                                                 => ! [V20__pow__phi] :
                                                                                      ( c_24__type__80907___24t(V0__R,V9__C,V19__E,V20__pow__phi)
                                                                                     => ! [V21__rpow] :
                                                                                          ( c_24__type__80916___24t(V0__R,V9__C,V19__E,V21__rpow)
                                                                                         => ( cCoq_2emicromega_2eRingMicromega_2eSORaddon___24a22(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__C,V10__cO,V11__cI,V12__cplus,V13__ctimes,V14__cminus,V15__copp,V16__ceqb,V17__cleb,V18__phi,V19__E,V20__pow__phi,V21__rpow)
                                                                                           => cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V9__C,V10__cO,V11__cI,V12__cplus,V13__ctimes,V14__cminus,V15__copp,V16__ceqb,V18__phi) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('Coq.micromega.RingMicromega.check_inconsistent_sound',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__1859___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__1859___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__1859___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__1868___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__76843___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__76843___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__76843___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__C] :
                                                ( cType___24t(V11__C)
                                               => ! [V12__cO] :
                                                    ( t(V12__cO,V11__C)
                                                   => ! [V13__cI] :
                                                        ( t(V13__cI,V11__C)
                                                       => ! [V14__cplus] :
                                                            ( c_24__type__82503___24t(V0__R,V11__C,V14__cplus)
                                                           => ! [V15__ctimes] :
                                                                ( c_24__type__82503___24t(V0__R,V11__C,V15__ctimes)
                                                               => ! [V16__cminus] :
                                                                    ( c_24__type__82503___24t(V0__R,V11__C,V16__cminus)
                                                                   => ! [V17__copp] :
                                                                        ( c_24__type__76882___24t(V0__R,V11__C,V17__copp)
                                                                       => ! [V18__ceqb] :
                                                                            ( c_24__type__82515___24t(V0__R,V11__C,V18__ceqb)
                                                                           => ! [V19__cleb] :
                                                                                ( c_24__type__82515___24t(V0__R,V11__C,V19__cleb)
                                                                               => ! [V20__phi] :
                                                                                    ( c_24__type__80902___24t(V0__R,V11__C,V20__phi)
                                                                                   => ! [V21__E] :
                                                                                        ( cType___24t(V21__E)
                                                                                       => ! [V22__pow__phi] :
                                                                                            ( c_24__type__80907___24t(V0__R,V11__C,V21__E,V22__pow__phi)
                                                                                           => ! [V23__rpow] :
                                                                                                ( c_24__type__80916___24t(V0__R,V11__C,V21__E,V23__rpow)
                                                                                               => ( cCoq_2emicromega_2eRingMicromega_2eSORaddon___24a22(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V11__C,V12__cO,V13__cI,V14__cplus,V15__ctimes,V16__cminus,V17__copp,V18__ceqb,V19__cleb,V20__phi,V21__E,V22__pow__phi,V23__rpow)
                                                                                                 => ! [V25__p] :
                                                                                                      ( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(V11__C,V25__p)
                                                                                                     => ! [V26__op] :
                                                                                                          ( cCoq_2emicromega_2eRingMicromega_2eOp1___24t(V26__op)
                                                                                                         => ( cCoq_2emicromega_2eRingMicromega_2echeck__inconsistent___24a5(V11__C,V12__cO,V18__ceqb,V19__cleb,cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2emicromega_2eRingMicromega_2ePolC___24a1(V11__C),cCoq_2emicromega_2eRingMicromega_2eOp1,V25__p,V26__op)) = cCoq_2eInit_2eDatatypes_2etrue
                                                                                                           => ! [V28__env] :
                                                                                                                ( cCoq_2emicromega_2eRingMicromega_2ePolEnv___24t(V0__R,V28__env)
                                                                                                               => ~ cCoq_2emicromega_2eRingMicromega_2eeval__op1___24a7(V0__R,V1__rO,V7__req,V8__rle,V9__rlt,V26__op,cCoq_2emicromega_2eRingMicromega_2eeval__pol___24a7(V0__R,V3__rplus,V4__rtimes,V11__C,V20__phi,V28__env,V25__p)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('Coq.micromega.RingMicromega.cleb_sound',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__1859___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__1859___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__1859___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__1868___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__76843___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__76843___24t(V0__R,V8__rle)
                                     => ! [V9__C] :
                                          ( cType___24t(V9__C)
                                         => ! [V10__cO] :
                                              ( t(V10__cO,V9__C)
                                             => ! [V11__cI] :
                                                  ( t(V11__cI,V9__C)
                                                 => ! [V12__cplus] :
                                                      ( c_24__type__82503___24t(V0__R,V9__C,V12__cplus)
                                                     => ! [V13__ctimes] :
                                                          ( c_24__type__82503___24t(V0__R,V9__C,V13__ctimes)
                                                         => ! [V14__cminus] :
                                                              ( c_24__type__82503___24t(V0__R,V9__C,V14__cminus)
                                                             => ! [V15__copp] :
                                                                  ( c_24__type__76882___24t(V0__R,V9__C,V15__copp)
                                                                 => ! [V16__ceqb] :
                                                                      ( c_24__type__82515___24t(V0__R,V9__C,V16__ceqb)
                                                                     => ! [V17__cleb] :
                                                                          ( c_24__type__82515___24t(V0__R,V9__C,V17__cleb)
                                                                         => ! [V18__phi] :
                                                                              ( c_24__type__80902___24t(V0__R,V9__C,V18__phi)
                                                                             => ! [V19__E] :
                                                                                  ( cType___24t(V19__E)
                                                                                 => ! [V20__pow__phi] :
                                                                                      ( c_24__type__80907___24t(V0__R,V9__C,V19__E,V20__pow__phi)
                                                                                     => ! [V21__rpow] :
                                                                                          ( c_24__type__80916___24t(V0__R,V9__C,V19__E,V21__rpow)
                                                                                         => ( cCoq_2emicromega_2eRingMicromega_2eSORaddon___24a22(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__C,V10__cO,V11__cI,V12__cplus,V13__ctimes,V14__cminus,V15__copp,V16__ceqb,V17__cleb,V18__phi,V19__E,V20__pow__phi,V21__rpow)
                                                                                           => ! [V23__x] :
                                                                                                ( t(V23__x,V9__C)
                                                                                               => ! [V24__y] :
                                                                                                    ( t(V24__y,V9__C)
                                                                                                   => ( happ(happ(V17__cleb,V23__x),V24__y) = cCoq_2eInit_2eDatatypes_2etrue
                                                                                                     => p(happ(happ(V8__rle,happ(V18__phi,V23__x)),happ(V18__phi,V24__y))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('Coq.micromega.RingMicromega.cltb_sound',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__1859___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__1859___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__1859___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__1868___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__76843___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__76843___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__76843___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__C] :
                                                ( cType___24t(V11__C)
                                               => ! [V12__cO] :
                                                    ( t(V12__cO,V11__C)
                                                   => ! [V13__cI] :
                                                        ( t(V13__cI,V11__C)
                                                       => ! [V14__cplus] :
                                                            ( c_24__type__82503___24t(V0__R,V11__C,V14__cplus)
                                                           => ! [V15__ctimes] :
                                                                ( c_24__type__82503___24t(V0__R,V11__C,V15__ctimes)
                                                               => ! [V16__cminus] :
                                                                    ( c_24__type__82503___24t(V0__R,V11__C,V16__cminus)
                                                                   => ! [V17__copp] :
                                                                        ( c_24__type__76882___24t(V0__R,V11__C,V17__copp)
                                                                       => ! [V18__ceqb] :
                                                                            ( c_24__type__82515___24t(V0__R,V11__C,V18__ceqb)
                                                                           => ! [V19__cleb] :
                                                                                ( c_24__type__82515___24t(V0__R,V11__C,V19__cleb)
                                                                               => ! [V20__phi] :
                                                                                    ( c_24__type__80902___24t(V0__R,V11__C,V20__phi)
                                                                                   => ! [V21__E] :
                                                                                        ( cType___24t(V21__E)
                                                                                       => ! [V22__pow__phi] :
                                                                                            ( c_24__type__80907___24t(V0__R,V11__C,V21__E,V22__pow__phi)
                                                                                           => ! [V23__rpow] :
                                                                                                ( c_24__type__80916___24t(V0__R,V11__C,V21__E,V23__rpow)
                                                                                               => ( cCoq_2emicromega_2eRingMicromega_2eSORaddon___24a22(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V11__C,V12__cO,V13__cI,V14__cplus,V15__ctimes,V16__cminus,V17__copp,V18__ceqb,V19__cleb,V20__phi,V21__E,V22__pow__phi,V23__rpow)
                                                                                                 => ! [V25__x] :
                                                                                                      ( t(V25__x,V11__C)
                                                                                                     => ! [V26__y] :
                                                                                                          ( t(V26__y,V11__C)
                                                                                                         => ( cCoq_2emicromega_2eRingMicromega_2ecltb___24a5(V11__C,V18__ceqb,V19__cleb,V25__x,V26__y) = cCoq_2eInit_2eDatatypes_2etrue
                                                                                                           => p(happ(happ(V9__rlt,happ(V20__phi,V25__x)),happ(V20__phi,V26__y))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('Coq.micromega.RingMicromega.cneqb_sound',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__1859___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__1859___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__1859___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__1868___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__76843___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__76843___24t(V0__R,V8__rle)
                                     => ! [V9__C] :
                                          ( cType___24t(V9__C)
                                         => ! [V10__cO] :
                                              ( t(V10__cO,V9__C)
                                             => ! [V11__cI] :
                                                  ( t(V11__cI,V9__C)
                                                 => ! [V12__cplus] :
                                                      ( c_24__type__82503___24t(V0__R,V9__C,V12__cplus)
                                                     => ! [V13__ctimes] :
                                                          ( c_24__type__82503___24t(V0__R,V9__C,V13__ctimes)
                                                         => ! [V14__cminus] :
                                                              ( c_24__type__82503___24t(V0__R,V9__C,V14__cminus)
                                                             => ! [V15__copp] :
                                                                  ( c_24__type__76882___24t(V0__R,V9__C,V15__copp)
                                                                 => ! [V16__ceqb] :
                                                                      ( c_24__type__82515___24t(V0__R,V9__C,V16__ceqb)
                                                                     => ! [V17__cleb] :
                                                                          ( c_24__type__82515___24t(V0__R,V9__C,V17__cleb)
                                                                         => ! [V18__phi] :
                                                                              ( c_24__type__80902___24t(V0__R,V9__C,V18__phi)
                                                                             => ! [V19__E] :
                                                                                  ( cType___24t(V19__E)
                                                                                 => ! [V20__pow__phi] :
                                                                                      ( c_24__type__80907___24t(V0__R,V9__C,V19__E,V20__pow__phi)
                                                                                     => ! [V21__rpow] :
                                                                                          ( c_24__type__80916___24t(V0__R,V9__C,V19__E,V21__rpow)
                                                                                         => ( cCoq_2emicromega_2eRingMicromega_2eSORaddon___24a22(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__C,V10__cO,V11__cI,V12__cplus,V13__ctimes,V14__cminus,V15__copp,V16__ceqb,V17__cleb,V18__phi,V19__E,V20__pow__phi,V21__rpow)
                                                                                           => ! [V23__x] :
                                                                                                ( t(V23__x,V9__C)
                                                                                               => ! [V24__y] :
                                                                                                    ( t(V24__y,V9__C)
                                                                                                   => ( cCoq_2emicromega_2eRingMicromega_2ecneqb___24a4(V9__C,V16__ceqb,V23__x,V24__y) = cCoq_2eInit_2eDatatypes_2etrue
                                                                                                     => ~ p(happ(happ(V7__req,happ(V18__phi,V23__x)),happ(V18__phi,V24__y))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('Coq.micromega.RingMicromega.eval_pol_add',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__1859___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__1859___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__1859___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__1868___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__76843___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__76843___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__76843___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__C] :
                                                ( cType___24t(V11__C)
                                               => ! [V12__cO] :
                                                    ( t(V12__cO,V11__C)
                                                   => ! [V13__cI] :
                                                        ( t(V13__cI,V11__C)
                                                       => ! [V14__cplus] :
                                                            ( c_24__type__82503___24t(V0__R,V11__C,V14__cplus)
                                                           => ! [V15__ctimes] :
                                                                ( c_24__type__82503___24t(V0__R,V11__C,V15__ctimes)
                                                               => ! [V16__cminus] :
                                                                    ( c_24__type__82503___24t(V0__R,V11__C,V16__cminus)
                                                                   => ! [V17__copp] :
                                                                        ( c_24__type__76882___24t(V0__R,V11__C,V17__copp)
                                                                       => ! [V18__ceqb] :
                                                                            ( c_24__type__82515___24t(V0__R,V11__C,V18__ceqb)
                                                                           => ! [V19__cleb] :
                                                                                ( c_24__type__82515___24t(V0__R,V11__C,V19__cleb)
                                                                               => ! [V20__phi] :
                                                                                    ( c_24__type__80902___24t(V0__R,V11__C,V20__phi)
                                                                                   => ! [V21__E] :
                                                                                        ( cType___24t(V21__E)
                                                                                       => ! [V22__pow__phi] :
                                                                                            ( c_24__type__80907___24t(V0__R,V11__C,V21__E,V22__pow__phi)
                                                                                           => ! [V23__rpow] :
                                                                                                ( c_24__type__80916___24t(V0__R,V11__C,V21__E,V23__rpow)
                                                                                               => ( cCoq_2emicromega_2eRingMicromega_2eSORaddon___24a22(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V11__C,V12__cO,V13__cI,V14__cplus,V15__ctimes,V16__cminus,V17__copp,V18__ceqb,V19__cleb,V20__phi,V21__E,V22__pow__phi,V23__rpow)
                                                                                                 => ! [V25__env] :
                                                                                                      ( cCoq_2emicromega_2eRingMicromega_2ePolEnv___24t(V0__R,V25__env)
                                                                                                     => ! [V26__lhs] :
                                                                                                          ( cCoq_2emicromega_2eEnvRing_2ePol___24t(V11__C,V26__lhs)
                                                                                                         => ! [V27__rhs] :
                                                                                                              ( cCoq_2emicromega_2eEnvRing_2ePol___24t(V11__C,V27__rhs)
                                                                                                             => p(happ(happ(V7__req,cCoq_2emicromega_2eRingMicromega_2eeval__pol___24a7(V0__R,V3__rplus,V4__rtimes,V11__C,V20__phi,V25__env,cCoq_2emicromega_2eRingMicromega_2epadd___24a6(V11__C,V12__cO,V14__cplus,V18__ceqb,V26__lhs,V27__rhs))),happ(happ(V3__rplus,cCoq_2emicromega_2eRingMicromega_2eeval__pol___24a7(V0__R,V3__rplus,V4__rtimes,V11__C,V20__phi,V25__env,V26__lhs)),cCoq_2emicromega_2eRingMicromega_2eeval__pol___24a7(V0__R,V3__rplus,V4__rtimes,V11__C,V20__phi,V25__env,V27__rhs)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('Coq.micromega.RingMicromega.micomega_sor_setoid',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__1859___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__1859___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__1859___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__1868___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__76843___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__76843___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__76843___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)
                                           => cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V7__req) ) ) ) ) ) ) ) ) ) ) ) ).

fof('Coq.micromega.RingMicromega.micomega_sor_setoid_Reflexive',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__1859___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__1859___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__1859___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__1868___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__76843___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__76843___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__76843___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)
                                           => cCoq_2eClasses_2eRelationClasses_2eReflexive___24a2(V0__R,V7__req) ) ) ) ) ) ) ) ) ) ) ) ).

fof('Coq.micromega.RingMicromega.micomega_sor_setoid_Symmetric',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__1859___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__1859___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__1859___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__1868___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__76843___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__76843___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__76843___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)
                                           => cCoq_2eClasses_2eRelationClasses_2eSymmetric___24a2(V0__R,V7__req) ) ) ) ) ) ) ) ) ) ) ) ).

fof('Coq.micromega.RingMicromega.rle_morph_Proper',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__1859___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__1859___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__1859___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__1868___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__76843___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__76843___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__76843___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)
                                           => cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__76843___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,c_24__type__78062___24a1(V0__R),V7__req,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,cProp,V7__req,c_3c_3d_3e)),V8__rle) ) ) ) ) ) ) ) ) ) ) ) ).

fof('Coq.micromega.RingMicromega.rlt_morph_Proper',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__1859___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__1859___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__1859___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__1868___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__76843___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__76843___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__76843___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)
                                           => cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__76843___24a1(V0__R),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,c_24__type__78062___24a1(V0__R),V7__req,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V0__R,cProp,V7__req,c_3c_3d_3e)),V9__rlt) ) ) ) ) ) ) ) ) ) ) ) ).

fof('Coq.micromega.ZMicromega.Zdiv_PX',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
     => ! [V1__p] :
          ( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(cCoq_2eNumbers_2eBinNums_2eZ,V1__p)
         => ! [V2__q] :
              ( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(cCoq_2eNumbers_2eBinNums_2eZ,V2__q)
             => ( cCoq_2emicromega_2eZMicromega_2eZdivide__pol___24a2(V0__x,V1__p)
               => ( cCoq_2emicromega_2eZMicromega_2eZdivide__pol___24a2(V0__x,V2__q)
                 => ! [V5__j] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V5__j)
                     => cCoq_2emicromega_2eZMicromega_2eZdivide__pol___24a2(V0__x,cCoq_2emicromega_2eEnvRing_2ePX___24a4(cCoq_2eNumbers_2eBinNums_2eZ,V1__p,V5__j,V2__q)) ) ) ) ) ) ) ).

fof('Coq.micromega.ZMicromega.Zdiv_Pc',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
     => ! [V1__c] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__c)
         => ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V0__x,V1__c)
           => cCoq_2emicromega_2eZMicromega_2eZdivide__pol___24a2(V0__x,cCoq_2emicromega_2eEnvRing_2ePc___24a2(cCoq_2eNumbers_2eBinNums_2eZ,V1__c)) ) ) ) ).

fof('Coq.micromega.ZMicromega.Zdiv_Pinj',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
     => ! [V1__p] :
          ( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(cCoq_2eNumbers_2eBinNums_2eZ,V1__p)
         => ( cCoq_2emicromega_2eZMicromega_2eZdivide__pol___24a2(V0__x,V1__p)
           => ! [V3__j] :
                ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__j)
               => cCoq_2emicromega_2eZMicromega_2eZdivide__pol___24a2(V0__x,cCoq_2emicromega_2eEnvRing_2ePinj___24a3(cCoq_2eNumbers_2eBinNums_2eZ,V3__j,V1__p)) ) ) ) ) ).

fof('Coq.micromega.ZMicromega.Zdivide_pol_Zdivide',axiom,
    ! [V0__p] :
      ( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(cCoq_2eNumbers_2eBinNums_2eZ,V0__p)
     => ! [V1__x] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__x)
         => ! [V2__y] :
              ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__y)
             => ( cCoq_2emicromega_2eZMicromega_2eZdivide__pol___24a2(V1__x,V0__p)
               => ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V2__y,V1__x)
                 => cCoq_2emicromega_2eZMicromega_2eZdivide__pol___24a2(V2__y,V0__p) ) ) ) ) ) ).

fof('Coq.micromega.ZMicromega.Zdivide_pol_one',axiom,
    ! [V0__p] :
      ( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(cCoq_2eNumbers_2eBinNums_2eZ,V0__p)
     => cCoq_2emicromega_2eZMicromega_2eZdivide__pol___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),V0__p) ) ).

fof('Coq.micromega.ZMicromega.Zgcd_pol_div',axiom,
    ! [V0__p] :
      ( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(cCoq_2eNumbers_2eBinNums_2eZ,V0__p)
     => ! [V1__g] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__g)
         => ! [V2__c] :
              ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__c)
             => ( cCoq_2emicromega_2eZMicromega_2eZgcd__pol___24a1(V0__p) = cCoq_2eInit_2eDatatypes_2epair___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ,V1__g,V2__c)
               => cCoq_2emicromega_2eZMicromega_2eZdivide__pol___24a2(V1__g,cCoq_2emicromega_2eEnvRing_2ePsubC___24a4(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eZArith_2eBinIntDef_2eZ_2esub,V0__p,V2__c)) ) ) ) ) ).

fof('Coq.micromega.ZMicromega.Zsor',axiom,
    cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd,cCoq_2eZArith_2eBinIntDef_2eZ_2emul,cCoq_2eZArith_2eBinIntDef_2eZ_2esub,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eZ),cCoq_2eZArith_2eBinInt_2eZ_2ele,cCoq_2eZArith_2eBinInt_2eZ_2elt) ).

fof('Coq.micromega.ZMicromega.narrow_interval_lower_bound',axiom,
    ! [V0__a] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
     => ! [V1__b] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
         => ! [V2__x] :
              ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__x)
             => ( cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V0__a,cCoq_2eNumbers_2eBinNums_2eZ0)
               => ( p(cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__a,V2__x),V1__b))
                 => p(cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(V2__x,cCoq_2emicromega_2eZMicromega_2eceiling___24a2(V1__b,V0__a))) ) ) ) ) ) ).

fof('Coq.omega.OmegaLemmas.OMEGA1',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
         => ( V0__x = V1__y
           => ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__x))
             => p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__y)) ) ) ) ) ).

fof('Coq.omega.OmegaLemmas.OMEGA17',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)
             => ( cCoq_2eZArith_2eBinInt_2eZne___24a2(V0__x,cCoq_2eNumbers_2eBinNums_2eZ0)
               => ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
                 => cCoq_2eZArith_2eBinInt_2eZne___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__y,V2__z)),cCoq_2eNumbers_2eBinNums_2eZ0) ) ) ) ) ) ).

fof('Coq.omega.OmegaLemmas.OMEGA2',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
         => ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__x))
           => ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__y))
             => p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y))) ) ) ) ) ).

fof('Coq.omega.OmegaLemmas.OMEGA6',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
         => ! [V2__z] :
              ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
             => ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__x))
               => ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
                 => p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__y,V2__z)))) ) ) ) ) ) ).

fof('Coq.omega.OmegaLemmas.OMEGA7',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)
             => ! [V3__t] :
                  ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__t)
                 => ( cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V2__z,cCoq_2eNumbers_2eBinNums_2eZ0)
                   => ( cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V3__t,cCoq_2eNumbers_2eBinNums_2eZ0)
                     => ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V0__x))
                       => ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,V1__y))
                         => p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V2__z),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__y,V3__t)))) ) ) ) ) ) ) ) ) ).

fof('Coq.omega.OmegaLemmas.fast_OMEGA12',axiom,
    ! [V0__v2] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__v2)
     => ! [V1__c2] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__c2)
         => ! [V2__l1] :
              ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__l1)
             => ! [V3__l2] :
                  ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__l2)
                 => ! [V4__k2] :
                      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V4__k2)
                     => ! [V5__P] :
                          ( c_24__type__1179___24t(V5__P)
                         => ( p(happ(V5__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v2,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__c2,V4__k2)),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V2__l1,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V3__l2,V4__k2)))))
                           => p(happ(V5__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V2__l1,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v2,V1__c2),V3__l2),V4__k2)))) ) ) ) ) ) ) ) ).

fof('Coq.omega.OmegaLemmas.fast_OMEGA13',axiom,
    ! [V0__v] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__v)
     => ! [V1__l1] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__l1)
         => ! [V2__l2] :
              ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__l2)
             => ! [V3__x] :
                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__x)
                 => ! [V4__P] :
                      ( c_24__type__1179___24t(V4__P)
                     => ( p(happ(V4__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__l1,V2__l2)))
                       => p(happ(V4__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(V3__x)),V1__l1),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v,cCoq_2eNumbers_2eBinNums_2eZneg___24a1(V3__x)),V2__l2)))) ) ) ) ) ) ) ).

fof('Coq.omega.OmegaLemmas.fast_OMEGA14',axiom,
    ! [V0__v] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__v)
     => ! [V1__l1] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__l1)
         => ! [V2__l2] :
              ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__l2)
             => ! [V3__x] :
                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V3__x)
                 => ! [V4__P] :
                      ( c_24__type__1179___24t(V4__P)
                     => ( p(happ(V4__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__l1,V2__l2)))
                       => p(happ(V4__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v,cCoq_2eNumbers_2eBinNums_2eZneg___24a1(V3__x)),V1__l1),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(V3__x)),V2__l2)))) ) ) ) ) ) ) ).

fof('Coq.omega.OmegaLemmas.fast_OMEGA15',axiom,
    ! [V0__v] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__v)
     => ! [V1__c1] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__c1)
         => ! [V2__c2] :
              ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__c2)
             => ! [V3__l1] :
                  ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V3__l1)
                 => ! [V4__l2] :
                      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V4__l2)
                     => ! [V5__k2] :
                          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V5__k2)
                         => ! [V6__P] :
                              ( c_24__type__1179___24t(V6__P)
                             => ( p(happ(V6__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__c1,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__c2,V5__k2))),cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V3__l1,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V4__l2,V5__k2)))))
                               => p(happ(V6__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v,V1__c1),V3__l1),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__v,V2__c2),V4__l2),V5__k2)))) ) ) ) ) ) ) ) ) ).

fof('Coq.omega.OmegaLemmas.fast_Zopp_eq_mult_neg_1',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
     => ! [V1__P] :
          ( c_24__type__1179___24t(V1__P)
         => ( p(happ(V1__P,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2eNumbers_2eBinNums_2exH))))
           => p(happ(V1__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__x))) ) ) ) ).

fof('Coq.omega.OmegaLemmas.fast_Zopp_mult_distr_r',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
         => ! [V2__P] :
              ( c_24__type__1179___24t(V2__P)
             => ( p(happ(V2__P,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__y))))
               => p(happ(V2__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y)))) ) ) ) ) ).

fof('Coq.omega.OmegaLemmas.fast_Zopp_plus_distr',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
         => ! [V2__P] :
              ( c_24__type__1179___24t(V2__P)
             => ( p(happ(V2__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__x),cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__y))))
               => p(happ(V2__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y)))) ) ) ) ) ).

fof('Coq.omega.OmegaLemmas.fast_Zplus_assoc',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
         => ! [V2__p] :
              ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
             => ! [V3__P] :
                  ( c_24__type__1179___24t(V3__P)
                 => ( p(happ(V3__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,V1__m),V2__p)))
                   => p(happ(V3__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__m,V2__p)))) ) ) ) ) ) ).

fof('Coq.omega.OmegaLemmas.fast_Zplus_assoc_reverse',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)
             => ! [V3__P] :
                  ( c_24__type__1179___24t(V3__P)
                 => ( p(happ(V3__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__m,V2__p))))
                   => p(happ(V3__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,V1__m),V2__p))) ) ) ) ) ) ).

fof('Coq.omega.OmegaLemmas.fast_Zplus_comm',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
         => ! [V2__P] :
              ( c_24__type__1179___24t(V2__P)
             => ( p(happ(V2__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__y,V0__x)))
               => p(happ(V2__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y))) ) ) ) ) ).

fof('Coq.omega.OmegaLemmas.fast_Zplus_permute',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)
             => ! [V3__P] :
                  ( c_24__type__1179___24t(V3__P)
                 => ( p(happ(V3__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__m,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,V2__p))))
                   => p(happ(V3__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__m,V2__p)))) ) ) ) ) ) ).

fof('Coq.omega.OmegaLemmas.fast_Zred_factor0',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
     => ! [V1__P] :
          ( c_24__type__1179___24t(V1__P)
         => ( p(happ(V1__P,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))))
           => p(happ(V1__P,V0__x)) ) ) ) ).

fof('Coq.omega.OmegaLemmas.fast_Zred_factor2',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
         => ! [V2__P] :
              ( c_24__type__1179___24t(V2__P)
             => ( p(happ(V2__P,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),V1__y))))
               => p(happ(V2__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y)))) ) ) ) ) ).

fof('Coq.omega.OmegaLemmas.fast_Zred_factor3',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
         => ! [V2__P] :
              ( c_24__type__1179___24t(V2__P)
             => ( p(happ(V2__P,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),V1__y))))
               => p(happ(V2__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y),V0__x))) ) ) ) ) ).

fof('Coq.omega.OmegaLemmas.fast_Zred_factor5',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
         => ! [V2__P] :
              ( c_24__type__1179___24t(V2__P)
             => ( p(happ(V2__P,V1__y))
               => p(happ(V2__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,cCoq_2eNumbers_2eBinNums_2eZ0),V1__y))) ) ) ) ) ).

fof('Coq.omega.OmegaLemmas.fast_Zred_factor6',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
     => ! [V1__P] :
          ( c_24__type__1179___24t(V1__P)
         => ( p(happ(V1__P,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,cCoq_2eNumbers_2eBinNums_2eZ0)))
           => p(happ(V1__P,V0__x)) ) ) ) ).

fof('Coq.omega.OmegaLemmas.intro_Z',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => ? [V1__y] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
          & cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V0__n) = V1__y
          & p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__y,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)),cCoq_2eNumbers_2eBinNums_2eZ0))) ) ) ).

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.morph0',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__1859___24t(V0__R,V3__radd)
                 => ! [V4__rmul] :
                      ( c_24__type__1859___24t(V0__R,V4__rmul)
                     => ! [V5__rsub] :
                          ( c_24__type__1859___24t(V0__R,V5__rsub)
                         => ! [V6__ropp] :
                              ( c_24__type__1868___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__76843___24t(V0__R,V7__req)
                                 => ! [V8__C] :
                                      ( cType___24t(V8__C)
                                     => ! [V9__cO] :
                                          ( t(V9__cO,V8__C)
                                         => ! [V10__cI] :
                                              ( t(V10__cI,V8__C)
                                             => ! [V11__cadd] :
                                                  ( c_24__type__82503___24t(V0__R,V8__C,V11__cadd)
                                                 => ! [V12__cmul] :
                                                      ( c_24__type__82503___24t(V0__R,V8__C,V12__cmul)
                                                     => ! [V13__csub] :
                                                          ( c_24__type__82503___24t(V0__R,V8__C,V13__csub)
                                                         => ! [V14__copp] :
                                                              ( c_24__type__76882___24t(V0__R,V8__C,V14__copp)
                                                             => ! [V15__ceqb] :
                                                                  ( c_24__type__82515___24t(V0__R,V8__C,V15__ceqb)
                                                                 => ! [V16__phi] :
                                                                      ( c_24__type__80902___24t(V0__R,V8__C,V16__phi)
                                                                     => ( cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__cO,V10__cI,V11__cadd,V12__cmul,V13__csub,V14__copp,V15__ceqb,V16__phi)
                                                                       => p(happ(happ(V7__req,happ(V16__phi,V9__cO)),V1__rO)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('Coq.setoid_ring.Ring_theory.morph_eq',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__1859___24t(V0__R,V3__radd)
                 => ! [V4__rmul] :
                      ( c_24__type__1859___24t(V0__R,V4__rmul)
                     => ! [V5__rsub] :
                          ( c_24__type__1859___24t(V0__R,V5__rsub)
                         => ! [V6__ropp] :
                              ( c_24__type__1868___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__76843___24t(V0__R,V7__req)
                                 => ! [V8__C] :
                                      ( cType___24t(V8__C)
                                     => ! [V9__cO] :
                                          ( t(V9__cO,V8__C)
                                         => ! [V10__cI] :
                                              ( t(V10__cI,V8__C)
                                             => ! [V11__cadd] :
                                                  ( c_24__type__82503___24t(V0__R,V8__C,V11__cadd)
                                                 => ! [V12__cmul] :
                                                      ( c_24__type__82503___24t(V0__R,V8__C,V12__cmul)
                                                     => ! [V13__csub] :
                                                          ( c_24__type__82503___24t(V0__R,V8__C,V13__csub)
                                                         => ! [V14__copp] :
                                                              ( c_24__type__76882___24t(V0__R,V8__C,V14__copp)
                                                             => ! [V15__ceqb] :
                                                                  ( c_24__type__82515___24t(V0__R,V8__C,V15__ceqb)
                                                                 => ! [V16__phi] :
                                                                      ( c_24__type__80902___24t(V0__R,V8__C,V16__phi)
                                                                     => ( cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req,V8__C,V9__cO,V10__cI,V11__cadd,V12__cmul,V13__csub,V14__copp,V15__ceqb,V16__phi)
                                                                       => ! [V18__x] :
                                                                            ( t(V18__x,V8__C)
                                                                           => ! [V19__y] :
                                                                                ( t(V19__y,V8__C)
                                                                               => ( happ(happ(V15__ceqb,V18__x),V19__y) = cCoq_2eInit_2eDatatypes_2etrue
                                                                                 => p(happ(happ(V7__req,happ(V16__phi,V18__x)),happ(V16__phi,V19__y))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('PLF.Imp.AExp.silly2',axiom,
    ! [V0__P] :
      ( cProp___24t(V0__P)
     => ( p(V0__P)
       => p(V0__P) ) ) ).

fof('PLF.LibTactics.equates_0',axiom,
    ! [V0__P] :
      ( cProp___24t(V0__P)
     => ! [V1__Q] :
          ( cProp___24t(V1__Q)
         => ( p(V0__P)
           => ( V0__P = V1__Q
             => p(V1__Q) ) ) ) ) ).

fof('PLF.LibTactics.equates_1',axiom,
    ! [V0__A0] :
      ( cType___24t(V0__A0)
     => ! [V1__P] :
          ( c_24__type__78062___24t(V0__A0,V1__P)
         => ! [V2__x1] :
              ( t(V2__x1,V0__A0)
             => ! [V3__y1] :
                  ( t(V3__y1,V0__A0)
                 => ( p(happ(V1__P,V3__y1))
                   => ( V2__x1 = V3__y1
                     => p(happ(V1__P,V2__x1)) ) ) ) ) ) ) ).

fof('PLF.LibTactics.equates_2',axiom,
    ! [V0__A0] :
      ( cType___24t(V0__A0)
     => ! [V1__A1] :
          ( cType___24t(V1__A1)
         => ! [V2__y1] :
              ( t(V2__y1,V0__A0)
             => ! [V3__P] :
                  ( c_24__type__84590___24t(V0__A0,V1__A1,V3__P)
                 => ! [V4__x1] :
                      ( t(V4__x1,V0__A0)
                     => ! [V5__x2] :
                          ( t(V5__x2,V1__A1)
                         => ( p(happ(happ(V3__P,V2__y1),V5__x2))
                           => ( V4__x1 = V2__y1
                             => p(happ(happ(V3__P,V4__x1),V5__x2)) ) ) ) ) ) ) ) ) ).

fof('PLF.LibTactics.equates_3',axiom,
    ! [V0__A0] :
      ( cType___24t(V0__A0)
     => ! [V1__A1] :
          ( cType___24t(V1__A1)
         => ! [V2__A2] :
              ( c_24__type__85086___24t(V1__A1,V2__A2)
             => ! [V3__y1] :
                  ( t(V3__y1,V0__A0)
                 => ! [V4__P] :
                      ( c_24__type__112996___24t(V0__A0,V1__A1,V2__A2,V4__P)
                     => ! [V5__x1] :
                          ( t(V5__x1,V0__A0)
                         => ! [V6__x2] :
                              ( t(V6__x2,V1__A1)
                             => ! [V7__x3] :
                                  ( t(V7__x3,happ(V2__A2,V6__x2))
                                 => ( p(happ(happ(happ(V4__P,V3__y1),V6__x2),V7__x3))
                                   => ( V5__x1 = V3__y1
                                     => p(happ(happ(happ(V4__P,V5__x1),V6__x2),V7__x3)) ) ) ) ) ) ) ) ) ) ) ).

fof('PLF.LibTactics.equates_4',axiom,
    ! [V0__A0] :
      ( cType___24t(V0__A0)
     => ! [V1__A1] :
          ( cType___24t(V1__A1)
         => ! [V2__A2] :
              ( c_24__type__85086___24t(V1__A1,V2__A2)
             => ! [V3__A3] :
                  ( c_24__type__113005___24t(V1__A1,V2__A2,V3__A3)
                 => ! [V4__y1] :
                      ( t(V4__y1,V0__A0)
                     => ! [V5__P] :
                          ( c_24__type__113037___24t(V0__A0,V1__A1,V2__A2,V3__A3,V5__P)
                         => ! [V6__x1] :
                              ( t(V6__x1,V0__A0)
                             => ! [V7__x2] :
                                  ( t(V7__x2,V1__A1)
                                 => ! [V8__x3] :
                                      ( t(V8__x3,happ(V2__A2,V7__x2))
                                     => ! [V9__x4] :
                                          ( t(V9__x4,happ(happ(V3__A3,V7__x2),V8__x3))
                                         => ( p(happ(happ(happ(happ(V5__P,V4__y1),V7__x2),V8__x3),V9__x4))
                                           => ( V6__x1 = V4__y1
                                             => p(happ(happ(happ(happ(V5__P,V6__x1),V7__x2),V8__x3),V9__x4)) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('PLF.LibTactics.equates_5',axiom,
    ! [V0__A0] :
      ( cType___24t(V0__A0)
     => ! [V1__A1] :
          ( cType___24t(V1__A1)
         => ! [V2__A2] :
              ( c_24__type__85086___24t(V1__A1,V2__A2)
             => ! [V3__A3] :
                  ( c_24__type__113046___24t(V1__A1,V2__A2,V3__A3)
                 => ! [V4__A4] :
                      ( c_24__type__113065___24t(V1__A1,V2__A2,V3__A3,V4__A4)
                     => ! [V5__y1] :
                          ( t(V5__y1,V0__A0)
                         => ! [V6__P] :
                              ( c_24__type__113122___24t(V0__A0,V1__A1,V2__A2,V3__A3,V4__A4,V6__P)
                             => ! [V7__x1] :
                                  ( t(V7__x1,V0__A0)
                                 => ! [V8__x2] :
                                      ( t(V8__x2,V1__A1)
                                     => ! [V9__x3] :
                                          ( t(V9__x3,happ(V2__A2,V8__x2))
                                         => ! [V10__x4] :
                                              ( t(V10__x4,happ(happ(V3__A3,V8__x2),V9__x3))
                                             => ! [V11__x5] :
                                                  ( t(V11__x5,happ(happ(happ(V4__A4,V8__x2),V9__x3),V10__x4))
                                                 => ( p(happ(happ(happ(happ(happ(V6__P,V5__y1),V8__x2),V9__x3),V10__x4),V11__x5))
                                                   => ( V7__x1 = V5__y1
                                                     => p(happ(happ(happ(happ(happ(V6__P,V7__x1),V8__x2),V9__x3),V10__x4),V11__x5)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('PLF.LibTactics.equates_6',axiom,
    ! [V0__A0] :
      ( cType___24t(V0__A0)
     => ! [V1__A1] :
          ( cType___24t(V1__A1)
         => ! [V2__A2] :
              ( c_24__type__85086___24t(V1__A1,V2__A2)
             => ! [V3__A3] :
                  ( c_24__type__113131___24t(V1__A1,V2__A2,V3__A3)
                 => ! [V4__A4] :
                      ( c_24__type__113150___24t(V1__A1,V2__A2,V3__A3,V4__A4)
                     => ! [V5__A5] :
                          ( c_24__type__113188___24t(V1__A1,V2__A2,V3__A3,V4__A4,V5__A5)
                         => ! [V6__y1] :
                              ( t(V6__y1,V0__A0)
                             => ! [V7__P] :
                                  ( c_24__type__113281___24t(V0__A0,V1__A1,V2__A2,V3__A3,V4__A4,V5__A5,V7__P)
                                 => ! [V8__x1] :
                                      ( t(V8__x1,V0__A0)
                                     => ! [V9__x2] :
                                          ( t(V9__x2,V1__A1)
                                         => ! [V10__x3] :
                                              ( t(V10__x3,happ(V2__A2,V9__x2))
                                             => ! [V11__x4] :
                                                  ( t(V11__x4,happ(happ(V3__A3,V9__x2),V10__x3))
                                                 => ! [V12__x5] :
                                                      ( t(V12__x5,happ(happ(happ(V4__A4,V9__x2),V10__x3),V11__x4))
                                                     => ! [V13__x6] :
                                                          ( t(V13__x6,happ(happ(happ(happ(V5__A5,V9__x2),V10__x3),V11__x4),V12__x5))
                                                         => ( p(happ(happ(happ(happ(happ(happ(V7__P,V6__y1),V9__x2),V10__x3),V11__x4),V12__x5),V13__x6))
                                                           => ( V8__x1 = V6__y1
                                                             => p(happ(happ(happ(happ(happ(happ(V7__P,V8__x1),V9__x2),V10__x3),V11__x4),V12__x5),V13__x6)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('PLF.LibTactics.ltac_mark',axiom,
    p(cPLF_2eLibTactics_2eltac__Mark) ).

fof('PLF.Maps.apply_empty',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__x] :
          ( cCoq_2eStrings_2eString_2estring___24t(V1__x)
         => cPLF_2eMaps_2eempty___24a2(V0__A,V1__x) = cCoq_2eInit_2eDatatypes_2eNone___24a1(V0__A) ) ) ).

fof('PLF.Maps.eqb_string_false_iff',axiom,
    ! [V0__x] :
      ( cCoq_2eStrings_2eString_2estring___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eStrings_2eString_2estring___24t(V1__y)
         => ( cPLF_2eMaps_2eeqb__string___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efalse
          <=> V0__x != V1__y ) ) ) ).

fof('PLF.Maps.false_eqb_string',axiom,
    ! [V0__x] :
      ( cCoq_2eStrings_2eString_2estring___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eStrings_2eString_2estring___24t(V1__y)
         => ( V0__x != V1__y
           => cPLF_2eMaps_2eeqb__string___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ).

fof('PLF.Maps.t_apply_empty',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__x] :
          ( cCoq_2eStrings_2eString_2estring___24t(V1__x)
         => ! [V2__v] :
              ( t(V2__v,V0__A)
             => cPLF_2eMaps_2et__empty___24a3(V0__A,V2__v,V1__x) = V2__v ) ) ) ).

fof('PLF.Maps.t_update_eq',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cPLF_2eMaps_2etotal__map___24t(V0__A,V1__m)
         => ! [V2__x] :
              ( cCoq_2eStrings_2eString_2estring___24t(V2__x)
             => ! [V3__v] :
                  ( t(V3__v,V0__A)
                 => cPLF_2eMaps_2et__update___24a5(V0__A,V1__m,V2__x,V3__v,V2__x) = V3__v ) ) ) ) ).

