TPTP Problem File: SEV662+1.p

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%------------------------------------------------------------------------------
% File     : SEV662+1 : TPTP v9.3.1. Released v9.3.0.
% Domain   : Set theory
% Problem  : CoqHammer - Norm value  normal
% 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    : Norm.value'.normal.p [Kal26]

% Status   : Unknown
% Rating   : 1.00 v9.3.0
% Syntax   : Number of formulae    : 3097 (1341 unt;   0 def)
%            Number of atoms       : 10676 (3244 equ)
%            Maximal formula atoms :  257 (   3 avg)
%            Number of connectives : 7679 ( 100   ~; 927   |;2449   &)
%                                         (1123 <=>;3080  =>;   0  <=;   0 <~>)
%            Maximal formula depth :  258 (   6 avg)
%            Maximal term depth    :   23 (   1 avg)
%            Number of predicates  :  632 ( 631 usr;   0 prp; 1-23 aty)
%            Number of functors    : 1853 (1853 usr;1230 con; 0-22 aty)
%            Number of variables   : 10094 (8995   !;1099   ?)
% SPC      : FOF_UNK_RFO_SEQ

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

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

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

fof('$_case_Coq.Init.Datatypes.bool$3576',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_243576___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_243576___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = c_24__fix__3546__v__CANONICAL__0___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3) ) ) ) ) ).

fof('$_case_Coq.Init.Datatypes.bool$3843',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_243843___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_243843___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = c_24__fix__3546__v__CANONICAL__0___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3) ) ) ) ) ).

fof('$_case_Coq.Init.Datatypes.bool$43239',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_2443322___24a2(Vv__CANONICAL__3,Vv__CANONICAL__4) = cCoq_2eInit_2eDatatypes_2etrue
            & c_24__case__Coq_2eInit_2eDatatypes_2ebool_2443239___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_2443322___24a2(Vv__CANONICAL__3,Vv__CANONICAL__4) = cCoq_2eInit_2eDatatypes_2efalse
            & c_24__case__Coq_2eInit_2eDatatypes_2ebool_2443239___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$43570',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_2443635___24a2(Vv__CANONICAL__3,Vv__CANONICAL__4) = cCoq_2eInit_2eDatatypes_2etrue
            & c_24__case__Coq_2eInit_2eDatatypes_2ebool_2443570___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_2443635___24a2(Vv__CANONICAL__3,Vv__CANONICAL__4) = cCoq_2eInit_2eDatatypes_2efalse
            & c_24__case__Coq_2eInit_2eDatatypes_2ebool_2443570___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$4574',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_244574___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_244574___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cNorm_2esubst___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3) ) ) ) ) ).

fof('$_case_Coq.Init.Datatypes.list$26705',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_2426792___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_2426705___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__26709] :
                ( t(Vvar__1___24Anonymous__26709,Vv__CANONICAL__0)
                & ? [Vvar__2___24Anonymous__26710] :
                    ( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vvar__2___24Anonymous__26710)
                    & c_24__case__Coq_2eInit_2eDatatypes_2elist_2426792___24a3(Vv__CANONICAL__0,Vv__CANONICAL__4,Vv__CANONICAL__5) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__26709,Vvar__2___24Anonymous__26710)
                    & c_24__case__Coq_2eInit_2eDatatypes_2elist_2426705___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__26709,c_24__fix__26837__v__CANONICAL__1___24a3(Vv__CANONICAL__0,Vvar__2___24Anonymous__26710,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$26792',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_2426792___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__26796] :
              ( t(Vvar__1___24Anonymous__26796,Vv__CANONICAL__0)
              & ? [Vvar__2___24Anonymous__26797] :
                  ( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vvar__2___24Anonymous__26797)
                  & Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__26796,Vvar__2___24Anonymous__26797)
                  & c_24__case__Coq_2eInit_2eDatatypes_2elist_2426792___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__26796,c_24__fix__26837__v__CANONICAL__1___24a3(Vv__CANONICAL__0,Vvar__2___24Anonymous__26797,cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,cCoq_2eInit_2eDatatypes_2enil___24a1(Vv__CANONICAL__0)))) ) ) ) ) ) ).

fof('$_case_Coq.Init.Datatypes.nat$101',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_24101___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vv__CANONICAL__3 )
        | ? [Vvar__0___24Anonymous__102] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__102)
            & Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__102)
            & c_24__case__Coq_2eInit_2eDatatypes_2enat_24101___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2eS___24a1(c_24__fix__120__v__CANONICAL__0___24a2(Vvar__0___24Anonymous__102,Vv__CANONICAL__3)) ) ) ) ).

fof('$_case_Coq.Init.Datatypes.nat$32693',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_2432693___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZ0 )
        | ? [Vvar__0___24Anonymous__32694] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__32694)
            & Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__32694)
            & c_24__case__Coq_2eInit_2eDatatypes_2enat_2432693___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__32694)) ) ) ) ).

fof('$_case_Coq.Init.Datatypes.nat$32715',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_2432715___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZ0 )
        | ? [Vvar__0___24Anonymous__32716] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__32716)
            & Vv__CANONICAL__0 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__32716)
            & c_24__case__Coq_2eInit_2eDatatypes_2enat_2432715___24a1(Vv__CANONICAL__0) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(Vvar__0___24Anonymous__32716)) ) ) ) ).

fof('$_case_Coq.Init.Datatypes.nat$42617',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_2442617___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vv__CANONICAL__3 )
        | ? [Vvar__0___24Anonymous__42618] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__42618)
            & Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__42618)
            & c_24__case__Coq_2eInit_2eDatatypes_2enat_2442617___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2eS___24a1(c_24__fix__120__v__CANONICAL__0___24a2(Vvar__0___24Anonymous__42618,Vv__CANONICAL__3)) ) ) ) ).

fof('$_case_Coq.Init.Datatypes.nat$42757',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_2442757___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = Vv__CANONICAL__4 )
        | ? [Vvar__0___24Anonymous__42758] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__42758)
            & Vv__CANONICAL__3 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__42758)
            & c_24__case__Coq_2eInit_2eDatatypes_2enat_2442757___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cCoq_2eInit_2eDatatypes_2eS___24a1(c_24__fix__120__v__CANONICAL__0___24a2(Vvar__0___24Anonymous__42758,Vv__CANONICAL__4)) ) ) ) ).

fof('$_case_Coq.Init.Datatypes.nat$42879',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_2442879___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = Vv__CANONICAL__3 )
        | ? [Vvar__0___24Anonymous__42880] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__42880)
            & ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__4)
             => ( Vv__CANONICAL__3 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__42880)
                & ( ( Vv__CANONICAL__4 = cCoq_2eInit_2eDatatypes_2eO
                    & c_24__case__Coq_2eInit_2eDatatypes_2enat_2442879___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = Vv__CANONICAL__3 )
                  | ? [Vvar__0___24Anonymous__42892] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__42892)
                      & Vv__CANONICAL__4 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__42892)
                      & c_24__case__Coq_2eInit_2eDatatypes_2enat_2442879___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = c_24__fix__42920__v__CANONICAL__0___24a2(Vvar__0___24Anonymous__42880,Vvar__0___24Anonymous__42892) ) ) ) ) ) ) ) ).

fof('$_case_Coq.Init.Datatypes.nat$42987',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_2442987___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cCoq_2eInit_2eDatatypes_2eO )
        | ? [Vvar__0___24Anonymous__42988] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__42988)
            & Vv__CANONICAL__3 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__42988)
            & c_24__case__Coq_2eInit_2eDatatypes_2enat_2442987___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__43006__v__CANONICAL__0___24a2(Vvar__0___24Anonymous__42988,Vv__CANONICAL__4)) ) ) ) ).

fof('$_case_Coq.Init.Datatypes.nat$43322',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_2443322___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eInit_2eDatatypes_2etrue )
              | ? [Vvar__0___24Anonymous__43323] :
                  ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__43323)
                  & Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__43323)
                  & c_24__case__Coq_2eInit_2eDatatypes_2enat_2443322___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) )
        | ? [Vvar__0___24Anonymous__43324] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__43324)
            & ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
             => ( Vv__CANONICAL__0 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__43324)
                & ( ( Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2eO
                    & c_24__case__Coq_2eInit_2eDatatypes_2enat_2443322___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eInit_2eDatatypes_2efalse )
                  | ? [Vvar__0___24Anonymous__43338] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__43338)
                      & Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__43338)
                      & c_24__case__Coq_2eInit_2eDatatypes_2enat_2443322___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = c_24__fix__43374__v__CANONICAL__0___24a2(Vvar__0___24Anonymous__43324,Vvar__0___24Anonymous__43338) ) ) ) ) ) ) ) ).