fof('PLF.Maps.update_eq',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cPLF_2eMaps_2epartial__map___24t(V0__A,V1__m)
         => ! [V2__x] :
              ( cCoq_2eStrings_2eString_2estring___24t(V2__x)
             => ! [V3__v] :
                  ( t(V3__v,V0__A)
                 => cPLF_2eMaps_2eupdate___24a5(V0__A,V1__m,V2__x,V3__v,V2__x) = cCoq_2eInit_2eDatatypes_2eSome___24a2(V0__A,V3__v) ) ) ) ) ).

fof('PLF.Maps.update_neq',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cPLF_2eMaps_2epartial__map___24t(V0__A,V1__m)
         => ! [V2__x1] :
              ( cCoq_2eStrings_2eString_2estring___24t(V2__x1)
             => ! [V3__x2] :
                  ( cCoq_2eStrings_2eString_2estring___24t(V3__x2)
                 => ! [V4__v] :
                      ( t(V4__v,V0__A)
                     => ( V3__x2 != V2__x1
                       => cPLF_2eMaps_2eupdate___24a5(V0__A,V1__m,V3__x2,V4__v,V2__x1) = happ(V1__m,V2__x1) ) ) ) ) ) ) ).

fof('PLF.Maps.update_shadow',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__m] :
          ( cPLF_2eMaps_2epartial__map___24t(V0__A,V1__m)
         => ! [V2__x] :
              ( cCoq_2eStrings_2eString_2estring___24t(V2__x)
             => ! [V3__v1] :
                  ( t(V3__v1,V0__A)
                 => ! [V4__v2] :
                      ( t(V4__v2,V0__A)
                     => cPLF_2eMaps_2eupdate___24a4(V0__A,cPLF_2eMaps_2eupdate___24a4(V0__A,V1__m,V2__x,V3__v1),V2__x,V4__v2) = cPLF_2eMaps_2eupdate___24a4(V0__A,V1__m,V2__x,V4__v2) ) ) ) ) ) ).

fof('PLF.References.STLCRef.RefsAndNontermination.factorial_type',axiom,
    cPLF_2eReferences_2eSTLCRef_2ehas__type___24a4(cPLF_2eMaps_2eempty___24a1(cPLF_2eReferences_2eSTLCRef_2ety),cCoq_2eInit_2eDatatypes_2enil___24a1(cPLF_2eReferences_2eSTLCRef_2ety),cPLF_2eReferences_2eSTLCRef_2eRefsAndNontermination_2efactorial,cPLF_2eReferences_2eSTLCRef_2eArrow___24a2(cPLF_2eReferences_2eSTLCRef_2eNat,cPLF_2eReferences_2eSTLCRef_2eNat)) ).

fof('PLF.References.STLCRef.RefsAndNontermination.loop_typeable',axiom,
    ? [V0__T] :
      ( cPLF_2eReferences_2eSTLCRef_2ety___24t(V0__T)
      & cPLF_2eReferences_2eSTLCRef_2ehas__type___24a4(cPLF_2eMaps_2eempty___24a1(cPLF_2eReferences_2eSTLCRef_2ety),cCoq_2eInit_2eDatatypes_2enil___24a1(cPLF_2eReferences_2eSTLCRef_2ety),cPLF_2eReferences_2eSTLCRef_2eRefsAndNontermination_2eloop,V0__T) ) ).

fof('PLF.References.STLCRef.RefsAndNontermination.sc_one',axiom,
    ! [V0__X] :
      ( cType___24t(V0__X)
     => ! [V1__R] :
          ( cPLF_2eSmallstep_2erelation___24t(V0__X,V1__R)
         => ! [V2__x] :
              ( t(V2__x,V0__X)
             => ! [V3__y] :
                  ( t(V3__y,V0__X)
                 => ( p(happ(happ(V1__R,V2__x),V3__y))
                   => cPLF_2eReferences_2eSTLCRef_2eRefsAndNontermination_2estep__closure___24a4(V0__X,V1__R,V2__x,V3__y) ) ) ) ) ) ).

fof('PLF.References.STLCRef.RefsAndNontermination.sc_step',axiom,
    ! [V0__X] :
      ( cType___24t(V0__X)
     => ! [V1__R] :
          ( cPLF_2eSmallstep_2erelation___24t(V0__X,V1__R)
         => ! [V2__x] :
              ( t(V2__x,V0__X)
             => ! [V3__y] :
                  ( t(V3__y,V0__X)
                 => ! [V4__z] :
                      ( t(V4__z,V0__X)
                     => ( p(happ(happ(V1__R,V2__x),V3__y))
                       => ( cPLF_2eReferences_2eSTLCRef_2eRefsAndNontermination_2estep__closure___24a4(V0__X,V1__R,V3__y,V4__z)
                         => cPLF_2eReferences_2eSTLCRef_2eRefsAndNontermination_2estep__closure___24a4(V0__X,V1__R,V2__x,V4__z) ) ) ) ) ) ) ) ).

fof('PLF.References.STLCRef.ST_App1',axiom,
    ! [V0__t1] :
      ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V0__t1)
     => ! [V1__t1_27] :
          ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V1__t1_27)
         => ! [V2__t2] :
              ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V2__t2)
             => ! [V3__st] :
                  ( cPLF_2eReferences_2eSTLCRef_2estore___24t(V3__st)
                 => ! [V4__st_27] :
                      ( cPLF_2eReferences_2eSTLCRef_2estore___24t(V4__st_27)
                     => ( cPLF_2eReferences_2eSTLCRef_2estep___24a2(cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cPLF_2eReferences_2eSTLCRef_2estore,V0__t1,V3__st),cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cPLF_2eReferences_2eSTLCRef_2estore,V1__t1_27,V4__st_27))
                       => cPLF_2eReferences_2eSTLCRef_2estep___24a2(cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cPLF_2eReferences_2eSTLCRef_2estore,cPLF_2eReferences_2eSTLCRef_2eapp___24a2(V0__t1,V2__t2),V3__st),cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cPLF_2eReferences_2eSTLCRef_2estore,cPLF_2eReferences_2eSTLCRef_2eapp___24a2(V1__t1_27,V2__t2),V4__st_27)) ) ) ) ) ) ) ).

fof('PLF.References.STLCRef.ST_App2',axiom,
    ! [V0__v1] :
      ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V0__v1)
     => ! [V1__t2] :
          ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V1__t2)
         => ! [V2__t2_27] :
              ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V2__t2_27)
             => ! [V3__st] :
                  ( cPLF_2eReferences_2eSTLCRef_2estore___24t(V3__st)
                 => ! [V4__st_27] :
                      ( cPLF_2eReferences_2eSTLCRef_2estore___24t(V4__st_27)
                     => ( cPLF_2eReferences_2eSTLCRef_2evalue___24a1(V0__v1)
                       => ( cPLF_2eReferences_2eSTLCRef_2estep___24a2(cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cPLF_2eReferences_2eSTLCRef_2estore,V1__t2,V3__st),cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cPLF_2eReferences_2eSTLCRef_2estore,V2__t2_27,V4__st_27))
                         => cPLF_2eReferences_2eSTLCRef_2estep___24a2(cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cPLF_2eReferences_2eSTLCRef_2estore,cPLF_2eReferences_2eSTLCRef_2eapp___24a2(V0__v1,V1__t2),V3__st),cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cPLF_2eReferences_2eSTLCRef_2estore,cPLF_2eReferences_2eSTLCRef_2eapp___24a2(V0__v1,V2__t2_27),V4__st_27)) ) ) ) ) ) ) ) ).

fof('PLF.References.STLCRef.ST_AppAbs',axiom,
    ! [V0__x] :
      ( cCoq_2eStrings_2eString_2estring___24t(V0__x)
     => ! [V1__T] :
          ( cPLF_2eReferences_2eSTLCRef_2ety___24t(V1__T)
         => ! [V2__t12] :
              ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V2__t12)
             => ! [V3__v2] :
                  ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V3__v2)
                 => ! [V4__st] :
                      ( cPLF_2eReferences_2eSTLCRef_2estore___24t(V4__st)
                     => ( cPLF_2eReferences_2eSTLCRef_2evalue___24a1(V3__v2)
                       => cPLF_2eReferences_2eSTLCRef_2estep___24a2(cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cPLF_2eReferences_2eSTLCRef_2estore,cPLF_2eReferences_2eSTLCRef_2eapp___24a2(cPLF_2eReferences_2eSTLCRef_2eabs___24a3(V0__x,V1__T,V2__t12),V3__v2),V4__st),cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cPLF_2eReferences_2eSTLCRef_2estore,cPLF_2eReferences_2eSTLCRef_2esubst___24a3(V0__x,V3__v2,V2__t12),V4__st)) ) ) ) ) ) ) ).

fof('PLF.References.STLCRef.ST_Assign',axiom,
    ! [V0__v2] :
      ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V0__v2)
     => ! [V1__l] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__l)
         => ! [V2__st] :
              ( cCoq_2eInit_2eDatatypes_2elist___24t(cPLF_2eReferences_2eSTLCRef_2etm,V2__st)
             => ( cPLF_2eReferences_2eSTLCRef_2evalue___24a1(V0__v2)
               => ( p(cCoq_2eInit_2ePeano_2elt___24a2(V1__l,cCoq_2eInit_2eDatatypes_2elength___24a2(cPLF_2eReferences_2eSTLCRef_2etm,V2__st)))
                 => cPLF_2eReferences_2eSTLCRef_2estep___24a2(cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cCoq_2eInit_2eDatatypes_2elist___24a1(cPLF_2eReferences_2eSTLCRef_2etm),cPLF_2eReferences_2eSTLCRef_2eassign___24a2(cPLF_2eReferences_2eSTLCRef_2eloc___24a1(V1__l),V0__v2),V2__st),cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cCoq_2eInit_2eDatatypes_2elist___24a1(cPLF_2eReferences_2eSTLCRef_2etm),cPLF_2eReferences_2eSTLCRef_2eunit,cPLF_2eReferences_2eSTLCRef_2ereplace___24a4(cPLF_2eReferences_2eSTLCRef_2etm,V1__l,V0__v2,V2__st))) ) ) ) ) ) ).

fof('PLF.References.STLCRef.ST_Assign1',axiom,
    ! [V0__t1] :
      ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V0__t1)
     => ! [V1__t1_27] :
          ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V1__t1_27)
         => ! [V2__t2] :
              ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V2__t2)
             => ! [V3__st] :
                  ( cPLF_2eReferences_2eSTLCRef_2estore___24t(V3__st)
                 => ! [V4__st_27] :
                      ( cPLF_2eReferences_2eSTLCRef_2estore___24t(V4__st_27)
                     => ( cPLF_2eReferences_2eSTLCRef_2estep___24a2(cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cPLF_2eReferences_2eSTLCRef_2estore,V0__t1,V3__st),cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cPLF_2eReferences_2eSTLCRef_2estore,V1__t1_27,V4__st_27))
                       => cPLF_2eReferences_2eSTLCRef_2estep___24a2(cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cPLF_2eReferences_2eSTLCRef_2estore,cPLF_2eReferences_2eSTLCRef_2eassign___24a2(V0__t1,V2__t2),V3__st),cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cPLF_2eReferences_2eSTLCRef_2estore,cPLF_2eReferences_2eSTLCRef_2eassign___24a2(V1__t1_27,V2__t2),V4__st_27)) ) ) ) ) ) ) ).

fof('PLF.References.STLCRef.ST_Assign2',axiom,
    ! [V0__v1] :
      ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V0__v1)
     => ! [V1__t2] :
          ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V1__t2)
         => ! [V2__t2_27] :
              ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V2__t2_27)
             => ! [V3__st] :
                  ( cPLF_2eReferences_2eSTLCRef_2estore___24t(V3__st)
                 => ! [V4__st_27] :
                      ( cPLF_2eReferences_2eSTLCRef_2estore___24t(V4__st_27)
                     => ( cPLF_2eReferences_2eSTLCRef_2evalue___24a1(V0__v1)
                       => ( cPLF_2eReferences_2eSTLCRef_2estep___24a2(cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cPLF_2eReferences_2eSTLCRef_2estore,V1__t2,V3__st),cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cPLF_2eReferences_2eSTLCRef_2estore,V2__t2_27,V4__st_27))
                         => cPLF_2eReferences_2eSTLCRef_2estep___24a2(cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cPLF_2eReferences_2eSTLCRef_2estore,cPLF_2eReferences_2eSTLCRef_2eassign___24a2(V0__v1,V1__t2),V3__st),cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cPLF_2eReferences_2eSTLCRef_2estore,cPLF_2eReferences_2eSTLCRef_2eassign___24a2(V0__v1,V2__t2_27),V4__st_27)) ) ) ) ) ) ) ) ).

fof('PLF.References.STLCRef.ST_Deref',axiom,
    ! [V0__t1] :
      ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V0__t1)
     => ! [V1__t1_27] :
          ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V1__t1_27)
         => ! [V2__st] :
              ( cPLF_2eReferences_2eSTLCRef_2estore___24t(V2__st)
             => ! [V3__st_27] :
                  ( cPLF_2eReferences_2eSTLCRef_2estore___24t(V3__st_27)
                 => ( cPLF_2eReferences_2eSTLCRef_2estep___24a2(cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cPLF_2eReferences_2eSTLCRef_2estore,V0__t1,V2__st),cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cPLF_2eReferences_2eSTLCRef_2estore,V1__t1_27,V3__st_27))
                   => cPLF_2eReferences_2eSTLCRef_2estep___24a2(cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cPLF_2eReferences_2eSTLCRef_2estore,cPLF_2eReferences_2eSTLCRef_2ederef___24a1(V0__t1),V2__st),cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cPLF_2eReferences_2eSTLCRef_2estore,cPLF_2eReferences_2eSTLCRef_2ederef___24a1(V1__t1_27),V3__st_27)) ) ) ) ) ) ).

fof('PLF.References.STLCRef.ST_DerefLoc',axiom,
    ! [V0__st] :
      ( cCoq_2eInit_2eDatatypes_2elist___24t(cPLF_2eReferences_2eSTLCRef_2etm,V0__st)
     => ! [V1__l] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__l)
         => ( p(cCoq_2eInit_2ePeano_2elt___24a2(V1__l,cCoq_2eInit_2eDatatypes_2elength___24a2(cPLF_2eReferences_2eSTLCRef_2etm,V0__st)))
           => cPLF_2eReferences_2eSTLCRef_2estep___24a2(cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cCoq_2eInit_2eDatatypes_2elist___24a1(cPLF_2eReferences_2eSTLCRef_2etm),cPLF_2eReferences_2eSTLCRef_2ederef___24a1(cPLF_2eReferences_2eSTLCRef_2eloc___24a1(V1__l)),V0__st),cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cCoq_2eInit_2eDatatypes_2elist___24a1(cPLF_2eReferences_2eSTLCRef_2etm),cPLF_2eReferences_2eSTLCRef_2estore__lookup___24a2(V1__l,V0__st),V0__st)) ) ) ) ).

fof('PLF.References.STLCRef.ST_If0',axiom,
    ! [V0__t1] :
      ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V0__t1)
     => ! [V1__t1_27] :
          ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V1__t1_27)
         => ! [V2__t2] :
              ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V2__t2)
             => ! [V3__t3] :
                  ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V3__t3)
                 => ! [V4__st] :
                      ( cPLF_2eReferences_2eSTLCRef_2estore___24t(V4__st)
                     => ! [V5__st_27] :
                          ( cPLF_2eReferences_2eSTLCRef_2estore___24t(V5__st_27)
                         => ( cPLF_2eReferences_2eSTLCRef_2estep___24a2(cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cPLF_2eReferences_2eSTLCRef_2estore,V0__t1,V4__st),cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cPLF_2eReferences_2eSTLCRef_2estore,V1__t1_27,V5__st_27))
                           => cPLF_2eReferences_2eSTLCRef_2estep___24a2(cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cPLF_2eReferences_2eSTLCRef_2estore,cPLF_2eReferences_2eSTLCRef_2etest0___24a3(V0__t1,V2__t2,V3__t3),V4__st),cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cPLF_2eReferences_2eSTLCRef_2estore,cPLF_2eReferences_2eSTLCRef_2etest0___24a3(V1__t1_27,V2__t2,V3__t3),V5__st_27)) ) ) ) ) ) ) ) ).

fof('PLF.References.STLCRef.ST_If0_Nonzero',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => ! [V1__t2] :
          ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V1__t2)
         => ! [V2__t3] :
              ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V2__t3)
             => ! [V3__st] :
                  ( cPLF_2eReferences_2eSTLCRef_2estore___24t(V3__st)
                 => cPLF_2eReferences_2eSTLCRef_2estep___24a2(cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cPLF_2eReferences_2eSTLCRef_2estore,cPLF_2eReferences_2eSTLCRef_2etest0___24a3(cPLF_2eReferences_2eSTLCRef_2econst___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n)),V1__t2,V2__t3),V3__st),cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cPLF_2eReferences_2eSTLCRef_2estore,V2__t3,V3__st)) ) ) ) ) ).

fof('PLF.References.STLCRef.ST_If0_Zero',axiom,
    ! [V0__t2] :
      ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V0__t2)
     => ! [V1__t3] :
          ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V1__t3)
         => ! [V2__st] :
              ( cPLF_2eReferences_2eSTLCRef_2estore___24t(V2__st)
             => cPLF_2eReferences_2eSTLCRef_2estep___24a2(cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cPLF_2eReferences_2eSTLCRef_2estore,cPLF_2eReferences_2eSTLCRef_2etest0___24a3(cPLF_2eReferences_2eSTLCRef_2econst___24a1(cCoq_2eInit_2eDatatypes_2eO),V0__t2,V1__t3),V2__st),cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cPLF_2eReferences_2eSTLCRef_2estore,V0__t2,V2__st)) ) ) ) ).

fof('PLF.References.STLCRef.ST_Mult1',axiom,
    ! [V0__t1] :
      ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V0__t1)
     => ! [V1__t2] :
          ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V1__t2)
         => ! [V2__t1_27] :
              ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V2__t1_27)
             => ! [V3__st] :
                  ( cPLF_2eReferences_2eSTLCRef_2estore___24t(V3__st)
                 => ! [V4__st_27] :
                      ( cPLF_2eReferences_2eSTLCRef_2estore___24t(V4__st_27)
                     => ( cPLF_2eReferences_2eSTLCRef_2estep___24a2(cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cPLF_2eReferences_2eSTLCRef_2estore,V0__t1,V3__st),cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cPLF_2eReferences_2eSTLCRef_2estore,V2__t1_27,V4__st_27))
                       => cPLF_2eReferences_2eSTLCRef_2estep___24a2(cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cPLF_2eReferences_2eSTLCRef_2estore,cPLF_2eReferences_2eSTLCRef_2emlt___24a2(V0__t1,V1__t2),V3__st),cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cPLF_2eReferences_2eSTLCRef_2estore,cPLF_2eReferences_2eSTLCRef_2emlt___24a2(V2__t1_27,V1__t2),V4__st_27)) ) ) ) ) ) ) ).

fof('PLF.References.STLCRef.ST_Mult2',axiom,
    ! [V0__v1] :
      ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V0__v1)
     => ! [V1__t2] :
          ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V1__t2)
         => ! [V2__t2_27] :
              ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V2__t2_27)
             => ! [V3__st] :
                  ( cPLF_2eReferences_2eSTLCRef_2estore___24t(V3__st)
                 => ! [V4__st_27] :
                      ( cPLF_2eReferences_2eSTLCRef_2estore___24t(V4__st_27)
                     => ( cPLF_2eReferences_2eSTLCRef_2evalue___24a1(V0__v1)
                       => ( cPLF_2eReferences_2eSTLCRef_2estep___24a2(cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cPLF_2eReferences_2eSTLCRef_2estore,V1__t2,V3__st),cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cPLF_2eReferences_2eSTLCRef_2estore,V2__t2_27,V4__st_27))
                         => cPLF_2eReferences_2eSTLCRef_2estep___24a2(cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cPLF_2eReferences_2eSTLCRef_2estore,cPLF_2eReferences_2eSTLCRef_2emlt___24a2(V0__v1,V1__t2),V3__st),cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cPLF_2eReferences_2eSTLCRef_2estore,cPLF_2eReferences_2eSTLCRef_2emlt___24a2(V0__v1,V2__t2_27),V4__st_27)) ) ) ) ) ) ) ) ).

fof('PLF.References.STLCRef.ST_MultNats',axiom,
    ! [V0__n1] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n1)
     => ! [V1__n2] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n2)
         => ! [V2__st] :
              ( cPLF_2eReferences_2eSTLCRef_2estore___24t(V2__st)
             => cPLF_2eReferences_2eSTLCRef_2estep___24a2(cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cPLF_2eReferences_2eSTLCRef_2estore,cPLF_2eReferences_2eSTLCRef_2emlt___24a2(cPLF_2eReferences_2eSTLCRef_2econst___24a1(V0__n1),cPLF_2eReferences_2eSTLCRef_2econst___24a1(V1__n2)),V2__st),cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cPLF_2eReferences_2eSTLCRef_2estore,cPLF_2eReferences_2eSTLCRef_2econst___24a1(cCoq_2eInit_2eNat_2emul___24a2(V0__n1,V1__n2)),V2__st)) ) ) ) ).

fof('PLF.References.STLCRef.ST_Pred',axiom,
    ! [V0__t1] :
      ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V0__t1)
     => ! [V1__t1_27] :
          ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V1__t1_27)
         => ! [V2__st] :
              ( cPLF_2eReferences_2eSTLCRef_2estore___24t(V2__st)
             => ! [V3__st_27] :
                  ( cPLF_2eReferences_2eSTLCRef_2estore___24t(V3__st_27)
                 => ( cPLF_2eReferences_2eSTLCRef_2estep___24a2(cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cPLF_2eReferences_2eSTLCRef_2estore,V0__t1,V2__st),cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cPLF_2eReferences_2eSTLCRef_2estore,V1__t1_27,V3__st_27))
                   => cPLF_2eReferences_2eSTLCRef_2estep___24a2(cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cPLF_2eReferences_2eSTLCRef_2estore,cPLF_2eReferences_2eSTLCRef_2eprd___24a1(V0__t1),V2__st),cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cPLF_2eReferences_2eSTLCRef_2estore,cPLF_2eReferences_2eSTLCRef_2eprd___24a1(V1__t1_27),V3__st_27)) ) ) ) ) ) ).

fof('PLF.References.STLCRef.ST_PredNat',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => ! [V1__st] :
          ( cPLF_2eReferences_2eSTLCRef_2estore___24t(V1__st)
         => cPLF_2eReferences_2eSTLCRef_2estep___24a2(cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cPLF_2eReferences_2eSTLCRef_2estore,cPLF_2eReferences_2eSTLCRef_2eprd___24a1(cPLF_2eReferences_2eSTLCRef_2econst___24a1(V0__n)),V1__st),cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cPLF_2eReferences_2eSTLCRef_2estore,cPLF_2eReferences_2eSTLCRef_2econst___24a1(cCoq_2eInit_2eNat_2epred___24a1(V0__n)),V1__st)) ) ) ).

fof('PLF.References.STLCRef.ST_Ref',axiom,
    ! [V0__t1] :
      ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V0__t1)
     => ! [V1__t1_27] :
          ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V1__t1_27)
         => ! [V2__st] :
              ( cPLF_2eReferences_2eSTLCRef_2estore___24t(V2__st)
             => ! [V3__st_27] :
                  ( cPLF_2eReferences_2eSTLCRef_2estore___24t(V3__st_27)
                 => ( cPLF_2eReferences_2eSTLCRef_2estep___24a2(cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cPLF_2eReferences_2eSTLCRef_2estore,V0__t1,V2__st),cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cPLF_2eReferences_2eSTLCRef_2estore,V1__t1_27,V3__st_27))
                   => cPLF_2eReferences_2eSTLCRef_2estep___24a2(cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cPLF_2eReferences_2eSTLCRef_2estore,cPLF_2eReferences_2eSTLCRef_2eref___24a1(V0__t1),V2__st),cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cPLF_2eReferences_2eSTLCRef_2estore,cPLF_2eReferences_2eSTLCRef_2eref___24a1(V1__t1_27),V3__st_27)) ) ) ) ) ) ).

fof('PLF.References.STLCRef.ST_RefValue',axiom,
    ! [V0__v1] :
      ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V0__v1)
     => ! [V1__st] :
          ( cPLF_2eReferences_2eSTLCRef_2estore___24t(V1__st)
         => ( cPLF_2eReferences_2eSTLCRef_2evalue___24a1(V0__v1)
           => cPLF_2eReferences_2eSTLCRef_2estep___24a2(cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cPLF_2eReferences_2eSTLCRef_2estore,cPLF_2eReferences_2eSTLCRef_2eref___24a1(V0__v1),V1__st),cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cCoq_2eInit_2eDatatypes_2elist___24a1(cPLF_2eReferences_2eSTLCRef_2etm),cPLF_2eReferences_2eSTLCRef_2eloc___24a1(cCoq_2eInit_2eDatatypes_2elength___24a2(cPLF_2eReferences_2eSTLCRef_2etm,V1__st)),cCoq_2eInit_2eDatatypes_2eapp___24a3(cPLF_2eReferences_2eSTLCRef_2etm,V1__st,cCoq_2eInit_2eDatatypes_2econs___24a3(cPLF_2eReferences_2eSTLCRef_2etm,V0__v1,cCoq_2eInit_2eDatatypes_2enil___24a1(cPLF_2eReferences_2eSTLCRef_2etm))))) ) ) ) ).

fof('PLF.References.STLCRef.ST_Succ',axiom,
    ! [V0__t1] :
      ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V0__t1)
     => ! [V1__t1_27] :
          ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V1__t1_27)
         => ! [V2__st] :
              ( cPLF_2eReferences_2eSTLCRef_2estore___24t(V2__st)
             => ! [V3__st_27] :
                  ( cPLF_2eReferences_2eSTLCRef_2estore___24t(V3__st_27)
                 => ( cPLF_2eReferences_2eSTLCRef_2estep___24a2(cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cPLF_2eReferences_2eSTLCRef_2estore,V0__t1,V2__st),cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cPLF_2eReferences_2eSTLCRef_2estore,V1__t1_27,V3__st_27))
                   => cPLF_2eReferences_2eSTLCRef_2estep___24a2(cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cPLF_2eReferences_2eSTLCRef_2estore,cPLF_2eReferences_2eSTLCRef_2escc___24a1(V0__t1),V2__st),cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cPLF_2eReferences_2eSTLCRef_2estore,cPLF_2eReferences_2eSTLCRef_2escc___24a1(V1__t1_27),V3__st_27)) ) ) ) ) ) ).

fof('PLF.References.STLCRef.ST_SuccNat',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => ! [V1__st] :
          ( cPLF_2eReferences_2eSTLCRef_2estore___24t(V1__st)
         => cPLF_2eReferences_2eSTLCRef_2estep___24a2(cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cPLF_2eReferences_2eSTLCRef_2estore,cPLF_2eReferences_2eSTLCRef_2escc___24a1(cPLF_2eReferences_2eSTLCRef_2econst___24a1(V0__n)),V1__st),cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cPLF_2eReferences_2eSTLCRef_2estore,cPLF_2eReferences_2eSTLCRef_2econst___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(V0__n)),V1__st)) ) ) ).

fof('PLF.References.STLCRef.T_Abs',axiom,
    ! [V0__Gamma] :
      ( cPLF_2eMaps_2epartial__map___24t(cPLF_2eReferences_2eSTLCRef_2ety,V0__Gamma)
     => ! [V1__ST] :
          ( cPLF_2eReferences_2eSTLCRef_2estore__ty___24t(V1__ST)
         => ! [V2__x] :
              ( cCoq_2eStrings_2eString_2estring___24t(V2__x)
             => ! [V3__T11] :
                  ( cPLF_2eReferences_2eSTLCRef_2ety___24t(V3__T11)
                 => ! [V4__T12] :
                      ( cPLF_2eReferences_2eSTLCRef_2ety___24t(V4__T12)
                     => ! [V5__t12] :
                          ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V5__t12)
                         => ( cPLF_2eReferences_2eSTLCRef_2ehas__type___24a4(cPLF_2eMaps_2eupdate___24a4(cPLF_2eReferences_2eSTLCRef_2ety,V0__Gamma,V2__x,V3__T11),V1__ST,V5__t12,V4__T12)
                           => cPLF_2eReferences_2eSTLCRef_2ehas__type___24a4(V0__Gamma,V1__ST,cPLF_2eReferences_2eSTLCRef_2eabs___24a3(V2__x,V3__T11,V5__t12),cPLF_2eReferences_2eSTLCRef_2eArrow___24a2(V3__T11,V4__T12)) ) ) ) ) ) ) ) ).

fof('PLF.References.STLCRef.T_App',axiom,
    ! [V0__T1] :
      ( cPLF_2eReferences_2eSTLCRef_2ety___24t(V0__T1)
     => ! [V1__T2] :
          ( cPLF_2eReferences_2eSTLCRef_2ety___24t(V1__T2)
         => ! [V2__Gamma] :
              ( cPLF_2eReferences_2eSTLCRef_2econtext___24t(V2__Gamma)
             => ! [V3__ST] :
                  ( cPLF_2eReferences_2eSTLCRef_2estore__ty___24t(V3__ST)
                 => ! [V4__t1] :
                      ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V4__t1)
                     => ! [V5__t2] :
                          ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V5__t2)
                         => ( cPLF_2eReferences_2eSTLCRef_2ehas__type___24a4(V2__Gamma,V3__ST,V4__t1,cPLF_2eReferences_2eSTLCRef_2eArrow___24a2(V0__T1,V1__T2))
                           => ( cPLF_2eReferences_2eSTLCRef_2ehas__type___24a4(V2__Gamma,V3__ST,V5__t2,V0__T1)
                             => cPLF_2eReferences_2eSTLCRef_2ehas__type___24a4(V2__Gamma,V3__ST,cPLF_2eReferences_2eSTLCRef_2eapp___24a2(V4__t1,V5__t2),V1__T2) ) ) ) ) ) ) ) ) ).

fof('PLF.References.STLCRef.T_Assign',axiom,
    ! [V0__Gamma] :
      ( cPLF_2eReferences_2eSTLCRef_2econtext___24t(V0__Gamma)
     => ! [V1__ST] :
          ( cPLF_2eReferences_2eSTLCRef_2estore__ty___24t(V1__ST)
         => ! [V2__t1] :
              ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V2__t1)
             => ! [V3__t2] :
                  ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V3__t2)
                 => ! [V4__T11] :
                      ( cPLF_2eReferences_2eSTLCRef_2ety___24t(V4__T11)
                     => ( cPLF_2eReferences_2eSTLCRef_2ehas__type___24a4(V0__Gamma,V1__ST,V2__t1,cPLF_2eReferences_2eSTLCRef_2eRef___24a1(V4__T11))
                       => ( cPLF_2eReferences_2eSTLCRef_2ehas__type___24a4(V0__Gamma,V1__ST,V3__t2,V4__T11)
                         => cPLF_2eReferences_2eSTLCRef_2ehas__type___24a4(V0__Gamma,V1__ST,cPLF_2eReferences_2eSTLCRef_2eassign___24a2(V2__t1,V3__t2),cPLF_2eReferences_2eSTLCRef_2eUnit) ) ) ) ) ) ) ) ).

fof('PLF.References.STLCRef.T_Deref',axiom,
    ! [V0__Gamma] :
      ( cPLF_2eReferences_2eSTLCRef_2econtext___24t(V0__Gamma)
     => ! [V1__ST] :
          ( cPLF_2eReferences_2eSTLCRef_2estore__ty___24t(V1__ST)
         => ! [V2__t1] :
              ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V2__t1)
             => ! [V3__T11] :
                  ( cPLF_2eReferences_2eSTLCRef_2ety___24t(V3__T11)
                 => ( cPLF_2eReferences_2eSTLCRef_2ehas__type___24a4(V0__Gamma,V1__ST,V2__t1,cPLF_2eReferences_2eSTLCRef_2eRef___24a1(V3__T11))
                   => cPLF_2eReferences_2eSTLCRef_2ehas__type___24a4(V0__Gamma,V1__ST,cPLF_2eReferences_2eSTLCRef_2ederef___24a1(V2__t1),V3__T11) ) ) ) ) ) ).

fof('PLF.References.STLCRef.T_If0',axiom,
    ! [V0__Gamma] :
      ( cPLF_2eReferences_2eSTLCRef_2econtext___24t(V0__Gamma)
     => ! [V1__ST] :
          ( cPLF_2eReferences_2eSTLCRef_2estore__ty___24t(V1__ST)
         => ! [V2__t1] :
              ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V2__t1)
             => ! [V3__t2] :
                  ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V3__t2)
                 => ! [V4__t3] :
                      ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V4__t3)
                     => ! [V5__T] :
                          ( cPLF_2eReferences_2eSTLCRef_2ety___24t(V5__T)
                         => ( cPLF_2eReferences_2eSTLCRef_2ehas__type___24a4(V0__Gamma,V1__ST,V2__t1,cPLF_2eReferences_2eSTLCRef_2eNat)
                           => ( cPLF_2eReferences_2eSTLCRef_2ehas__type___24a4(V0__Gamma,V1__ST,V3__t2,V5__T)
                             => ( cPLF_2eReferences_2eSTLCRef_2ehas__type___24a4(V0__Gamma,V1__ST,V4__t3,V5__T)
                               => cPLF_2eReferences_2eSTLCRef_2ehas__type___24a4(V0__Gamma,V1__ST,cPLF_2eReferences_2eSTLCRef_2etest0___24a3(V2__t1,V3__t2,V4__t3),V5__T) ) ) ) ) ) ) ) ) ) ).

fof('PLF.References.STLCRef.T_Loc',axiom,
    ! [V0__Gamma] :
      ( cPLF_2eReferences_2eSTLCRef_2econtext___24t(V0__Gamma)
     => ! [V1__ST] :
          ( cCoq_2eInit_2eDatatypes_2elist___24t(cPLF_2eReferences_2eSTLCRef_2ety,V1__ST)
         => ! [V2__l] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__l)
             => ( p(cCoq_2eInit_2ePeano_2elt___24a2(V2__l,cCoq_2eInit_2eDatatypes_2elength___24a2(cPLF_2eReferences_2eSTLCRef_2ety,V1__ST)))
               => cPLF_2eReferences_2eSTLCRef_2ehas__type___24a4(V0__Gamma,V1__ST,cPLF_2eReferences_2eSTLCRef_2eloc___24a1(V2__l),cPLF_2eReferences_2eSTLCRef_2eRef___24a1(cPLF_2eReferences_2eSTLCRef_2estore__Tlookup___24a2(V2__l,V1__ST))) ) ) ) ) ).

fof('PLF.References.STLCRef.T_Mult',axiom,
    ! [V0__Gamma] :
      ( cPLF_2eReferences_2eSTLCRef_2econtext___24t(V0__Gamma)
     => ! [V1__ST] :
          ( cPLF_2eReferences_2eSTLCRef_2estore__ty___24t(V1__ST)
         => ! [V2__t1] :
              ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V2__t1)
             => ! [V3__t2] :
                  ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V3__t2)
                 => ( cPLF_2eReferences_2eSTLCRef_2ehas__type___24a4(V0__Gamma,V1__ST,V2__t1,cPLF_2eReferences_2eSTLCRef_2eNat)
                   => ( cPLF_2eReferences_2eSTLCRef_2ehas__type___24a4(V0__Gamma,V1__ST,V3__t2,cPLF_2eReferences_2eSTLCRef_2eNat)
                     => cPLF_2eReferences_2eSTLCRef_2ehas__type___24a4(V0__Gamma,V1__ST,cPLF_2eReferences_2eSTLCRef_2emlt___24a2(V2__t1,V3__t2),cPLF_2eReferences_2eSTLCRef_2eNat) ) ) ) ) ) ) ).

fof('PLF.References.STLCRef.T_Nat',axiom,
    ! [V0__Gamma] :
      ( cPLF_2eReferences_2eSTLCRef_2econtext___24t(V0__Gamma)
     => ! [V1__ST] :
          ( cPLF_2eReferences_2eSTLCRef_2estore__ty___24t(V1__ST)
         => ! [V2__n] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
             => cPLF_2eReferences_2eSTLCRef_2ehas__type___24a4(V0__Gamma,V1__ST,cPLF_2eReferences_2eSTLCRef_2econst___24a1(V2__n),cPLF_2eReferences_2eSTLCRef_2eNat) ) ) ) ).

fof('PLF.References.STLCRef.T_Pred',axiom,
    ! [V0__Gamma] :
      ( cPLF_2eReferences_2eSTLCRef_2econtext___24t(V0__Gamma)
     => ! [V1__ST] :
          ( cPLF_2eReferences_2eSTLCRef_2estore__ty___24t(V1__ST)
         => ! [V2__t1] :
              ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V2__t1)
             => ( cPLF_2eReferences_2eSTLCRef_2ehas__type___24a4(V0__Gamma,V1__ST,V2__t1,cPLF_2eReferences_2eSTLCRef_2eNat)
               => cPLF_2eReferences_2eSTLCRef_2ehas__type___24a4(V0__Gamma,V1__ST,cPLF_2eReferences_2eSTLCRef_2eprd___24a1(V2__t1),cPLF_2eReferences_2eSTLCRef_2eNat) ) ) ) ) ).

fof('PLF.References.STLCRef.T_Ref',axiom,
    ! [V0__Gamma] :
      ( cPLF_2eReferences_2eSTLCRef_2econtext___24t(V0__Gamma)
     => ! [V1__ST] :
          ( cPLF_2eReferences_2eSTLCRef_2estore__ty___24t(V1__ST)
         => ! [V2__t1] :
              ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V2__t1)
             => ! [V3__T1] :
                  ( cPLF_2eReferences_2eSTLCRef_2ety___24t(V3__T1)
                 => ( cPLF_2eReferences_2eSTLCRef_2ehas__type___24a4(V0__Gamma,V1__ST,V2__t1,V3__T1)
                   => cPLF_2eReferences_2eSTLCRef_2ehas__type___24a4(V0__Gamma,V1__ST,cPLF_2eReferences_2eSTLCRef_2eref___24a1(V2__t1),cPLF_2eReferences_2eSTLCRef_2eRef___24a1(V3__T1)) ) ) ) ) ) ).

fof('PLF.References.STLCRef.T_Succ',axiom,
    ! [V0__Gamma] :
      ( cPLF_2eReferences_2eSTLCRef_2econtext___24t(V0__Gamma)
     => ! [V1__ST] :
          ( cPLF_2eReferences_2eSTLCRef_2estore__ty___24t(V1__ST)
         => ! [V2__t1] :
              ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V2__t1)
             => ( cPLF_2eReferences_2eSTLCRef_2ehas__type___24a4(V0__Gamma,V1__ST,V2__t1,cPLF_2eReferences_2eSTLCRef_2eNat)
               => cPLF_2eReferences_2eSTLCRef_2ehas__type___24a4(V0__Gamma,V1__ST,cPLF_2eReferences_2eSTLCRef_2escc___24a1(V2__t1),cPLF_2eReferences_2eSTLCRef_2eNat) ) ) ) ) ).

fof('PLF.References.STLCRef.T_Unit',axiom,
    ! [V0__Gamma] :
      ( cPLF_2eReferences_2eSTLCRef_2econtext___24t(V0__Gamma)
     => ! [V1__ST] :
          ( cPLF_2eReferences_2eSTLCRef_2estore__ty___24t(V1__ST)
         => cPLF_2eReferences_2eSTLCRef_2ehas__type___24a4(V0__Gamma,V1__ST,cPLF_2eReferences_2eSTLCRef_2eunit,cPLF_2eReferences_2eSTLCRef_2eUnit) ) ) ).

fof('PLF.References.STLCRef.T_Var',axiom,
    ! [V0__Gamma] :
      ( c_24__type__212230___24t(V0__Gamma)
     => ! [V1__ST] :
          ( cPLF_2eReferences_2eSTLCRef_2estore__ty___24t(V1__ST)
         => ! [V2__x] :
              ( cCoq_2eStrings_2eString_2estring___24t(V2__x)
             => ! [V3__T] :
                  ( cPLF_2eReferences_2eSTLCRef_2ety___24t(V3__T)
                 => ( happ(V0__Gamma,V2__x) = cCoq_2eInit_2eDatatypes_2eSome___24a2(cPLF_2eReferences_2eSTLCRef_2ety,V3__T)
                   => cPLF_2eReferences_2eSTLCRef_2ehas__type___24a4(V0__Gamma,V1__ST,cPLF_2eReferences_2eSTLCRef_2evar___24a1(V2__x),V3__T) ) ) ) ) ) ).

fof('PLF.References.STLCRef.afi_abs',axiom,
    ! [V0__x] :
      ( cCoq_2eStrings_2eString_2estring___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eStrings_2eString_2estring___24t(V1__y)
         => ! [V2__T11] :
              ( cPLF_2eReferences_2eSTLCRef_2ety___24t(V2__T11)
             => ! [V3__t12] :
                  ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V3__t12)
                 => ( V1__y != V0__x
                   => ( cPLF_2eReferences_2eSTLCRef_2eappears__free__in___24a2(V0__x,V3__t12)
                     => cPLF_2eReferences_2eSTLCRef_2eappears__free__in___24a2(V0__x,cPLF_2eReferences_2eSTLCRef_2eabs___24a3(V1__y,V2__T11,V3__t12)) ) ) ) ) ) ) ).

fof('PLF.References.STLCRef.afi_app1',axiom,
    ! [V0__x] :
      ( cCoq_2eStrings_2eString_2estring___24t(V0__x)
     => ! [V1__t1] :
          ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V1__t1)
         => ! [V2__t2] :
              ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V2__t2)
             => ( cPLF_2eReferences_2eSTLCRef_2eappears__free__in___24a2(V0__x,V1__t1)
               => cPLF_2eReferences_2eSTLCRef_2eappears__free__in___24a2(V0__x,cPLF_2eReferences_2eSTLCRef_2eapp___24a2(V1__t1,V2__t2)) ) ) ) ) ).