fof('$_case_Coq.Init.Datatypes.nat$43635',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_2443635___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eInit_2eDatatypes_2etrue )
        | ? [Vvar__0___24Anonymous__43636] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__43636)
            & ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
             => ( Vv__CANONICAL__0 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__43636)
                & ( ( Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2eO
                    & c_24__case__Coq_2eInit_2eDatatypes_2enat_2443635___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eInit_2eDatatypes_2efalse )
                  | ? [Vvar__0___24Anonymous__43648] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__43648)
                      & Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__43648)
                      & c_24__case__Coq_2eInit_2eDatatypes_2enat_2443635___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = c_24__fix__43676__v__CANONICAL__0___24a2(Vvar__0___24Anonymous__43636,Vvar__0___24Anonymous__43648) ) ) ) ) ) ) ) ).

fof('$_case_Coq.Init.Datatypes.nat$44186',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_2444186___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vv__CANONICAL__3 )
        | ? [Vvar__0___24Anonymous__44187] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__44187)
            & Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__44187)
            & c_24__case__Coq_2eInit_2eDatatypes_2enat_2444186___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2eS___24a1(c_24__fix__120__v__CANONICAL__0___24a2(Vvar__0___24Anonymous__44187,Vv__CANONICAL__3)) ) ) ) ).

fof('$_case_Coq.Init.Datatypes.nat$44295',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_2444295___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vv__CANONICAL__2 )
        | ? [Vvar__0___24Anonymous__44296] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__44296)
            & ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
             => ( Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__44296)
                & ( ( Vv__CANONICAL__3 = cCoq_2eInit_2eDatatypes_2eO
                    & c_24__case__Coq_2eInit_2eDatatypes_2enat_2444295___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vv__CANONICAL__2 )
                  | ? [Vvar__0___24Anonymous__44308] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__44308)
                      & Vv__CANONICAL__3 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__44308)
                      & c_24__case__Coq_2eInit_2eDatatypes_2enat_2444295___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = c_24__fix__42920__v__CANONICAL__0___24a2(Vvar__0___24Anonymous__44296,Vvar__0___24Anonymous__44308) ) ) ) ) ) ) ) ).

fof('$_case_Coq.Init.Datatypes.nat$44389',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_2444389___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2eO )
        | ? [Vvar__0___24Anonymous__44390] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__44390)
            & Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__44390)
            & c_24__case__Coq_2eInit_2eDatatypes_2enat_2444389___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eNat_2eadd___24a2(Vv__CANONICAL__3,c_24__fix__43006__v__CANONICAL__0___24a2(Vvar__0___24Anonymous__44390,Vv__CANONICAL__3)) ) ) ) ).

fof('$_case_Coq.Init.Datatypes.nat$44509',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_2444509___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vv__CANONICAL__3 )
        | ? [Vvar__0___24Anonymous__44510] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__44510)
            & Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__44510)
            & c_24__case__Coq_2eInit_2eDatatypes_2enat_2444509___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2eS___24a1(c_24__fix__120__v__CANONICAL__0___24a2(Vvar__0___24Anonymous__44510,Vv__CANONICAL__3)) ) ) ) ).

fof('$_case_Coq.Init.Datatypes.nat$45138',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_2445138___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vv__CANONICAL__3 )
        | ? [Vvar__0___24Anonymous__45139] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__45139)
            & Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__45139)
            & c_24__case__Coq_2eInit_2eDatatypes_2enat_2445138___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2eS___24a1(c_24__fix__120__v__CANONICAL__0___24a2(Vvar__0___24Anonymous__45139,Vv__CANONICAL__3)) ) ) ) ).

fof('$_case_Coq.Init.Datatypes.nat$45247',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_2445247___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vv__CANONICAL__2 )
        | ? [Vvar__0___24Anonymous__45248] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__45248)
            & ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
             => ( Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__45248)
                & ( ( Vv__CANONICAL__3 = cCoq_2eInit_2eDatatypes_2eO
                    & c_24__case__Coq_2eInit_2eDatatypes_2enat_2445247___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vv__CANONICAL__2 )
                  | ? [Vvar__0___24Anonymous__45260] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__45260)
                      & Vv__CANONICAL__3 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__45260)
                      & c_24__case__Coq_2eInit_2eDatatypes_2enat_2445247___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = c_24__fix__42920__v__CANONICAL__0___24a2(Vvar__0___24Anonymous__45248,Vvar__0___24Anonymous__45260) ) ) ) ) ) ) ) ).

fof('$_case_Coq.Init.Datatypes.nat$45341',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_2445341___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2eO )
        | ? [Vvar__0___24Anonymous__45342] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__45342)
            & Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__45342)
            & c_24__case__Coq_2eInit_2eDatatypes_2enat_2445341___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eNat_2eadd___24a2(Vv__CANONICAL__3,c_24__fix__43006__v__CANONICAL__0___24a2(Vvar__0___24Anonymous__45342,Vv__CANONICAL__3)) ) ) ) ).