fof('PLF.References.STLCRef.afi_app2',axiom,
    ! [V0__x] :
      ( cCoq_2eStrings_2eString_2estring___24t(V0__x)
     => ! [V1__t1] :
          ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V1__t1)
         => ! [V2__t2] :
              ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V2__t2)
             => ( cPLF_2eReferences_2eSTLCRef_2eappears__free__in___24a2(V0__x,V2__t2)
               => cPLF_2eReferences_2eSTLCRef_2eappears__free__in___24a2(V0__x,cPLF_2eReferences_2eSTLCRef_2eapp___24a2(V1__t1,V2__t2)) ) ) ) ) ).

fof('PLF.References.STLCRef.afi_assign1',axiom,
    ! [V0__x] :
      ( cCoq_2eStrings_2eString_2estring___24t(V0__x)
     => ! [V1__t1] :
          ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V1__t1)
         => ! [V2__t2] :
              ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V2__t2)
             => ( cPLF_2eReferences_2eSTLCRef_2eappears__free__in___24a2(V0__x,V1__t1)
               => cPLF_2eReferences_2eSTLCRef_2eappears__free__in___24a2(V0__x,cPLF_2eReferences_2eSTLCRef_2eassign___24a2(V1__t1,V2__t2)) ) ) ) ) ).

fof('PLF.References.STLCRef.afi_assign2',axiom,
    ! [V0__x] :
      ( cCoq_2eStrings_2eString_2estring___24t(V0__x)
     => ! [V1__t1] :
          ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V1__t1)
         => ! [V2__t2] :
              ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V2__t2)
             => ( cPLF_2eReferences_2eSTLCRef_2eappears__free__in___24a2(V0__x,V2__t2)
               => cPLF_2eReferences_2eSTLCRef_2eappears__free__in___24a2(V0__x,cPLF_2eReferences_2eSTLCRef_2eassign___24a2(V1__t1,V2__t2)) ) ) ) ) ).

fof('PLF.References.STLCRef.afi_deref',axiom,
    ! [V0__x] :
      ( cCoq_2eStrings_2eString_2estring___24t(V0__x)
     => ! [V1__t1] :
          ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V1__t1)
         => ( cPLF_2eReferences_2eSTLCRef_2eappears__free__in___24a2(V0__x,V1__t1)
           => cPLF_2eReferences_2eSTLCRef_2eappears__free__in___24a2(V0__x,cPLF_2eReferences_2eSTLCRef_2ederef___24a1(V1__t1)) ) ) ) ).

fof('PLF.References.STLCRef.afi_if0_1',axiom,
    ! [V0__x] :
      ( cCoq_2eStrings_2eString_2estring___24t(V0__x)
     => ! [V1__t1] :
          ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V1__t1)
         => ! [V2__t2] :
              ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V2__t2)
             => ! [V3__t3] :
                  ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V3__t3)
                 => ( cPLF_2eReferences_2eSTLCRef_2eappears__free__in___24a2(V0__x,V1__t1)
                   => cPLF_2eReferences_2eSTLCRef_2eappears__free__in___24a2(V0__x,cPLF_2eReferences_2eSTLCRef_2etest0___24a3(V1__t1,V2__t2,V3__t3)) ) ) ) ) ) ).

fof('PLF.References.STLCRef.afi_if0_2',axiom,
    ! [V0__x] :
      ( cCoq_2eStrings_2eString_2estring___24t(V0__x)
     => ! [V1__t1] :
          ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V1__t1)
         => ! [V2__t2] :
              ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V2__t2)
             => ! [V3__t3] :
                  ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V3__t3)
                 => ( cPLF_2eReferences_2eSTLCRef_2eappears__free__in___24a2(V0__x,V2__t2)
                   => cPLF_2eReferences_2eSTLCRef_2eappears__free__in___24a2(V0__x,cPLF_2eReferences_2eSTLCRef_2etest0___24a3(V1__t1,V2__t2,V3__t3)) ) ) ) ) ) ).

fof('PLF.References.STLCRef.afi_if0_3',axiom,
    ! [V0__x] :
      ( cCoq_2eStrings_2eString_2estring___24t(V0__x)
     => ! [V1__t1] :
          ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V1__t1)
         => ! [V2__t2] :
              ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V2__t2)
             => ! [V3__t3] :
                  ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V3__t3)
                 => ( cPLF_2eReferences_2eSTLCRef_2eappears__free__in___24a2(V0__x,V3__t3)
                   => cPLF_2eReferences_2eSTLCRef_2eappears__free__in___24a2(V0__x,cPLF_2eReferences_2eSTLCRef_2etest0___24a3(V1__t1,V2__t2,V3__t3)) ) ) ) ) ) ).

fof('PLF.References.STLCRef.afi_mult1',axiom,
    ! [V0__x] :
      ( cCoq_2eStrings_2eString_2estring___24t(V0__x)
     => ! [V1__t1] :
          ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V1__t1)
         => ! [V2__t2] :
              ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V2__t2)
             => ( cPLF_2eReferences_2eSTLCRef_2eappears__free__in___24a2(V0__x,V1__t1)
               => cPLF_2eReferences_2eSTLCRef_2eappears__free__in___24a2(V0__x,cPLF_2eReferences_2eSTLCRef_2emlt___24a2(V1__t1,V2__t2)) ) ) ) ) ).

fof('PLF.References.STLCRef.afi_mult2',axiom,
    ! [V0__x] :
      ( cCoq_2eStrings_2eString_2estring___24t(V0__x)
     => ! [V1__t1] :
          ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V1__t1)
         => ! [V2__t2] :
              ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V2__t2)
             => ( cPLF_2eReferences_2eSTLCRef_2eappears__free__in___24a2(V0__x,V2__t2)
               => cPLF_2eReferences_2eSTLCRef_2eappears__free__in___24a2(V0__x,cPLF_2eReferences_2eSTLCRef_2emlt___24a2(V1__t1,V2__t2)) ) ) ) ) ).

fof('PLF.References.STLCRef.afi_pred',axiom,
    ! [V0__x] :
      ( cCoq_2eStrings_2eString_2estring___24t(V0__x)
     => ! [V1__t1] :
          ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V1__t1)
         => ( cPLF_2eReferences_2eSTLCRef_2eappears__free__in___24a2(V0__x,V1__t1)
           => cPLF_2eReferences_2eSTLCRef_2eappears__free__in___24a2(V0__x,cPLF_2eReferences_2eSTLCRef_2eprd___24a1(V1__t1)) ) ) ) ).

fof('PLF.References.STLCRef.afi_ref',axiom,
    ! [V0__x] :
      ( cCoq_2eStrings_2eString_2estring___24t(V0__x)
     => ! [V1__t1] :
          ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V1__t1)
         => ( cPLF_2eReferences_2eSTLCRef_2eappears__free__in___24a2(V0__x,V1__t1)
           => cPLF_2eReferences_2eSTLCRef_2eappears__free__in___24a2(V0__x,cPLF_2eReferences_2eSTLCRef_2eref___24a1(V1__t1)) ) ) ) ).

fof('PLF.References.STLCRef.afi_succ',axiom,
    ! [V0__x] :
      ( cCoq_2eStrings_2eString_2estring___24t(V0__x)
     => ! [V1__t1] :
          ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V1__t1)
         => ( cPLF_2eReferences_2eSTLCRef_2eappears__free__in___24a2(V0__x,V1__t1)
           => cPLF_2eReferences_2eSTLCRef_2eappears__free__in___24a2(V0__x,cPLF_2eReferences_2eSTLCRef_2escc___24a1(V1__t1)) ) ) ) ).

fof('PLF.References.STLCRef.afi_var',axiom,
    ! [V0__x] :
      ( cCoq_2eStrings_2eString_2estring___24t(V0__x)
     => cPLF_2eReferences_2eSTLCRef_2eappears__free__in___24a2(V0__x,cPLF_2eReferences_2eSTLCRef_2evar___24a1(V0__x)) ) ).

fof('PLF.References.STLCRef.appears_free_in_ind',axiom,
    ! [V0__P] :
      ( c_24__type__212563___24t(V0__P)
     => ( ! [V1__x] :
            ( cCoq_2eStrings_2eString_2estring___24t(V1__x)
           => p(happ(happ(V0__P,V1__x),cPLF_2eReferences_2eSTLCRef_2evar___24a1(V1__x))) )
       => ( ! [V2__x] :
              ( cCoq_2eStrings_2eString_2estring___24t(V2__x)
             => ! [V3__t1] :
                  ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V3__t1)
                 => ! [V4__t2] :
                      ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V4__t2)
                     => ( cPLF_2eReferences_2eSTLCRef_2eappears__free__in___24a2(V2__x,V3__t1)
                       => ( p(happ(happ(V0__P,V2__x),V3__t1))
                         => p(happ(happ(V0__P,V2__x),cPLF_2eReferences_2eSTLCRef_2eapp___24a2(V3__t1,V4__t2))) ) ) ) ) )
         => ( ! [V3__x] :
                ( cCoq_2eStrings_2eString_2estring___24t(V3__x)
               => ! [V4__t1] :
                    ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V4__t1)
                   => ! [V5__t2] :
                        ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V5__t2)
                       => ( cPLF_2eReferences_2eSTLCRef_2eappears__free__in___24a2(V3__x,V5__t2)
                         => ( p(happ(happ(V0__P,V3__x),V5__t2))
                           => p(happ(happ(V0__P,V3__x),cPLF_2eReferences_2eSTLCRef_2eapp___24a2(V4__t1,V5__t2))) ) ) ) ) )
           => ( ! [V4__x] :
                  ( cCoq_2eStrings_2eString_2estring___24t(V4__x)
                 => ! [V5__y] :
                      ( cCoq_2eStrings_2eString_2estring___24t(V5__y)
                     => ! [V6__T11] :
                          ( cPLF_2eReferences_2eSTLCRef_2ety___24t(V6__T11)
                         => ! [V7__t12] :
                              ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V7__t12)
                             => ( V5__y != V4__x
                               => ( cPLF_2eReferences_2eSTLCRef_2eappears__free__in___24a2(V4__x,V7__t12)
                                 => ( p(happ(happ(V0__P,V4__x),V7__t12))
                                   => p(happ(happ(V0__P,V4__x),cPLF_2eReferences_2eSTLCRef_2eabs___24a3(V5__y,V6__T11,V7__t12))) ) ) ) ) ) ) )
             => ( ! [V5__x] :
                    ( cCoq_2eStrings_2eString_2estring___24t(V5__x)
                   => ! [V6__t1] :
                        ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V6__t1)
                       => ( cPLF_2eReferences_2eSTLCRef_2eappears__free__in___24a2(V5__x,V6__t1)
                         => ( p(happ(happ(V0__P,V5__x),V6__t1))
                           => p(happ(happ(V0__P,V5__x),cPLF_2eReferences_2eSTLCRef_2escc___24a1(V6__t1))) ) ) ) )
               => ( ! [V6__x] :
                      ( cCoq_2eStrings_2eString_2estring___24t(V6__x)
                     => ! [V7__t1] :
                          ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V7__t1)
                         => ( cPLF_2eReferences_2eSTLCRef_2eappears__free__in___24a2(V6__x,V7__t1)
                           => ( p(happ(happ(V0__P,V6__x),V7__t1))
                             => p(happ(happ(V0__P,V6__x),cPLF_2eReferences_2eSTLCRef_2eprd___24a1(V7__t1))) ) ) ) )
                 => ( ! [V7__x] :
                        ( cCoq_2eStrings_2eString_2estring___24t(V7__x)
                       => ! [V8__t1] :
                            ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V8__t1)
                           => ! [V9__t2] :
                                ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V9__t2)
                               => ( cPLF_2eReferences_2eSTLCRef_2eappears__free__in___24a2(V7__x,V8__t1)
                                 => ( p(happ(happ(V0__P,V7__x),V8__t1))
                                   => p(happ(happ(V0__P,V7__x),cPLF_2eReferences_2eSTLCRef_2emlt___24a2(V8__t1,V9__t2))) ) ) ) ) )
                   => ( ! [V8__x] :
                          ( cCoq_2eStrings_2eString_2estring___24t(V8__x)
                         => ! [V9__t1] :
                              ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V9__t1)
                             => ! [V10__t2] :
                                  ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V10__t2)
                                 => ( cPLF_2eReferences_2eSTLCRef_2eappears__free__in___24a2(V8__x,V10__t2)
                                   => ( p(happ(happ(V0__P,V8__x),V10__t2))
                                     => p(happ(happ(V0__P,V8__x),cPLF_2eReferences_2eSTLCRef_2emlt___24a2(V9__t1,V10__t2))) ) ) ) ) )
                     => ( ! [V9__x] :
                            ( cCoq_2eStrings_2eString_2estring___24t(V9__x)
                           => ! [V10__t1] :
                                ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V10__t1)
                               => ! [V11__t2] :
                                    ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V11__t2)
                                   => ! [V12__t3] :
                                        ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V12__t3)
                                       => ( cPLF_2eReferences_2eSTLCRef_2eappears__free__in___24a2(V9__x,V10__t1)
                                         => ( p(happ(happ(V0__P,V9__x),V10__t1))
                                           => p(happ(happ(V0__P,V9__x),cPLF_2eReferences_2eSTLCRef_2etest0___24a3(V10__t1,V11__t2,V12__t3))) ) ) ) ) ) )
                       => ( ! [V10__x] :
                              ( cCoq_2eStrings_2eString_2estring___24t(V10__x)
                             => ! [V11__t1] :
                                  ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V11__t1)
                                 => ! [V12__t2] :
                                      ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V12__t2)
                                     => ! [V13__t3] :
                                          ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V13__t3)
                                         => ( cPLF_2eReferences_2eSTLCRef_2eappears__free__in___24a2(V10__x,V12__t2)
                                           => ( p(happ(happ(V0__P,V10__x),V12__t2))
                                             => p(happ(happ(V0__P,V10__x),cPLF_2eReferences_2eSTLCRef_2etest0___24a3(V11__t1,V12__t2,V13__t3))) ) ) ) ) ) )
                         => ( ! [V11__x] :
                                ( cCoq_2eStrings_2eString_2estring___24t(V11__x)
                               => ! [V12__t1] :
                                    ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V12__t1)
                                   => ! [V13__t2] :
                                        ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V13__t2)
                                       => ! [V14__t3] :
                                            ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V14__t3)
                                           => ( cPLF_2eReferences_2eSTLCRef_2eappears__free__in___24a2(V11__x,V14__t3)
                                             => ( p(happ(happ(V0__P,V11__x),V14__t3))
                                               => p(happ(happ(V0__P,V11__x),cPLF_2eReferences_2eSTLCRef_2etest0___24a3(V12__t1,V13__t2,V14__t3))) ) ) ) ) ) )
                           => ( ! [V12__x] :
                                  ( cCoq_2eStrings_2eString_2estring___24t(V12__x)
                                 => ! [V13__t1] :
                                      ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V13__t1)
                                     => ( cPLF_2eReferences_2eSTLCRef_2eappears__free__in___24a2(V12__x,V13__t1)
                                       => ( p(happ(happ(V0__P,V12__x),V13__t1))
                                         => p(happ(happ(V0__P,V12__x),cPLF_2eReferences_2eSTLCRef_2eref___24a1(V13__t1))) ) ) ) )
                             => ( ! [V13__x] :
                                    ( cCoq_2eStrings_2eString_2estring___24t(V13__x)
                                   => ! [V14__t1] :
                                        ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V14__t1)
                                       => ( cPLF_2eReferences_2eSTLCRef_2eappears__free__in___24a2(V13__x,V14__t1)
                                         => ( p(happ(happ(V0__P,V13__x),V14__t1))
                                           => p(happ(happ(V0__P,V13__x),cPLF_2eReferences_2eSTLCRef_2ederef___24a1(V14__t1))) ) ) ) )
                               => ( ! [V14__x] :
                                      ( cCoq_2eStrings_2eString_2estring___24t(V14__x)
                                     => ! [V15__t1] :
                                          ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V15__t1)
                                         => ! [V16__t2] :
                                              ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V16__t2)
                                             => ( cPLF_2eReferences_2eSTLCRef_2eappears__free__in___24a2(V14__x,V15__t1)
                                               => ( p(happ(happ(V0__P,V14__x),V15__t1))
                                                 => p(happ(happ(V0__P,V14__x),cPLF_2eReferences_2eSTLCRef_2eassign___24a2(V15__t1,V16__t2))) ) ) ) ) )
                                 => ( ! [V15__x] :
                                        ( cCoq_2eStrings_2eString_2estring___24t(V15__x)
                                       => ! [V16__t1] :
                                            ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V16__t1)
                                           => ! [V17__t2] :
                                                ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V17__t2)
                                               => ( cPLF_2eReferences_2eSTLCRef_2eappears__free__in___24a2(V15__x,V17__t2)
                                                 => ( p(happ(happ(V0__P,V15__x),V17__t2))
                                                   => p(happ(happ(V0__P,V15__x),cPLF_2eReferences_2eSTLCRef_2eassign___24a2(V16__t1,V17__t2))) ) ) ) ) )
                                   => ! [V16__s] :
                                        ( cCoq_2eStrings_2eString_2estring___24t(V16__s)
                                       => ! [V17__t] :
                                            ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V17__t)
                                           => ( cPLF_2eReferences_2eSTLCRef_2eappears__free__in___24a2(V16__s,V17__t)
                                             => p(happ(happ(V0__P,V16__s),V17__t)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('PLF.References.STLCRef.assign_pres_store_typing',axiom,
    ! [V0__ST] :
      ( cPLF_2eReferences_2eSTLCRef_2estore__ty___24t(V0__ST)
     => ! [V1__st] :
          ( cCoq_2eInit_2eDatatypes_2elist___24t(cPLF_2eReferences_2eSTLCRef_2etm,V1__st)
         => ! [V2__l] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__l)
             => ! [V3__t] :
                  ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V3__t)
                 => ( p(cCoq_2eInit_2ePeano_2elt___24a2(V2__l,cCoq_2eInit_2eDatatypes_2elength___24a2(cPLF_2eReferences_2eSTLCRef_2etm,V1__st)))
                   => ( cPLF_2eReferences_2eSTLCRef_2estore__well__typed___24a2(V0__ST,V1__st)
                     => ( cPLF_2eReferences_2eSTLCRef_2ehas__type___24a4(cPLF_2eMaps_2eempty___24a1(cPLF_2eReferences_2eSTLCRef_2ety),V0__ST,V3__t,cPLF_2eReferences_2eSTLCRef_2estore__Tlookup___24a2(V2__l,V0__ST))
                       => cPLF_2eReferences_2eSTLCRef_2estore__well__typed___24a2(V0__ST,cPLF_2eReferences_2eSTLCRef_2ereplace___24a4(cPLF_2eReferences_2eSTLCRef_2etm,V2__l,V3__t,V1__st)) ) ) ) ) ) ) ) ).

fof('PLF.References.STLCRef.context_invariance',axiom,
    ! [V0__Gamma] :
      ( cPLF_2eReferences_2eSTLCRef_2econtext___24t(V0__Gamma)
     => ! [V1__Gamma_27] :
          ( c_24__type__212230___24t(V1__Gamma_27)
         => ! [V2__ST] :
              ( cPLF_2eReferences_2eSTLCRef_2estore__ty___24t(V2__ST)
             => ! [V3__t] :
                  ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V3__t)
                 => ! [V4__T] :
                      ( cPLF_2eReferences_2eSTLCRef_2ety___24t(V4__T)
                     => ( cPLF_2eReferences_2eSTLCRef_2ehas__type___24a4(V0__Gamma,V2__ST,V3__t,V4__T)
                       => ( ! [V6__x] :
                              ( cCoq_2eStrings_2eString_2estring___24t(V6__x)
                             => ( cPLF_2eReferences_2eSTLCRef_2eappears__free__in___24a2(V6__x,V3__t)
                               => happ(V0__Gamma,V6__x) = happ(V1__Gamma_27,V6__x) ) )
                         => cPLF_2eReferences_2eSTLCRef_2ehas__type___24a4(V1__Gamma_27,V2__ST,V3__t,V4__T) ) ) ) ) ) ) ) ).

fof('PLF.References.STLCRef.extends_app',axiom,
    ! [V0__ST] :
      ( cCoq_2eInit_2eDatatypes_2elist___24t(cPLF_2eReferences_2eSTLCRef_2ety,V0__ST)
     => ! [V1__T] :
          ( cCoq_2eInit_2eDatatypes_2elist___24t(cPLF_2eReferences_2eSTLCRef_2ety,V1__T)
         => cPLF_2eReferences_2eSTLCRef_2eextends___24a2(cCoq_2eInit_2eDatatypes_2eapp___24a3(cPLF_2eReferences_2eSTLCRef_2ety,V0__ST,V1__T),V0__ST) ) ) ).

fof('PLF.References.STLCRef.extends_cons',axiom,
    ! [V0__x] :
      ( cPLF_2eReferences_2eSTLCRef_2ety___24t(V0__x)
     => ! [V1__ST_27] :
          ( cPLF_2eReferences_2eSTLCRef_2estore__ty___24t(V1__ST_27)
         => ! [V2__ST] :
              ( cPLF_2eReferences_2eSTLCRef_2estore__ty___24t(V2__ST)
             => ( cPLF_2eReferences_2eSTLCRef_2eextends___24a2(V1__ST_27,V2__ST)
               => cPLF_2eReferences_2eSTLCRef_2eextends___24a2(cCoq_2eInit_2eDatatypes_2econs___24a3(cPLF_2eReferences_2eSTLCRef_2ety,V0__x,V1__ST_27),cCoq_2eInit_2eDatatypes_2econs___24a3(cPLF_2eReferences_2eSTLCRef_2ety,V0__x,V2__ST)) ) ) ) ) ).

fof('PLF.References.STLCRef.extends_ind',axiom,
    ! [V0__P] :
      ( c_24__type__212493___24t(V0__P)
     => ( ! [V1__ST_27] :
            ( cPLF_2eReferences_2eSTLCRef_2estore__ty___24t(V1__ST_27)
           => p(happ(happ(V0__P,V1__ST_27),cCoq_2eInit_2eDatatypes_2enil___24a1(cPLF_2eReferences_2eSTLCRef_2ety))) )
       => ( ! [V2__x] :
              ( cPLF_2eReferences_2eSTLCRef_2ety___24t(V2__x)
             => ! [V3__ST_27] :
                  ( cPLF_2eReferences_2eSTLCRef_2estore__ty___24t(V3__ST_27)
                 => ! [V4__ST] :
                      ( cPLF_2eReferences_2eSTLCRef_2estore__ty___24t(V4__ST)
                     => ( cPLF_2eReferences_2eSTLCRef_2eextends___24a2(V3__ST_27,V4__ST)
                       => ( p(happ(happ(V0__P,V3__ST_27),V4__ST))
                         => p(happ(happ(V0__P,cCoq_2eInit_2eDatatypes_2econs___24a3(cPLF_2eReferences_2eSTLCRef_2ety,V2__x,V3__ST_27)),cCoq_2eInit_2eDatatypes_2econs___24a3(cPLF_2eReferences_2eSTLCRef_2ety,V2__x,V4__ST))) ) ) ) ) )
         => ! [V3__s] :
              ( cPLF_2eReferences_2eSTLCRef_2estore__ty___24t(V3__s)
             => ! [V4__s] :
                  ( cPLF_2eReferences_2eSTLCRef_2estore__ty___24t(V4__s)
                 => ( cPLF_2eReferences_2eSTLCRef_2eextends___24a2(V3__s,V4__s)
                   => p(happ(happ(V0__P,V3__s),V4__s)) ) ) ) ) ) ) ).

fof('PLF.References.STLCRef.extends_lookup',axiom,
    ! [V0__l] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__l)
     => ! [V1__ST] :
          ( cCoq_2eInit_2eDatatypes_2elist___24t(cPLF_2eReferences_2eSTLCRef_2ety,V1__ST)
         => ! [V2__ST_27] :
              ( cPLF_2eReferences_2eSTLCRef_2estore__ty___24t(V2__ST_27)
             => ( p(cCoq_2eInit_2ePeano_2elt___24a2(V0__l,cCoq_2eInit_2eDatatypes_2elength___24a2(cPLF_2eReferences_2eSTLCRef_2ety,V1__ST)))
               => ( cPLF_2eReferences_2eSTLCRef_2eextends___24a2(V2__ST_27,V1__ST)
                 => cPLF_2eReferences_2eSTLCRef_2estore__Tlookup___24a2(V0__l,V2__ST_27) = cPLF_2eReferences_2eSTLCRef_2estore__Tlookup___24a2(V0__l,V1__ST) ) ) ) ) ) ).

fof('PLF.References.STLCRef.extends_nil',axiom,
    ! [V0__ST_27] :
      ( cPLF_2eReferences_2eSTLCRef_2estore__ty___24t(V0__ST_27)
     => cPLF_2eReferences_2eSTLCRef_2eextends___24a2(V0__ST_27,cCoq_2eInit_2eDatatypes_2enil___24a1(cPLF_2eReferences_2eSTLCRef_2ety)) ) ).

fof('PLF.References.STLCRef.extends_refl',axiom,
    ! [V0__ST] :
      ( cPLF_2eReferences_2eSTLCRef_2estore__ty___24t(V0__ST)
     => cPLF_2eReferences_2eSTLCRef_2eextends___24a2(V0__ST,V0__ST) ) ).

fof('PLF.References.STLCRef.free_in_context',axiom,
    ! [V0__x] :
      ( cCoq_2eStrings_2eString_2estring___24t(V0__x)
     => ! [V1__t] :
          ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V1__t)
         => ! [V2__T] :
              ( cPLF_2eReferences_2eSTLCRef_2ety___24t(V2__T)
             => ! [V3__Gamma] :
                  ( cPLF_2eReferences_2eSTLCRef_2econtext___24t(V3__Gamma)
                 => ! [V4__ST] :
                      ( cPLF_2eReferences_2eSTLCRef_2estore__ty___24t(V4__ST)
                     => ( cPLF_2eReferences_2eSTLCRef_2eappears__free__in___24a2(V0__x,V1__t)
                       => ( cPLF_2eReferences_2eSTLCRef_2ehas__type___24a4(V3__Gamma,V4__ST,V1__t,V2__T)
                         => ? [V7__T_27] :
                              ( cPLF_2eReferences_2eSTLCRef_2ety___24t(V7__T_27)
                              & happ(V3__Gamma,V0__x) = cCoq_2eInit_2eDatatypes_2eSome___24a2(cPLF_2eReferences_2eSTLCRef_2ety,V7__T_27) ) ) ) ) ) ) ) ) ).

fof('PLF.References.STLCRef.has_type_ind',axiom,
    ! [V0__P] :
      ( c_24__type__212228___24t(V0__P)
     => ( ! [V1__Gamma] :
            ( c_24__type__212230___24t(V1__Gamma)
           => ! [V2__ST] :
                ( cPLF_2eReferences_2eSTLCRef_2estore__ty___24t(V2__ST)
               => ! [V3__x] :
                    ( cCoq_2eStrings_2eString_2estring___24t(V3__x)
                   => ! [V4__T] :
                        ( cPLF_2eReferences_2eSTLCRef_2ety___24t(V4__T)
                       => ( happ(V1__Gamma,V3__x) = cCoq_2eInit_2eDatatypes_2eSome___24a2(cPLF_2eReferences_2eSTLCRef_2ety,V4__T)
                         => p(happ(happ(happ(happ(V0__P,V1__Gamma),V2__ST),cPLF_2eReferences_2eSTLCRef_2evar___24a1(V3__x)),V4__T)) ) ) ) ) )
       => ( ! [V2__Gamma] :
              ( cPLF_2eMaps_2epartial__map___24t(cPLF_2eReferences_2eSTLCRef_2ety,V2__Gamma)
             => ! [V3__ST] :
                  ( cPLF_2eReferences_2eSTLCRef_2estore__ty___24t(V3__ST)
                 => ! [V4__x] :
                      ( cCoq_2eStrings_2eString_2estring___24t(V4__x)
                     => ! [V5__T11] :
                          ( cPLF_2eReferences_2eSTLCRef_2ety___24t(V5__T11)
                         => ! [V6__T12] :
                              ( cPLF_2eReferences_2eSTLCRef_2ety___24t(V6__T12)
                             => ! [V7__t12] :
                                  ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V7__t12)
                                 => ( cPLF_2eReferences_2eSTLCRef_2ehas__type___24a4(cPLF_2eMaps_2eupdate___24a4(cPLF_2eReferences_2eSTLCRef_2ety,V2__Gamma,V4__x,V5__T11),V3__ST,V7__t12,V6__T12)
                                   => ( p(happ(happ(happ(happ(V0__P,cPLF_2eMaps_2eupdate___24a4(cPLF_2eReferences_2eSTLCRef_2ety,V2__Gamma,V4__x,V5__T11)),V3__ST),V7__t12),V6__T12))
                                     => p(happ(happ(happ(happ(V0__P,V2__Gamma),V3__ST),cPLF_2eReferences_2eSTLCRef_2eabs___24a3(V4__x,V5__T11,V7__t12)),cPLF_2eReferences_2eSTLCRef_2eArrow___24a2(V5__T11,V6__T12))) ) ) ) ) ) ) ) )
         => ( ! [V3__T1] :
                ( cPLF_2eReferences_2eSTLCRef_2ety___24t(V3__T1)
               => ! [V4__T2] :
                    ( cPLF_2eReferences_2eSTLCRef_2ety___24t(V4__T2)
                   => ! [V5__Gamma] :
                        ( cPLF_2eReferences_2eSTLCRef_2econtext___24t(V5__Gamma)
                       => ! [V6__ST] :
                            ( cPLF_2eReferences_2eSTLCRef_2estore__ty___24t(V6__ST)
                           => ! [V7__t1] :
                                ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V7__t1)
                               => ! [V8__t2] :
                                    ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V8__t2)
                                   => ( cPLF_2eReferences_2eSTLCRef_2ehas__type___24a4(V5__Gamma,V6__ST,V7__t1,cPLF_2eReferences_2eSTLCRef_2eArrow___24a2(V3__T1,V4__T2))
                                     => ( p(happ(happ(happ(happ(V0__P,V5__Gamma),V6__ST),V7__t1),cPLF_2eReferences_2eSTLCRef_2eArrow___24a2(V3__T1,V4__T2)))
                                       => ( cPLF_2eReferences_2eSTLCRef_2ehas__type___24a4(V5__Gamma,V6__ST,V8__t2,V3__T1)
                                         => ( p(happ(happ(happ(happ(V0__P,V5__Gamma),V6__ST),V8__t2),V3__T1))
                                           => p(happ(happ(happ(happ(V0__P,V5__Gamma),V6__ST),cPLF_2eReferences_2eSTLCRef_2eapp___24a2(V7__t1,V8__t2)),V4__T2)) ) ) ) ) ) ) ) ) ) )
           => ( ! [V4__Gamma] :
                  ( cPLF_2eReferences_2eSTLCRef_2econtext___24t(V4__Gamma)
                 => ! [V5__ST] :
                      ( cPLF_2eReferences_2eSTLCRef_2estore__ty___24t(V5__ST)
                     => ! [V6__n] :
                          ( cCoq_2eInit_2eDatatypes_2enat___24t(V6__n)
                         => p(happ(happ(happ(happ(V0__P,V4__Gamma),V5__ST),cPLF_2eReferences_2eSTLCRef_2econst___24a1(V6__n)),cPLF_2eReferences_2eSTLCRef_2eNat)) ) ) )
             => ( ! [V5__Gamma] :
                    ( cPLF_2eReferences_2eSTLCRef_2econtext___24t(V5__Gamma)
                   => ! [V6__ST] :
                        ( cPLF_2eReferences_2eSTLCRef_2estore__ty___24t(V6__ST)
                       => ! [V7__t1] :
                            ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V7__t1)
                           => ( cPLF_2eReferences_2eSTLCRef_2ehas__type___24a4(V5__Gamma,V6__ST,V7__t1,cPLF_2eReferences_2eSTLCRef_2eNat)
                             => ( p(happ(happ(happ(happ(V0__P,V5__Gamma),V6__ST),V7__t1),cPLF_2eReferences_2eSTLCRef_2eNat))
                               => p(happ(happ(happ(happ(V0__P,V5__Gamma),V6__ST),cPLF_2eReferences_2eSTLCRef_2escc___24a1(V7__t1)),cPLF_2eReferences_2eSTLCRef_2eNat)) ) ) ) ) )
               => ( ! [V6__Gamma] :
                      ( cPLF_2eReferences_2eSTLCRef_2econtext___24t(V6__Gamma)
                     => ! [V7__ST] :
                          ( cPLF_2eReferences_2eSTLCRef_2estore__ty___24t(V7__ST)
                         => ! [V8__t1] :
                              ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V8__t1)
                             => ( cPLF_2eReferences_2eSTLCRef_2ehas__type___24a4(V6__Gamma,V7__ST,V8__t1,cPLF_2eReferences_2eSTLCRef_2eNat)
                               => ( p(happ(happ(happ(happ(V0__P,V6__Gamma),V7__ST),V8__t1),cPLF_2eReferences_2eSTLCRef_2eNat))
                                 => p(happ(happ(happ(happ(V0__P,V6__Gamma),V7__ST),cPLF_2eReferences_2eSTLCRef_2eprd___24a1(V8__t1)),cPLF_2eReferences_2eSTLCRef_2eNat)) ) ) ) ) )
                 => ( ! [V7__Gamma] :
                        ( cPLF_2eReferences_2eSTLCRef_2econtext___24t(V7__Gamma)
                       => ! [V8__ST] :
                            ( cPLF_2eReferences_2eSTLCRef_2estore__ty___24t(V8__ST)
                           => ! [V9__t1] :
                                ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V9__t1)
                               => ! [V10__t2] :
                                    ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V10__t2)
                                   => ( cPLF_2eReferences_2eSTLCRef_2ehas__type___24a4(V7__Gamma,V8__ST,V9__t1,cPLF_2eReferences_2eSTLCRef_2eNat)
                                     => ( p(happ(happ(happ(happ(V0__P,V7__Gamma),V8__ST),V9__t1),cPLF_2eReferences_2eSTLCRef_2eNat))
                                       => ( cPLF_2eReferences_2eSTLCRef_2ehas__type___24a4(V7__Gamma,V8__ST,V10__t2,cPLF_2eReferences_2eSTLCRef_2eNat)
                                         => ( p(happ(happ(happ(happ(V0__P,V7__Gamma),V8__ST),V10__t2),cPLF_2eReferences_2eSTLCRef_2eNat))
                                           => p(happ(happ(happ(happ(V0__P,V7__Gamma),V8__ST),cPLF_2eReferences_2eSTLCRef_2emlt___24a2(V9__t1,V10__t2)),cPLF_2eReferences_2eSTLCRef_2eNat)) ) ) ) ) ) ) ) )
                   => ( ! [V8__Gamma] :
                          ( cPLF_2eReferences_2eSTLCRef_2econtext___24t(V8__Gamma)
                         => ! [V9__ST] :
                              ( cPLF_2eReferences_2eSTLCRef_2estore__ty___24t(V9__ST)
                             => ! [V10__t1] :
                                  ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V10__t1)
                                 => ! [V11__t2] :
                                      ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V11__t2)
                                     => ! [V12__t3] :
                                          ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V12__t3)
                                         => ! [V13__T] :
                                              ( cPLF_2eReferences_2eSTLCRef_2ety___24t(V13__T)
                                             => ( cPLF_2eReferences_2eSTLCRef_2ehas__type___24a4(V8__Gamma,V9__ST,V10__t1,cPLF_2eReferences_2eSTLCRef_2eNat)
                                               => ( p(happ(happ(happ(happ(V0__P,V8__Gamma),V9__ST),V10__t1),cPLF_2eReferences_2eSTLCRef_2eNat))
                                                 => ( cPLF_2eReferences_2eSTLCRef_2ehas__type___24a4(V8__Gamma,V9__ST,V11__t2,V13__T)
                                                   => ( p(happ(happ(happ(happ(V0__P,V8__Gamma),V9__ST),V11__t2),V13__T))
                                                     => ( cPLF_2eReferences_2eSTLCRef_2ehas__type___24a4(V8__Gamma,V9__ST,V12__t3,V13__T)
                                                       => ( p(happ(happ(happ(happ(V0__P,V8__Gamma),V9__ST),V12__t3),V13__T))
                                                         => p(happ(happ(happ(happ(V0__P,V8__Gamma),V9__ST),cPLF_2eReferences_2eSTLCRef_2etest0___24a3(V10__t1,V11__t2,V12__t3)),V13__T)) ) ) ) ) ) ) ) ) ) ) ) )
                     => ( ! [V9__Gamma] :
                            ( cPLF_2eReferences_2eSTLCRef_2econtext___24t(V9__Gamma)
                           => ! [V10__ST] :
                                ( cPLF_2eReferences_2eSTLCRef_2estore__ty___24t(V10__ST)
                               => p(happ(happ(happ(happ(V0__P,V9__Gamma),V10__ST),cPLF_2eReferences_2eSTLCRef_2eunit),cPLF_2eReferences_2eSTLCRef_2eUnit)) ) )
                       => ( ! [V10__Gamma] :
                              ( cPLF_2eReferences_2eSTLCRef_2econtext___24t(V10__Gamma)
                             => ! [V11__ST] :
                                  ( cCoq_2eInit_2eDatatypes_2elist___24t(cPLF_2eReferences_2eSTLCRef_2ety,V11__ST)
                                 => ! [V12__l] :
                                      ( cCoq_2eInit_2eDatatypes_2enat___24t(V12__l)
                                     => ( p(cCoq_2eInit_2ePeano_2elt___24a2(V12__l,cCoq_2eInit_2eDatatypes_2elength___24a2(cPLF_2eReferences_2eSTLCRef_2ety,V11__ST)))
                                       => p(happ(happ(happ(happ(V0__P,V10__Gamma),V11__ST),cPLF_2eReferences_2eSTLCRef_2eloc___24a1(V12__l)),cPLF_2eReferences_2eSTLCRef_2eRef___24a1(cPLF_2eReferences_2eSTLCRef_2estore__Tlookup___24a2(V12__l,V11__ST)))) ) ) ) )
                         => ( ! [V11__Gamma] :
                                ( cPLF_2eReferences_2eSTLCRef_2econtext___24t(V11__Gamma)
                               => ! [V12__ST] :
                                    ( cPLF_2eReferences_2eSTLCRef_2estore__ty___24t(V12__ST)
                                   => ! [V13__t1] :
                                        ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V13__t1)
                                       => ! [V14__T1] :
                                            ( cPLF_2eReferences_2eSTLCRef_2ety___24t(V14__T1)
                                           => ( cPLF_2eReferences_2eSTLCRef_2ehas__type___24a4(V11__Gamma,V12__ST,V13__t1,V14__T1)
                                             => ( p(happ(happ(happ(happ(V0__P,V11__Gamma),V12__ST),V13__t1),V14__T1))
                                               => p(happ(happ(happ(happ(V0__P,V11__Gamma),V12__ST),cPLF_2eReferences_2eSTLCRef_2eref___24a1(V13__t1)),cPLF_2eReferences_2eSTLCRef_2eRef___24a1(V14__T1))) ) ) ) ) ) )
                           => ( ! [V12__Gamma] :
                                  ( cPLF_2eReferences_2eSTLCRef_2econtext___24t(V12__Gamma)
                                 => ! [V13__ST] :
                                      ( cPLF_2eReferences_2eSTLCRef_2estore__ty___24t(V13__ST)
                                     => ! [V14__t1] :
                                          ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V14__t1)
                                         => ! [V15__T11] :
                                              ( cPLF_2eReferences_2eSTLCRef_2ety___24t(V15__T11)
                                             => ( cPLF_2eReferences_2eSTLCRef_2ehas__type___24a4(V12__Gamma,V13__ST,V14__t1,cPLF_2eReferences_2eSTLCRef_2eRef___24a1(V15__T11))
                                               => ( p(happ(happ(happ(happ(V0__P,V12__Gamma),V13__ST),V14__t1),cPLF_2eReferences_2eSTLCRef_2eRef___24a1(V15__T11)))
                                                 => p(happ(happ(happ(happ(V0__P,V12__Gamma),V13__ST),cPLF_2eReferences_2eSTLCRef_2ederef___24a1(V14__t1)),V15__T11)) ) ) ) ) ) )
                             => ( ! [V13__Gamma] :
                                    ( cPLF_2eReferences_2eSTLCRef_2econtext___24t(V13__Gamma)
                                   => ! [V14__ST] :
                                        ( cPLF_2eReferences_2eSTLCRef_2estore__ty___24t(V14__ST)
                                       => ! [V15__t1] :
                                            ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V15__t1)
                                           => ! [V16__t2] :
                                                ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V16__t2)
                                               => ! [V17__T11] :
                                                    ( cPLF_2eReferences_2eSTLCRef_2ety___24t(V17__T11)
                                                   => ( cPLF_2eReferences_2eSTLCRef_2ehas__type___24a4(V13__Gamma,V14__ST,V15__t1,cPLF_2eReferences_2eSTLCRef_2eRef___24a1(V17__T11))
                                                     => ( p(happ(happ(happ(happ(V0__P,V13__Gamma),V14__ST),V15__t1),cPLF_2eReferences_2eSTLCRef_2eRef___24a1(V17__T11)))
                                                       => ( cPLF_2eReferences_2eSTLCRef_2ehas__type___24a4(V13__Gamma,V14__ST,V16__t2,V17__T11)
                                                         => ( p(happ(happ(happ(happ(V0__P,V13__Gamma),V14__ST),V16__t2),V17__T11))
                                                           => p(happ(happ(happ(happ(V0__P,V13__Gamma),V14__ST),cPLF_2eReferences_2eSTLCRef_2eassign___24a2(V15__t1,V16__t2)),cPLF_2eReferences_2eSTLCRef_2eUnit)) ) ) ) ) ) ) ) ) )
                               => ! [V14__c] :
                                    ( cPLF_2eReferences_2eSTLCRef_2econtext___24t(V14__c)
                                   => ! [V15__s] :
                                        ( cPLF_2eReferences_2eSTLCRef_2estore__ty___24t(V15__s)
                                       => ! [V16__t] :
                                            ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V16__t)
                                           => ! [V17__t] :
                                                ( cPLF_2eReferences_2eSTLCRef_2ety___24t(V17__t)
                                               => ( cPLF_2eReferences_2eSTLCRef_2ehas__type___24a4(V14__c,V15__s,V16__t,V17__t)
                                                 => p(happ(happ(happ(happ(V0__P,V14__c),V15__s),V16__t),V17__t)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('PLF.References.STLCRef.length_extends',axiom,
    ! [V0__l] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__l)
     => ! [V1__ST] :
          ( cCoq_2eInit_2eDatatypes_2elist___24t(cPLF_2eReferences_2eSTLCRef_2ety,V1__ST)
         => ! [V2__ST_27] :
              ( cPLF_2eReferences_2eSTLCRef_2estore__ty___24t(V2__ST_27)
             => ( p(cCoq_2eInit_2ePeano_2elt___24a2(V0__l,cCoq_2eInit_2eDatatypes_2elength___24a2(cPLF_2eReferences_2eSTLCRef_2ety,V1__ST)))
               => ( cPLF_2eReferences_2eSTLCRef_2eextends___24a2(V2__ST_27,V1__ST)
                 => p(cCoq_2eInit_2ePeano_2elt___24a2(V0__l,cCoq_2eInit_2eDatatypes_2elength___24a2(cPLF_2eReferences_2eSTLCRef_2ety,V2__ST_27))) ) ) ) ) ) ).