fof('$_case_Coq.Init.Datatypes.nat$45451',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_2445451___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vv__CANONICAL__3 )
        | ? [Vvar__0___24Anonymous__45452] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__45452)
            & Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__45452)
            & c_24__case__Coq_2eInit_2eDatatypes_2enat_2445451___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2eS___24a1(c_24__fix__120__v__CANONICAL__0___24a2(Vvar__0___24Anonymous__45452,Vv__CANONICAL__3)) ) ) ) ).

fof('$_case_Coq.Init.Datatypes.nat$45560',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_2445560___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vv__CANONICAL__2 )
        | ? [Vvar__0___24Anonymous__45561] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__45561)
            & ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
             => ( Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__45561)
                & ( ( Vv__CANONICAL__3 = cCoq_2eInit_2eDatatypes_2eO
                    & c_24__case__Coq_2eInit_2eDatatypes_2enat_2445560___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vv__CANONICAL__2 )
                  | ? [Vvar__0___24Anonymous__45573] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__45573)
                      & Vv__CANONICAL__3 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__45573)
                      & c_24__case__Coq_2eInit_2eDatatypes_2enat_2445560___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = c_24__fix__42920__v__CANONICAL__0___24a2(Vvar__0___24Anonymous__45561,Vvar__0___24Anonymous__45573) ) ) ) ) ) ) ) ).

fof('$_case_Coq.Init.Datatypes.nat$45654',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_2445654___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2eO )
        | ? [Vvar__0___24Anonymous__45655] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__45655)
            & Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__45655)
            & c_24__case__Coq_2eInit_2eDatatypes_2enat_2445654___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eNat_2eadd___24a2(Vv__CANONICAL__3,c_24__fix__43006__v__CANONICAL__0___24a2(Vvar__0___24Anonymous__45655,Vv__CANONICAL__3)) ) ) ) ).

fof('$_case_Coq.Init.Datatypes.prod$15423',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8] :
      ( cType___24t(Vv__CANONICAL__0)
     => ( cType___24t(Vv__CANONICAL__2)
       => ( c_24__type__15436___24t(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__6)
         => ( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
           => ( t(Vv__CANONICAL__8,Vv__CANONICAL__2)
             => ? [Vvar__2___24Anonymous__15428] :
                  ( t(Vvar__2___24Anonymous__15428,Vv__CANONICAL__2)
                  & ? [Vvar__3___24Anonymous__15429] :
                      ( t(Vvar__3___24Anonymous__15429,Vv__CANONICAL__2)
                      & happ(happ(Vv__CANONICAL__6,Vv__CANONICAL__7),Vv__CANONICAL__8) = cCoq_2eInit_2eDatatypes_2epair___24a4(Vv__CANONICAL__2,Vv__CANONICAL__2,Vvar__2___24Anonymous__15428,Vvar__3___24Anonymous__15429)
                      & ( c_24__case__Coq_2eInit_2eDatatypes_2eprod_2415423___24a9(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8)
                      <=> p(happ(happ(Vv__CANONICAL__1,happ(Vv__CANONICAL__5,Vv__CANONICAL__7)),happ(Vv__CANONICAL__5,happ(happ(Vv__CANONICAL__3,happ(happ(Vv__CANONICAL__4,Vv__CANONICAL__8),Vvar__2___24Anonymous__15428)),Vvar__3___24Anonymous__15429)))) ) ) ) ) ) ) ) ) ).

fof('$_case_Coq.Numbers.BinNums.Z$32710',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_2432715___24a1(Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZ0
          & c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2432710___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZ0 )
        | ? [Vvar__0___24Anonymous__32711] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__32711)
            & c_24__case__Coq_2eInit_2eDatatypes_2enat_2432715___24a1(Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__32711)
            & c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2432710___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__32711) )
        | ? [Vvar__0___24Anonymous__32712] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__32712)
            & c_24__case__Coq_2eInit_2eDatatypes_2enat_2432715___24a1(Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__32712)
            & c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2432710___24a3(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__32712) ) ) ) ).