fof('PLF.References.STLCRef.length_replace',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__n] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
         => ! [V2__x] :
              ( t(V2__x,V0__A)
             => ! [V3__l] :
                  ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
                 => cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,cPLF_2eReferences_2eSTLCRef_2ereplace___24a4(V0__A,V1__n,V2__x,V3__l)) = cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V3__l) ) ) ) ) ).

fof('PLF.References.STLCRef.lookup_replace_eq',axiom,
    ! [V0__l] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__l)
     => ! [V1__t] :
          ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V1__t)
         => ! [V2__st] :
              ( cCoq_2eInit_2eDatatypes_2elist___24t(cPLF_2eReferences_2eSTLCRef_2etm,V2__st)
             => ( p(cCoq_2eInit_2ePeano_2elt___24a2(V0__l,cCoq_2eInit_2eDatatypes_2elength___24a2(cPLF_2eReferences_2eSTLCRef_2etm,V2__st)))
               => cPLF_2eReferences_2eSTLCRef_2estore__lookup___24a2(V0__l,cPLF_2eReferences_2eSTLCRef_2ereplace___24a4(cPLF_2eReferences_2eSTLCRef_2etm,V0__l,V1__t,V2__st)) = V1__t ) ) ) ) ).

fof('PLF.References.STLCRef.lookup_replace_neq',axiom,
    ! [V0__l1] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__l1)
     => ! [V1__l2] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__l2)
         => ! [V2__t] :
              ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V2__t)
             => ! [V3__st] :
                  ( cCoq_2eInit_2eDatatypes_2elist___24t(cPLF_2eReferences_2eSTLCRef_2etm,V3__st)
                 => ( V0__l1 != V1__l2
                   => cPLF_2eReferences_2eSTLCRef_2estore__lookup___24a2(V0__l1,cPLF_2eReferences_2eSTLCRef_2ereplace___24a4(cPLF_2eReferences_2eSTLCRef_2etm,V1__l2,V2__t,V3__st)) = cPLF_2eReferences_2eSTLCRef_2estore__lookup___24a2(V0__l1,V3__st) ) ) ) ) ) ).

fof('PLF.References.STLCRef.nth_eq_last',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__l] :
          ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
         => ! [V2__x] :
              ( t(V2__x,V0__A)
             => ! [V3__d] :
                  ( t(V3__d,V0__A)
                 => cCoq_2eLists_2eList_2enth___24a4(V0__A,cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V1__l),cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__l,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__x,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A))),V3__d) = V2__x ) ) ) ) ).

fof('PLF.References.STLCRef.preservation',axiom,
    ! [V0__ST] :
      ( cPLF_2eReferences_2eSTLCRef_2estore__ty___24t(V0__ST)
     => ! [V1__t] :
          ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V1__t)
         => ! [V2__t_27] :
              ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V2__t_27)
             => ! [V3__T] :
                  ( cPLF_2eReferences_2eSTLCRef_2ety___24t(V3__T)
                 => ! [V4__st] :
                      ( cPLF_2eReferences_2eSTLCRef_2estore___24t(V4__st)
                     => ! [V5__st_27] :
                          ( cPLF_2eReferences_2eSTLCRef_2estore___24t(V5__st_27)
                         => ( cPLF_2eReferences_2eSTLCRef_2ehas__type___24a4(cPLF_2eMaps_2eempty___24a1(cPLF_2eReferences_2eSTLCRef_2ety),V0__ST,V1__t,V3__T)
                           => ( cPLF_2eReferences_2eSTLCRef_2estore__well__typed___24a2(V0__ST,V4__st)
                             => ( cPLF_2eReferences_2eSTLCRef_2estep___24a2(cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cPLF_2eReferences_2eSTLCRef_2estore,V1__t,V4__st),cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cPLF_2eReferences_2eSTLCRef_2estore,V2__t_27,V5__st_27))
                               => ? [V9__ST_27] :
                                    ( cPLF_2eReferences_2eSTLCRef_2estore__ty___24t(V9__ST_27)
                                    & cPLF_2eReferences_2eSTLCRef_2eextends___24a2(V9__ST_27,V0__ST)
                                    & cPLF_2eReferences_2eSTLCRef_2ehas__type___24a4(cPLF_2eMaps_2eempty___24a1(cPLF_2eReferences_2eSTLCRef_2ety),V9__ST_27,V2__t_27,V3__T)
                                    & cPLF_2eReferences_2eSTLCRef_2estore__well__typed___24a2(V9__ST_27,V5__st_27) ) ) ) ) ) ) ) ) ) ) ).

fof('PLF.References.STLCRef.progress',axiom,
    ! [V0__ST] :
      ( cPLF_2eReferences_2eSTLCRef_2estore__ty___24t(V0__ST)
     => ! [V1__t] :
          ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V1__t)
         => ! [V2__T] :
              ( cPLF_2eReferences_2eSTLCRef_2ety___24t(V2__T)
             => ! [V3__st] :
                  ( cPLF_2eReferences_2eSTLCRef_2estore___24t(V3__st)
                 => ( cPLF_2eReferences_2eSTLCRef_2ehas__type___24a4(cPLF_2eMaps_2eempty___24a1(cPLF_2eReferences_2eSTLCRef_2ety),V0__ST,V1__t,V2__T)
                   => ( cPLF_2eReferences_2eSTLCRef_2estore__well__typed___24a2(V0__ST,V3__st)
                     => ( cPLF_2eReferences_2eSTLCRef_2evalue___24a1(V1__t)
                        | ? [V6__t_27] :
                            ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V6__t_27)
                            & ? [V7__st_27] :
                                ( cPLF_2eReferences_2eSTLCRef_2estore___24t(V7__st_27)
                                & cPLF_2eReferences_2eSTLCRef_2estep___24a2(cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cPLF_2eReferences_2eSTLCRef_2estore,V1__t,V3__st),cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cPLF_2eReferences_2eSTLCRef_2estore,V6__t_27,V7__st_27)) ) ) ) ) ) ) ) ) ) ).

fof('PLF.References.STLCRef.store_weakening',axiom,
    ! [V0__Gamma] :
      ( cPLF_2eReferences_2eSTLCRef_2econtext___24t(V0__Gamma)
     => ! [V1__ST] :
          ( cPLF_2eReferences_2eSTLCRef_2estore__ty___24t(V1__ST)
         => ! [V2__ST_27] :
              ( cPLF_2eReferences_2eSTLCRef_2estore__ty___24t(V2__ST_27)
             => ! [V3__t] :
                  ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V3__t)
                 => ! [V4__T] :
                      ( cPLF_2eReferences_2eSTLCRef_2ety___24t(V4__T)
                     => ( cPLF_2eReferences_2eSTLCRef_2eextends___24a2(V2__ST_27,V1__ST)
                       => ( cPLF_2eReferences_2eSTLCRef_2ehas__type___24a4(V0__Gamma,V1__ST,V3__t,V4__T)
                         => cPLF_2eReferences_2eSTLCRef_2ehas__type___24a4(V0__Gamma,V2__ST_27,V3__t,V4__T) ) ) ) ) ) ) ) ).

fof('PLF.References.STLCRef.store_well_typed_app',axiom,
    ! [V0__ST] :
      ( cPLF_2eReferences_2eSTLCRef_2estore__ty___24t(V0__ST)
     => ! [V1__st] :
          ( cPLF_2eReferences_2eSTLCRef_2estore___24t(V1__st)
         => ! [V2__t1] :
              ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V2__t1)
             => ! [V3__T1] :
                  ( cPLF_2eReferences_2eSTLCRef_2ety___24t(V3__T1)
                 => ( cPLF_2eReferences_2eSTLCRef_2estore__well__typed___24a2(V0__ST,V1__st)
                   => ( cPLF_2eReferences_2eSTLCRef_2ehas__type___24a4(cPLF_2eMaps_2eempty___24a1(cPLF_2eReferences_2eSTLCRef_2ety),V0__ST,V2__t1,V3__T1)
                     => cPLF_2eReferences_2eSTLCRef_2estore__well__typed___24a2(cCoq_2eInit_2eDatatypes_2eapp___24a3(cPLF_2eReferences_2eSTLCRef_2ety,V0__ST,cCoq_2eInit_2eDatatypes_2econs___24a3(cPLF_2eReferences_2eSTLCRef_2ety,V3__T1,cCoq_2eInit_2eDatatypes_2enil___24a1(cPLF_2eReferences_2eSTLCRef_2ety))),cCoq_2eInit_2eDatatypes_2eapp___24a3(cPLF_2eReferences_2eSTLCRef_2etm,V1__st,cCoq_2eInit_2eDatatypes_2econs___24a3(cPLF_2eReferences_2eSTLCRef_2etm,V2__t1,cCoq_2eInit_2eDatatypes_2enil___24a1(cPLF_2eReferences_2eSTLCRef_2etm)))) ) ) ) ) ) ) ).

fof('PLF.References.STLCRef.substitution_preserves_typing',axiom,
    ! [V0__Gamma] :
      ( cPLF_2eMaps_2epartial__map___24t(cPLF_2eReferences_2eSTLCRef_2ety,V0__Gamma)
     => ! [V1__ST] :
          ( cPLF_2eReferences_2eSTLCRef_2estore__ty___24t(V1__ST)
         => ! [V2__x] :
              ( cCoq_2eStrings_2eString_2estring___24t(V2__x)
             => ! [V3__s] :
                  ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V3__s)
                 => ! [V4__S] :
                      ( cPLF_2eReferences_2eSTLCRef_2ety___24t(V4__S)
                     => ! [V5__t] :
                          ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V5__t)
                         => ! [V6__T] :
                              ( cPLF_2eReferences_2eSTLCRef_2ety___24t(V6__T)
                             => ( cPLF_2eReferences_2eSTLCRef_2ehas__type___24a4(cPLF_2eMaps_2eempty___24a1(cPLF_2eReferences_2eSTLCRef_2ety),V1__ST,V3__s,V4__S)
                               => ( cPLF_2eReferences_2eSTLCRef_2ehas__type___24a4(cPLF_2eMaps_2eupdate___24a4(cPLF_2eReferences_2eSTLCRef_2ety,V0__Gamma,V2__x,V4__S),V1__ST,V5__t,V6__T)
                                 => cPLF_2eReferences_2eSTLCRef_2ehas__type___24a4(V0__Gamma,V1__ST,cPLF_2eReferences_2eSTLCRef_2esubst___24a3(V2__x,V3__s,V5__t),V6__T) ) ) ) ) ) ) ) ) ) ).

fof('PLF.References.STLCRef.tm_ind',axiom,
    ! [V0__P] :
      ( c_24__type__212347___24t(V0__P)
     => ( ! [V1__s] :
            ( cCoq_2eStrings_2eString_2estring___24t(V1__s)
           => p(happ(V0__P,cPLF_2eReferences_2eSTLCRef_2evar___24a1(V1__s))) )
       => ( ! [V2__t] :
              ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V2__t)
             => ( p(happ(V0__P,V2__t))
               => ! [V4__t] :
                    ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V4__t)
                   => ( p(happ(V0__P,V4__t))
                     => p(happ(V0__P,cPLF_2eReferences_2eSTLCRef_2eapp___24a2(V2__t,V4__t))) ) ) ) )
         => ( ! [V3__s] :
                ( cCoq_2eStrings_2eString_2estring___24t(V3__s)
               => ! [V4__t] :
                    ( cPLF_2eReferences_2eSTLCRef_2ety___24t(V4__t)
                   => ! [V5__t] :
                        ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V5__t)
                       => ( p(happ(V0__P,V5__t))
                         => p(happ(V0__P,cPLF_2eReferences_2eSTLCRef_2eabs___24a3(V3__s,V4__t,V5__t))) ) ) ) )
           => ( ! [V4__n] :
                  ( cCoq_2eInit_2eDatatypes_2enat___24t(V4__n)
                 => p(happ(V0__P,cPLF_2eReferences_2eSTLCRef_2econst___24a1(V4__n))) )
             => ( ! [V5__t] :
                    ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V5__t)
                   => ( p(happ(V0__P,V5__t))
                     => p(happ(V0__P,cPLF_2eReferences_2eSTLCRef_2escc___24a1(V5__t))) ) )
               => ( ! [V6__t] :
                      ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V6__t)
                     => ( p(happ(V0__P,V6__t))
                       => p(happ(V0__P,cPLF_2eReferences_2eSTLCRef_2eprd___24a1(V6__t))) ) )
                 => ( ! [V7__t] :
                        ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V7__t)
                       => ( p(happ(V0__P,V7__t))
                         => ! [V9__t] :
                              ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V9__t)
                             => ( p(happ(V0__P,V9__t))
                               => p(happ(V0__P,cPLF_2eReferences_2eSTLCRef_2emlt___24a2(V7__t,V9__t))) ) ) ) )
                   => ( ! [V8__t] :
                          ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V8__t)
                         => ( p(happ(V0__P,V8__t))
                           => ! [V10__t] :
                                ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V10__t)
                               => ( p(happ(V0__P,V10__t))
                                 => ! [V12__t] :
                                      ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V12__t)
                                     => ( p(happ(V0__P,V12__t))
                                       => p(happ(V0__P,cPLF_2eReferences_2eSTLCRef_2etest0___24a3(V8__t,V10__t,V12__t))) ) ) ) ) ) )
                     => ( p(happ(V0__P,cPLF_2eReferences_2eSTLCRef_2eunit))
                       => ( ! [V10__t] :
                              ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V10__t)
                             => ( p(happ(V0__P,V10__t))
                               => p(happ(V0__P,cPLF_2eReferences_2eSTLCRef_2eref___24a1(V10__t))) ) )
                         => ( ! [V11__t] :
                                ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V11__t)
                               => ( p(happ(V0__P,V11__t))
                                 => p(happ(V0__P,cPLF_2eReferences_2eSTLCRef_2ederef___24a1(V11__t))) ) )
                           => ( ! [V12__t] :
                                  ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V12__t)
                                 => ( p(happ(V0__P,V12__t))
                                   => ! [V14__t] :
                                        ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V14__t)
                                       => ( p(happ(V0__P,V14__t))
                                         => p(happ(V0__P,cPLF_2eReferences_2eSTLCRef_2eassign___24a2(V12__t,V14__t))) ) ) ) )
                             => ( ! [V13__n] :
                                    ( cCoq_2eInit_2eDatatypes_2enat___24t(V13__n)
                                   => p(happ(V0__P,cPLF_2eReferences_2eSTLCRef_2eloc___24a1(V13__n))) )
                               => ! [V14__t] :
                                    ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V14__t)
                                   => p(happ(V0__P,V14__t)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('PLF.References.STLCRef.ty_ind',axiom,
    ! [V0__P] :
      ( c_24__type__219182___24t(V0__P)
     => ( p(happ(V0__P,cPLF_2eReferences_2eSTLCRef_2eNat))
       => ( p(happ(V0__P,cPLF_2eReferences_2eSTLCRef_2eUnit))
         => ( ! [V3__t] :
                ( cPLF_2eReferences_2eSTLCRef_2ety___24t(V3__t)
               => ( p(happ(V0__P,V3__t))
                 => ! [V5__t] :
                      ( cPLF_2eReferences_2eSTLCRef_2ety___24t(V5__t)
                     => ( p(happ(V0__P,V5__t))
                       => p(happ(V0__P,cPLF_2eReferences_2eSTLCRef_2eArrow___24a2(V3__t,V5__t))) ) ) ) )
           => ( ! [V4__t] :
                  ( cPLF_2eReferences_2eSTLCRef_2ety___24t(V4__t)
                 => ( p(happ(V0__P,V4__t))
                   => p(happ(V0__P,cPLF_2eReferences_2eSTLCRef_2eRef___24a1(V4__t))) ) )
             => ! [V5__t] :
                  ( cPLF_2eReferences_2eSTLCRef_2ety___24t(V5__t)
                 => p(happ(V0__P,V5__t)) ) ) ) ) ) ) ).

fof('PLF.References.STLCRef.v_abs',axiom,
    ! [V0__x] :
      ( cCoq_2eStrings_2eString_2estring___24t(V0__x)
     => ! [V1__T] :
          ( cPLF_2eReferences_2eSTLCRef_2ety___24t(V1__T)
         => ! [V2__t] :
              ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V2__t)
             => cPLF_2eReferences_2eSTLCRef_2evalue___24a1(cPLF_2eReferences_2eSTLCRef_2eabs___24a3(V0__x,V1__T,V2__t)) ) ) ) ).

fof('PLF.References.STLCRef.v_loc',axiom,
    ! [V0__l] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__l)
     => cPLF_2eReferences_2eSTLCRef_2evalue___24a1(cPLF_2eReferences_2eSTLCRef_2eloc___24a1(V0__l)) ) ).

fof('PLF.References.STLCRef.v_nat',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => cPLF_2eReferences_2eSTLCRef_2evalue___24a1(cPLF_2eReferences_2eSTLCRef_2econst___24a1(V0__n)) ) ).

fof('PLF.References.STLCRef.v_unit',axiom,
    cPLF_2eReferences_2eSTLCRef_2evalue___24a1(cPLF_2eReferences_2eSTLCRef_2eunit) ).

fof('PLF.References.STLCRef.value_ind',axiom,
    ! [V0__P] :
      ( c_24__type__212347___24t(V0__P)
     => ( ! [V1__x] :
            ( cCoq_2eStrings_2eString_2estring___24t(V1__x)
           => ! [V2__T] :
                ( cPLF_2eReferences_2eSTLCRef_2ety___24t(V2__T)
               => ! [V3__t] :
                    ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V3__t)
                   => p(happ(V0__P,cPLF_2eReferences_2eSTLCRef_2eabs___24a3(V1__x,V2__T,V3__t))) ) ) )
       => ( ! [V2__n] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
             => p(happ(V0__P,cPLF_2eReferences_2eSTLCRef_2econst___24a1(V2__n))) )
         => ( p(happ(V0__P,cPLF_2eReferences_2eSTLCRef_2eunit))
           => ( ! [V4__l] :
                  ( cCoq_2eInit_2eDatatypes_2enat___24t(V4__l)
                 => p(happ(V0__P,cPLF_2eReferences_2eSTLCRef_2eloc___24a1(V4__l))) )
             => ! [V5__t] :
                  ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V5__t)
                 => ( cPLF_2eReferences_2eSTLCRef_2evalue___24a1(V5__t)
                   => p(happ(V0__P,V5__t)) ) ) ) ) ) ) ) ).

fof('PLF.Smallstep.CImp.CS_Par1',axiom,
    ! [V0__st] :
      ( cPLF_2eImp_2estate___24t(V0__st)
     => ! [V1__c1] :
          ( cPLF_2eSmallstep_2eCImp_2ecom___24t(V1__c1)
         => ! [V2__c1_27] :
              ( cPLF_2eSmallstep_2eCImp_2ecom___24t(V2__c1_27)
             => ! [V3__c2] :
                  ( cPLF_2eSmallstep_2eCImp_2ecom___24t(V3__c2)
                 => ! [V4__st_27] :
                      ( cPLF_2eImp_2estate___24t(V4__st_27)
                     => ( cPLF_2eSmallstep_2eCImp_2ecstep___24a2(cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eSmallstep_2eCImp_2ecom,cPLF_2eImp_2estate,V1__c1,V0__st),cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eSmallstep_2eCImp_2ecom,cPLF_2eImp_2estate,V2__c1_27,V4__st_27))
                       => cPLF_2eSmallstep_2eCImp_2ecstep___24a2(cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eSmallstep_2eCImp_2ecom,cPLF_2eImp_2estate,cPLF_2eSmallstep_2eCImp_2eCPar___24a2(V1__c1,V3__c2),V0__st),cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eSmallstep_2eCImp_2ecom,cPLF_2eImp_2estate,cPLF_2eSmallstep_2eCImp_2eCPar___24a2(V2__c1_27,V3__c2),V4__st_27)) ) ) ) ) ) ) ).

fof('PLF.Smallstep.CImp.CS_Par2',axiom,
    ! [V0__st] :
      ( cPLF_2eImp_2estate___24t(V0__st)
     => ! [V1__c1] :
          ( cPLF_2eSmallstep_2eCImp_2ecom___24t(V1__c1)
         => ! [V2__c2] :
              ( cPLF_2eSmallstep_2eCImp_2ecom___24t(V2__c2)
             => ! [V3__c2_27] :
                  ( cPLF_2eSmallstep_2eCImp_2ecom___24t(V3__c2_27)
                 => ! [V4__st_27] :
                      ( cPLF_2eImp_2estate___24t(V4__st_27)
                     => ( cPLF_2eSmallstep_2eCImp_2ecstep___24a2(cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eSmallstep_2eCImp_2ecom,cPLF_2eImp_2estate,V2__c2,V0__st),cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eSmallstep_2eCImp_2ecom,cPLF_2eImp_2estate,V3__c2_27,V4__st_27))
                       => cPLF_2eSmallstep_2eCImp_2ecstep___24a2(cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eSmallstep_2eCImp_2ecom,cPLF_2eImp_2estate,cPLF_2eSmallstep_2eCImp_2eCPar___24a2(V1__c1,V2__c2),V0__st),cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eSmallstep_2eCImp_2ecom,cPLF_2eImp_2estate,cPLF_2eSmallstep_2eCImp_2eCPar___24a2(V1__c1,V3__c2_27),V4__st_27)) ) ) ) ) ) ) ).

fof('PLF.Smallstep.CImp.CS_SeqStep',axiom,
    ! [V0__st] :
      ( cPLF_2eImp_2estate___24t(V0__st)
     => ! [V1__c1] :
          ( cPLF_2eSmallstep_2eCImp_2ecom___24t(V1__c1)
         => ! [V2__c1_27] :
              ( cPLF_2eSmallstep_2eCImp_2ecom___24t(V2__c1_27)
             => ! [V3__st_27] :
                  ( cPLF_2eImp_2estate___24t(V3__st_27)
                 => ! [V4__c2] :
                      ( cPLF_2eSmallstep_2eCImp_2ecom___24t(V4__c2)
                     => ( cPLF_2eSmallstep_2eCImp_2ecstep___24a2(cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eSmallstep_2eCImp_2ecom,cPLF_2eImp_2estate,V1__c1,V0__st),cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eSmallstep_2eCImp_2ecom,cPLF_2eImp_2estate,V2__c1_27,V3__st_27))
                       => cPLF_2eSmallstep_2eCImp_2ecstep___24a2(cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eSmallstep_2eCImp_2ecom,cPLF_2eImp_2estate,cPLF_2eSmallstep_2eCImp_2eCSeq___24a2(V1__c1,V4__c2),V0__st),cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eSmallstep_2eCImp_2ecom,cPLF_2eImp_2estate,cPLF_2eSmallstep_2eCImp_2eCSeq___24a2(V2__c1_27,V4__c2),V3__st_27)) ) ) ) ) ) ) ).

fof('PLF.Smallstep.CS_SeqStep',axiom,
    ! [V0__st] :
      ( cPLF_2eImp_2estate___24t(V0__st)
     => ! [V1__c1] :
          ( cPLF_2eImp_2ecom___24t(V1__c1)
         => ! [V2__c1_27] :
              ( cPLF_2eImp_2ecom___24t(V2__c1_27)
             => ! [V3__st_27] :
                  ( cPLF_2eImp_2estate___24t(V3__st_27)
                 => ! [V4__c2] :
                      ( cPLF_2eImp_2ecom___24t(V4__c2)
                     => ( cPLF_2eSmallstep_2ecstep___24a2(cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eImp_2ecom,cPLF_2eImp_2estate,V1__c1,V0__st),cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eImp_2ecom,cPLF_2eImp_2estate,V2__c1_27,V3__st_27))
                       => cPLF_2eSmallstep_2ecstep___24a2(cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eImp_2ecom,cPLF_2eImp_2estate,cPLF_2eImp_2eCSeq___24a2(V1__c1,V4__c2),V0__st),cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eImp_2ecom,cPLF_2eImp_2estate,cPLF_2eImp_2eCSeq___24a2(V2__c1_27,V4__c2),V3__st_27)) ) ) ) ) ) ) ).

fof('PLF.Smallstep.multi_refl',axiom,
    ! [V0__X] :
      ( cType___24t(V0__X)
     => ! [V1__R] :
          ( cPLF_2eSmallstep_2erelation___24t(V0__X,V1__R)
         => ! [V2__x] :
              ( t(V2__x,V0__X)
             => cPLF_2eSmallstep_2emulti___24a4(V0__X,V1__R,V2__x,V2__x) ) ) ) ).

fof('PLF.Smallstep.multi_step',axiom,
    ! [V0__X] :
      ( cType___24t(V0__X)
     => ! [V1__R] :
          ( cPLF_2eSmallstep_2erelation___24t(V0__X,V1__R)
         => ! [V2__x] :
              ( t(V2__x,V0__X)
             => ! [V3__y] :
                  ( t(V3__y,V0__X)
                 => ! [V4__z] :
                      ( t(V4__z,V0__X)
                     => ( p(happ(happ(V1__R,V2__x),V3__y))
                       => ( cPLF_2eSmallstep_2emulti___24a4(V0__X,V1__R,V3__y,V4__z)
                         => cPLF_2eSmallstep_2emulti___24a4(V0__X,V1__R,V2__x,V4__z) ) ) ) ) ) ) ) ).

fof('PLF.Smallstep.multi_trans',axiom,
    ! [V0__X] :
      ( cType___24t(V0__X)
     => ! [V1__R] :
          ( cPLF_2eSmallstep_2erelation___24t(V0__X,V1__R)
         => ! [V2__x] :
              ( t(V2__x,V0__X)
             => ! [V3__y] :
                  ( t(V3__y,V0__X)
                 => ! [V4__z] :
                      ( t(V4__z,V0__X)
                     => ( cPLF_2eSmallstep_2emulti___24a4(V0__X,V1__R,V2__x,V3__y)
                       => ( cPLF_2eSmallstep_2emulti___24a4(V0__X,V1__R,V3__y,V4__z)
                         => cPLF_2eSmallstep_2emulti___24a4(V0__X,V1__R,V2__x,V4__z) ) ) ) ) ) ) ) ).

fof('PLF.Stlc.STLC.ST_App1',axiom,
    ! [V0__t1] :
      ( cPLF_2eStlc_2eSTLC_2etm___24t(V0__t1)
     => ! [V1__t1_27] :
          ( cPLF_2eStlc_2eSTLC_2etm___24t(V1__t1_27)
         => ! [V2__t2] :
              ( cPLF_2eStlc_2eSTLC_2etm___24t(V2__t2)
             => ( cPLF_2eStlc_2eSTLC_2estep___24a2(V0__t1,V1__t1_27)
               => cPLF_2eStlc_2eSTLC_2estep___24a2(cPLF_2eStlc_2eSTLC_2eapp___24a2(V0__t1,V2__t2),cPLF_2eStlc_2eSTLC_2eapp___24a2(V1__t1_27,V2__t2)) ) ) ) ) ).

fof('PLF.Stlc.STLC.ST_App2',axiom,
    ! [V0__v1] :
      ( cPLF_2eStlc_2eSTLC_2etm___24t(V0__v1)
     => ! [V1__t2] :
          ( cPLF_2eStlc_2eSTLC_2etm___24t(V1__t2)
         => ! [V2__t2_27] :
              ( cPLF_2eStlc_2eSTLC_2etm___24t(V2__t2_27)
             => ( cPLF_2eStlc_2eSTLC_2evalue___24a1(V0__v1)
               => ( cPLF_2eStlc_2eSTLC_2estep___24a2(V1__t2,V2__t2_27)
                 => cPLF_2eStlc_2eSTLC_2estep___24a2(cPLF_2eStlc_2eSTLC_2eapp___24a2(V0__v1,V1__t2),cPLF_2eStlc_2eSTLC_2eapp___24a2(V0__v1,V2__t2_27)) ) ) ) ) ) ).

fof('PLF.Stlc.STLC.ST_Test',axiom,
    ! [V0__t1] :
      ( cPLF_2eStlc_2eSTLC_2etm___24t(V0__t1)
     => ! [V1__t1_27] :
          ( cPLF_2eStlc_2eSTLC_2etm___24t(V1__t1_27)
         => ! [V2__t2] :
              ( cPLF_2eStlc_2eSTLC_2etm___24t(V2__t2)
             => ! [V3__t3] :
                  ( cPLF_2eStlc_2eSTLC_2etm___24t(V3__t3)
                 => ( cPLF_2eStlc_2eSTLC_2estep___24a2(V0__t1,V1__t1_27)
                   => cPLF_2eStlc_2eSTLC_2estep___24a2(cPLF_2eStlc_2eSTLC_2etest___24a3(V0__t1,V2__t2,V3__t3),cPLF_2eStlc_2eSTLC_2etest___24a3(V1__t1_27,V2__t2,V3__t3)) ) ) ) ) ) ).

fof('PLF.Stlc.STLC.ST_TestFls',axiom,
    ! [V0__t1] :
      ( cPLF_2eStlc_2eSTLC_2etm___24t(V0__t1)
     => ! [V1__t2] :
          ( cPLF_2eStlc_2eSTLC_2etm___24t(V1__t2)
         => cPLF_2eStlc_2eSTLC_2estep___24a2(cPLF_2eStlc_2eSTLC_2etest___24a3(cPLF_2eStlc_2eSTLC_2efls,V0__t1,V1__t2),V1__t2) ) ) ).

fof('PLF.Stlc.STLC.ST_TestTru',axiom,
    ! [V0__t1] :
      ( cPLF_2eStlc_2eSTLC_2etm___24t(V0__t1)
     => ! [V1__t2] :
          ( cPLF_2eStlc_2eSTLC_2etm___24t(V1__t2)
         => cPLF_2eStlc_2eSTLC_2estep___24a2(cPLF_2eStlc_2eSTLC_2etest___24a3(cPLF_2eStlc_2eSTLC_2etru,V0__t1,V1__t2),V0__t1) ) ) ).

fof('PLF.Stlc.STLC.T_App',axiom,
    ! [V0__T11] :
      ( cPLF_2eStlc_2eSTLC_2ety___24t(V0__T11)
     => ! [V1__T12] :
          ( cPLF_2eStlc_2eSTLC_2ety___24t(V1__T12)
         => ! [V2__Gamma] :
              ( cPLF_2eStlc_2eSTLC_2econtext___24t(V2__Gamma)
             => ! [V3__t1] :
                  ( cPLF_2eStlc_2eSTLC_2etm___24t(V3__t1)
                 => ! [V4__t2] :
                      ( cPLF_2eStlc_2eSTLC_2etm___24t(V4__t2)
                     => ( cPLF_2eStlc_2eSTLC_2ehas__type___24a3(V2__Gamma,V3__t1,cPLF_2eStlc_2eSTLC_2eArrow___24a2(V0__T11,V1__T12))
                       => ( cPLF_2eStlc_2eSTLC_2ehas__type___24a3(V2__Gamma,V4__t2,V0__T11)
                         => cPLF_2eStlc_2eSTLC_2ehas__type___24a3(V2__Gamma,cPLF_2eStlc_2eSTLC_2eapp___24a2(V3__t1,V4__t2),V1__T12) ) ) ) ) ) ) ) ).

fof('PLF.Stlc.STLC.T_Fls',axiom,
    ! [V0__Gamma] :
      ( cPLF_2eStlc_2eSTLC_2econtext___24t(V0__Gamma)
     => cPLF_2eStlc_2eSTLC_2ehas__type___24a3(V0__Gamma,cPLF_2eStlc_2eSTLC_2efls,cPLF_2eStlc_2eSTLC_2eBool) ) ).

fof('PLF.Stlc.STLC.T_Test',axiom,
    ! [V0__t1] :
      ( cPLF_2eStlc_2eSTLC_2etm___24t(V0__t1)
     => ! [V1__t2] :
          ( cPLF_2eStlc_2eSTLC_2etm___24t(V1__t2)
         => ! [V2__t3] :
              ( cPLF_2eStlc_2eSTLC_2etm___24t(V2__t3)
             => ! [V3__T] :
                  ( cPLF_2eStlc_2eSTLC_2ety___24t(V3__T)
                 => ! [V4__Gamma] :
                      ( cPLF_2eStlc_2eSTLC_2econtext___24t(V4__Gamma)
                     => ( cPLF_2eStlc_2eSTLC_2ehas__type___24a3(V4__Gamma,V0__t1,cPLF_2eStlc_2eSTLC_2eBool)
                       => ( cPLF_2eStlc_2eSTLC_2ehas__type___24a3(V4__Gamma,V1__t2,V3__T)
                         => ( cPLF_2eStlc_2eSTLC_2ehas__type___24a3(V4__Gamma,V2__t3,V3__T)
                           => cPLF_2eStlc_2eSTLC_2ehas__type___24a3(V4__Gamma,cPLF_2eStlc_2eSTLC_2etest___24a3(V0__t1,V1__t2,V2__t3),V3__T) ) ) ) ) ) ) ) ) ).

fof('PLF.Stlc.STLC.T_Tru',axiom,
    ! [V0__Gamma] :
      ( cPLF_2eStlc_2eSTLC_2econtext___24t(V0__Gamma)
     => cPLF_2eStlc_2eSTLC_2ehas__type___24a3(V0__Gamma,cPLF_2eStlc_2eSTLC_2etru,cPLF_2eStlc_2eSTLC_2eBool) ) ).

fof('PLF.Stlc.STLC.T_Var',axiom,
    ! [V0__Gamma] :
      ( c_24__type__185353___24t(V0__Gamma)
     => ! [V1__x] :
          ( cCoq_2eStrings_2eString_2estring___24t(V1__x)
         => ! [V2__T] :
              ( cPLF_2eStlc_2eSTLC_2ety___24t(V2__T)
             => ( happ(V0__Gamma,V1__x) = cCoq_2eInit_2eDatatypes_2eSome___24a2(cPLF_2eStlc_2eSTLC_2ety,V2__T)
               => cPLF_2eStlc_2eSTLC_2ehas__type___24a3(V0__Gamma,cPLF_2eStlc_2eSTLC_2evar___24a1(V1__x),V2__T) ) ) ) ) ).

fof('PLF.Stlc.STLC.v_abs',axiom,
    ! [V0__x] :
      ( cCoq_2eStrings_2eString_2estring___24t(V0__x)
     => ! [V1__T] :
          ( cPLF_2eStlc_2eSTLC_2ety___24t(V1__T)
         => ! [V2__t] :
              ( cPLF_2eStlc_2eSTLC_2etm___24t(V2__t)
             => cPLF_2eStlc_2eSTLC_2evalue___24a1(cPLF_2eStlc_2eSTLC_2eabs___24a3(V0__x,V1__T,V2__t)) ) ) ) ).

fof('PLF.Stlc.STLC.v_fls',axiom,
    cPLF_2eStlc_2eSTLC_2evalue___24a1(cPLF_2eStlc_2eSTLC_2efls) ).

fof('PLF.Stlc.STLC.v_tru',axiom,
    cPLF_2eStlc_2eSTLC_2evalue___24a1(cPLF_2eStlc_2eSTLC_2etru) ).

fof('PLF.StlcProp.STLCProp.preservation',axiom,
    ! [V0__t] :
      ( cPLF_2eStlc_2eSTLC_2etm___24t(V0__t)
     => ! [V1__t_27] :
          ( cPLF_2eStlc_2eSTLC_2etm___24t(V1__t_27)
         => ! [V2__T] :
              ( cPLF_2eStlc_2eSTLC_2ety___24t(V2__T)
             => ( cPLF_2eStlc_2eSTLC_2ehas__type___24a3(cPLF_2eMaps_2eempty___24a1(cPLF_2eStlc_2eSTLC_2ety),V0__t,V2__T)
               => ( cPLF_2eStlc_2eSTLC_2estep___24a2(V0__t,V1__t_27)
                 => cPLF_2eStlc_2eSTLC_2ehas__type___24a3(cPLF_2eMaps_2eempty___24a1(cPLF_2eStlc_2eSTLC_2ety),V1__t_27,V2__T) ) ) ) ) ) ).

fof('PLF.StlcProp.STLCProp.progress',axiom,
    ! [V0__t] :
      ( cPLF_2eStlc_2eSTLC_2etm___24t(V0__t)
     => ! [V1__T] :
          ( cPLF_2eStlc_2eSTLC_2ety___24t(V1__T)
         => ( cPLF_2eStlc_2eSTLC_2ehas__type___24a3(cPLF_2eMaps_2eempty___24a1(cPLF_2eStlc_2eSTLC_2ety),V0__t,V1__T)
           => ( cPLF_2eStlc_2eSTLC_2evalue___24a1(V0__t)
              | ? [V3__t_27] :
                  ( cPLF_2eStlc_2eSTLC_2etm___24t(V3__t_27)
                  & cPLF_2eStlc_2eSTLC_2estep___24a2(V0__t,V3__t_27) ) ) ) ) ) ).

fof('PLF.StlcProp.STLCProp.progress\'',axiom,
    ! [V0__t] :
      ( cPLF_2eStlc_2eSTLC_2etm___24t(V0__t)
     => ! [V1__T] :
          ( cPLF_2eStlc_2eSTLC_2ety___24t(V1__T)
         => ( cPLF_2eStlc_2eSTLC_2ehas__type___24a3(cPLF_2eMaps_2eempty___24a1(cPLF_2eStlc_2eSTLC_2ety),V0__t,V1__T)
           => ( cPLF_2eStlc_2eSTLC_2evalue___24a1(V0__t)
              | ? [V3__t_27] :
                  ( cPLF_2eStlc_2eSTLC_2etm___24t(V3__t_27)
                  & cPLF_2eStlc_2eSTLC_2estep___24a2(V0__t,V3__t_27) ) ) ) ) ) ).

fof('PLF.StlcProp.STLCProp.substitution_preserves_typing',axiom,
    ! [V0__Gamma] :
      ( cPLF_2eMaps_2epartial__map___24t(cPLF_2eStlc_2eSTLC_2ety,V0__Gamma)
     => ! [V1__x] :
          ( cCoq_2eStrings_2eString_2estring___24t(V1__x)
         => ! [V2__U] :
              ( cPLF_2eStlc_2eSTLC_2ety___24t(V2__U)
             => ! [V3__t] :
                  ( cPLF_2eStlc_2eSTLC_2etm___24t(V3__t)
                 => ! [V4__v] :
                      ( cPLF_2eStlc_2eSTLC_2etm___24t(V4__v)
                     => ! [V5__T] :
                          ( cPLF_2eStlc_2eSTLC_2ety___24t(V5__T)
                         => ( cPLF_2eStlc_2eSTLC_2ehas__type___24a3(cPLF_2eMaps_2eupdate___24a4(cPLF_2eStlc_2eSTLC_2ety,V0__Gamma,V1__x,V2__U),V3__t,V5__T)
                           => ( cPLF_2eStlc_2eSTLC_2ehas__type___24a3(cPLF_2eMaps_2eempty___24a1(cPLF_2eStlc_2eSTLC_2ety),V4__v,V2__U)
                             => cPLF_2eStlc_2eSTLC_2ehas__type___24a3(V0__Gamma,cPLF_2eStlc_2eSTLC_2esubst___24a3(V1__x,V4__v,V3__t),V5__T) ) ) ) ) ) ) ) ) ).

fof('PLF.StlcProp.STLCProp.typable_empty__closed',axiom,
    ! [V0__t] :
      ( cPLF_2eStlc_2eSTLC_2etm___24t(V0__t)
     => ! [V1__T] :
          ( cPLF_2eStlc_2eSTLC_2ety___24t(V1__T)
         => ( cPLF_2eStlc_2eSTLC_2ehas__type___24a3(cPLF_2eMaps_2eempty___24a1(cPLF_2eStlc_2eSTLC_2ety),V0__t,V1__T)
           => cPLF_2eStlcProp_2eSTLCProp_2eclosed___24a1(V0__t) ) ) ) ).

fof('UseAuto.PreservationProgressReferences.nth_eq_last\'',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__l] :
          ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V1__l)
         => ! [V2__x] :
              ( t(V2__x,V0__A)
             => ! [V3__d] :
                  ( t(V3__d,V0__A)
                 => ! [V4__n] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(V4__n)
                     => ( V4__n = cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V1__l)
                       => cCoq_2eLists_2eList_2enth___24a4(V0__A,V4__n,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V1__l,cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,V2__x,cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A))),V3__d) = V2__x ) ) ) ) ) ) ).

fof('UseAuto.PreservationProgressReferences.preservation',axiom,
    ! [V0__ST] :
      ( cPLF_2eReferences_2eSTLCRef_2estore__ty___24t(V0__ST)
     => ! [V1__t] :
          ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V1__t)
         => ! [V2__t_27] :
              ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V2__t_27)
             => ! [V3__T] :
                  ( cPLF_2eReferences_2eSTLCRef_2ety___24t(V3__T)
                 => ! [V4__st] :
                      ( cPLF_2eReferences_2eSTLCRef_2estore___24t(V4__st)
                     => ! [V5__st_27] :
                          ( cPLF_2eReferences_2eSTLCRef_2estore___24t(V5__st_27)
                         => ( cPLF_2eReferences_2eSTLCRef_2ehas__type___24a4(cPLF_2eMaps_2eempty___24a1(cPLF_2eReferences_2eSTLCRef_2ety),V0__ST,V1__t,V3__T)
                           => ( cPLF_2eReferences_2eSTLCRef_2estore__well__typed___24a2(V0__ST,V4__st)
                             => ( cPLF_2eReferences_2eSTLCRef_2estep___24a2(cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cPLF_2eReferences_2eSTLCRef_2estore,V1__t,V4__st),cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cPLF_2eReferences_2eSTLCRef_2estore,V2__t_27,V5__st_27))
                               => ? [V9__ST_27] :
                                    ( cPLF_2eReferences_2eSTLCRef_2estore__ty___24t(V9__ST_27)
                                    & cPLF_2eReferences_2eSTLCRef_2eextends___24a2(V9__ST_27,V0__ST)
                                    & cPLF_2eReferences_2eSTLCRef_2ehas__type___24a4(cPLF_2eMaps_2eempty___24a1(cPLF_2eReferences_2eSTLCRef_2ety),V9__ST_27,V2__t_27,V3__T)
                                    & cPLF_2eReferences_2eSTLCRef_2estore__well__typed___24a2(V9__ST_27,V5__st_27) ) ) ) ) ) ) ) ) ) ) ).

fof('UseAuto.PreservationProgressReferences.preservation_ref',axiom,
    ! [V0__st] :
      ( cPLF_2eReferences_2eSTLCRef_2estore___24t(V0__st)
     => ! [V1__ST] :
          ( cPLF_2eReferences_2eSTLCRef_2estore__ty___24t(V1__ST)
         => ! [V2__T1] :
              ( cPLF_2eReferences_2eSTLCRef_2ety___24t(V2__T1)
             => ( cCoq_2eInit_2eDatatypes_2elength___24a2(cPLF_2eReferences_2eSTLCRef_2ety,V1__ST) = cCoq_2eInit_2eDatatypes_2elength___24a2(cPLF_2eReferences_2eSTLCRef_2etm,V0__st)
               => cPLF_2eReferences_2eSTLCRef_2eRef___24a1(V2__T1) = cPLF_2eReferences_2eSTLCRef_2eRef___24a1(cPLF_2eReferences_2eSTLCRef_2estore__Tlookup___24a2(cCoq_2eInit_2eDatatypes_2elength___24a2(cPLF_2eReferences_2eSTLCRef_2etm,V0__st),cCoq_2eInit_2eDatatypes_2eapp___24a3(cPLF_2eReferences_2eSTLCRef_2ety,V1__ST,cCoq_2eInit_2eDatatypes_2econs___24a3(cPLF_2eReferences_2eSTLCRef_2ety,V2__T1,cCoq_2eInit_2eDatatypes_2enil___24a1(cPLF_2eReferences_2eSTLCRef_2ety))))) ) ) ) ) ).

fof('UseAuto.PreservationProgressStlc.preservation',axiom,
    ! [V0__t] :
      ( cPLF_2eStlc_2eSTLC_2etm___24t(V0__t)
     => ! [V1__t_27] :
          ( cPLF_2eStlc_2eSTLC_2etm___24t(V1__t_27)
         => ! [V2__T] :
              ( cPLF_2eStlc_2eSTLC_2ety___24t(V2__T)
             => ( cPLF_2eStlc_2eSTLC_2ehas__type___24a3(cPLF_2eMaps_2eempty___24a1(cPLF_2eStlc_2eSTLC_2ety),V0__t,V2__T)
               => ( cPLF_2eStlc_2eSTLC_2estep___24a2(V0__t,V1__t_27)
                 => cPLF_2eStlc_2eSTLC_2ehas__type___24a3(cPLF_2eMaps_2eempty___24a1(cPLF_2eStlc_2eSTLC_2ety),V1__t_27,V2__T) ) ) ) ) ) ).

fof('UseAuto.PreservationProgressStlc.preservation\'',axiom,
    ! [V0__t] :
      ( cPLF_2eStlc_2eSTLC_2etm___24t(V0__t)
     => ! [V1__t_27] :
          ( cPLF_2eStlc_2eSTLC_2etm___24t(V1__t_27)
         => ! [V2__T] :
              ( cPLF_2eStlc_2eSTLC_2ety___24t(V2__T)
             => ( cPLF_2eStlc_2eSTLC_2ehas__type___24a3(cPLF_2eMaps_2eempty___24a1(cPLF_2eStlc_2eSTLC_2ety),V0__t,V2__T)
               => ( cPLF_2eStlc_2eSTLC_2estep___24a2(V0__t,V1__t_27)
                 => cPLF_2eStlc_2eSTLC_2ehas__type___24a3(cPLF_2eMaps_2eempty___24a1(cPLF_2eStlc_2eSTLC_2ety),V1__t_27,V2__T) ) ) ) ) ) ).

fof('UseAuto.PreservationProgressStlc.progress',axiom,
    ! [V0__t] :
      ( cPLF_2eStlc_2eSTLC_2etm___24t(V0__t)
     => ! [V1__T] :
          ( cPLF_2eStlc_2eSTLC_2ety___24t(V1__T)
         => ( cPLF_2eStlc_2eSTLC_2ehas__type___24a3(cPLF_2eMaps_2eempty___24a1(cPLF_2eStlc_2eSTLC_2ety),V0__t,V1__T)
           => ( cPLF_2eStlc_2eSTLC_2evalue___24a1(V0__t)
              | ? [V3__t_27] :
                  ( cPLF_2eStlc_2eSTLC_2etm___24t(V3__t_27)
                  & cPLF_2eStlc_2eSTLC_2estep___24a2(V0__t,V3__t_27) ) ) ) ) ) ).

fof('UseAuto.PreservationProgressStlc.progress\'',axiom,
    ! [V0__t] :
      ( cPLF_2eStlc_2eSTLC_2etm___24t(V0__t)
     => ! [V1__T] :
          ( cPLF_2eStlc_2eSTLC_2ety___24t(V1__T)
         => ( cPLF_2eStlc_2eSTLC_2ehas__type___24a3(cPLF_2eMaps_2eempty___24a1(cPLF_2eStlc_2eSTLC_2ety),V0__t,V1__T)
           => ( cPLF_2eStlc_2eSTLC_2evalue___24a1(V0__t)
              | ? [V3__t_27] :
                  ( cPLF_2eStlc_2eSTLC_2etm___24t(V3__t_27)
                  & cPLF_2eStlc_2eSTLC_2estep___24a2(V0__t,V3__t_27) ) ) ) ) ) ).

fof('UseAuto.nat_le_refl',axiom,
    ! [V0__x] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
     => cCoq_2eInit_2ePeano_2ele___24a2(V0__x,V0__x) ) ).

fof('UseAuto.solving_conj_hyp',axiom,
    ! [V0__F] :
      ( cProp___24t(V0__F)
     => ! [V1__F_27] :
          ( cProp___24t(V1__F_27)
         => ( ( p(V0__F)
              & p(V1__F_27) )
           => p(V0__F) ) ) ) ).

fof('UseAuto.solving_conj_hyp\'',axiom,
    ! [V0__F] :
      ( cProp___24t(V0__F)
     => ! [V1__F_27] :
          ( cProp___24t(V1__F_27)
         => ( ( p(V0__F)
              & p(V1__F_27) )
           => p(V0__F) ) ) ) ).

fof('UseAuto.solving_disj_goal',axiom,
    ! [V0__F] :
      ( cProp___24t(V0__F)
     => ! [V1__F_27] :
          ( cProp___24t(V1__F_27)
         => ( p(V0__F)
           => ( p(V0__F)
              | p(V1__F_27) ) ) ) ) ).

fof('UseAuto.solving_disj_hyp',axiom,
    ! [V0__F] :
      ( cProp___24t(V0__F)
     => ! [V1__F_27] :
          ( cProp___24t(V1__F_27)
         => ( ( p(V0__F)
              | p(V1__F_27) )
           => ( p(V1__F_27)
              | p(V0__F) ) ) ) ) ).

fof('UseAuto.solving_exists_hyp',axiom,
    ! [V0__f] :
      ( c_24__type__592___24t(V0__f)
     => ! [V1__g] :
          ( c_24__type__592___24t(V1__g)
         => ( ! [V2__x] :
                ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__x)
               => ( p(happ(V0__f,V2__x))
                 => p(happ(V1__g,V2__x)) ) )
           => ( ? [V3__a] :
                  ( cCoq_2eInit_2eDatatypes_2enat___24t(V3__a)
                  & p(happ(V0__f,V3__a)) )
             => ? [V4__a] :
                  ( cCoq_2eInit_2eDatatypes_2enat___24t(V4__a)
                  & p(happ(V1__g,V4__a)) ) ) ) ) ) ).

fof('$adef_Coq.PArith.BinPos.Pos.SqrtSpec_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2ePArith_2eBinPos_2ePos_2eSqrtSpec,V_24X1),V_24X2))
    <=> cCoq_2ePArith_2eBinPos_2ePos_2eSqrtSpec___24a2(V_24X1,V_24X2) ) ).

fof('$adef_$_lam_102438_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(c_24__lam__102438,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> c_24__lam__102438___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).

fof('$adef_PLF.Smallstep.P_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cPLF_2eSmallstep_2eP,V_24X1),V_24X2) = cPLF_2eSmallstep_2eP___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('$adef_Coq.Reals.Rdefinitions.IZR_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eReals_2eRdefinitions_2eIZR,V_24X1) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V_24X1) ).

fof('$adef_PLF.StlcProp.STLCArith.abs_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cPLF_2eStlcProp_2eSTLCArith_2eabs,V_24X1),V_24X2),V_24X3) = cPLF_2eStlcProp_2eSTLCArith_2eabs___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_PLF.StlcProp.STLCArith.prd_$a1',axiom,
    ! [V_24X1] : happ(cPLF_2eStlcProp_2eSTLCArith_2eprd,V_24X1) = cPLF_2eStlcProp_2eSTLCArith_2eprd___24a1(V_24X1) ).

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('$adef_PLF.Smallstep.multi_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cPLF_2eSmallstep_2emulti,V_24X1),V_24X2) = cPLF_2eSmallstep_2emulti___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.NArith.BinNat.N.lt_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eNArith_2eBinNat_2eN_2elt,V_24X1),V_24X2))
    <=> cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.ZArith.BinIntDef.Z.of_N_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(V_24X1) ).

fof('$adef_Coq.Vectors.VectorDef.cons_$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('$adef_Coq.FSets.FSetPositive.PositiveSet.filter_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2efilter,V_24X1),V_24X2) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2efilter___24a2(V_24X1,V_24X2) ).

fof('$adef_PLF.Maps.empty_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cPLF_2eMaps_2eempty,V_24X1),V_24X2) = cPLF_2eMaps_2eempty___24a2(V_24X1,V_24X2) ).

fof('$adef_PLF.References.STLCRef.ref_$a1',axiom,
    ! [V_24X1] : happ(cPLF_2eReferences_2eSTLCRef_2eref,V_24X1) = cPLF_2eReferences_2eSTLCRef_2eref___24a1(V_24X1) ).

fof('$adef_Coq.Init.Datatypes.BoolSpec_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] :
      ( p(happ(happ(happ(cCoq_2eInit_2eDatatypes_2eBoolSpec,V_24X1),V_24X2),V_24X3))
    <=> cCoq_2eInit_2eDatatypes_2eBoolSpec___24a3(V_24X1,V_24X2,V_24X3) ) ).

fof('$adef_$_lam_112898_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__112898,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__112898___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

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('$adef_Coq.FSets.FSetPositive.PositiveSet.rev_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2erev,V_24X1) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2erev___24a1(V_24X1) ).

fof('$adef_PLF.Types.bvalue_$a1',axiom,
    ! [V_24X1] :
      ( p(happ(cPLF_2eTypes_2ebvalue,V_24X1))
    <=> cPLF_2eTypes_2ebvalue___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('$adef_Coq.setoid_ring.Ring_polynom.mk_monpol_list_$a10',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2emk__monpol__list,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10) = cCoq_2esetoid__ring_2eRing__polynom_2emk__monpol__list___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10) ).

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('$adef_Coq.micromega.RingMicromega.eval_pol_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2eeval__pol,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2emicromega_2eRingMicromega_2eeval__pol___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_Coq.setoid_ring.Ring_theory.sring_eq_ext_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2esring__eq__ext,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> cCoq_2esetoid__ring_2eRing__theory_2esring__eq__ext___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).

fof('$adef_Coq.micromega.RingMicromega.psubC_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRingMicromega_2epsubC,V_24X1),V_24X2) = cCoq_2emicromega_2eRingMicromega_2epsubC___24a2(V_24X1,V_24X2) ).

fof('$adef_$_case_Coq.Init.Datatypes.nat$77172_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2enat_2477172,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__case__Coq_2eInit_2eDatatypes_2enat_2477172___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

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('$adef_PLF.Smallstep.stack_step_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] :
      ( p(happ(happ(happ(cPLF_2eSmallstep_2estack__step,V_24X1),V_24X2),V_24X3))
    <=> cPLF_2eSmallstep_2estack__step___24a3(V_24X1,V_24X2,V_24X3) ) ).

fof('$adef_PLF.Smallstep.SimpleArith1.step_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cPLF_2eSmallstep_2eSimpleArith1_2estep,V_24X1),V_24X2))
    <=> cPLF_2eSmallstep_2eSimpleArith1_2estep___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.Arith.Compare_dec.le_lt_eq_dec_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eArith_2eCompare__dec_2ele__lt__eq__dec,V_24X1),V_24X2) = cCoq_2eArith_2eCompare__dec_2ele__lt__eq__dec___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.micromega.EnvRing.Pol_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2emicromega_2eEnvRing_2ePol,V_24X1) = cCoq_2emicromega_2eEnvRing_2ePol___24a1(V_24X1) ).

fof('$adef_Coq.micromega.Tauto.Cj_$a6',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eCj,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2emicromega_2eTauto_2eCj___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).

fof('$adef_Coq.ZArith.BinIntDef.Z.sgn_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2esgn,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2esgn___24a1(V_24X1) ).

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('$adef_PLF.References.STLCRef.scc_$a1',axiom,
    ! [V_24X1] : happ(cPLF_2eReferences_2eSTLCRef_2escc,V_24X1) = cPLF_2eReferences_2eSTLCRef_2escc___24a1(V_24X1) ).

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('$adef_Coq.Lists.List.partition_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eLists_2eList_2epartition,V_24X1),V_24X2),V_24X3) = cCoq_2eLists_2eList_2epartition___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_$_case_Coq.Init.Datatypes.nat$212097_$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_2enat_24212097,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__case__Coq_2eInit_2eDatatypes_2enat_24212097___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).

fof('$adef_Coq.setoid_ring.Ring_polynom.Pc_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePc,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.PArith.BinPos.Pos.iter_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2ePArith_2eBinPos_2ePos_2eiter,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2ePArith_2eBinPos_2ePos_2eiter___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_PLF.References.STLCRef.value_$a1',axiom,
    ! [V_24X1] :
      ( p(happ(cPLF_2eReferences_2eSTLCRef_2evalue,V_24X1))
    <=> cPLF_2eReferences_2eSTLCRef_2evalue___24a1(V_24X1) ) ).

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('$adef_$_prop_154310_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__prop__154310,V_24X1),V_24X2) = c_24__prop__154310___24a2(V_24X1,V_24X2) ).

fof('$adef_PLF.Smallstep.Temp1.step_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cPLF_2eSmallstep_2eTemp1_2estep,V_24X1),V_24X2))
    <=> cPLF_2eSmallstep_2eTemp1_2estep___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('$adef_PLF.StlcProp.STLCArith.var_$a1',axiom,
    ! [V_24X1] : happ(cPLF_2eStlcProp_2eSTLCArith_2evar,V_24X1) = cPLF_2eStlcProp_2eSTLCArith_2evar___24a1(V_24X1) ).

fof('$adef_Coq.setoid_ring.Ring_polynom.vmon_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2evmon,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Logic.JMeq.JMeq_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(cCoq_2eLogic_2eJMeq_2eJMeq,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> cCoq_2eLogic_2eJMeq_2eJMeq___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).

fof('$adef_Coq.Init.Decimal.Pos_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2ePos,V_24X1) = cCoq_2eInit_2eDecimal_2ePos___24a1(V_24X1) ).

fof('$adef_Coq.FSets.FSetPositive.PositiveSet.mem_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem,V_24X1),V_24X2) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V_24X1,V_24X2) ).

fof('$adef_$_prop_92116_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__92116,V_24X1),V_24X2),V_24X3) = c_24__prop__92116___24a3(V_24X1,V_24X2,V_24X3) ).

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('$adef_$_case_Coq.Init.Datatypes.nat$211329_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2enat_24211329,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__case__Coq_2eInit_2eDatatypes_2enat_24211329___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.Arith.Between.P_nth_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
      ( p(happ(happ(happ(happ(happ(cCoq_2eArith_2eBetween_2eP__nth,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
    <=> cCoq_2eArith_2eBetween_2eP__nth___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).

fof('$adef_PLF.StlcProp.STLCArith.test0_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cPLF_2eStlcProp_2eSTLCArith_2etest0,V_24X1),V_24X2),V_24X3) = cPLF_2eStlcProp_2eSTLCArith_2etest0___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_$_case_Coq.Init.Datatypes.nat$163138_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2enat_24163138,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__case__Coq_2eInit_2eDatatypes_2enat_24163138___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

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('$adef_$_case_Coq.Init.Datatypes.list$211097_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2elist_24211097,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__case__Coq_2eInit_2eDatatypes_2elist_24211097___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.micromega.ZMicromega.Vars.Facts.MP.Dec.FSetDecideAuxiliary.FSet_elt_Prop_$a1',axiom,
    ! [V_24X1] :
      ( p(happ(cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop,V_24X1))
    <=> cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(V_24X1) ) ).

fof('$adef_PLF.StlcProp.STLCArith.mlt_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cPLF_2eStlcProp_2eSTLCArith_2emlt,V_24X1),V_24X2) = cPLF_2eStlcProp_2eSTLCArith_2emlt___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.setoid_ring.Field_theory.FEdiv_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEdiv,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.micromega.ZMicromega.ceiling_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eZMicromega_2eceiling,V_24X1),V_24X2) = cCoq_2emicromega_2eZMicromega_2eceiling___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('$adef_$_lam_2126_$a1',axiom,
    ! [V_24X1] : happ(c_24__lam__2126,V_24X1) = c_24__lam__2126___24a1(V_24X1) ).

fof('$adef_Coq.Init.Datatypes.app_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2eapp,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2eapp___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.Init.Specif.existT_$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('$adef_PLF.Types.step_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cPLF_2eTypes_2estep,V_24X1),V_24X2))
    <=> cPLF_2eTypes_2estep___24a2(V_24X1,V_24X2) ) ).

fof('$adef_PLF.References.STLCRef.subst_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cPLF_2eReferences_2eSTLCRef_2esubst,V_24X1),V_24X2),V_24X3) = cPLF_2eReferences_2eSTLCRef_2esubst___24a3(V_24X1,V_24X2,V_24X3) ).

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('$adef_Coq.setoid_ring.Field_theory.FEmul_$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('$adef_Coq.Vectors.Vector.nil_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eVectors_2eVector_2enil,V_24X1) = cCoq_2eVectors_2eVector_2enil___24a1(V_24X1) ).

fof('$adef_PLF.References.STLCRef.ty_rect_$a1',axiom,
    ! [V_24X1] : happ(cPLF_2eReferences_2eSTLCRef_2ety__rect,V_24X1) = cPLF_2eReferences_2eSTLCRef_2ety__rect___24a1(V_24X1) ).

fof('$adef_Coq.ZArith.BinIntDef.Z.mul_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2emul,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V_24X1,V_24X2) ).

fof('$adef_PLF.Smallstep.Temp3.value_$a1',axiom,
    ! [V_24X1] :
      ( p(happ(cPLF_2eSmallstep_2eTemp3_2evalue,V_24X1))
    <=> cPLF_2eSmallstep_2eTemp3_2evalue___24a1(V_24X1) ) ).

fof('$adef_Coq.micromega.ZMicromega.Vars.ct_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] :
      ( p(happ(happ(happ(cCoq_2emicromega_2eZMicromega_2eVars_2ect,V_24X1),V_24X2),V_24X3))
    <=> cCoq_2emicromega_2eZMicromega_2eVars_2ect___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('$adef_$_fix_1042_v_CANONICAL_0_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__fix__1042__v__CANONICAL__0,V_24X1),V_24X2) = c_24__fix__1042__v__CANONICAL__0___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Relations.Relation_Operators.symprod_$a6',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] :
      ( p(happ(happ(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2esymprod,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6))
    <=> cCoq_2eRelations_2eRelation__Operators_2esymprod___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ) ).

fof('$adef_$_fix_212205_v_CANONICAL_0_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__fix__212205__v__CANONICAL__0,V_24X1),V_24X2),V_24X3) = c_24__fix__212205__v__CANONICAL__0___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.Init.Decimal.D4_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD4,V_24X1) = cCoq_2eInit_2eDecimal_2eD4___24a1(V_24X1) ).

fof('$adef_Coq.micromega.RingMicromega.Build_Formula_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2eBuild__Formula,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.setoid_ring.Ring_polynom.mkmult_pow_$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('$adef_PLF.References.STLCRef.replace_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cPLF_2eReferences_2eSTLCRef_2ereplace,V_24X1),V_24X2),V_24X3),V_24X4) = cPLF_2eReferences_2eSTLCRef_2ereplace___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.Init.Specif.sumbool_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eSpecif_2esumbool,V_24X1),V_24X2) = cCoq_2eInit_2eSpecif_2esumbool___24a2(V_24X1,V_24X2) ).

fof('$adef_PLF.Smallstep.CImp.CPar_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cPLF_2eSmallstep_2eCImp_2eCPar,V_24X1),V_24X2) = cPLF_2eSmallstep_2eCImp_2eCPar___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.PArith.BinPos.Pos.IsPos_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2ePArith_2eBinPos_2ePos_2eIsPos,V_24X1) = cCoq_2ePArith_2eBinPos_2ePos_2eIsPos___24a1(V_24X1) ).

fof('$adef_Coq.setoid_ring.Field_theory.mk_rsplit_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2emk__rsplit,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_PLF.Imp.BLe_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cPLF_2eImp_2eBLe,V_24X1),V_24X2) = cPLF_2eImp_2eBLe___24a2(V_24X1,V_24X2) ).

fof('$adef_PLF.References.STLCRef.ty_rec_$a1',axiom,
    ! [V_24X1] : happ(cPLF_2eReferences_2eSTLCRef_2ety__rec,V_24X1) = cPLF_2eReferences_2eSTLCRef_2ety__rec___24a1(V_24X1) ).

fof('$adef_Coq.micromega.EnvRing.zmon_pred_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eEnvRing_2ezmon__pred,V_24X1),V_24X2) = cCoq_2emicromega_2eEnvRing_2ezmon__pred___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Sets.Relations_1.Relation_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eSets_2eRelations__1_2eRelation,V_24X1) = cCoq_2eSets_2eRelations__1_2eRelation___24a1(V_24X1) ).

fof('$adef_$_fix_211742_v_CANONICAL_0_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__fix__211742__v__CANONICAL__0,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__fix__211742__v__CANONICAL__0___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.setoid_ring.Ring_theory.semi_ring_theory_$a6',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] :
      ( p(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2esemi__ring__theory,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6))
    <=> cCoq_2esetoid__ring_2eRing__theory_2esemi__ring__theory___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ) ).

fof('$adef_Coq.Reals.RIneq.mknonposreal_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eReals_2eRIneq_2emknonposreal,V_24X1) = cCoq_2eReals_2eRIneq_2emknonposreal___24a1(V_24X1) ).

fof('$adef_Coq.Lists.SetoidList.transpose_restr2_$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('$adef_PLF.Imp.AMinus_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cPLF_2eImp_2eAMinus,V_24X1),V_24X2) = cPLF_2eImp_2eAMinus___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.micromega.EnvRing.PsubC_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eEnvRing_2ePsubC,V_24X1),V_24X2) = cCoq_2emicromega_2eEnvRing_2ePsubC___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.FSets.FSetPositive.PositiveSet.xfilter_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2exfilter,V_24X1),V_24X2),V_24X3) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2exfilter___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_$_fix_111186_v_CANONICAL_0_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__fix__111186__v__CANONICAL__0,V_24X1),V_24X2),V_24X3) = c_24__fix__111186__v__CANONICAL__0___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.setoid_ring.Ring_polynom.PEsub_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEsub,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.micromega.EnvRing.mkZmon_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eEnvRing_2emkZmon,V_24X1),V_24X2) = cCoq_2emicromega_2eEnvRing_2emkZmon___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.micromega.Env.jump_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eEnv_2ejump,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eEnv_2ejump___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.FSets.FSetPositive.PositiveSet.ct_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] :
      ( p(happ(happ(happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2ect,V_24X1),V_24X2),V_24X3))
    <=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2ect___24a3(V_24X1,V_24X2,V_24X3) ) ).

fof('$adef_Coq.Init.Nat.max_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2emax,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2emax___24a2(V_24X1,V_24X2) ).

fof('$adef_PLF.Imp.BreakImp.CIf_$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('$adef_$_case_PLF.References.STLCRef.tm$208442_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__case__PLF_2eReferences_2eSTLCRef_2etm_24208442,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__case__PLF_2eReferences_2eSTLCRef_2etm_24208442___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_Coq.Init.Byte.of_bits_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eByte_2eof__bits,V_24X1) = cCoq_2eInit_2eByte_2eof__bits___24a1(V_24X1) ).

fof('$adef_Coq.Init.Datatypes.option_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2eoption,V_24X1) = cCoq_2eInit_2eDatatypes_2eoption___24a1(V_24X1) ).

fof('$adef_Coq.Relations.Relation_Definitions.relation_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eRelations_2eRelation__Definitions_2erelation,V_24X1) = cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V_24X1) ).

fof('$adef_Coq.Init.Decimal.revapp_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDecimal_2erevapp,V_24X1),V_24X2) = cCoq_2eInit_2eDecimal_2erevapp___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.NArith.BinNatDef.N.sub_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2esub,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2esub___24a2(V_24X1,V_24X2) ).

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('$adef_$_lam_2102_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__2102,V_24X1),V_24X2),V_24X3) = c_24__lam__2102___24a3(V_24X1,V_24X2,V_24X3) ).

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('$adef_$_prop_92096_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__92096,V_24X1),V_24X2),V_24X3) = c_24__prop__92096___24a3(V_24X1,V_24X2,V_24X3) ).

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('$adef_PLF.Maps.t_update_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cPLF_2eMaps_2et__update,V_24X1),V_24X2),V_24X3),V_24X4) = cPLF_2eMaps_2et__update___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.FSets.FSetPositive.PositiveSet.rev_append_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2erev__append,V_24X1),V_24X2) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2erev__append___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.setoid_ring.Ring_theory.ring_morph_$a17',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17] :
      ( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2ering__morph,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14),V_24X15),V_24X16),V_24X17))
    <=> cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17) ) ).

fof('$adef_Coq.Init.Datatypes.CompOpp_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2eCompOpp,V_24X1) = cCoq_2eInit_2eDatatypes_2eCompOpp___24a1(V_24X1) ).

fof('$adef_Coq.micromega.EnvRing.PEopp_$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('$adef_Coq.Arith.Lt.le_not_lt_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eArith_2eLt_2ele__not__lt,V_24X1),V_24X2) = cCoq_2eArith_2eLt_2ele__not__lt___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.micromega.RingMicromega.SORaddon_$a22',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22] :
      ( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2eSORaddon,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14),V_24X15),V_24X16),V_24X17),V_24X18),V_24X19),V_24X20),V_24X21),V_24X22))
    <=> cCoq_2emicromega_2eRingMicromega_2eSORaddon___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22) ) ).

fof('$adef_Coq.ZArith.Zpower.two_power_pos_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eZArith_2eZpower_2etwo__power__pos,V_24X1) = cCoq_2eZArith_2eZpower_2etwo__power__pos___24a1(V_24X1) ).

fof('$adef_Coq.Arith.Between.exists_between_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] :
      ( p(happ(happ(happ(cCoq_2eArith_2eBetween_2eexists__between,V_24X1),V_24X2),V_24X3))
    <=> cCoq_2eArith_2eBetween_2eexists__between___24a3(V_24X1,V_24X2,V_24X3) ) ).

fof('$adef_PLF.StlcProp.STLCArith.scc_$a1',axiom,
    ! [V_24X1] : happ(cPLF_2eStlcProp_2eSTLCArith_2escc,V_24X1) = cPLF_2eStlcProp_2eSTLCArith_2escc___24a1(V_24X1) ).

fof('$adef_$_case_Coq.Init.Datatypes.nat$210921_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2enat_24210921,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__case__Coq_2eInit_2eDatatypes_2enat_24210921___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

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('$adef_PLF.References.STLCRef.store_lookup_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cPLF_2eReferences_2eSTLCRef_2estore__lookup,V_24X1),V_24X2) = cPLF_2eReferences_2eSTLCRef_2estore__lookup___24a2(V_24X1,V_24X2) ).

fof('$adef_$_case_Coq.Numbers.BinNums.positive$109181_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__case__Coq_2eNumbers_2eBinNums_2epositive_24109181,V_24X1),V_24X2) = c_24__case__Coq_2eNumbers_2eBinNums_2epositive_24109181___24a2(V_24X1,V_24X2) ).

fof('$adef_$_case_Coq.Init.Datatypes.nat$77615_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2enat_2477615,V_24X1),V_24X2) = c_24__case__Coq_2eInit_2eDatatypes_2enat_2477615___24a2(V_24X1,V_24X2) ).

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('$adef_PLF.Stlc.STLC.value_$a1',axiom,
    ! [V_24X1] :
      ( p(happ(cPLF_2eStlc_2eSTLC_2evalue,V_24X1))
    <=> cPLF_2eStlc_2eSTLC_2evalue___24a1(V_24X1) ) ).

fof('$adef_PLF.Imp.ANum_$a1',axiom,
    ! [V_24X1] : happ(cPLF_2eImp_2eANum,V_24X1) = cPLF_2eImp_2eANum___24a1(V_24X1) ).

fof('$adef_PLF.Smallstep.CImp.cstep_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cPLF_2eSmallstep_2eCImp_2ecstep,V_24X1),V_24X2))
    <=> cPLF_2eSmallstep_2eCImp_2ecstep___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('$adef_Coq.micromega.Tauto.and_cnf_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eand__cnf,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eTauto_2eand__cnf___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_PLF.Smallstep.cstep_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cPLF_2eSmallstep_2ecstep,V_24X1),V_24X2))
    <=> cPLF_2eSmallstep_2ecstep___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('$adef_PLF.Smallstep.Temp3.step_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cPLF_2eSmallstep_2eTemp3_2estep,V_24X1),V_24X2))
    <=> cPLF_2eSmallstep_2eTemp3_2estep___24a2(V_24X1,V_24X2) ) ).

fof('$adef_$_case_Coq.Init.Datatypes.nat$113335_$a1',axiom,
    ! [V_24X1] : happ(c_24__case__Coq_2eInit_2eDatatypes_2enat_24113335,V_24X1) = c_24__case__Coq_2eInit_2eDatatypes_2enat_24113335___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('$adef_PLF.LibTactics.boxer_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cPLF_2eLibTactics_2eboxer,V_24X1),V_24X2) = cPLF_2eLibTactics_2eboxer___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.setoid_ring.Ring_polynom.mkPinj_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2emkPinj,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eRing__polynom_2emkPinj___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_PLF.Smallstep.multi_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(cPLF_2eSmallstep_2emulti,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> cPLF_2eSmallstep_2emulti___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).

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('$adef_Coq.PArith.BinPosDef.Pos.pred_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2epred,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2epred___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('$adef_Coq.Sorting.Sorted.HdRel_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(cCoq_2eSorting_2eSorted_2eHdRel,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> cCoq_2eSorting_2eSorted_2eHdRel___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).

fof('$adef_Hammer.Tactics.Reconstr.rdone_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cHammer_2eTactics_2eReconstr_2erdone,V_24X1),V_24X2))
    <=> cHammer_2eTactics_2eReconstr_2erdone___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.Reals.Rfunctions.Z_spec_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRfunctions_2eZ__spec,V_24X1),V_24X2) = cCoq_2eReals_2eRfunctions_2eZ__spec___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Init.Datatypes.inl_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2einl,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2einl___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.setoid_ring.Ring_polynom.mkZmon_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2emkZmon,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__polynom_2emkZmon___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('$adef_$_case_Coq.Init.Datatypes.nat$163035_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2enat_24163035,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__case__Coq_2eInit_2eDatatypes_2enat_24163035___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_Coq.setoid_ring.Ring_theory.ring_eq_ext_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
      ( p(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
    <=> cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).

fof('$adef_Coq.micromega.RingMicromega.cltb_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2ecltb,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2emicromega_2eRingMicromega_2ecltb___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_PLF.References.STLCRef.appears_free_in_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cPLF_2eReferences_2eSTLCRef_2eappears__free__in,V_24X1),V_24X2))
    <=> cPLF_2eReferences_2eSTLCRef_2eappears__free__in___24a2(V_24X1,V_24X2) ) ).

fof('$adef_PLF.Maps.t_empty_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cPLF_2eMaps_2et__empty,V_24X1),V_24X2) = cPLF_2eMaps_2et__empty___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Vectors.VectorDef.append_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eVectors_2eVectorDef_2eappend,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eVectors_2eVectorDef_2eappend___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_PLF.Smallstep.CImp.CWhile_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cPLF_2eSmallstep_2eCImp_2eCWhile,V_24X1),V_24X2) = cPLF_2eSmallstep_2eCImp_2eCWhile___24a2(V_24X1,V_24X2) ).

fof('$adef_PLF.References.STLCRef.var_$a1',axiom,
    ! [V_24X1] : happ(cPLF_2eReferences_2eSTLCRef_2evar,V_24X1) = cPLF_2eReferences_2eSTLCRef_2evar___24a1(V_24X1) ).

fof('$adef_$_lam_79669_$a6',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__79669,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__79669___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).

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('$adef_$_prop_154311_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__prop__154311,V_24X1),V_24X2) = c_24__prop__154311___24a2(V_24X1,V_24X2) ).

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('$adef_Coq.ZArith.BinIntDef.Z.of_int_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__int,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eof__int___24a1(V_24X1) ).

fof('$adef_$_case_Coq.Init.Datatypes.list$115259_$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_24115259,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__case__Coq_2eInit_2eDatatypes_2elist_24115259___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).

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('$adef_Coq.ZArith.Zpower.shift_pos_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eZpower_2eshift__pos,V_24X1),V_24X2) = cCoq_2eZArith_2eZpower_2eshift__pos___24a2(V_24X1,V_24X2) ).

fof('$adef_PLF.Types.nvalue_$a1',axiom,
    ! [V_24X1] :
      ( p(happ(cPLF_2eTypes_2envalue,V_24X1))
    <=> cPLF_2eTypes_2envalue___24a1(V_24X1) ) ).

fof('$adef_PLF.References.STLCRef.test0_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cPLF_2eReferences_2eSTLCRef_2etest0,V_24X1),V_24X2),V_24X3) = cPLF_2eReferences_2eSTLCRef_2etest0___24a3(V_24X1,V_24X2,V_24X3) ).

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('$adef_Coq.Init.Datatypes.CompGtT_$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('$adef_Coq.Reals.Rfunctions.ZintNeg_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRfunctions_2eZintNeg,V_24X1),V_24X2) = cCoq_2eReals_2eRfunctions_2eZintNeg___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.ZArith.Znumtheory.Bezout_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] :
      ( p(happ(happ(happ(cCoq_2eZArith_2eZnumtheory_2eBezout,V_24X1),V_24X2),V_24X3))
    <=> cCoq_2eZArith_2eZnumtheory_2eBezout___24a3(V_24X1,V_24X2,V_24X3) ) ).

fof('$adef_Coq.micromega.Tauto.cnf_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eTauto_2ecnf,V_24X1),V_24X2) = cCoq_2emicromega_2eTauto_2ecnf___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.micromega.Tauto.GFormula_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eGFormula,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eTauto_2eGFormula___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.Numbers.BinNums.Npos_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2eNpos,V_24X1) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(V_24X1) ).

fof('$adef_Coq.setoid_ring.Ring_theory.Morphism_$a17',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2eMorphism,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14),V_24X15),V_24X16),V_24X17) = cCoq_2esetoid__ring_2eRing__theory_2eMorphism___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17) ).

fof('$adef_Coq.setoid_ring.Ring_theory.IDphi_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__theory_2eIDphi,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__theory_2eIDphi___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.micromega.Env.jump_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eEnv_2ejump,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eEnv_2ejump___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.setoid_ring.Ring_polynom.P0_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2eP0,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__polynom_2eP0___24a2(V_24X1,V_24X2) ).

fof('$adef_PLF.Smallstep.bstep_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] :
      ( p(happ(happ(happ(cPLF_2eSmallstep_2ebstep,V_24X1),V_24X2),V_24X3))
    <=> cPLF_2eSmallstep_2ebstep___24a3(V_24X1,V_24X2,V_24X3) ) ).

fof('$adef_Coq.ZArith.BinIntDef.Z.of_uint_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__uint,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eof__uint___24a1(V_24X1) ).

fof('$adef_PLF.LibTactics.ltac_something_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cPLF_2eLibTactics_2eltac__something,V_24X1),V_24X2) = cPLF_2eLibTactics_2eltac__something___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Numbers.BinNums.xI_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2exI,V_24X1) = cCoq_2eNumbers_2eBinNums_2exI___24a1(V_24X1) ).

fof('$adef_Coq.ZArith.Zeven.Zodd_$a1',axiom,
    ! [V_24X1] :
      ( p(happ(cCoq_2eZArith_2eZeven_2eZodd,V_24X1))
    <=> cCoq_2eZArith_2eZeven_2eZodd___24a1(V_24X1) ) ).

fof('$adef_PLF.Stlc.STLC.step_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cPLF_2eStlc_2eSTLC_2estep,V_24X1),V_24X2))
    <=> cPLF_2eStlc_2eSTLC_2estep___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.ZArith.BinIntDef.Z.ltb_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eltb,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2eltb___24a2(V_24X1,V_24X2) ).

fof('$adef_PLF.Stlc.STLC.abs_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cPLF_2eStlc_2eSTLC_2eabs,V_24X1),V_24X2),V_24X3) = cPLF_2eStlc_2eSTLC_2eabs___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_$_fix_209397_v_CANONICAL_0_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__fix__209397__v__CANONICAL__0,V_24X1),V_24X2),V_24X3) = c_24__fix__209397__v__CANONICAL__0___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_PLF.LibTactics.ltac_tag_subst_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cPLF_2eLibTactics_2eltac__tag__subst,V_24X1),V_24X2) = cPLF_2eLibTactics_2eltac__tag__subst___24a2(V_24X1,V_24X2) ).

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('$adef_$_case_Coq.Init.Datatypes.nat$77928_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2enat_2477928,V_24X1),V_24X2) = c_24__case__Coq_2eInit_2eDatatypes_2enat_2477928___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.micromega.RMicromega.CPlus_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRMicromega_2eCPlus,V_24X1),V_24X2) = cCoq_2emicromega_2eRMicromega_2eCPlus___24a2(V_24X1,V_24X2) ).

fof('$adef_$_lam_2119_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__2119,V_24X1),V_24X2),V_24X3) = c_24__lam__2119___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('$adef_PLF.References.STLCRef.loc_$a1',axiom,
    ! [V_24X1] : happ(cPLF_2eReferences_2eSTLCRef_2eloc,V_24X1) = cPLF_2eReferences_2eSTLCRef_2eloc___24a1(V_24X1) ).

fof('$adef_PLF.References.STLCRef.app_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cPLF_2eReferences_2eSTLCRef_2eapp,V_24X1),V_24X2) = cPLF_2eReferences_2eSTLCRef_2eapp___24a2(V_24X1,V_24X2) ).

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('$adef_Coq.Init.Datatypes.negb_$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('$adef_$_prop_92114_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__prop__92114,V_24X1),V_24X2) = c_24__prop__92114___24a2(V_24X1,V_24X2) ).

fof('$adef_$_case_Coq.Init.Datatypes.bool$111428_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2ebool_24111428,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_24111428___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

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('$adef_Coq.PArith.BinPosDef.Pos.ggcdn_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eggcdn,V_24X1),V_24X2),V_24X3) = cCoq_2ePArith_2eBinPosDef_2ePos_2eggcdn___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('$adef_$_let_11_subst_l_1650_$a10',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__let__11__subst__l__1650,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10) = c_24__let__11__subst__l__1650___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10) ).

fof('$adef_Coq.Lists.List.combine_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eLists_2eList_2ecombine,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eLists_2eList_2ecombine___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_PLF.Smallstep.Combined.P_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cPLF_2eSmallstep_2eCombined_2eP,V_24X1),V_24X2) = cPLF_2eSmallstep_2eCombined_2eP___24a2(V_24X1,V_24X2) ).

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('$adef_PLF.Smallstep.astep_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] :
      ( p(happ(happ(happ(cPLF_2eSmallstep_2eastep,V_24X1),V_24X2),V_24X3))
    <=> cPLF_2eSmallstep_2eastep___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('$adef_Coq.Init.Logic_Type.notT_$a1',axiom,
    ! [V_24X1] :
      ( p(happ(cCoq_2eInit_2eLogic__Type_2enotT,V_24X1))
    <=> cCoq_2eInit_2eLogic__Type_2enotT___24a1(V_24X1) ) ).

fof('$adef_Coq.Init.Nat.add_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2eadd,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2eadd___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Init.Specif.sigT2_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2esigT2,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2esigT2___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.Structures.OrderedType.Compare_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eStructures_2eOrderedType_2eCompare,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eStructures_2eOrderedType_2eCompare___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_$_fix_211134_v_CANONICAL_0_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__fix__211134__v__CANONICAL__0,V_24X1),V_24X2) = c_24__fix__211134__v__CANONICAL__0___24a2(V_24X1,V_24X2) ).

fof('$adef_$_prop_168302_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__prop__168302,V_24X1),V_24X2) = c_24__prop__168302___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.setoid_ring.Field_theory.FEc_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEc,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Classes.Morphisms.Proper_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] :
      ( p(happ(happ(happ(cCoq_2eClasses_2eMorphisms_2eProper,V_24X1),V_24X2),V_24X3))
    <=> cCoq_2eClasses_2eMorphisms_2eProper___24a3(V_24X1,V_24X2,V_24X3) ) ).

fof('$adef_Coq.Init.Decimal.rev_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2erev,V_24X1) = cCoq_2eInit_2eDecimal_2erev___24a1(V_24X1) ).

fof('$adef_Coq.ZArith.BinIntDef.Z.pos_sub_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(V_24X1,V_24X2) ).

fof('$adef_$_lam_102438_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__102438,V_24X1),V_24X2),V_24X3) = c_24__lam__102438___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.Init.Specif.right_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eSpecif_2eright,V_24X1),V_24X2) = cCoq_2eInit_2eSpecif_2eright___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.setoid_ring.Ring_theory.power_theory_$a7',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] :
      ( p(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2epower__theory,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7))
    <=> cCoq_2esetoid__ring_2eRing__theory_2epower__theory___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ) ).

fof('$adef_PLF.Imp.AExp.AMinus_$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('$adef_PLF.LibTactics.ltac_to_generalize_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cPLF_2eLibTactics_2eltac__to__generalize,V_24X1),V_24X2) = cPLF_2eLibTactics_2eltac__to__generalize___24a2(V_24X1,V_24X2) ).

fof('$adef_$_case_Coq.Init.Datatypes.nat$162913_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2enat_24162913,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__case__Coq_2eInit_2eDatatypes_2enat_24162913___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

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('$adef_Coq.micromega.Env.hd_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eEnv_2ehd,V_24X1),V_24X2) = cCoq_2emicromega_2eEnv_2ehd___24a2(V_24X1,V_24X2) ).

fof('$adef_PLF.Smallstep.value_$a1',axiom,
    ! [V_24X1] :
      ( p(happ(cPLF_2eSmallstep_2evalue,V_24X1))
    <=> cPLF_2eSmallstep_2evalue___24a1(V_24X1) ) ).

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('$adef_Coq.ZArith.BinIntDef.Z.div_eucl_$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('$adef_Coq.micromega.RMicromega.CMinus_$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('$adef_$_fix_211437_v_CANONICAL_0_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__fix__211437__v__CANONICAL__0,V_24X1),V_24X2),V_24X3) = c_24__fix__211437__v__CANONICAL__0___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.Bool.Bool.ifb_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eBool_2eBool_2eifb,V_24X1),V_24X2),V_24X3) = cCoq_2eBool_2eBool_2eifb___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_$_lam_1722_$a11',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__lam__1722,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11) = c_24__lam__1722___24a11(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11) ).

fof('$adef_$_prop_92115_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__92115,V_24X1),V_24X2),V_24X3) = c_24__prop__92115___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_$_case_Coq.Init.Datatypes.bool$109396_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2ebool_24109396,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_24109396___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.setoid_ring.Field_theory.FEadd_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEadd,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_$_lam_2109_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__2109,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__2109___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.Init.Datatypes.S_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2eS,V_24X1) = cCoq_2eInit_2eDatatypes_2eS___24a1(V_24X1) ).

fof('$adef_Coq.Strings.Ascii.Ascii_$a8',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8] : happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2eStrings_2eAscii_2eAscii,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8) = cCoq_2eStrings_2eAscii_2eAscii___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8) ).

fof('$adef_$_let_var_6_p_113399_113402_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__let__var__6__p__113399__113402,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__let__var__6__p__113399__113402___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.micromega.EnvRing.PEpow_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePEpow,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eEnvRing_2ePEpow___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.setoid_ring.Ring_polynom.zmon_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ezmon,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.setoid_ring.Ring_theory.semi_morph_$a13',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13] :
      ( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2esemi__morph,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13))
    <=> cCoq_2esetoid__ring_2eRing__theory_2esemi__morph___24a13(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13) ) ).

fof('$adef_PLF.Smallstep.CImp.CAss_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cPLF_2eSmallstep_2eCImp_2eCAss,V_24X1),V_24X2) = cPLF_2eSmallstep_2eCImp_2eCAss___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.ZArith.BinIntDef.Z.add_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.micromega.RingMicromega.Formula_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2emicromega_2eRingMicromega_2eFormula,V_24X1) = cCoq_2emicromega_2eRingMicromega_2eFormula___24a1(V_24X1) ).

fof('$adef_Coq.Reals.RIneq.mknegreal_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eReals_2eRIneq_2emknegreal,V_24X1) = cCoq_2eReals_2eRIneq_2emknegreal___24a1(V_24X1) ).

fof('$adef_Coq.setoid_ring.InitialRing.gen_phiPOS1_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_Coq.micromega.ZMicromega.RatProof_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eZMicromega_2eRatProof,V_24X1),V_24X2) = cCoq_2emicromega_2eZMicromega_2eRatProof___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.micromega.RingMicromega.PolC_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2emicromega_2eRingMicromega_2ePolC,V_24X1) = cCoq_2emicromega_2eRingMicromega_2ePolC___24a1(V_24X1) ).

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('$adef_$_prop_92098_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__92098,V_24X1),V_24X2),V_24X3) = c_24__prop__92098___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.Lists.SetoidList.InA_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(cCoq_2eLists_2eSetoidList_2eInA,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> cCoq_2eLists_2eSetoidList_2eInA___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).

fof('$adef_Coq.Reals.Rdefinitions.Rlt_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eReals_2eRdefinitions_2eRlt,V_24X1),V_24X2))
    <=> cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V_24X1,V_24X2) ) ).

fof('$adef_PLF.Imp.CSeq_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cPLF_2eImp_2eCSeq,V_24X1),V_24X2) = cPLF_2eImp_2eCSeq___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.ZArith.BinIntDef.Z.sub_$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('$adef_$_prop_168309_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__prop__168309,V_24X1),V_24X2) = c_24__prop__168309___24a2(V_24X1,V_24X2) ).

fof('$adef_PLF.Types.scc_$a1',axiom,
    ! [V_24X1] : happ(cPLF_2eTypes_2escc,V_24X1) = cPLF_2eTypes_2escc___24a1(V_24X1) ).

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('$adef_PLF.StlcProp.STLCArith.const_$a1',axiom,
    ! [V_24X1] : happ(cPLF_2eStlcProp_2eSTLCArith_2econst,V_24X1) = cPLF_2eStlcProp_2eSTLCArith_2econst___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('$adef_Coq.micromega.Env.tail_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eEnv_2etail,V_24X1),V_24X2) = cCoq_2emicromega_2eEnv_2etail___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.setoid_ring.Ring_theory.pow_pos_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2epow__pos,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_$_lam_2126_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__2126,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__2126___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.micromega.EnvRing.Psub_$a6',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePsub,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2emicromega_2eEnvRing_2ePsub___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).

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('$adef_PLF.Imp.AExp.APlus_$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('$adef_Coq.ZArith.BinInt.Z.gt_$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('$adef_Coq.Classes.RelationClasses.Symmetric_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eClasses_2eRelationClasses_2eSymmetric,V_24X1),V_24X2))
    <=> cCoq_2eClasses_2eRelationClasses_2eSymmetric___24a2(V_24X1,V_24X2) ) ).

fof('$adef_$_let_var_6_p_113401_113403_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__let__var__6__p__113401__113403,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__let__var__6__p__113401__113403___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

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('$adef_Coq.Lists.List.flat_map_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eLists_2eList_2eflat__map,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eLists_2eList_2eflat__map___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

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('$adef_$_prop_198720_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__prop__198720,V_24X1),V_24X2) = c_24__prop__198720___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.micromega.RingMicromega.eval_op1_$a7',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] :
      ( p(happ(happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2eeval__op1,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7))
    <=> cCoq_2emicromega_2eRingMicromega_2eeval__op1___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ) ).

fof('$adef_Coq.micromega.EnvRing.Pphi_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePphi,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2emicromega_2eEnvRing_2ePphi___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_Coq.Lists.SetoidList.transpose_restr_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
      ( p(happ(happ(happ(happ(happ(cCoq_2eLists_2eSetoidList_2etranspose__restr,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
    <=> cCoq_2eLists_2eSetoidList_2etranspose__restr___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).

fof('$adef_$_fix_77969_v_CANONICAL_0_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__fix__77969__v__CANONICAL__0,V_24X1),V_24X2) = c_24__fix__77969__v__CANONICAL__0___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Vectors.Vector.t_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eVectors_2eVector_2et,V_24X1),V_24X2) = cCoq_2eVectors_2eVector_2et___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.setoid_ring.Field_theory.FEinv_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEinv,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.ZArith.Zpower.Zdiv_rest_proof_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eZArith_2eZpower_2eZdiv__rest__proof,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eZArith_2eZpower_2eZdiv__rest__proof___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.Init.Wf.Acc_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] :
      ( p(happ(happ(happ(cCoq_2eInit_2eWf_2eAcc,V_24X1),V_24X2),V_24X3))
    <=> cCoq_2eInit_2eWf_2eAcc___24a3(V_24X1,V_24X2,V_24X3) ) ).

fof('$adef_Coq.setoid_ring.Ring_theory.pow_N_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2epow__N,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2esetoid__ring_2eRing__theory_2epow__N___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_PLF.Smallstep.Temp4.test_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cPLF_2eSmallstep_2eTemp4_2etest,V_24X1),V_24X2),V_24X3) = cPLF_2eSmallstep_2eTemp4_2etest___24a3(V_24X1,V_24X2,V_24X3) ).

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('$adef_PLF.Types.test_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cPLF_2eTypes_2etest,V_24X1),V_24X2),V_24X3) = cPLF_2eTypes_2etest___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.ZArith.BinInt.Z.ge_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2ege,V_24X1),V_24X2) = cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.ZArith.Zbool.Zeq_bool_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eZbool_2eZeq__bool,V_24X1),V_24X2) = cCoq_2eZArith_2eZbool_2eZeq__bool___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.micromega.RMicromega.CQ_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2emicromega_2eRMicromega_2eCQ,V_24X1) = cCoq_2emicromega_2eRMicromega_2eCQ___24a1(V_24X1) ).

fof('$adef_Coq.QArith.QArith_base.Qmake_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eQArith_2eQArith__base_2eQmake,V_24X1),V_24X2) = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.setoid_ring.Ring_polynom.PEX_$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('$adef_PLF.References.STLCRef.Arrow_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cPLF_2eReferences_2eSTLCRef_2eArrow,V_24X1),V_24X2) = cPLF_2eReferences_2eSTLCRef_2eArrow___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.micromega.OrderedRing.SOR_$a10',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10] :
      ( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eOrderedRing_2eSOR,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10))
    <=> cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10) ) ).

fof('$adef_Coq.Init.Datatypes.sum_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2esum,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2esum___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.ZArith.Znumtheory.Zis_gcd_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] :
      ( p(happ(happ(happ(cCoq_2eZArith_2eZnumtheory_2eZis__gcd,V_24X1),V_24X2),V_24X3))
    <=> cCoq_2eZArith_2eZnumtheory_2eZis__gcd___24a3(V_24X1,V_24X2,V_24X3) ) ).

fof('$adef_Coq.PArith.BinPosDef.Pos.iter_op_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eiter__op,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2ePArith_2eBinPosDef_2ePos_2eiter__op___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.Vectors.VectorDef.tl_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eVectors_2eVectorDef_2etl,V_24X1) = cCoq_2eVectors_2eVectorDef_2etl___24a1(V_24X1) ).

fof('$adef_Coq.setoid_ring.Ring_polynom.norm_aux_$a9',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9] : happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2enorm__aux,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9) = cCoq_2esetoid__ring_2eRing__polynom_2enorm__aux___24a9(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9) ).

fof('$adef_Coq.micromega.ZMicromega.Vars.Node_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eZMicromega_2eVars_2eNode,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eZMicromega_2eVars_2eNode___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_$_lam_102446_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(c_24__lam__102446,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> c_24__lam__102446___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).

fof('$adef_Coq.setoid_ring.InitialRing.triv_div_$a6',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eInitialRing_2etriv__div,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2esetoid__ring_2eInitialRing_2etriv__div___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).

fof('$adef_Coq.Init.Logic.False_rec_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eLogic_2eFalse__rec,V_24X1),V_24X2) = cCoq_2eInit_2eLogic_2eFalse__rec___24a2(V_24X1,V_24X2) ).

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('$adef_PLF.Stlc.STLC.subst_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cPLF_2eStlc_2eSTLC_2esubst,V_24X1),V_24X2),V_24X3) = cPLF_2eStlc_2eSTLC_2esubst___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.Lists.List.In_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] :
      ( p(happ(happ(happ(cCoq_2eLists_2eList_2eIn,V_24X1),V_24X2),V_24X3))
    <=> cCoq_2eLists_2eList_2eIn___24a3(V_24X1,V_24X2,V_24X3) ) ).

fof('$adef_Coq.Init.Datatypes.andb_$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] : happ(happ(cCoq_2eInit_2ePeano_2elt,V_24X1),V_24X2) = cCoq_2eInit_2ePeano_2elt___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('$adef_Coq.PArith.BinPos.Pos.le_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2ePArith_2eBinPos_2ePos_2ele,V_24X1),V_24X2))
    <=> cCoq_2ePArith_2eBinPos_2ePos_2ele___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.Init.Nat.mul_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2emul,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2emul___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.FSets.FSetPositive.PositiveSet.Node_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode,V_24X1),V_24X2),V_24X3) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.Init.Peano.le_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eInit_2ePeano_2ele,V_24X1),V_24X2))
    <=> cCoq_2eInit_2ePeano_2ele___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.Init.Decimal.D7_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD7,V_24X1) = cCoq_2eInit_2eDecimal_2eD7___24a1(V_24X1) ).

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('$adef_PLF.References.STLCRef.prd_$a1',axiom,
    ! [V_24X1] : happ(cPLF_2eReferences_2eSTLCRef_2eprd,V_24X1) = cPLF_2eReferences_2eSTLCRef_2eprd___24a1(V_24X1) ).

fof('$adef_Coq.micromega.ZMicromega.ZgcdM_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eZMicromega_2eZgcdM,V_24X1),V_24X2) = cCoq_2emicromega_2eZMicromega_2eZgcdM___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.micromega.EnvRing.PEmul_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePEmul,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.Init.Datatypes.snd_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2esnd,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2esnd___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_$_lam_102430_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(c_24__lam__102430,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> c_24__lam__102430___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).

fof('$adef_Coq.ZArith.BinIntDef.Z.gcd_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2egcd,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2egcd___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('$adef_Coq.Init.Datatypes.prod_rec_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2eprod__rec,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2eprod__rec___24a3(V_24X1,V_24X2,V_24X3) ).

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('$adef_Coq.Lists.List.nth_$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('$adef_PLF.StlcProp.STLCProp.closed_$a1',axiom,
    ! [V_24X1] :
      ( p(happ(cPLF_2eStlcProp_2eSTLCProp_2eclosed,V_24X1))
    <=> cPLF_2eStlcProp_2eSTLCProp_2eclosed___24a1(V_24X1) ) ).

fof('$adef_Coq.micromega.EnvRing.Padd_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePadd,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eEnvRing_2ePadd___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('$adef_Coq.micromega.RingMicromega.psub_$a6',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2epsub,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2emicromega_2eRingMicromega_2epsub___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).

fof('$adef_$_prop_168303_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__prop__168303,V_24X1),V_24X2) = c_24__prop__168303___24a2(V_24X1,V_24X2) ).

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('$adef_PLF.Smallstep.CImp.CIf_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cPLF_2eSmallstep_2eCImp_2eCIf,V_24X1),V_24X2),V_24X3) = cPLF_2eSmallstep_2eCImp_2eCIf___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_$_fix_80266_1_add_carry_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__fix__80266__1__add__carry,V_24X1),V_24X2) = c_24__fix__80266__1__add__carry___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.setoid_ring.Ring_polynom.zmon_pred_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ezmon__pred,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__polynom_2ezmon__pred___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.micromega.EnvRing.mkPinj_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eEnvRing_2emkPinj,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eEnvRing_2emkPinj___24a3(V_24X1,V_24X2,V_24X3) ).

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('$adef_PLF.References.STLCRef.step_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cPLF_2eReferences_2eSTLCRef_2estep,V_24X1),V_24X2))
    <=> cPLF_2eReferences_2eSTLCRef_2estep___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.Init.Datatypes.inr_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2einr,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2einr___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_$_case_Coq.Init.Datatypes.nat$113313_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2enat_24113313,V_24X1),V_24X2),V_24X3) = c_24__case__Coq_2eInit_2eDatatypes_2enat_24113313___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('$adef_$_case_Coq.Init.Datatypes.nat$210866_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2enat_24210866,V_24X1),V_24X2),V_24X3) = c_24__case__Coq_2eInit_2eDatatypes_2enat_24210866___24a3(V_24X1,V_24X2,V_24X3) ).

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('$adef_Coq.micromega.RingMicromega.padd_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2epadd,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eRingMicromega_2epadd___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.Strings.Ascii.byte_of_ascii_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eStrings_2eAscii_2ebyte__of__ascii,V_24X1) = cCoq_2eStrings_2eAscii_2ebyte__of__ascii___24a1(V_24X1) ).

fof('$adef_$_case_Coq.Init.Datatypes.nat$77280_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2enat_2477280,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__case__Coq_2eInit_2eDatatypes_2enat_2477280___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_Coq.setoid_ring.Ring_polynom.PNSubstL_$a11',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePNSubstL,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11) = cCoq_2esetoid__ring_2eRing__polynom_2ePNSubstL___24a11(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11) ).

fof('$adef_Coq.NArith.BinNatDef.N.succ_double_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2esucc__double,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2esucc__double___24a1(V_24X1) ).

fof('$adef_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.bits_lt_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt,V_24X1),V_24X2))
    <=> cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(V_24X1,V_24X2) ) ).

fof('$adef_PLF.Smallstep.Combined.C_$a1',axiom,
    ! [V_24X1] : happ(cPLF_2eSmallstep_2eCombined_2eC,V_24X1) = cPLF_2eSmallstep_2eCombined_2eC___24a1(V_24X1) ).

fof('$adef_$_prop_92095_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__92095,V_24X1),V_24X2),V_24X3) = c_24__prop__92095___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.PArith.BinPosDef.Pos.succ_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(V_24X1) ).

fof('$adef_Coq.setoid_ring.Field_theory.FEsub_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEsub,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_PLF.Maps.t_update_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cPLF_2eMaps_2et__update,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cPLF_2eMaps_2et__update___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_PLF.LibTactics.COIND_$a1',axiom,
    ! [V_24X1] :
      ( p(happ(cPLF_2eLibTactics_2eCOIND,V_24X1))
    <=> cPLF_2eLibTactics_2eCOIND___24a1(V_24X1) ) ).

fof('$adef_Coq.FSets.FSetPositive.PositiveSet.E.bits_lt_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eE_2ebits__lt,V_24X1),V_24X2))
    <=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eE_2ebits__lt___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.Relations.Relation_Operators.Desc_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] :
      ( p(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eDesc,V_24X1),V_24X2),V_24X3))
    <=> cCoq_2eRelations_2eRelation__Operators_2eDesc___24a3(V_24X1,V_24X2,V_24X3) ) ).

fof('$adef_$_lam_168764_$a6',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__168764,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__168764___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).

fof('$adef_Coq.micromega.ZMicromega.Zgcd_pol_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2emicromega_2eZMicromega_2eZgcd__pol,V_24X1) = cCoq_2emicromega_2eZMicromega_2eZgcd__pol___24a1(V_24X1) ).

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('$adef_PLF.Smallstep.Temp2.step_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cPLF_2eSmallstep_2eTemp2_2estep,V_24X1),V_24X2))
    <=> cPLF_2eSmallstep_2eTemp2_2estep___24a2(V_24X1,V_24X2) ) ).

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('$adef_$_fix_109197_v_CANONICAL_0_$a1',axiom,
    ! [V_24X1] : happ(c_24__fix__109197__v__CANONICAL__0,V_24X1) = c_24__fix__109197__v__CANONICAL__0___24a1(V_24X1) ).

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('$adef_$_prop_92099_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__92099,V_24X1),V_24X2),V_24X3) = c_24__prop__92099___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.setoid_ring.Ring_polynom.norm_subst_$a12',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] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2enorm__subst,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12) = cCoq_2esetoid__ring_2eRing__polynom_2enorm__subst___24a12(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12) ).

fof('$adef_Coq.micromega.DeclConstant.DeclaredConstant_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2emicromega_2eDeclConstant_2eDeclaredConstant,V_24X1),V_24X2))
    <=> cCoq_2emicromega_2eDeclConstant_2eDeclaredConstant___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.ZArith.BinIntDef.Z.compare_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.setoid_ring.Ring_theory.ring_theory_$a8',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8] :
      ( p(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2ering__theory,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8))
    <=> cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8) ) ).

fof('$adef_Coq.QArith.QArith_base.Qden_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eQArith_2eQArith__base_2eQden,V_24X1) = cCoq_2eQArith_2eQArith__base_2eQden___24a1(V_24X1) ).

fof('$adef_PLF.Imp.BreakImp.CWhile_$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('$adef_$_prop_154313_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__prop__154313,V_24X1),V_24X2) = c_24__prop__154313___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('$adef_Coq.Init.Datatypes.eq_true_$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('$adef_PLF.Smallstep.Combined.test_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cPLF_2eSmallstep_2eCombined_2etest,V_24X1),V_24X2),V_24X3) = cPLF_2eSmallstep_2eCombined_2etest___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.micromega.ZMicromega.valid_cut_sign_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2emicromega_2eZMicromega_2evalid__cut__sign,V_24X1) = cCoq_2emicromega_2eZMicromega_2evalid__cut__sign___24a1(V_24X1) ).

fof('$adef_$_prop_92094_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__prop__92094,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__prop__92094___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.Init.Decimal.Decimal_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDecimal_2eDecimal,V_24X1),V_24X2) = cCoq_2eInit_2eDecimal_2eDecimal___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Strings.Ascii.nat_of_ascii_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eStrings_2eAscii_2enat__of__ascii,V_24X1) = cCoq_2eStrings_2eAscii_2enat__of__ascii___24a1(V_24X1) ).

fof('$adef_Coq.micromega.ZMicromega.Vars.E.bits_lt_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2emicromega_2eZMicromega_2eVars_2eE_2ebits__lt,V_24X1),V_24X2))
    <=> cCoq_2emicromega_2eZMicromega_2eVars_2eE_2ebits__lt___24a2(V_24X1,V_24X2) ) ).

fof('$adef_PLF.References.STLCRef.RefsAndNontermination.step_closure_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cPLF_2eReferences_2eSTLCRef_2eRefsAndNontermination_2estep__closure,V_24X1),V_24X2) = cPLF_2eReferences_2eSTLCRef_2eRefsAndNontermination_2estep__closure___24a2(V_24X1,V_24X2) ).

fof('$adef_$_lam_102454_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__102454,V_24X1),V_24X2),V_24X3) = c_24__lam__102454___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_PLF.Smallstep.step_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cPLF_2eSmallstep_2estep,V_24X1),V_24X2))
    <=> cPLF_2eSmallstep_2estep___24a2(V_24X1,V_24X2) ) ).

fof('$adef_PLF.References.STLCRef.extends_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cPLF_2eReferences_2eSTLCRef_2eextends,V_24X1),V_24X2))
    <=> cPLF_2eReferences_2eSTLCRef_2eextends___24a2(V_24X1,V_24X2) ) ).

fof('$adef_PLF.References.STLCRef.tseq_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cPLF_2eReferences_2eSTLCRef_2etseq,V_24X1),V_24X2) = cPLF_2eReferences_2eSTLCRef_2etseq___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.micromega.Env.nth_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eEnv_2enth,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eEnv_2enth___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_PLF.Stlc.STLC.app_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cPLF_2eStlc_2eSTLC_2eapp,V_24X1),V_24X2) = cPLF_2eStlc_2eSTLC_2eapp___24a2(V_24X1,V_24X2) ).

fof('$adef_$_case_Coq.Init.Datatypes.list$210988_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2elist_24210988,V_24X1),V_24X2),V_24X3) = c_24__case__Coq_2eInit_2eDatatypes_2elist_24210988___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_PLF.References.STLCRef.store_Tlookup_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cPLF_2eReferences_2eSTLCRef_2estore__Tlookup,V_24X1),V_24X2) = cPLF_2eReferences_2eSTLCRef_2estore__Tlookup___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Bool.Bool.eqb_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eBool_2eBool_2eeqb,V_24X1),V_24X2) = cCoq_2eBool_2eBool_2eeqb___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.NArith.BinNatDef.N.div_eucl_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2ediv__eucl,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2ediv__eucl___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('$adef_PLF.StlcProp.STLCArith.Arrow_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cPLF_2eStlcProp_2eSTLCArith_2eArrow,V_24X1),V_24X2) = cPLF_2eStlcProp_2eSTLCArith_2eArrow___24a2(V_24X1,V_24X2) ).

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('$adef_Coq.micromega.RingMicromega.padd_$a6',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2epadd,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2emicromega_2eRingMicromega_2epadd___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).

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('$adef_$_case_Coq.Init.Datatypes.list$115346_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2elist_24115346,V_24X1),V_24X2),V_24X3) = c_24__case__Coq_2eInit_2eDatatypes_2elist_24115346___24a3(V_24X1,V_24X2,V_24X3) ).

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('$adef_$_prop_92100_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__prop__92100,V_24X1),V_24X2) = c_24__prop__92100___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.ZArith.Zpower.two_power_nat_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eZArith_2eZpower_2etwo__power__nat,V_24X1) = cCoq_2eZArith_2eZpower_2etwo__power__nat___24a1(V_24X1) ).

fof('$adef_Coq.Numbers.BinNums.Zneg_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2eZneg,V_24X1) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(V_24X1) ).

fof('$adef_Coq.Reals.RIneq.mknonnegreal_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eReals_2eRIneq_2emknonnegreal,V_24X1) = cCoq_2eReals_2eRIneq_2emknonnegreal___24a1(V_24X1) ).

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('$adef_Coq.ZArith.Zeven.Zeven_$a1',axiom,
    ! [V_24X1] :
      ( p(happ(cCoq_2eZArith_2eZeven_2eZeven,V_24X1))
    <=> cCoq_2eZArith_2eZeven_2eZeven___24a1(V_24X1) ) ).

fof('$adef_Coq.Init.Wf.well_founded_induction_type_2_$a7',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] : happ(happ(happ(happ(happ(happ(happ(cCoq_2eInit_2eWf_2ewell__founded__induction__type__2,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = cCoq_2eInit_2eWf_2ewell__founded__induction__type__2___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).

fof('$adef_PLF.Stlc.STLC.var_$a1',axiom,
    ! [V_24X1] : happ(cPLF_2eStlc_2eSTLC_2evar,V_24X1) = cPLF_2eStlc_2eSTLC_2evar___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('$adef_PLF.LibTactics.rm_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cPLF_2eLibTactics_2erm,V_24X1),V_24X2) = cPLF_2eLibTactics_2erm___24a2(V_24X1,V_24X2) ).

fof('$adef_$_lam_218144_$a9',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9] : happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__lam__218144,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9) = c_24__lam__218144___24a9(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9) ).

fof('$adef_Coq.NArith.BinNatDef.N.leb_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2eleb,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2eleb___24a2(V_24X1,V_24X2) ).

fof('$adef_$_case_Coq.Init.Datatypes.nat$1023_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2enat_241023,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__case__Coq_2eInit_2eDatatypes_2enat_241023___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.Arith.Between.between_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] :
      ( p(happ(happ(happ(cCoq_2eArith_2eBetween_2ebetween,V_24X1),V_24X2),V_24X3))
    <=> cCoq_2eArith_2eBetween_2ebetween___24a3(V_24X1,V_24X2,V_24X3) ) ).

fof('$adef_Coq.micromega.RingMicromega.eval_nformula_$a11',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11] :
      ( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2eeval__nformula,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11))
    <=> cCoq_2emicromega_2eRingMicromega_2eeval__nformula___24a11(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11) ) ).

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('$adef_PLF.References.STLCRef.const_$a1',axiom,
    ! [V_24X1] : happ(cPLF_2eReferences_2eSTLCRef_2econst,V_24X1) = cPLF_2eReferences_2eSTLCRef_2econst___24a1(V_24X1) ).

fof('$adef_$_prop_168301_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__prop__168301,V_24X1),V_24X2) = c_24__prop__168301___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Init.Wf.Fix_F_2_$a8',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8] : happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2eInit_2eWf_2eFix__F__2,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8) = cCoq_2eInit_2eWf_2eFix__F__2___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8) ).

fof('$adef_Coq.PArith.BinPosDef.Pos.sub_mask_$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('$adef_$_lam_2109_$a1',axiom,
    ! [V_24X1] : happ(c_24__lam__2109,V_24X1) = c_24__lam__2109___24a1(V_24X1) ).

fof('$adef_Coq.ZArith.BinIntDef.Z.gtb_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2egtb,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2egtb___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('$adef_Coq.Init.Datatypes.prod_uncurry_$a6',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2eInit_2eDatatypes_2eprod__uncurry,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2eInit_2eDatatypes_2eprod__uncurry___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).

fof('$adef_Coq.NArith.BinNatDef.N.pos_div_eucl_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2epos__div__eucl,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2epos__div__eucl___24a2(V_24X1,V_24X2) ).

fof('$adef_$_fix_211015_v_CANONICAL_0_$a1',axiom,
    ! [V_24X1] : happ(c_24__fix__211015__v__CANONICAL__0,V_24X1) = c_24__fix__211015__v__CANONICAL__0___24a1(V_24X1) ).

fof('$adef_Coq.Init.Datatypes.prod_rect_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eInit_2eDatatypes_2eprod__rect,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eInit_2eDatatypes_2eprod__rect___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_Coq.Arith.Compare_dec.lt_eq_lt_dec_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eArith_2eCompare__dec_2elt__eq__lt__dec,V_24X1),V_24X2) = cCoq_2eArith_2eCompare__dec_2elt__eq__lt__dec___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.setoid_ring.Ring_polynom.PEadd_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEadd,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.micromega.RingMicromega.check_inconsistent_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2echeck__inconsistent,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2emicromega_2eRingMicromega_2echeck__inconsistent___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_Coq.Vectors.VectorDef.splitat_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eVectors_2eVectorDef_2esplitat,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eVectors_2eVectorDef_2esplitat___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

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('$adef_Coq.micromega.RingMicromega.map_option2_$a6',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2emap__option2,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2emicromega_2eRingMicromega_2emap__option2___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).

fof('$adef_Coq.Init.Datatypes.xorb_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2exorb,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2exorb___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Strings.String.String_$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('$adef_PLF.Smallstep.Temp2.value_$a1',axiom,
    ! [V_24X1] :
      ( p(happ(cPLF_2eSmallstep_2eTemp2_2evalue,V_24X1))
    <=> cPLF_2eSmallstep_2eTemp2_2evalue___24a1(V_24X1) ) ).

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('$adef_Coq.micromega.Tauto.FF_$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('$adef_$_lam_218144_$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__218144,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = c_24__lam__218144___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).

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('$adef_$_lam_112906_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__112906,V_24X1),V_24X2),V_24X3) = c_24__lam__112906___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_$_lam_1722_$a12',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] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__lam__1722,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12) = c_24__lam__1722___24a12(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12) ).

fof('$adef_Coq.Structures.OrderedType.GT_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eStructures_2eOrderedType_2eGT,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eStructures_2eOrderedType_2eGT___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_Hammer.Tactics.Tactics.rdone_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cHammer_2eTactics_2eTactics_2erdone,V_24X1),V_24X2))
    <=> cHammer_2eTactics_2eTactics_2erdone___24a2(V_24X1,V_24X2) ) ).

fof('$adef_$_lam_112906_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__112906,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__112906___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

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('$adef_$_lam_102454_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(c_24__lam__102454,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> c_24__lam__102454___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).

fof('$adef_Coq.setoid_ring.Ring_theory.id_phi_N_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2esetoid__ring_2eRing__theory_2eid__phi__N,V_24X1) = cCoq_2esetoid__ring_2eRing__theory_2eid__phi__N___24a1(V_24X1) ).

fof('$adef_Coq.Vectors.Fin.FS_$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('$adef_$_case_PLF.Stlc.STLC.tm$110793_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__case__PLF_2eStlc_2eSTLC_2etm_24110793,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__case__PLF_2eStlc_2eSTLC_2etm_24110793___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

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('$adef_PLF.Smallstep.aval_$a1',axiom,
    ! [V_24X1] :
      ( p(happ(cPLF_2eSmallstep_2eaval,V_24X1))
    <=> cPLF_2eSmallstep_2eaval___24a1(V_24X1) ) ).

fof('$adef_Coq.Setoids.Setoid.Setoid_Theory_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eSetoids_2eSetoid_2eSetoid__Theory,V_24X1),V_24X2))
    <=> cCoq_2eSetoids_2eSetoid_2eSetoid__Theory___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.Init.Peano.ge_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2ePeano_2ege,V_24X1),V_24X2) = cCoq_2eInit_2ePeano_2ege___24a2(V_24X1,V_24X2) ).

fof('$adef_PLF.References.STLCRef.assign_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cPLF_2eReferences_2eSTLCRef_2eassign,V_24X1),V_24X2) = cPLF_2eReferences_2eSTLCRef_2eassign___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Init.Decimal.Neg_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eNeg,V_24X1) = cCoq_2eInit_2eDecimal_2eNeg___24a1(V_24X1) ).

fof('$adef_PLF.Stlc.STLC.test_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cPLF_2eStlc_2eSTLC_2etest,V_24X1),V_24X2),V_24X3) = cPLF_2eStlc_2eSTLC_2etest___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.Lists.SetoidList.NoDupA_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] :
      ( p(happ(happ(happ(cCoq_2eLists_2eSetoidList_2eNoDupA,V_24X1),V_24X2),V_24X3))
    <=> cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(V_24X1,V_24X2,V_24X3) ) ).

fof('$adef_PLF.Imp.SLoad_$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('$adef_$_fix_77667_v_CANONICAL_0_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__fix__77667__v__CANONICAL__0,V_24X1),V_24X2) = c_24__fix__77667__v__CANONICAL__0___24a2(V_24X1,V_24X2) ).

fof('$adef_PLF.References.STLCRef.RefsAndNontermination.step_closure_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(cPLF_2eReferences_2eSTLCRef_2eRefsAndNontermination_2estep__closure,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> cPLF_2eReferences_2eSTLCRef_2eRefsAndNontermination_2estep__closure___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).

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('$adef_Coq.Init.Decimal.D9_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD9,V_24X1) = cCoq_2eInit_2eDecimal_2eD9___24a1(V_24X1) ).

fof('$adef_Coq.PArith.BinPosDef.Pos.leb_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eleb,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2eleb___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Classes.RelationClasses.Reflexive_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eClasses_2eRelationClasses_2eReflexive,V_24X1),V_24X2))
    <=> cCoq_2eClasses_2eRelationClasses_2eReflexive___24a2(V_24X1,V_24X2) ) ).

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('$adef_PLF.Maps.partial_map_$a1',axiom,
    ! [V_24X1] : happ(cPLF_2eMaps_2epartial__map,V_24X1) = cPLF_2eMaps_2epartial__map___24a1(V_24X1) ).

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('$adef_$_lam_2102_$a1',axiom,
    ! [V_24X1] : happ(c_24__lam__2102,V_24X1) = c_24__lam__2102___24a1(V_24X1) ).

fof('$adef_PLF.References.STLCRef.deref_$a1',axiom,
    ! [V_24X1] : happ(cPLF_2eReferences_2eSTLCRef_2ederef,V_24X1) = cPLF_2eReferences_2eSTLCRef_2ederef___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('$adef_PLF.References.STLCRef.abs_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cPLF_2eReferences_2eSTLCRef_2eabs,V_24X1),V_24X2),V_24X3) = cPLF_2eReferences_2eSTLCRef_2eabs___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.Init.Wf.Acc_inv_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eInit_2eWf_2eAcc__inv,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eInit_2eWf_2eAcc__inv___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.micromega.RMicromega.CInv_$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('$adef_Coq.ZArith.Znumtheory.rel_prime_$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('$adef_Coq.Init.Nat.pred_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eNat_2epred,V_24X1) = cCoq_2eInit_2eNat_2epred___24a1(V_24X1) ).

fof('$adef_$_prop_92097_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__92097,V_24X1),V_24X2),V_24X3) = c_24__prop__92097___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_$_case_Coq.Init.Datatypes.bool$111211_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2ebool_24111211,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_24111211___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

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('$adef_Coq.micromega.ZMicromega.Zdiv_pol_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eZMicromega_2eZdiv__pol,V_24X1),V_24X2) = cCoq_2emicromega_2eZMicromega_2eZdiv__pol___24a2(V_24X1,V_24X2) ).

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('$adef_$_case_Coq.Init.Datatypes.bool$77863_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2ebool_2477863,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_2477863___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_$_prop_168300_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__prop__168300,V_24X1),V_24X2) = c_24__prop__168300___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Lists.List.map_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eLists_2eList_2emap,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eLists_2eList_2emap___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_PLF.Imp.aevalR_extended.AMinus_$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('$adef_PLF.References.STLCRef.store_well_typed_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cPLF_2eReferences_2eSTLCRef_2estore__well__typed,V_24X1),V_24X2))
    <=> cPLF_2eReferences_2eSTLCRef_2estore__well__typed___24a2(V_24X1,V_24X2) ) ).

fof('$adef_$_prop_154312_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__prop__154312,V_24X1),V_24X2) = c_24__prop__154312___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.micromega.EnvRing.PsubC_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePsubC,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eEnvRing_2ePsubC___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

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('$adef_$_case_Coq.Init.Datatypes.bool$77532_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2ebool_2477532,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_2477532___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_PLF.Maps.update_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cPLF_2eMaps_2eupdate,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cPLF_2eMaps_2eupdate___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

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('$adef_PLF.References.STLCRef.Ref_$a1',axiom,
    ! [V_24X1] : happ(cPLF_2eReferences_2eSTLCRef_2eRef,V_24X1) = cPLF_2eReferences_2eSTLCRef_2eRef___24a1(V_24X1) ).

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('$adef_$_fix_77299_v_CANONICAL_0_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__fix__77299__v__CANONICAL__0,V_24X1),V_24X2) = c_24__fix__77299__v__CANONICAL__0___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Init.Datatypes.cons_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2econs,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2econs___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.setoid_ring.Field_theory.field_theory_$a10',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10] :
      ( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2efield__theory,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10))
    <=> cCoq_2esetoid__ring_2eField__theory_2efield__theory___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10) ) ).

fof('$adef_Coq.setoid_ring.Ring_theory.Computational_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2eComputational,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eRing__theory_2eComputational___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.micromega.RingMicromega.PsatzSquare_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRingMicromega_2ePsatzSquare,V_24X1),V_24X2) = cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Strings.String.string_dec_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eStrings_2eString_2estring__dec,V_24X1),V_24X2) = cCoq_2eStrings_2eString_2estring__dec___24a2(V_24X1,V_24X2) ).

fof('$adef_$_lam_102446_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__102446,V_24X1),V_24X2),V_24X3) = c_24__lam__102446___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.ZArith.BinIntDef.Z.of_nat_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V_24X1) ).

fof('$adef_Coq.Init.Datatypes.pair_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eInit_2eDatatypes_2epair,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eInit_2eDatatypes_2epair___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.PArith.BinPosDef.Pos.IsPos_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(V_24X1) ).

fof('$adef_Coq.micromega.Tauto.cnf_tt_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eTauto_2ecnf__tt,V_24X1),V_24X2) = cCoq_2emicromega_2eTauto_2ecnf__tt___24a2(V_24X1,V_24X2) ).

fof('$adef_$_let_3_s_168284_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__let__3__s__168284,V_24X1),V_24X2) = c_24__let__3__s__168284___24a2(V_24X1,V_24X2) ).

fof('$adef_PLF.Stlc.STLC.Arrow_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cPLF_2eStlc_2eSTLC_2eArrow,V_24X1),V_24X2) = cPLF_2eStlc_2eSTLC_2eArrow___24a2(V_24X1,V_24X2) ).

fof('$adef_$_case_Coq.Numbers.BinNums.Z$113330_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__case__Coq_2eNumbers_2eBinNums_2eZ_24113330,V_24X1),V_24X2),V_24X3) = c_24__case__Coq_2eNumbers_2eBinNums_2eZ_24113330___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.micromega.RingMicromega.Psatz_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2emicromega_2eRingMicromega_2ePsatz,V_24X1) = cCoq_2emicromega_2eRingMicromega_2ePsatz___24a1(V_24X1) ).

fof('$adef_Coq.Init.Datatypes.Some_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2eSome,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2eSome___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.micromega.EnvRing.Pc_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eEnvRing_2ePc,V_24X1),V_24X2) = cCoq_2emicromega_2eEnvRing_2ePc___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Structures.OrderedType.EQ_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eStructures_2eOrderedType_2eEQ,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eStructures_2eOrderedType_2eEQ___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_Coq.Vectors.VectorDef.caseS_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eVectors_2eVectorDef_2ecaseS,V_24X1),V_24X2),V_24X3) = cCoq_2eVectors_2eVectorDef_2ecaseS___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.Numbers.BinNums.Zpos_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2eZpos,V_24X1) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(V_24X1) ).

fof('$adef_Coq.NArith.BinNatDef.N.double_$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('$adef_PLF.Stlc.STLC.has_type_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] :
      ( p(happ(happ(happ(cPLF_2eStlc_2eSTLC_2ehas__type,V_24X1),V_24X2),V_24X3))
    <=> cPLF_2eStlc_2eSTLC_2ehas__type___24a3(V_24X1,V_24X2,V_24X3) ) ).

fof('$adef_Coq.Init.Nat.sub_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2esub,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2esub___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.micromega.Tauto.clause_$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('$adef_$_lam_79669_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__79669,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__79669___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

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('$adef_Coq.PArith.BinPosDef.Pos.gcd_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2egcd,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2egcd___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Bool.Bool.ReflectF_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eBool_2eBool_2eReflectF,V_24X1) = cCoq_2eBool_2eBool_2eReflectF___24a1(V_24X1) ).

fof('$adef_Coq.setoid_ring.Ring_polynom.add_pow_list_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2eadd__pow__list,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eRing__polynom_2eadd__pow__list___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.PArith.BinPos.Pos.iter_op_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2ePArith_2eBinPos_2ePos_2eiter__op,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2ePArith_2eBinPos_2ePos_2eiter__op___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

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('$adef_Coq.setoid_ring.Ring_polynom.norm_subst_$a11',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2enorm__subst,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11) = cCoq_2esetoid__ring_2eRing__polynom_2enorm__subst___24a11(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11) ).

fof('$adef_$_lam_102430_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__102430,V_24X1),V_24X2),V_24X3) = c_24__lam__102430___24a3(V_24X1,V_24X2,V_24X3) ).

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('$adef_PLF.StlcProp.STLCArith.app_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cPLF_2eStlcProp_2eSTLCArith_2eapp,V_24X1),V_24X2) = cPLF_2eStlcProp_2eSTLCArith_2eapp___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Arith.PeanoNat.Nat.pred_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eArith_2ePeanoNat_2eNat_2epred,V_24X1) = cCoq_2eArith_2ePeanoNat_2eNat_2epred___24a1(V_24X1) ).

fof('$adef_Coq.Lists.List.Forall_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] :
      ( p(happ(happ(happ(cCoq_2eLists_2eList_2eForall,V_24X1),V_24X2),V_24X3))
    <=> cCoq_2eLists_2eList_2eForall___24a3(V_24X1,V_24X2,V_24X3) ) ).

fof('$adef_$_fix_77213_v_CANONICAL_0_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__fix__77213__v__CANONICAL__0,V_24X1),V_24X2) = c_24__fix__77213__v__CANONICAL__0___24a2(V_24X1,V_24X2) ).

fof('$adef_$_lam_108016_$a1',axiom,
    ! [V_24X1] : happ(c_24__lam__108016,V_24X1) = c_24__lam__108016___24a1(V_24X1) ).

fof('$adef_Coq.Init.Decimal.nb_digits_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2enb__digits,V_24X1) = cCoq_2eInit_2eDecimal_2enb__digits___24a1(V_24X1) ).

fof('$adef_$_prop_94743_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__prop__94743,V_24X1),V_24X2) = c_24__prop__94743___24a2(V_24X1,V_24X2) ).

fof('$adef_PLF.Smallstep.C_$a1',axiom,
    ! [V_24X1] : happ(cPLF_2eSmallstep_2eC,V_24X1) = cPLF_2eSmallstep_2eC___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('$adef_Coq.Init.Datatypes.prod_rect_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2eprod__rect,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2eprod__rect___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_PLF.Types.iszro_$a1',axiom,
    ! [V_24X1] : happ(cPLF_2eTypes_2eiszro,V_24X1) = cPLF_2eTypes_2eiszro___24a1(V_24X1) ).

fof('$adef_Coq.Init.Datatypes.fst_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2efst,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2efst___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.ZArith.Zpower.shift_nat_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eZpower_2eshift__nat,V_24X1),V_24X2) = cCoq_2eZArith_2eZpower_2eshift__nat___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.setoid_ring.Ring_polynom.mon_of_pol_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2emon__of__pol,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eRing__polynom_2emon__of__pol___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.Arith.PeanoNat.Nat.sub_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eArith_2ePeanoNat_2eNat_2esub,V_24X1),V_24X2) = cCoq_2eArith_2ePeanoNat_2eNat_2esub___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('$adef_Coq.ZArith.BinIntDef.Z.quotrem_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2equotrem___24a2(V_24X1,V_24X2) ).

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('$adef_Coq.micromega.Tauto.N_$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('$adef_PLF.Maps.update_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cPLF_2eMaps_2eupdate,V_24X1),V_24X2),V_24X3),V_24X4) = cPLF_2eMaps_2eupdate___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.PArith.BinPosDef.Pos.ggcd_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eggcd,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2eggcd___24a2(V_24X1,V_24X2) ).

fof('$adef_PLF.Smallstep.Temp1.value_$a1',axiom,
    ! [V_24X1] :
      ( p(happ(cPLF_2eSmallstep_2eTemp1_2evalue,V_24X1))
    <=> cPLF_2eSmallstep_2eTemp1_2evalue___24a1(V_24X1) ) ).

fof('$adef_Coq.Init.Wf.Fix_F_2_$a7',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] : happ(happ(happ(happ(happ(happ(happ(cCoq_2eInit_2eWf_2eFix__F__2,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = cCoq_2eInit_2eWf_2eFix__F__2___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).

fof('$adef_$_lam_168764_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__lam__168764,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__lam__168764___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_$_case_Coq.Init.Specif.sumor$168291_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__case__Coq_2eInit_2eSpecif_2esumor_24168291,V_24X1),V_24X2) = c_24__case__Coq_2eInit_2eSpecif_2esumor_24168291___24a2(V_24X1,V_24X2) ).

fof('$adef_PLF.Types.prd_$a1',axiom,
    ! [V_24X1] : happ(cPLF_2eTypes_2eprd,V_24X1) = cPLF_2eTypes_2eprd___24a1(V_24X1) ).

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('$adef_PLF.Smallstep.relation_$a1',axiom,
    ! [V_24X1] : happ(cPLF_2eSmallstep_2erelation,V_24X1) = cPLF_2eSmallstep_2erelation___24a1(V_24X1) ).

fof('$adef_$_fix_115391_v_CANONICAL_1_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__fix__115391__v__CANONICAL__1,V_24X1),V_24X2),V_24X3) = c_24__fix__115391__v__CANONICAL__1___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.Init.Nat.min_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2emin,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2emin___24a2(V_24X1,V_24X2) ).

fof('$adef_PLF.Imp.AExp.BLe_$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('$adef_Coq.PArith.BinPosDef.Pos.compare_$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('$adef_Coq.NArith.BinNat.N.div_eucl_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNat_2eN_2ediv__eucl,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNat_2eN_2ediv__eucl___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('$adef_Coq.micromega.RingMicromega.PsatzZ_$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('$adef_PLF.Imp.SPush_$a1',axiom,
    ! [V_24X1] : happ(cPLF_2eImp_2eSPush,V_24X1) = cPLF_2eImp_2eSPush___24a1(V_24X1) ).

fof('$adef_PLF.StlcProp.STLCProp.appears_free_in_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cPLF_2eStlcProp_2eSTLCProp_2eappears__free__in,V_24X1),V_24X2))
    <=> cPLF_2eStlcProp_2eSTLCProp_2eappears__free__in___24a2(V_24X1,V_24X2) ) ).

fof('$adef_$_case_Coq.Init.Datatypes.list$211642_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2elist_24211642,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__case__Coq_2eInit_2eDatatypes_2elist_24211642___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

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('$adef_$_case_Coq.Init.Datatypes.bool$108704_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2ebool_24108704,V_24X1),V_24X2))
    <=> c_24__case__Coq_2eInit_2eDatatypes_2ebool_24108704___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('$adef_PLF.Maps.total_map_$a1',axiom,
    ! [V_24X1] : happ(cPLF_2eMaps_2etotal__map,V_24X1) = cPLF_2eMaps_2etotal__map___24a1(V_24X1) ).

fof('$adef_Coq.Vectors.VectorDef.nil_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eVectors_2eVectorDef_2enil,V_24X1) = cCoq_2eVectors_2eVectorDef_2enil___24a1(V_24X1) ).

fof('$adef_Coq.Init.Specif.left_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eSpecif_2eleft,V_24X1),V_24X2) = cCoq_2eInit_2eSpecif_2eleft___24a2(V_24X1,V_24X2) ).

fof('$adef_PLF.Maps.t_empty_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cPLF_2eMaps_2et__empty,V_24X1),V_24X2),V_24X3) = cPLF_2eMaps_2et__empty___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.Init.Specif.sigT_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eSpecif_2esigT,V_24X1),V_24X2) = cCoq_2eInit_2eSpecif_2esigT___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.micromega.RingMicromega.map_option_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2emap__option,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eRingMicromega_2emap__option___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.Init.Decimal.D3_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD3,V_24X1) = cCoq_2eInit_2eDecimal_2eD3___24a1(V_24X1) ).

fof('$adef_Coq.micromega.RingMicromega.NFormula_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2emicromega_2eRingMicromega_2eNFormula,V_24X1) = cCoq_2emicromega_2eRingMicromega_2eNFormula___24a1(V_24X1) ).

fof('$adef_Coq.Arith.PeanoNat.Nat.divmod_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eArith_2ePeanoNat_2eNat_2edivmod,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eArith_2ePeanoNat_2eNat_2edivmod___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_PLF.Maps.empty_$a1',axiom,
    ! [V_24X1] : happ(cPLF_2eMaps_2eempty,V_24X1) = cPLF_2eMaps_2eempty___24a1(V_24X1) ).

fof('$adef_$_case_Coq.Init.Datatypes.nat$77050_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2enat_2477050,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__case__Coq_2eInit_2eDatatypes_2enat_2477050___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_$_lam_112898_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__112898,V_24X1),V_24X2),V_24X3) = c_24__lam__112898___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_PLF.Smallstep.CImp.CSeq_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cPLF_2eSmallstep_2eCImp_2eCSeq,V_24X1),V_24X2) = cPLF_2eSmallstep_2eCImp_2eCSeq___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('$adef_Coq.Init.Specif.sig2_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2esig2,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2esig2___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.setoid_ring.Field_theory.FEpow_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEpow,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.Init.Datatypes.length_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2elength,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2elength___24a2(V_24X1,V_24X2) ).

fof('$adef_PLF.References.STLCRef.mlt_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cPLF_2eReferences_2eSTLCRef_2emlt,V_24X1),V_24X2) = cPLF_2eReferences_2eSTLCRef_2emlt___24a2(V_24X1,V_24X2) ).

fof('$adef_PLF.References.STLCRef.has_type_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(cPLF_2eReferences_2eSTLCRef_2ehas__type,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> cPLF_2eReferences_2eSTLCRef_2ehas__type___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).

fof('$adef_Coq.micromega.ZMicromega.is_diff_env_elt_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(cCoq_2emicromega_2eZMicromega_2eis__diff__env__elt,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> cCoq_2emicromega_2eZMicromega_2eis__diff__env__elt___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).

fof('$adef_Coq.NArith.BinNat.N.le_$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_112334_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__prop__112334,V_24X1),V_24X2) = c_24__prop__112334___24a2(V_24X1,V_24X2) ).

fof('$adef_PLF.References.STLCRef.ty_rect_$a6',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cPLF_2eReferences_2eSTLCRef_2ety__rect,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cPLF_2eReferences_2eSTLCRef_2ety__rect___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).

fof('$adef_Coq.Vectors.VectorDef.hd_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eVectors_2eVectorDef_2ehd,V_24X1) = cCoq_2eVectors_2eVectorDef_2ehd___24a1(V_24X1) ).

fof('$adef_Coq.Vectors.Vector.cons_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eVectors_2eVector_2econs,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eVectors_2eVector_2econs___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.micromega.RingMicromega.eval_pol_$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_2eRingMicromega_2eeval__pol,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = cCoq_2emicromega_2eRingMicromega_2eeval__pol___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).

fof('$adef_Coq.Init.Nat.divmod_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eInit_2eNat_2edivmod,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eInit_2eNat_2edivmod___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.ZArith.Zpower.Zdiv_rest_proofs_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eZpower_2eZdiv__rest__proofs,V_24X1),V_24X2) = cCoq_2eZArith_2eZpower_2eZdiv__rest__proofs___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.PArith.BinPosDef.Pos.of_succ_nat_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(V_24X1) ).

fof('$adef_Coq.micromega.EnvRing.PEsub_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePEsub,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eEnvRing_2ePEsub___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.micromega.RingMicromega.eval_nformula_$a9',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9] : happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2eeval__nformula,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9) = cCoq_2emicromega_2eRingMicromega_2eeval__nformula___24a9(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9) ).

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('$adef_$_lam_2119_$a1',axiom,
    ! [V_24X1] : happ(c_24__lam__2119,V_24X1) = c_24__lam__2119___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('$tdef_$_type_1383',axiom,
    ! [V_24Y] :
      ( c_24__type__1383___24t(V_24Y)
    <=> t(V_24Y,c_24__type__1383) ) ).

fof('$tdef_$_type_76882',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__76882___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__76882___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_94747',axiom,
    ! [V_24Y] :
      ( c_24__type__94747___24t(V_24Y)
    <=> t(V_24Y,c_24__type__94747) ) ).

fof('$tdef_$_type_113458',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__113458___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__113458___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_$_type_214684',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__214684___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__214684___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_Coq.micromega.ZMicromega.Vars.E.t',axiom,
    ! [V_24Y] :
      ( cCoq_2emicromega_2eZMicromega_2eVars_2eE_2et___24t(V_24Y)
    <=> t(V_24Y,cCoq_2emicromega_2eZMicromega_2eVars_2eE_2et) ) ).

fof('$tdef_$_type_76446',axiom,
    ! [V_24Y] :
      ( c_24__type__76446___24t(V_24Y)
    <=> t(V_24Y,c_24__type__76446) ) ).

fof('$tdef_$_type_81409',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
      ( c_24__type__81409___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
    <=> t(V_24Y,c_24__type__81409___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).

fof('$tdef_$_type_104869',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__104869___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__104869___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_161927',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__161927___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__161927___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_89572',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__89572___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__89572___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_Coq.micromega.VarMap.t',axiom,
    ! [V_24X1,V_24Y] :
      ( cCoq_2emicromega_2eVarMap_2et___24t(V_24X1,V_24Y)
    <=> t(V_24Y,cCoq_2emicromega_2eVarMap_2et___24a1(V_24X1)) ) ).

fof('$tdef_$_type_93894',axiom,
    ! [V_24Y] :
      ( c_24__type__93894___24t(V_24Y)
    <=> t(V_24Y,c_24__type__93894) ) ).

fof('$tdef_$_type_75718',axiom,
    ! [V_24Y] :
      ( c_24__type__75718___24t(V_24Y)
    <=> t(V_24Y,c_24__type__75718) ) ).

fof('$tdef_$_type_203683',axiom,
    ! [V_24Y] :
      ( c_24__type__203683___24t(V_24Y)
    <=> t(V_24Y,c_24__type__203683) ) ).

fof('$tdef_$_type_108018',axiom,
    ! [V_24Y] :
      ( c_24__type__108018___24t(V_24Y)
    <=> t(V_24Y,c_24__type__108018) ) ).

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_1859',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__1859___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__1859___24a1(V_24X1)) ) ).

fof('$tdef_$_type_549',axiom,
    ! [V_24Y] :
      ( c_24__type__549___24t(V_24Y)
    <=> t(V_24Y,c_24__type__549) ) ).

fof('$tdef_$_type_91246',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
      ( c_24__type__91246___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__91246___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).

fof('$tdef_$_type_81197',axiom,
    ! [V_24Y] :
      ( c_24__type__81197___24t(V_24Y)
    <=> t(V_24Y,c_24__type__81197) ) ).

fof('$tdef_$_type_113131',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__113131___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__113131___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_112932',axiom,
    ! [V_24Y] :
      ( c_24__type__112932___24t(V_24Y)
    <=> t(V_24Y,c_24__type__112932) ) ).

fof('$tdef_$_type_91812',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__91812___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__91812___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_219180',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__219180___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__219180___24a1(V_24X1)) ) ).

fof('$tdef_$_type_218279',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__218279___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__218279___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_$_type_84765',axiom,
    ! [V_24Y] :
      ( c_24__type__84765___24t(V_24Y)
    <=> t(V_24Y,c_24__type__84765) ) ).

fof('$tdef_$_type_214597',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__214597___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__214597___24a1(V_24X1)) ) ).

fof('$tdef_$_type_83500',axiom,
    ! [V_24Y] :
      ( c_24__type__83500___24t(V_24Y)
    <=> t(V_24Y,c_24__type__83500) ) ).

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_75629',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__75629___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__75629___24a1(V_24X1)) ) ).

fof('$tdef_$_type_2363',axiom,
    ! [V_24Y] :
      ( c_24__type__2363___24t(V_24Y)
    <=> t(V_24Y,c_24__type__2363) ) ).

fof('$tdef_$_type_203741',axiom,
    ! [V_24Y] :
      ( c_24__type__203741___24t(V_24Y)
    <=> t(V_24Y,c_24__type__203741) ) ).

fof('$tdef_PLF.Smallstep.relation',axiom,
    ! [V_24X1,V_24Y] :
      ( cPLF_2eSmallstep_2erelation___24t(V_24X1,V_24Y)
    <=> t(V_24Y,cPLF_2eSmallstep_2erelation___24a1(V_24X1)) ) ).

fof('$tdef_$_type_2377',axiom,
    ! [V_24Y] :
      ( c_24__type__2377___24t(V_24Y)
    <=> t(V_24Y,c_24__type__2377) ) ).

fof('$tdef_Coq.Structures.OrdersTac.ord',axiom,
    ! [V_24Y] :
      ( cCoq_2eStructures_2eOrdersTac_2eord___24t(V_24Y)
    <=> t(V_24Y,cCoq_2eStructures_2eOrdersTac_2eord) ) ).

fof('$tdef_Coq.micromega.EnvRing.PExpr',axiom,
    ! [V_24X1,V_24Y] :
      ( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(V_24X1,V_24Y)
    <=> t(V_24Y,cCoq_2emicromega_2eEnvRing_2ePExpr___24a1(V_24X1)) ) ).

fof('$tdef_$_type_94773',axiom,
    ! [V_24Y] :
      ( c_24__type__94773___24t(V_24Y)
    <=> t(V_24Y,c_24__type__94773) ) ).

fof('$tdef_$_type_88647',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
      ( c_24__type__88647___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
    <=> t(V_24Y,c_24__type__88647___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).

fof('$tdef_$_type_112890',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__112890___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__112890___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_86652',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
      ( c_24__type__86652___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
    <=> t(V_24Y,c_24__type__86652___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).

fof('$tdef_$_type_80907',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__80907___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__80907___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_1876',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__1876___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__1876___24a1(V_24X1)) ) ).

fof('$tdef_$_type_84590',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__84590___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__84590___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_Coq.PArith.BinPos.Pos.mask',axiom,
    ! [V_24Y] :
      ( cCoq_2ePArith_2eBinPos_2ePos_2emask___24t(V_24Y)
    <=> t(V_24Y,cCoq_2ePArith_2eBinPos_2ePos_2emask) ) ).

fof('$tdef_$_type_91686',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__91686___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__91686___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_$_type_90863',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
      ( c_24__type__90863___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
    <=> t(V_24Y,c_24__type__90863___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).

fof('$tdef_$_type_80621',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__80621___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__80621___24a1(V_24X1)) ) ).

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_98251',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__98251___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__98251___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_114845',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
      ( c_24__type__114845___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
    <=> t(V_24Y,c_24__type__114845___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).

fof('$tdef_PLF.Smallstep.tm',axiom,
    ! [V_24Y] :
      ( cPLF_2eSmallstep_2etm___24t(V_24Y)
    <=> t(V_24Y,cPLF_2eSmallstep_2etm) ) ).

fof('$tdef_$_type_219182',axiom,
    ! [V_24Y] :
      ( c_24__type__219182___24t(V_24Y)
    <=> t(V_24Y,c_24__type__219182) ) ).

fof('$tdef_$_type_91622',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__91622___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__91622___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_$_type_75738',axiom,
    ! [V_24Y] :
      ( c_24__type__75738___24t(V_24Y)
    <=> t(V_24Y,c_24__type__75738) ) ).

fof('$tdef_$_type_1640',axiom,
    ! [V_24Y] :
      ( c_24__type__1640___24t(V_24Y)
    <=> t(V_24Y,c_24__type__1640) ) ).

fof('$tdef_PLF.Imp.state',axiom,
    ! [V_24Y] :
      ( cPLF_2eImp_2estate___24t(V_24Y)
    <=> t(V_24Y,cPLF_2eImp_2estate) ) ).

fof('$tdef_$_type_79576',axiom,
    ! [V_24Y] :
      ( c_24__type__79576___24t(V_24Y)
    <=> t(V_24Y,c_24__type__79576) ) ).

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_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('$tdef_$_type_89665',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__89665___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__89665___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_$_type_100304',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__100304___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__100304___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_89690',axiom,
    ! [V_24Y] :
      ( c_24__type__89690___24t(V_24Y)
    <=> t(V_24Y,c_24__type__89690) ) ).

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_Coq.micromega.Tauto.GFormula',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( cCoq_2emicromega_2eTauto_2eGFormula___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,cCoq_2emicromega_2eTauto_2eGFormula___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_Coq.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_76838',axiom,
    ! [V_24Y] :
      ( c_24__type__76838___24t(V_24Y)
    <=> t(V_24Y,c_24__type__76838) ) ).

fof('$tdef_$_type_109200',axiom,
    ! [V_24Y] :
      ( c_24__type__109200___24t(V_24Y)
    <=> t(V_24Y,c_24__type__109200) ) ).

fof('$tdef_$_type_219161',axiom,
    ! [V_24Y] :
      ( c_24__type__219161___24t(V_24Y)
    <=> t(V_24Y,c_24__type__219161) ) ).

fof('$tdef_$_type_261',axiom,
    ! [V_24Y] :
      ( c_24__type__261___24t(V_24Y)
    <=> t(V_24Y,c_24__type__261) ) ).

fof('$tdef_$_type_198718',axiom,
    ! [V_24Y] :
      ( c_24__type__198718___24t(V_24Y)
    <=> t(V_24Y,c_24__type__198718) ) ).

fof('$tdef_$_type_168747',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__168747___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__168747___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_101642',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__101642___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__101642___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_113342',axiom,
    ! [V_24Y] :
      ( c_24__type__113342___24t(V_24Y)
    <=> t(V_24Y,c_24__type__113342) ) ).

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_82801',axiom,
    ! [V_24Y] :
      ( c_24__type__82801___24t(V_24Y)
    <=> t(V_24Y,c_24__type__82801) ) ).

fof('$tdef_$_type_391',axiom,
    ! [V_24Y] :
      ( c_24__type__391___24t(V_24Y)
    <=> t(V_24Y,c_24__type__391) ) ).

fof('$tdef_$_type_80586',axiom,
    ! [V_24Y] :
      ( c_24__type__80586___24t(V_24Y)
    <=> t(V_24Y,c_24__type__80586) ) ).

fof('$tdef_$_type_80296',axiom,
    ! [V_24Y] :
      ( c_24__type__80296___24t(V_24Y)
    <=> t(V_24Y,c_24__type__80296) ) ).

fof('$tdef_$_type_115492',axiom,
    ! [V_24Y] :
      ( c_24__type__115492___24t(V_24Y)
    <=> t(V_24Y,c_24__type__115492) ) ).

fof('$tdef_$_type_214288',axiom,
    ! [V_24Y] :
      ( c_24__type__214288___24t(V_24Y)
    <=> t(V_24Y,c_24__type__214288) ) ).

fof('$tdef_$_type_109351',axiom,
    ! [V_24Y] :
      ( c_24__type__109351___24t(V_24Y)
    <=> t(V_24Y,c_24__type__109351) ) ).

fof('$tdef_$_type_106979',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
      ( c_24__type__106979___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
    <=> t(V_24Y,c_24__type__106979___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).

fof('$tdef_$_type_105703',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__105703___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__105703___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_96925',axiom,
    ! [V_24Y] :
      ( c_24__type__96925___24t(V_24Y)
    <=> t(V_24Y,c_24__type__96925) ) ).

fof('$tdef_$_type_109241',axiom,
    ! [V_24Y] :
      ( c_24__type__109241___24t(V_24Y)
    <=> t(V_24Y,c_24__type__109241) ) ).

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_76925',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__76925___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__76925___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_85086',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__85086___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__85086___24a1(V_24X1)) ) ).

fof('$tdef_$_type_90125',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__90125___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__90125___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_Coq.setoid_ring.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_218526',axiom,
    ! [V_24Y] :
      ( c_24__type__218526___24t(V_24Y)
    <=> t(V_24Y,c_24__type__218526) ) ).

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_75611',axiom,
    ! [V_24Y] :
      ( c_24__type__75611___24t(V_24Y)
    <=> t(V_24Y,c_24__type__75611) ) ).

fof('$tdef_$_type_212347',axiom,
    ! [V_24Y] :
      ( c_24__type__212347___24t(V_24Y)
    <=> t(V_24Y,c_24__type__212347) ) ).

fof('$tdef_Coq.micromega.RingMicromega.PolEnv',axiom,
    ! [V_24X1,V_24Y] :
      ( cCoq_2emicromega_2eRingMicromega_2ePolEnv___24t(V_24X1,V_24Y)
    <=> t(V_24Y,cCoq_2emicromega_2eRingMicromega_2ePolEnv___24a1(V_24X1)) ) ).

fof('$tdef_$_type_107073',axiom,
    ! [V_24Y] :
      ( c_24__type__107073___24t(V_24Y)
    <=> t(V_24Y,c_24__type__107073) ) ).

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_113046',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__113046___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__113046___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_2088',axiom,
    ! [V_24Y] :
      ( c_24__type__2088___24t(V_24Y)
    <=> t(V_24Y,c_24__type__2088) ) ).

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_155065',axiom,
    ! [V_24Y] :
      ( c_24__type__155065___24t(V_24Y)
    <=> t(V_24Y,c_24__type__155065) ) ).

fof('$tdef_$_type_214554',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__214554___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__214554___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_Coq.Relations.Relation_Definitions.relation',axiom,
    ! [V_24X1,V_24Y] :
      ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(V_24X1,V_24Y)
    <=> t(V_24Y,cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V_24X1)) ) ).

fof('$tdef_$_type_88617',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
      ( c_24__type__88617___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
    <=> t(V_24Y,c_24__type__88617___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).

fof('$tdef_$_type_115610',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__115610___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__115610___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_PLF.Maps.partial_map',axiom,
    ! [V_24X1,V_24Y] :
      ( cPLF_2eMaps_2epartial__map___24t(V_24X1,V_24Y)
    <=> t(V_24Y,cPLF_2eMaps_2epartial__map___24a1(V_24X1)) ) ).

fof('$tdef_$_type_96796',axiom,
    ! [V_24Y] :
      ( c_24__type__96796___24t(V_24Y)
    <=> t(V_24Y,c_24__type__96796) ) ).

fof('$tdef_$_type_92261',axiom,
    ! [V_24Y] :
      ( c_24__type__92261___24t(V_24Y)
    <=> t(V_24Y,c_24__type__92261) ) ).

fof('$tdef_$_type_82725',axiom,
    ! [V_24Y] :
      ( c_24__type__82725___24t(V_24Y)
    <=> t(V_24Y,c_24__type__82725) ) ).

fof('$tdef_$_type_75646',axiom,
    ! [V_24Y] :
      ( c_24__type__75646___24t(V_24Y)
    <=> t(V_24Y,c_24__type__75646) ) ).

fof('$tdef_$_type_87130',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__87130___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__87130___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_$_type_113662',axiom,
    ! [V_24Y] :
      ( c_24__type__113662___24t(V_24Y)
    <=> t(V_24Y,c_24__type__113662) ) ).

fof('$tdef_$_type_97905',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__97905___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__97905___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_212724',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__212724___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__212724___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_99958',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__99958___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__99958___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_85946',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__85946___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__85946___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_214641',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__214641___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__214641___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_88195',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
      ( c_24__type__88195___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__88195___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).

fof('$tdef_$_type_97559',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__97559___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__97559___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_212230',axiom,
    ! [V_24Y] :
      ( c_24__type__212230___24t(V_24Y)
    <=> t(V_24Y,c_24__type__212230) ) ).

fof('$tdef_PLF.Imp.com',axiom,
    ! [V_24Y] :
      ( cPLF_2eImp_2ecom___24t(V_24Y)
    <=> t(V_24Y,cPLF_2eImp_2ecom) ) ).

fof('$tdef_$_type_2492',axiom,
    ! [V_24Y] :
      ( c_24__type__2492___24t(V_24Y)
    <=> t(V_24Y,c_24__type__2492) ) ).

fof('$tdef_Coq.Structures.DecidableTypeEx.Z_as_DT.t',axiom,
    ! [V_24Y] :
      ( cCoq_2eStructures_2eDecidableTypeEx_2eZ__as__DT_2et___24t(V_24Y)
    <=> t(V_24Y,cCoq_2eStructures_2eDecidableTypeEx_2eZ__as__DT_2et) ) ).

fof('$tdef_$_type_218312',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
      ( c_24__type__218312___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
    <=> t(V_24Y,c_24__type__218312___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).

fof('$tdef_$_type_89222',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__89222___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__89222___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_$_type_151260',axiom,
    ! [V_24Y] :
      ( c_24__type__151260___24t(V_24Y)
    <=> t(V_24Y,c_24__type__151260) ) ).

fof('$tdef_$_type_88321',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
      ( c_24__type__88321___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__88321___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).

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_212493',axiom,
    ! [V_24Y] :
      ( c_24__type__212493___24t(V_24Y)
    <=> t(V_24Y,c_24__type__212493) ) ).

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_Coq.Init.Byte.byte',axiom,
    ! [V_24Y] :
      ( cCoq_2eInit_2eByte_2ebyte___24t(V_24Y)
    <=> t(V_24Y,cCoq_2eInit_2eByte_2ebyte) ) ).

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_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_87552',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
      ( c_24__type__87552___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__87552___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).

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_934',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__934___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__934___24a1(V_24X1)) ) ).

fof('$tdef_$_type_80902',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__80902___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__80902___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_Coq.Vectors.Vector.t',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( cCoq_2eVectors_2eVector_2et___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,cCoq_2eVectors_2eVector_2et___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_2615',axiom,
    ! [V_24Y] :
      ( c_24__type__2615___24t(V_24Y)
    <=> t(V_24Y,c_24__type__2615) ) ).

fof('$tdef_Coq.Structures.DecidableTypeEx.Positive_as_DT.t',axiom,
    ! [V_24Y] :
      ( cCoq_2eStructures_2eDecidableTypeEx_2ePositive__as__DT_2et___24t(V_24Y)
    <=> t(V_24Y,cCoq_2eStructures_2eDecidableTypeEx_2ePositive__as__DT_2et) ) ).

fof('$tdef_$_type_1094',axiom,
    ! [V_24Y] :
      ( c_24__type__1094___24t(V_24Y)
    <=> t(V_24Y,c_24__type__1094) ) ).

fof('$tdef_$_type_78059',axiom,
    ! [V_24Y] :
      ( c_24__type__78059___24t(V_24Y)
    <=> t(V_24Y,c_24__type__78059) ) ).

fof('$tdef_$_type_102311',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__102311___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__102311___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.Stlc.STLC.tm',axiom,
    ! [V_24Y] :
      ( cPLF_2eStlc_2eSTLC_2etm___24t(V_24Y)
    <=> t(V_24Y,cPLF_2eStlc_2eSTLC_2etm) ) ).

fof('$tdef_$_type_108195',axiom,
    ! [V_24Y] :
      ( c_24__type__108195___24t(V_24Y)
    <=> t(V_24Y,c_24__type__108195) ) ).

fof('$tdef_$_type_212563',axiom,
    ! [V_24Y] :
      ( c_24__type__212563___24t(V_24Y)
    <=> t(V_24Y,c_24__type__212563) ) ).

fof('$tdef_$_type_115061',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__115061___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__115061___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_Coq.Init.Specif.sigT',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( cCoq_2eInit_2eSpecif_2esigT___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,cCoq_2eInit_2eSpecif_2esigT___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_78062',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__78062___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__78062___24a1(V_24X1)) ) ).

fof('$tdef_$_type_1372',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__1372___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__1372___24a1(V_24X1)) ) ).

fof('$tdef_$_type_166416',axiom,
    ! [V_24Y] :
      ( c_24__type__166416___24t(V_24Y)
    <=> t(V_24Y,c_24__type__166416) ) ).

fof('$tdef_$_type_154315',axiom,
    ! [V_24Y] :
      ( c_24__type__154315___24t(V_24Y)
    <=> t(V_24Y,c_24__type__154315) ) ).

fof('$tdef_$_type_1133',axiom,
    ! [V_24Y] :
      ( c_24__type__1133___24t(V_24Y)
    <=> t(V_24Y,c_24__type__1133) ) ).

fof('$tdef_PLF.Imp.sinstr',axiom,
    ! [V_24Y] :
      ( cPLF_2eImp_2esinstr___24t(V_24Y)
    <=> t(V_24Y,cPLF_2eImp_2esinstr) ) ).

fof('$tdef_$_type_1117',axiom,
    ! [V_24Y] :
      ( c_24__type__1117___24t(V_24Y)
    <=> t(V_24Y,c_24__type__1117) ) ).

fof('$tdef_$_type_1868',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__1868___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__1868___24a1(V_24X1)) ) ).

fof('$tdef_$_type_199306',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__199306___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__199306___24a1(V_24X1)) ) ).

fof('$tdef_$_type_109400',axiom,
    ! [V_24Y] :
      ( c_24__type__109400___24t(V_24Y)
    <=> t(V_24Y,c_24__type__109400) ) ).

fof('$tdef_$_type_1155',axiom,
    ! [V_24Y] :
      ( c_24__type__1155___24t(V_24Y)
    <=> t(V_24Y,c_24__type__1155) ) ).

fof('$tdef_$_type_113285',axiom,
    ! [V_24Y] :
      ( c_24__type__113285___24t(V_24Y)
    <=> t(V_24Y,c_24__type__113285) ) ).

fof('$tdef_$_type_203691',axiom,
    ! [V_24Y] :
      ( c_24__type__203691___24t(V_24Y)
    <=> t(V_24Y,c_24__type__203691) ) ).

fof('$tdef_$_type_79936',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__79936___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__79936___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_113392',axiom,
    ! [V_24Y] :
      ( c_24__type__113392___24t(V_24Y)
    <=> t(V_24Y,c_24__type__113392) ) ).

fof('$tdef_$_type_113065',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__113065___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__113065___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_83648',axiom,
    ! [V_24Y] :
      ( c_24__type__83648___24t(V_24Y)
    <=> t(V_24Y,c_24__type__83648) ) ).

fof('$tdef_$_type_99612',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__99612___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__99612___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_219163',axiom,
    ! [V_24Y] :
      ( c_24__type__219163___24t(V_24Y)
    <=> t(V_24Y,c_24__type__219163) ) ).

fof('$tdef_$_type_85185',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
      ( c_24__type__85185___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
    <=> t(V_24Y,c_24__type__85185___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).

fof('$tdef_$_type_1087',axiom,
    ! [V_24Y] :
      ( c_24__type__1087___24t(V_24Y)
    <=> t(V_24Y,c_24__type__1087) ) ).

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_215129',axiom,
    ! [V_24Y] :
      ( c_24__type__215129___24t(V_24Y)
    <=> t(V_24Y,c_24__type__215129) ) ).

fof('$tdef_$_type_115508',axiom,
    ! [V_24Y] :
      ( c_24__type__115508___24t(V_24Y)
    <=> t(V_24Y,c_24__type__115508) ) ).

fof('$tdef_$_type_98574',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__98574___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__98574___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_85531',axiom,
    ! [V_24Y] :
      ( c_24__type__85531___24t(V_24Y)
    <=> t(V_24Y,c_24__type__85531) ) ).

fof('$tdef_$_type_203673',axiom,
    ! [V_24Y] :
      ( c_24__type__203673___24t(V_24Y)
    <=> t(V_24Y,c_24__type__203673) ) ).

fof('$tdef_$_type_151257',axiom,
    ! [V_24Y] :
      ( c_24__type__151257___24t(V_24Y)
    <=> t(V_24Y,c_24__type__151257) ) ).

fof('$tdef_$_type_91876',axiom,
    ! [V_24Y] :
      ( c_24__type__91876___24t(V_24Y)
    <=> t(V_24Y,c_24__type__91876) ) ).

fof('$tdef_$_type_113413',axiom,
    ! [V_24Y] :
      ( c_24__type__113413___24t(V_24Y)
    <=> t(V_24Y,c_24__type__113413) ) ).

fof('$tdef_$_type_203761',axiom,
    ! [V_24Y] :
      ( c_24__type__203761___24t(V_24Y)
    <=> t(V_24Y,c_24__type__203761) ) ).

fof('$tdef_$_type_952',axiom,
    ! [V_24Y] :
      ( c_24__type__952___24t(V_24Y)
    <=> t(V_24Y,c_24__type__952) ) ).

fof('$tdef_Coq.micromega.Tauto.cnf',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( cCoq_2emicromega_2eTauto_2ecnf___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,cCoq_2emicromega_2eTauto_2ecnf___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_104035',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__104035___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__104035___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_177135',axiom,
    ! [V_24Y] :
      ( c_24__type__177135___24t(V_24Y)
    <=> t(V_24Y,c_24__type__177135) ) ).

fof('$tdef_$_type_96822',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__96822___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__96822___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_76419',axiom,
    ! [V_24Y] :
      ( c_24__type__76419___24t(V_24Y)
    <=> t(V_24Y,c_24__type__76419) ) ).

fof('$tdef_$_type_218221',axiom,
    ! [V_24Y] :
      ( c_24__type__218221___24t(V_24Y)
    <=> t(V_24Y,c_24__type__218221) ) ).

fof('$tdef_$_type_90226',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__90226___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__90226___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

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_82594',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__82594___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__82594___24a1(V_24X1)) ) ).

fof('$tdef_$_type_75666',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__75666___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__75666___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_Coq.QArith.QArith_base.Q',axiom,
    ! [V_24Y] :
      ( cCoq_2eQArith_2eQArith__base_2eQ___24t(V_24Y)
    <=> t(V_24Y,cCoq_2eQArith_2eQArith__base_2eQ) ) ).

fof('$tdef_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_Coq.Init.Datatypes.nat',axiom,
    ! [V_24Y] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V_24Y)
    <=> t(V_24Y,cCoq_2eInit_2eDatatypes_2enat) ) ).

fof('$tdef_$_type_86955',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__86955___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__86955___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_$_type_83489',axiom,
    ! [V_24Y] :
      ( c_24__type__83489___24t(V_24Y)
    <=> t(V_24Y,c_24__type__83489) ) ).

fof('$tdef_$_type_112806',axiom,
    ! [V_24Y] :
      ( c_24__type__112806___24t(V_24Y)
    <=> t(V_24Y,c_24__type__112806) ) ).

fof('$tdef_$_type_76873',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__76873___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__76873___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_75648',axiom,
    ! [V_24Y] :
      ( c_24__type__75648___24t(V_24Y)
    <=> t(V_24Y,c_24__type__75648) ) ).

fof('$tdef_$_type_218487',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
      ( c_24__type__218487___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
    <=> t(V_24Y,c_24__type__218487___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).

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_80340',axiom,
    ! [V_24Y] :
      ( c_24__type__80340___24t(V_24Y)
    <=> t(V_24Y,c_24__type__80340) ) ).

fof('$tdef_Coq.Init.Datatypes.prod',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( cCoq_2eInit_2eDatatypes_2eprod___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,cCoq_2eInit_2eDatatypes_2eprod___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_212317',axiom,
    ! [V_24Y] :
      ( c_24__type__212317___24t(V_24Y)
    <=> t(V_24Y,c_24__type__212317) ) ).

fof('$tdef_PLF.Types.ty',axiom,
    ! [V_24Y] :
      ( cPLF_2eTypes_2ety___24t(V_24Y)
    <=> t(V_24Y,cPLF_2eTypes_2ety) ) ).

fof('$tdef_$_type_90978',axiom,
    ! [V_24Y] :
      ( c_24__type__90978___24t(V_24Y)
    <=> t(V_24Y,c_24__type__90978) ) ).

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_108021',axiom,
    ! [V_24Y] :
      ( c_24__type__108021___24t(V_24Y)
    <=> t(V_24Y,c_24__type__108021) ) ).

fof('$tdef_$_type_87398',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__87398___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__87398___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_$_type_554',axiom,
    ! [V_24Y] :
      ( c_24__type__554___24t(V_24Y)
    <=> t(V_24Y,c_24__type__554) ) ).

fof('$tdef_$_type_203676',axiom,
    ! [V_24Y] :
      ( c_24__type__203676___24t(V_24Y)
    <=> t(V_24Y,c_24__type__203676) ) ).

fof('$tdef_$_type_198772',axiom,
    ! [V_24Y] :
      ( c_24__type__198772___24t(V_24Y)
    <=> t(V_24Y,c_24__type__198772) ) ).

fof('$tdef_PLF.Smallstep.Combined.tm',axiom,
    ! [V_24Y] :
      ( cPLF_2eSmallstep_2eCombined_2etm___24t(V_24Y)
    <=> t(V_24Y,cPLF_2eSmallstep_2eCombined_2etm) ) ).

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_PLF.Imp.bexp',axiom,
    ! [V_24Y] :
      ( cPLF_2eImp_2ebexp___24t(V_24Y)
    <=> t(V_24Y,cPLF_2eImp_2ebexp) ) ).

fof('$tdef_$_type_82244',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__82244___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__82244___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_85971',axiom,
    ! [V_24Y] :
      ( c_24__type__85971___24t(V_24Y)
    <=> t(V_24Y,c_24__type__85971) ) ).

fof('$tdef_$_type_203383',axiom,
    ! [V_24Y] :
      ( c_24__type__203383___24t(V_24Y)
    <=> t(V_24Y,c_24__type__203383) ) ).

fof('$tdef_$_type_113630',axiom,
    ! [V_24Y] :
      ( c_24__type__113630___24t(V_24Y)
    <=> t(V_24Y,c_24__type__113630) ) ).

fof('$tdef_$_type_90327',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__90327___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__90327___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_$_type_80052',axiom,
    ! [V_24Y] :
      ( c_24__type__80052___24t(V_24Y)
    <=> t(V_24Y,c_24__type__80052) ) ).

fof('$tdef_$_type_75693',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__75693___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__75693___24a1(V_24X1)) ) ).

fof('$tdef_$_type_115650',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__115650___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__115650___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_$_type_2356',axiom,
    ! [V_24Y] :
      ( c_24__type__2356___24t(V_24Y)
    <=> t(V_24Y,c_24__type__2356) ) ).

fof('$tdef_$_type_112884',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__112884___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__112884___24a1(V_24X1)) ) ).

fof('$tdef_Coq.setoid_ring.Ring_theory.ring_kind',axiom,
    ! [V_24Y] :
      ( cCoq_2esetoid__ring_2eRing__theory_2ering__kind___24t(V_24Y)
    <=> t(V_24Y,cCoq_2esetoid__ring_2eRing__theory_2ering__kind) ) ).

fof('$tdef_PLF.Smallstep.stack',axiom,
    ! [V_24Y] :
      ( cPLF_2eSmallstep_2estack___24t(V_24Y)
    <=> t(V_24Y,cPLF_2eSmallstep_2estack) ) ).

fof('$tdef_$_type_96930',axiom,
    ! [V_24Y] :
      ( c_24__type__96930___24t(V_24Y)
    <=> t(V_24Y,c_24__type__96930) ) ).

fof('$tdef_PLF.StlcProp.STLCArith.ty',axiom,
    ! [V_24Y] :
      ( cPLF_2eStlcProp_2eSTLCArith_2ety___24t(V_24Y)
    <=> t(V_24Y,cPLF_2eStlcProp_2eSTLCArith_2ety) ) ).

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_83593',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
      ( c_24__type__83593___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
    <=> t(V_24Y,c_24__type__83593___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).

fof('$tdef_$_type_13',axiom,
    ! [V_24Y] :
      ( c_24__type__13___24t(V_24Y)
    <=> t(V_24Y,c_24__type__13) ) ).

fof('$tdef_$_type_106899',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
      ( c_24__type__106899___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
    <=> t(V_24Y,c_24__type__106899___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).

fof('$tdef_$_type_212709',axiom,
    ! [V_24Y] :
      ( c_24__type__212709___24t(V_24Y)
    <=> t(V_24Y,c_24__type__212709) ) ).

fof('$tdef_$_type_76603',axiom,
    ! [V_24Y] :
      ( c_24__type__76603___24t(V_24Y)
    <=> t(V_24Y,c_24__type__76603) ) ).

fof('$tdef_$_type_76843',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__76843___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__76843___24a1(V_24X1)) ) ).

fof('$tdef_$_type_114912',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__114912___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__114912___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_$_type_76444',axiom,
    ! [V_24Y] :
      ( c_24__type__76444___24t(V_24Y)
    <=> t(V_24Y,c_24__type__76444) ) ).

fof('$tdef_$_type_218454',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__218454___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__218454___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_$_type_168307',axiom,
    ! [V_24Y] :
      ( c_24__type__168307___24t(V_24Y)
    <=> t(V_24Y,c_24__type__168307) ) ).

fof('$tdef_Coq.micromega.ZMicromega.Vars.tree',axiom,
    ! [V_24Y] :
      ( cCoq_2emicromega_2eZMicromega_2eVars_2etree___24t(V_24Y)
    <=> t(V_24Y,cCoq_2emicromega_2eZMicromega_2eVars_2etree) ) ).

fof('$tdef_$_type_82503',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__82503___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__82503___24a2(V_24X1,V_24X2)) ) ).

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_113560',axiom,
    ! [V_24Y] :
      ( c_24__type__113560___24t(V_24Y)
    <=> t(V_24Y,c_24__type__113560) ) ).

fof('$tdef_$_type_96920',axiom,
    ! [V_24Y] :
      ( c_24__type__96920___24t(V_24Y)
    <=> t(V_24Y,c_24__type__96920) ) ).

fof('$tdef_$_type_88258',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
      ( c_24__type__88258___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__88258___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).

fof('$tdef_$_type_86862',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__86862___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__86862___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_$_type_120971',axiom,
    ! [V_24Y] :
      ( c_24__type__120971___24t(V_24Y)
    <=> t(V_24Y,c_24__type__120971) ) ).

fof('$tdef_$_type_214637',axiom,
    ! [V_24Y] :
      ( c_24__type__214637___24t(V_24Y)
    <=> t(V_24Y,c_24__type__214637) ) ).

fof('$tdef_$_type_83764',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__83764___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__83764___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_1635',axiom,
    ! [V_24Y] :
      ( c_24__type__1635___24t(V_24Y)
    <=> t(V_24Y,c_24__type__1635) ) ).

fof('$tdef_$_type_113150',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__113150___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__113150___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_216915',axiom,
    ! [V_24Y] :
      ( c_24__type__216915___24t(V_24Y)
    <=> t(V_24Y,c_24__type__216915) ) ).

fof('$tdef_$_type_88785',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
      ( c_24__type__88785___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
    <=> t(V_24Y,c_24__type__88785___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).

fof('$tdef_$_type_115951',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__115951___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__115951___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_$_type_105916',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__105916___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__105916___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_79565',axiom,
    ! [V_24Y] :
      ( c_24__type__79565___24t(V_24Y)
    <=> t(V_24Y,c_24__type__79565) ) ).

fof('$tdef_$_type_113',axiom,
    ! [V_24Y] :
      ( c_24__type__113___24t(V_24Y)
    <=> t(V_24Y,c_24__type__113) ) ).

fof('$tdef_$_type_90619',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__90619___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__90619___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_Coq.micromega.Env.Env',axiom,
    ! [V_24X1,V_24Y] :
      ( cCoq_2emicromega_2eEnv_2eEnv___24t(V_24X1,V_24Y)
    <=> t(V_24Y,cCoq_2emicromega_2eEnv_2eEnv___24a1(V_24X1)) ) ).

fof('$tdef_Coq.ZArith.Znumtheory.Euclid',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( cCoq_2eZArith_2eZnumtheory_2eEuclid___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,cCoq_2eZArith_2eZnumtheory_2eEuclid___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_Coq.micromega.RingMicromega.Psatz',axiom,
    ! [V_24X1,V_24Y] :
      ( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(V_24X1,V_24Y)
    <=> t(V_24Y,cCoq_2emicromega_2eRingMicromega_2ePsatz___24a1(V_24X1)) ) ).

fof('$tdef_$_type_82369',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__82369___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__82369___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_82624',axiom,
    ! [V_24Y] :
      ( c_24__type__82624___24t(V_24Y)
    <=> t(V_24Y,c_24__type__82624) ) ).

fof('$tdef_$_type_80916',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__80916___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__80916___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_91645',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__91645___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__91645___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

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_PLF.StlcProp.STLCArith.tm',axiom,
    ! [V_24Y] :
      ( cPLF_2eStlcProp_2eSTLCArith_2etm___24t(V_24Y)
    <=> t(V_24Y,cPLF_2eStlcProp_2eSTLCArith_2etm) ) ).

fof('$tdef_$_type_91804',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__91804___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__91804___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_212773',axiom,
    ! [V_24Y] :
      ( c_24__type__212773___24t(V_24Y)
    <=> t(V_24Y,c_24__type__212773) ) ).

fof('$tdef_$_type_105508',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__105508___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__105508___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).

fof('$tdef_Coq.ZArith.BinInt.Z.t',axiom,
    ! [V_24Y] :
      ( cCoq_2eZArith_2eBinInt_2eZ_2et___24t(V_24Y)
    <=> t(V_24Y,cCoq_2eZArith_2eBinInt_2eZ_2et) ) ).

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_Coq.NArith.BinNat.N.t',axiom,
    ! [V_24Y] :
      ( cCoq_2eNArith_2eBinNat_2eN_2et___24t(V_24Y)
    <=> t(V_24Y,cCoq_2eNArith_2eBinNat_2eN_2et) ) ).

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_113122',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
      ( c_24__type__113122___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
    <=> t(V_24Y,c_24__type__113122___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).

fof('$tdef_$_type_104461',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__104461___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__104461___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_218396',axiom,
    ! [V_24Y] :
      ( c_24__type__218396___24t(V_24Y)
    <=> t(V_24Y,c_24__type__218396) ) ).

fof('$tdef_$_type_87615',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
      ( c_24__type__87615___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__87615___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).

fof('$tdef_$_type_90883',axiom,
    ! [V_24Y] :
      ( c_24__type__90883___24t(V_24Y)
    <=> t(V_24Y,c_24__type__90883) ) ).

fof('$tdef_PLF.References.STLCRef.ty',axiom,
    ! [V_24Y] :
      ( cPLF_2eReferences_2eSTLCRef_2ety___24t(V_24Y)
    <=> t(V_24Y,cPLF_2eReferences_2eSTLCRef_2ety) ) ).

fof('$tdef_$_type_1160',axiom,
    ! [V_24Y] :
      ( c_24__type__1160___24t(V_24Y)
    <=> t(V_24Y,c_24__type__1160) ) ).

fof('$tdef_$_type_109359',axiom,
    ! [V_24Y] :
      ( c_24__type__109359___24t(V_24Y)
    <=> t(V_24Y,c_24__type__109359) ) ).

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_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_Coq.FSets.FSetPositive.PositiveSet.E.t',axiom,
    ! [V_24Y] :
      ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eE_2et___24t(V_24Y)
    <=> t(V_24Y,cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eE_2et) ) ).

fof('$tdef_Coq.Arith.PeanoNat.Nat.t',axiom,
    ! [V_24Y] :
      ( cCoq_2eArith_2ePeanoNat_2eNat_2et___24t(V_24Y)
    <=> t(V_24Y,cCoq_2eArith_2ePeanoNat_2eNat_2et) ) ).

fof('$tdef_$_type_214401',axiom,
    ! [V_24Y] :
      ( c_24__type__214401___24t(V_24Y)
    <=> t(V_24Y,c_24__type__214401) ) ).

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_PLF.Types.tm',axiom,
    ! [V_24Y] :
      ( cPLF_2eTypes_2etm___24t(V_24Y)
    <=> t(V_24Y,cPLF_2eTypes_2etm) ) ).

fof('$tdef_$_type_113704',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__113704___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__113704___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_109354',axiom,
    ! [V_24Y] :
      ( c_24__type__109354___24t(V_24Y)
    <=> t(V_24Y,c_24__type__109354) ) ).

fof('$tdef_$_type_87305',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__87305___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__87305___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_Coq.Init.Datatypes.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_114870',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
      ( c_24__type__114870___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
    <=> t(V_24Y,c_24__type__114870___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).

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_112833',axiom,
    ! [V_24Y] :
      ( c_24__type__112833___24t(V_24Y)
    <=> t(V_24Y,c_24__type__112833) ) ).

fof('$tdef_$_type_113869',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
      ( c_24__type__113869___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
    <=> t(V_24Y,c_24__type__113869___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).

fof('$tdef_$_type_108024',axiom,
    ! [V_24Y] :
      ( c_24__type__108024___24t(V_24Y)
    <=> t(V_24Y,c_24__type__108024) ) ).

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_76490',axiom,
    ! [V_24Y] :
      ( c_24__type__76490___24t(V_24Y)
    <=> t(V_24Y,c_24__type__76490) ) ).

fof('$tdef_$_type_113822',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__113822___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__113822___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_2130',axiom,
    ! [V_24Y] :
      ( c_24__type__2130___24t(V_24Y)
    <=> t(V_24Y,c_24__type__2130) ) ).

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_198715',axiom,
    ! [V_24Y] :
      ( c_24__type__198715___24t(V_24Y)
    <=> t(V_24Y,c_24__type__198715) ) ).

fof('$tdef_$_type_1179',axiom,
    ! [V_24Y] :
      ( c_24__type__1179___24t(V_24Y)
    <=> t(V_24Y,c_24__type__1179) ) ).

fof('$tdef_$_type_211757',axiom,
    ! [V_24Y] :
      ( c_24__type__211757___24t(V_24Y)
    <=> t(V_24Y,c_24__type__211757) ) ).

fof('$tdef_$_type_79573',axiom,
    ! [V_24Y] :
      ( c_24__type__79573___24t(V_24Y)
    <=> t(V_24Y,c_24__type__79573) ) ).

fof('$tdef_$_type_2475',axiom,
    ! [V_24Y] :
      ( c_24__type__2475___24t(V_24Y)
    <=> t(V_24Y,c_24__type__2475) ) ).

fof('$tdef_$_type_1107',axiom,
    ! [V_24Y] :
      ( c_24__type__1107___24t(V_24Y)
    <=> t(V_24Y,c_24__type__1107) ) ).

fof('$tdef_$_type_100627',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__100627___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__100627___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.LibTactics.ltac_Wild',axiom,
    ! [V_24Y] :
      ( cPLF_2eLibTactics_2eltac__Wild___24t(V_24Y)
    <=> t(V_24Y,cPLF_2eLibTactics_2eltac__Wild) ) ).

fof('$tdef_$_type_86036',axiom,
    ! [V_24Y] :
      ( c_24__type__86036___24t(V_24Y)
    <=> t(V_24Y,c_24__type__86036) ) ).

fof('$tdef_$_type_75678',axiom,
    ! [V_24Y] :
      ( c_24__type__75678___24t(V_24Y)
    <=> t(V_24Y,c_24__type__75678) ) ).

fof('$tdef_$_type_98920',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__98920___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__98920___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_580',axiom,
    ! [V_24Y] :
      ( c_24__type__580___24t(V_24Y)
    <=> t(V_24Y,c_24__type__580) ) ).

fof('$tdef_$_type_214292',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__214292___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__214292___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_PLF.Imp.aexp',axiom,
    ! [V_24Y] :
      ( cPLF_2eImp_2eaexp___24t(V_24Y)
    <=> t(V_24Y,cPLF_2eImp_2eaexp) ) ).

fof('$tdef_$_type_87732',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
      ( c_24__type__87732___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__87732___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).

fof('$tdef_$_type_91668',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__91668___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__91668___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_$_type_199450',axiom,
    ! [V_24Y] :
      ( c_24__type__199450___24t(V_24Y)
    <=> t(V_24Y,c_24__type__199450) ) ).

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.LibTactics.Boxer',axiom,
    ! [V_24Y] :
      ( cPLF_2eLibTactics_2eBoxer___24t(V_24Y)
    <=> t(V_24Y,cPLF_2eLibTactics_2eBoxer) ) ).

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_2071',axiom,
    ! [V_24Y] :
      ( c_24__type__2071___24t(V_24Y)
    <=> t(V_24Y,c_24__type__2071) ) ).

fof('$tdef_$_type_182',axiom,
    ! [V_24Y] :
      ( c_24__type__182___24t(V_24Y)
    <=> t(V_24Y,c_24__type__182) ) ).

fof('$tdef_Coq.ZArith.BinIntDef.Z.t',axiom,
    ! [V_24Y] :
      ( cCoq_2eZArith_2eBinIntDef_2eZ_2et___24t(V_24Y)
    <=> t(V_24Y,cCoq_2eZArith_2eBinIntDef_2eZ_2et) ) ).

fof('$tdef_$_type_76465',axiom,
    ! [V_24Y] :
      ( c_24__type__76465___24t(V_24Y)
    <=> t(V_24Y,c_24__type__76465) ) ).

fof('$tdef_$_type_76741',axiom,
    ! [V_24Y] :
      ( c_24__type__76741___24t(V_24Y)
    <=> t(V_24Y,c_24__type__76741) ) ).

fof('$tdef_PLF.Smallstep.Temp4.tm',axiom,
    ! [V_24Y] :
      ( cPLF_2eSmallstep_2eTemp4_2etm___24t(V_24Y)
    <=> t(V_24Y,cPLF_2eSmallstep_2eTemp4_2etm) ) ).

fof('$tdef_PLF.Smallstep.CImp.com',axiom,
    ! [V_24Y] :
      ( cPLF_2eSmallstep_2eCImp_2ecom___24t(V_24Y)
    <=> t(V_24Y,cPLF_2eSmallstep_2eCImp_2ecom) ) ).

fof('$tdef_$_type_113715',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__113715___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__113715___24a2(V_24X1,V_24X2)) ) ).

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_113654',axiom,
    ! [V_24Y] :
      ( c_24__type__113654___24t(V_24Y)
    <=> t(V_24Y,c_24__type__113654) ) ).

fof('$tdef_$_type_102887',axiom,
    ! [V_24Y] :
      ( c_24__type__102887___24t(V_24Y)
    <=> t(V_24Y,c_24__type__102887) ) ).

fof('$tdef_$_type_76863',axiom,
    ! [V_24Y] :
      ( c_24__type__76863___24t(V_24Y)
    <=> t(V_24Y,c_24__type__76863) ) ).

fof('$tdef_$_type_109364',axiom,
    ! [V_24Y] :
      ( c_24__type__109364___24t(V_24Y)
    <=> t(V_24Y,c_24__type__109364) ) ).

fof('$tdef_$_type_115942',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__115942___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__115942___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_$_type_83534',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__83534___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__83534___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_93977',axiom,
    ! [V_24Y] :
      ( c_24__type__93977___24t(V_24Y)
    <=> t(V_24Y,c_24__type__93977) ) ).

fof('$tdef_$_type_212345',axiom,
    ! [V_24Y] :
      ( c_24__type__212345___24t(V_24Y)
    <=> t(V_24Y,c_24__type__212345) ) ).

fof('$tdef_PLF.LibTactics.ltac_Wilds',axiom,
    ! [V_24Y] :
      ( cPLF_2eLibTactics_2eltac__Wilds___24t(V_24Y)
    <=> t(V_24Y,cPLF_2eLibTactics_2eltac__Wilds) ) ).

fof('$tdef_$_type_115771',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__115771___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__115771___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_2471',axiom,
    ! [V_24Y] :
      ( c_24__type__2471___24t(V_24Y)
    <=> t(V_24Y,c_24__type__2471) ) ).

fof('$tdef_Coq.micromega.ZMicromega.ZWitness',axiom,
    ! [V_24Y] :
      ( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(V_24Y)
    <=> t(V_24Y,cCoq_2emicromega_2eZMicromega_2eZWitness) ) ).

fof('$tdef_$_type_921',axiom,
    ! [V_24Y] :
      ( c_24__type__921___24t(V_24Y)
    <=> t(V_24Y,c_24__type__921) ) ).

fof('$tdef_$_type_113188',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__113188___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__113188___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_$_type_106855',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
      ( c_24__type__106855___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
    <=> t(V_24Y,c_24__type__106855___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).

fof('$tdef_PLF.References.STLCRef.store',axiom,
    ! [V_24Y] :
      ( cPLF_2eReferences_2eSTLCRef_2estore___24t(V_24Y)
    <=> t(V_24Y,cPLF_2eReferences_2eSTLCRef_2estore) ) ).

fof('$tdef_$_type_79652',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__79652___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__79652___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_102497',axiom,
    ! [V_24Y] :
      ( c_24__type__102497___24t(V_24Y)
    <=> t(V_24Y,c_24__type__102497) ) ).

fof('$tdef_$_type_212713',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__212713___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__212713___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_82621',axiom,
    ! [V_24Y] :
      ( c_24__type__82621___24t(V_24Y)
    <=> t(V_24Y,c_24__type__82621) ) ).

fof('$tdef_$_type_106111',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__106111___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__106111___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_91309',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
      ( c_24__type__91309___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__91309___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).

fof('$tdef_PLF.Stlc.STLC.ty',axiom,
    ! [V_24Y] :
      ( cPLF_2eStlc_2eSTLC_2ety___24t(V_24Y)
    <=> t(V_24Y,cPLF_2eStlc_2eSTLC_2ety) ) ).

fof('$tdef_$_type_102413',axiom,
    ! [V_24Y] :
      ( c_24__type__102413___24t(V_24Y)
    <=> t(V_24Y,c_24__type__102413) ) ).

fof('$tdef_Coq.micromega.ZMicromega.ZArithProof',axiom,
    ! [V_24Y] :
      ( cCoq_2emicromega_2eZMicromega_2eZArithProof___24t(V_24Y)
    <=> t(V_24Y,cCoq_2emicromega_2eZMicromega_2eZArithProof) ) ).

fof('$tdef_$_type_101319',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__101319___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__101319___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).

fof('$tdef_Coq.Structures.DecidableTypeEx.Nat_as_DT.t',axiom,
    ! [V_24Y] :
      ( cCoq_2eStructures_2eDecidableTypeEx_2eNat__as__DT_2et___24t(V_24Y)
    <=> t(V_24Y,cCoq_2eStructures_2eDecidableTypeEx_2eNat__as__DT_2et) ) ).

fof('$tdef_$_type_212778',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__212778___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__212778___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_112996',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__112996___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__112996___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_Coq.Reals.RIneq.nonnegreal',axiom,
    ! [V_24Y] :
      ( cCoq_2eReals_2eRIneq_2enonnegreal___24t(V_24Y)
    <=> t(V_24Y,cCoq_2eReals_2eRIneq_2enonnegreal) ) ).

fof('$tdef_Coq.FSets.FSetPositive.PositiveSet.t',axiom,
    ! [V_24Y] :
      ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V_24Y)
    <=> t(V_24Y,cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et) ) ).

fof('$tdef_$_type_112801',axiom,
    ! [V_24Y] :
      ( c_24__type__112801___24t(V_24Y)
    <=> t(V_24Y,c_24__type__112801) ) ).

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_85967',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__85967___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__85967___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_155088',axiom,
    ! [V_24Y] :
      ( c_24__type__155088___24t(V_24Y)
    <=> t(V_24Y,c_24__type__155088) ) ).

fof('$tdef_$_type_87048',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__87048___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__87048___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_$_type_592',axiom,
    ! [V_24Y] :
      ( c_24__type__592___24t(V_24Y)
    <=> t(V_24Y,c_24__type__592) ) ).

fof('$tdef_$_type_212728',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__212728___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__212728___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_91820',axiom,
    ! [V_24Y] :
      ( c_24__type__91820___24t(V_24Y)
    <=> t(V_24Y,c_24__type__91820) ) ).

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_88593',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
      ( c_24__type__88593___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
    <=> t(V_24Y,c_24__type__88593___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).

fof('$tdef_$_type_949',axiom,
    ! [V_24Y] :
      ( c_24__type__949___24t(V_24Y)
    <=> t(V_24Y,c_24__type__949) ) ).

fof('$tdef_Coq.micromega.ZMicromega.Vars.elt',axiom,
    ! [V_24Y] :
      ( cCoq_2emicromega_2eZMicromega_2eVars_2eelt___24t(V_24Y)
    <=> t(V_24Y,cCoq_2emicromega_2eZMicromega_2eVars_2eelt) ) ).

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_82119',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__82119___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__82119___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_88563',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
      ( c_24__type__88563___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
    <=> t(V_24Y,c_24__type__88563___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).

fof('$tdef_$_type_75706',axiom,
    ! [V_24Y] :
      ( c_24__type__75706___24t(V_24Y)
    <=> t(V_24Y,c_24__type__75706) ) ).

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_393',axiom,
    ! [V_24Y] :
      ( c_24__type__393___24t(V_24Y)
    <=> t(V_24Y,c_24__type__393) ) ).

fof('$tdef_$_type_93898',axiom,
    ! [V_24Y] :
      ( c_24__type__93898___24t(V_24Y)
    <=> t(V_24Y,c_24__type__93898) ) ).

fof('$tdef_$_type_113710',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__113710___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__113710___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_214675',axiom,
    ! [V_24Y] :
      ( c_24__type__214675___24t(V_24Y)
    <=> t(V_24Y,c_24__type__214675) ) ).

fof('$tdef_$_type_113699',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__113699___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__113699___24a2(V_24X1,V_24X2)) ) ).

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_81869',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__81869___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__81869___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_219117',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__219117___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__219117___24a1(V_24X1)) ) ).

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_88375',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
      ( c_24__type__88375___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__88375___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).

fof('$tdef_$_type_212228',axiom,
    ! [V_24Y] :
      ( c_24__type__212228___24t(V_24Y)
    <=> t(V_24Y,c_24__type__212228) ) ).

fof('$tdef_$_type_219175',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__219175___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__219175___24a1(V_24X1)) ) ).

fof('$tdef_$_type_81370',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
      ( c_24__type__81370___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
    <=> t(V_24Y,c_24__type__81370___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).

fof('$tdef_$_type_79568',axiom,
    ! [V_24Y] :
      ( c_24__type__79568___24t(V_24Y)
    <=> t(V_24Y,c_24__type__79568) ) ).

fof('$tdef_$_type_566',axiom,
    ! [V_24Y] :
      ( c_24__type__566___24t(V_24Y)
    <=> t(V_24Y,c_24__type__566) ) ).

fof('$tdef_$_type_81448',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
      ( c_24__type__81448___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
    <=> t(V_24Y,c_24__type__81448___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).

fof('$tdef_$_type_203681',axiom,
    ! [V_24Y] :
      ( c_24__type__203681___24t(V_24Y)
    <=> t(V_24Y,c_24__type__203681) ) ).

fof('$tdef_$_type_83777',axiom,
    ! [V_24Y] :
      ( c_24__type__83777___24t(V_24Y)
    <=> t(V_24Y,c_24__type__83777) ) ).

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_91599',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__91599___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__91599___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_$_type_76596',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__76596___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__76596___24a1(V_24X1)) ) ).

fof('$tdef_$_type_115497',axiom,
    ! [V_24Y] :
      ( c_24__type__115497___24t(V_24Y)
    <=> t(V_24Y,c_24__type__115497) ) ).

fof('$tdef_$_type_109349',axiom,
    ! [V_24Y] :
      ( c_24__type__109349___24t(V_24Y)
    <=> t(V_24Y,c_24__type__109349) ) ).

fof('$tdef_$_type_89129',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__89129___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__89129___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_$_type_99266',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__99266___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__99266___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_75690',axiom,
    ! [V_24Y] :
      ( c_24__type__75690___24t(V_24Y)
    <=> t(V_24Y,c_24__type__75690) ) ).

fof('$tdef_$_type_101965',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__101965___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__101965___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_82538',axiom,
    ! [V_24Y] :
      ( c_24__type__82538___24t(V_24Y)
    <=> t(V_24Y,c_24__type__82538) ) ).

fof('$tdef_$_type_91489',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
      ( c_24__type__91489___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__91489___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).

fof('$tdef_PLF.References.STLCRef.context',axiom,
    ! [V_24Y] :
      ( cPLF_2eReferences_2eSTLCRef_2econtext___24t(V_24Y)
    <=> t(V_24Y,cPLF_2eReferences_2eSTLCRef_2econtext) ) ).

fof('$tdef_PLF.Smallstep.prog',axiom,
    ! [V_24Y] :
      ( cPLF_2eSmallstep_2eprog___24t(V_24Y)
    <=> t(V_24Y,cPLF_2eSmallstep_2eprog) ) ).

fof('$tdef_$_type_212675',axiom,
    ! [V_24Y] :
      ( c_24__type__212675___24t(V_24Y)
    <=> t(V_24Y,c_24__type__212675) ) ).

fof('$tdef_PLF.Stlc.STLC.context',axiom,
    ! [V_24Y] :
      ( cPLF_2eStlc_2eSTLC_2econtext___24t(V_24Y)
    <=> t(V_24Y,cPLF_2eStlc_2eSTLC_2econtext) ) ).

fof('$tdef_$_type_200033',axiom,
    ! [V_24Y] :
      ( c_24__type__200033___24t(V_24Y)
    <=> t(V_24Y,c_24__type__200033) ) ).

fof('$tdef_$_type_151265',axiom,
    ! [V_24Y] :
      ( c_24__type__151265___24t(V_24Y)
    <=> t(V_24Y,c_24__type__151265) ) ).

fof('$tdef_$_type_113005',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__113005___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__113005___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_88701',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
      ( c_24__type__88701___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
    <=> t(V_24Y,c_24__type__88701___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).

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_75624',axiom,
    ! [V_24Y] :
      ( c_24__type__75624___24t(V_24Y)
    <=> t(V_24Y,c_24__type__75624) ) ).

fof('$tdef_$_type_1854',axiom,
    ! [V_24Y] :
      ( c_24__type__1854___24t(V_24Y)
    <=> t(V_24Y,c_24__type__1854) ) ).

fof('$tdef_$_type_90844',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
      ( c_24__type__90844___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
    <=> t(V_24Y,c_24__type__90844___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).

fof('$tdef_$_type_89315',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__89315___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__89315___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_$_type_203685',axiom,
    ! [V_24Y] :
      ( c_24__type__203685___24t(V_24Y)
    <=> t(V_24Y,c_24__type__203685) ) ).

fof('$tdef_$_type_82515',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__82515___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__82515___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_91372',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
      ( c_24__type__91372___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__91372___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).

fof('$tdef_$_type_212989',axiom,
    ! [V_24Y] :
      ( c_24__type__212989___24t(V_24Y)
    <=> t(V_24Y,c_24__type__212989) ) ).

fof('$tdef_$_type_89490',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__89490___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__89490___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_Coq.setoid_ring.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_301',axiom,
    ! [V_24Y] :
      ( c_24__type__301___24t(V_24Y)
    <=> t(V_24Y,c_24__type__301) ) ).

fof('$tdef_$_type_203737',axiom,
    ! [V_24Y] :
      ( c_24__type__203737___24t(V_24Y)
    <=> t(V_24Y,c_24__type__203737) ) ).

fof('$tdef_$_type_2036',axiom,
    ! [V_24Y] :
      ( c_24__type__2036___24t(V_24Y)
    <=> t(V_24Y,c_24__type__2036) ) ).

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_88734',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
      ( c_24__type__88734___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
    <=> t(V_24Y,c_24__type__88734___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).

fof('$tdef_$_type_115784',axiom,
    ! [V_24Y] :
      ( c_24__type__115784___24t(V_24Y)
    <=> t(V_24Y,c_24__type__115784) ) ).

fof('$tdef_$_type_113037',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__113037___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__113037___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_$_type_85936',axiom,
    ! [V_24Y] :
      ( c_24__type__85936___24t(V_24Y)
    <=> t(V_24Y,c_24__type__85936) ) ).

fof('$tdef_$_type_185353',axiom,
    ! [V_24Y] :
      ( c_24__type__185353___24t(V_24Y)
    <=> t(V_24Y,c_24__type__185353) ) ).

fof('$tdef_$_type_105295',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__105295___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__105295___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_2384',axiom,
    ! [V_24Y] :
      ( c_24__type__2384___24t(V_24Y)
    <=> t(V_24Y,c_24__type__2384) ) ).

fof('$tdef_$_type_80354',axiom,
    ! [V_24Y] :
      ( c_24__type__80354___24t(V_24Y)
    <=> t(V_24Y,c_24__type__80354) ) ).

fof('$tdef_$_type_88438',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
      ( c_24__type__88438___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__88438___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).

fof('$tdef_$_type_2113',axiom,
    ! [V_24Y] :
      ( c_24__type__2113___24t(V_24Y)
    <=> t(V_24Y,c_24__type__2113) ) ).

fof('$tdef_$_type_91426',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
      ( c_24__type__91426___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__91426___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).

fof('$tdef_$_type_2096',axiom,
    ! [V_24Y] :
      ( c_24__type__2096___24t(V_24Y)
    <=> t(V_24Y,c_24__type__2096) ) ).

fof('$tdef_$_type_88758',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
      ( c_24__type__88758___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
    <=> t(V_24Y,c_24__type__88758___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).

fof('$tdef_Coq.Structures.DecidableTypeEx.N_as_DT.t',axiom,
    ! [V_24Y] :
      ( cCoq_2eStructures_2eDecidableTypeEx_2eN__as__DT_2et___24t(V_24Y)
    <=> t(V_24Y,cCoq_2eStructures_2eDecidableTypeEx_2eN__as__DT_2et) ) ).

fof('$tdef_$_type_91860',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__91860___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__91860___24a3(V_24X1,V_24X2,V_24X3)) ) ).

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_113281',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
      ( c_24__type__113281___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
    <=> t(V_24Y,c_24__type__113281___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).

fof('$tdef_$_type_104656',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__104656___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__104656___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_91730',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__91730___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__91730___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_$_type_104248',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__104248___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__104248___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_115736',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__115736___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__115736___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

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.PArith.BinPos.Pos.t',axiom,
    ! [V_24Y] :
      ( cCoq_2ePArith_2eBinPos_2ePos_2et___24t(V_24Y)
    <=> t(V_24Y,cCoq_2ePArith_2eBinPos_2ePos_2et) ) ).

fof('$tdef_Coq.setoid_ring.Ring_polynom.Pol',axiom,
    ! [V_24X1,V_24Y] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V_24X1,V_24Y)
    <=> t(V_24Y,cCoq_2esetoid__ring_2eRing__polynom_2ePol___24a1(V_24X1)) ) ).

fof('$tdef_$_type_6',axiom,
    ! [V_24Y] :
      ( c_24__type__6___24t(V_24Y)
    <=> t(V_24Y,c_24__type__6) ) ).

fof('$tdef_$_type_91893',axiom,
    ! [V_24Y] :
      ( c_24__type__91893___24t(V_24Y)
    <=> t(V_24Y,c_24__type__91893) ) ).

fof('$tdef_$_type_211861',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__211861___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__211861___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_$_type_91868',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__91868___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__91868___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_81744',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__81744___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__81744___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_114440',axiom,
    ! [V_24Y] :
      ( c_24__type__114440___24t(V_24Y)
    <=> t(V_24Y,c_24__type__114440) ) ).

fof('$tdef_$_type_90417',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__90417___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__90417___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_PLF.References.STLCRef.tm',axiom,
    ! [V_24Y] :
      ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V_24Y)
    <=> t(V_24Y,cPLF_2eReferences_2eSTLCRef_2etm) ) ).

fof('$tdef_$_type_79795',axiom,
    ! [V_24Y] :
      ( c_24__type__79795___24t(V_24Y)
    <=> t(V_24Y,c_24__type__79795) ) ).

fof('$tdef_$_type_115697',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__115697___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__115697___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_80690',axiom,
    ! [V_24Y] :
      ( c_24__type__80690___24t(V_24Y)
    <=> t(V_24Y,c_24__type__80690) ) ).

fof('$tdef_$_type_102623',axiom,
    ! [V_24Y] :
      ( c_24__type__102623___24t(V_24Y)
    <=> t(V_24Y,c_24__type__102623) ) ).

fof('$tdef_$_type_93878',axiom,
    ! [V_24Y] :
      ( c_24__type__93878___24t(V_24Y)
    <=> t(V_24Y,c_24__type__93878) ) ).

fof('$tdef_$_type_113614',axiom,
    ! [V_24Y] :
      ( c_24__type__113614___24t(V_24Y)
    <=> t(V_24Y,c_24__type__113614) ) ).

fof('$tdef_$_type_105082',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__105082___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__105082___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_1192',axiom,
    ! [V_24Y] :
      ( c_24__type__1192___24t(V_24Y)
    <=> t(V_24Y,c_24__type__1192) ) ).

fof('$tdef_$_type_90720',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__90720___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__90720___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_PLF.References.STLCRef.store_ty',axiom,
    ! [V_24Y] :
      ( cPLF_2eReferences_2eSTLCRef_2estore__ty___24t(V_24Y)
    <=> t(V_24Y,cPLF_2eReferences_2eSTLCRef_2estore__ty) ) ).

fof('$tdef_$_type_116',axiom,
    ! [V_24Y] :
      ( c_24__type__116___24t(V_24Y)
    <=> t(V_24Y,c_24__type__116) ) ).

fof('$tdef_$_type_91712',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__91712___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__91712___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

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_1632',axiom,
    ! [V_24Y] :
      ( c_24__type__1632___24t(V_24Y)
    <=> t(V_24Y,c_24__type__1632) ) ).

fof('$tdef_$_type_220585',axiom,
    ! [V_24Y] :
      ( c_24__type__220585___24t(V_24Y)
    <=> t(V_24Y,c_24__type__220585) ) ).

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_81994',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__81994___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__81994___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_121019',axiom,
    ! [V_24Y] :
      ( c_24__type__121019___24t(V_24Y)
    <=> t(V_24Y,c_24__type__121019) ) ).

fof('$tdef_$_type_78055',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__78055___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__78055___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_88677',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
      ( c_24__type__88677___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
    <=> t(V_24Y,c_24__type__88677___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).

fof('$tdef_$_type_174032',axiom,
    ! [V_24Y] :
      ( c_24__type__174032___24t(V_24Y)
    <=> t(V_24Y,c_24__type__174032) ) ).

fof('$tdef_$_type_203385',axiom,
    ! [V_24Y] :
      ( c_24__type__203385___24t(V_24Y)
    <=> t(V_24Y,c_24__type__203385) ) ).

fof('$tdef_$_type_87795',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
      ( c_24__type__87795___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__87795___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).

fof('$tdef_$_type_75607',axiom,
    ! [V_24Y] :
      ( c_24__type__75607___24t(V_24Y)
    <=> t(V_24Y,c_24__type__75607) ) ).

fof('$tdef_$_type_1074',axiom,
    ! [V_24Y] :
      ( c_24__type__1074___24t(V_24Y)
    <=> t(V_24Y,c_24__type__1074) ) ).

fof('$tdef_$_type_100973',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__100973___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__100973___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_83655',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__83655___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__83655___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_Type',axiom,
    ! [V_24Y] :
      ( cType___24t(V_24Y)
    <=> t(V_24Y,cType) ) ).

fof('$tdef_$_type_931',axiom,
    ! [V_24Y] :
      ( c_24__type__931___24t(V_24Y)
    <=> t(V_24Y,c_24__type__931) ) ).

fof('$tdef_$_type_90518',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__90518___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__90518___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_Coq.PArith.BinPosDef.Pos.mask',axiom,
    ! [V_24Y] :
      ( cCoq_2ePArith_2eBinPosDef_2ePos_2emask___24t(V_24Y)
    <=> t(V_24Y,cCoq_2ePArith_2eBinPosDef_2ePos_2emask) ) ).

fof('$tdef_$_type_80073',axiom,
    ! [V_24Y] :
      ( c_24__type__80073___24t(V_24Y)
    <=> t(V_24Y,c_24__type__80073) ) ).

fof('$tdef_$_type_113665',axiom,
    ! [V_24Y] :
      ( c_24__type__113665___24t(V_24Y)
    <=> t(V_24Y,c_24__type__113665) ) ).

fof('$tdef_Coq.micromega.RingMicromega.NFormula',axiom,
    ! [V_24X1,V_24Y] :
      ( cCoq_2emicromega_2eRingMicromega_2eNFormula___24t(V_24X1,V_24Y)
    <=> t(V_24Y,cCoq_2emicromega_2eRingMicromega_2eNFormula___24a1(V_24X1)) ) ).

fof('$tdef_$_type_396',axiom,
    ! [V_24Y] :
      ( c_24__type__396___24t(V_24Y)
    <=> t(V_24Y,c_24__type__396) ) ).

fof('$tdef_$_type_82480',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__82480___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__82480___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_76653',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__76653___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__76653___24a1(V_24X1)) ) ).

fof('$tdef_$_type_94744',axiom,
    ! [V_24Y] :
      ( c_24__type__94744___24t(V_24Y)
    <=> t(V_24Y,c_24__type__94744) ) ).

fof('$tdef_PLF.LibTactics.ltac_No_arg',axiom,
    ! [V_24Y] :
      ( cPLF_2eLibTactics_2eltac__No__arg___24t(V_24Y)
    <=> t(V_24Y,cPLF_2eLibTactics_2eltac__No__arg) ) ).

fof('$tdef_$_type_87678',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
      ( c_24__type__87678___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__87678___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).

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_89397',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__89397___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__89397___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

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_83555',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__83555___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__83555___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_83601',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
      ( c_24__type__83601___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
    <=> t(V_24Y,c_24__type__83601___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).

fof('$tdef_$_type_2559',axiom,
    ! [V_24Y] :
      ( c_24__type__2559___24t(V_24Y)
    <=> t(V_24Y,c_24__type__2559) ) ).

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_1141',axiom,
    ! [V_24Y] :
      ( c_24__type__1141___24t(V_24Y)
    <=> t(V_24Y,c_24__type__1141) ) ).

fof('$tdef_$_type_106935',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
      ( c_24__type__106935___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
    <=> t(V_24Y,c_24__type__106935___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).

fof('$tdef_$_type_212688',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__212688___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__212688___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_87223',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__87223___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__87223___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('_HAMMER_GOAL',conjecture,
    ! [V0__ST] :
      ( cPLF_2eReferences_2eSTLCRef_2estore__ty___24t(V0__ST)
     => ! [V1__t] :
          ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V1__t)
         => ! [V2__t_27] :
              ( cPLF_2eReferences_2eSTLCRef_2etm___24t(V2__t_27)
             => ! [V3__T] :
                  ( cPLF_2eReferences_2eSTLCRef_2ety___24t(V3__T)
                 => ! [V4__st] :
                      ( cPLF_2eReferences_2eSTLCRef_2estore___24t(V4__st)
                     => ! [V5__st_27] :
                          ( cPLF_2eReferences_2eSTLCRef_2estore___24t(V5__st_27)
                         => ( cPLF_2eReferences_2eSTLCRef_2ehas__type___24a4(cPLF_2eMaps_2eempty___24a1(cPLF_2eReferences_2eSTLCRef_2ety),V0__ST,V1__t,V3__T)
                           => ( cPLF_2eReferences_2eSTLCRef_2estore__well__typed___24a2(V0__ST,V4__st)
                             => ( cPLF_2eReferences_2eSTLCRef_2estep___24a2(cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cPLF_2eReferences_2eSTLCRef_2estore,V1__t,V4__st),cCoq_2eInit_2eDatatypes_2epair___24a4(cPLF_2eReferences_2eSTLCRef_2etm,cPLF_2eReferences_2eSTLCRef_2estore,V2__t_27,V5__st_27))
                               => ? [V9__ST_27] :
                                    ( cPLF_2eReferences_2eSTLCRef_2estore__ty___24t(V9__ST_27)
                                    & cPLF_2eReferences_2eSTLCRef_2eextends___24a2(V9__ST_27,V0__ST)
                                    & cPLF_2eReferences_2eSTLCRef_2ehas__type___24a4(cPLF_2eMaps_2eempty___24a1(cPLF_2eReferences_2eSTLCRef_2ety),V9__ST_27,V2__t_27,V3__T)
                                    & cPLF_2eReferences_2eSTLCRef_2estore__well__typed___24a2(V9__ST_27,V5__st_27) ) ) ) ) ) ) ) ) ) ) ).

%------------------------------------------------------------------------------