fof('$_case_Coq.Numbers.BinNums.positive$35167',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
     => ( ? [Vvar__0___24Anonymous__35168] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35168)
            & Vv__CANONICAL__1 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__35168)
            & c_24__case__Coq_2eNumbers_2eBinNums_2epositive_2435167___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2exO___24a1(c_24__fix__35183__v__CANONICAL__0___24a1(Vvar__0___24Anonymous__35168)) )
        | ? [Vvar__0___24Anonymous__35175] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35175)
            & Vv__CANONICAL__1 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__35175)
            & c_24__case__Coq_2eNumbers_2eBinNums_2epositive_2435167___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__35175) )
        | ( Vv__CANONICAL__1 = cCoq_2eNumbers_2eBinNums_2exH
          & c_24__case__Coq_2eNumbers_2eBinNums_2epositive_2435167___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ) ) ).

fof('$_case_Norm.tm$2929',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4] :
      ( cNorm_2etm___24t(Vv__CANONICAL__3)
     => ( ? [Vvar__0___24Anonymous__2930] :
            ( cCoq_2eStrings_2eString_2estring___24t(Vvar__0___24Anonymous__2930)
            & ( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__2)
             => ( cCoq_2eStrings_2eString_2estring___24t(Vvar__0___24Anonymous__2930)
               => ( Vv__CANONICAL__3 = cNorm_2evar___24a1(Vvar__0___24Anonymous__2930)
                  & ( ( cPLF_2eMaps_2eeqb__string___24a2(Vv__CANONICAL__2,Vvar__0___24Anonymous__2930) = cCoq_2eInit_2eDatatypes_2etrue
                      & c_24__case__Norm_2etm_242929___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__2930) = cCoq_2eInit_2eDatatypes_2efalse
                      & c_24__case__Norm_2etm_242929___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = Vv__CANONICAL__3 ) ) ) ) ) )
        | ? [Vvar__0___24Anonymous__2932] :
            ( cNorm_2etm___24t(Vvar__0___24Anonymous__2932)
            & ? [Vvar__1___24Anonymous__2933] :
                ( cNorm_2etm___24t(Vvar__1___24Anonymous__2933)
                & Vv__CANONICAL__3 = cNorm_2eapp___24a2(Vvar__0___24Anonymous__2932,Vvar__1___24Anonymous__2933)
                & c_24__case__Norm_2etm_242929___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cNorm_2eapp___24a2(c_24__fix__3546__v__CANONICAL__0___24a3(Vv__CANONICAL__2,Vv__CANONICAL__4,Vvar__0___24Anonymous__2932),c_24__fix__3546__v__CANONICAL__0___24a3(Vv__CANONICAL__2,Vv__CANONICAL__4,Vvar__1___24Anonymous__2933)) ) )
        | ? [Vvar__0___24Anonymous__3027] :
            ( cCoq_2eStrings_2eString_2estring___24t(Vvar__0___24Anonymous__3027)
            & ? [Vvar__1___24Anonymous__3028] :
                ( cNorm_2ety___24t(Vvar__1___24Anonymous__3028)
                & ? [Vvar__2___24Anonymous__3029] :
                    ( cNorm_2etm___24t(Vvar__2___24Anonymous__3029)
                    & Vv__CANONICAL__3 = cNorm_2eabs___24a3(Vvar__0___24Anonymous__3027,Vvar__1___24Anonymous__3028,Vvar__2___24Anonymous__3029)
                    & c_24__case__Norm_2etm_242929___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cNorm_2eabs___24a3(Vvar__0___24Anonymous__3027,Vvar__1___24Anonymous__3028,c_24__case__Coq_2eInit_2eDatatypes_2ebool_243843___24a4(Vv__CANONICAL__2,Vv__CANONICAL__4,Vvar__0___24Anonymous__3027,Vvar__2___24Anonymous__3029)) ) ) )
        | ? [Vvar__0___24Anonymous__3105] :
            ( cNorm_2etm___24t(Vvar__0___24Anonymous__3105)
            & ? [Vvar__1___24Anonymous__3106] :
                ( cNorm_2etm___24t(Vvar__1___24Anonymous__3106)
                & Vv__CANONICAL__3 = cNorm_2epair___24a2(Vvar__0___24Anonymous__3105,Vvar__1___24Anonymous__3106)
                & c_24__case__Norm_2etm_242929___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cNorm_2epair___24a2(c_24__fix__3546__v__CANONICAL__0___24a3(Vv__CANONICAL__2,Vv__CANONICAL__4,Vvar__0___24Anonymous__3105),c_24__fix__3546__v__CANONICAL__0___24a3(Vv__CANONICAL__2,Vv__CANONICAL__4,Vvar__1___24Anonymous__3106)) ) )
        | ? [Vvar__0___24Anonymous__3200] :
            ( cNorm_2etm___24t(Vvar__0___24Anonymous__3200)
            & Vv__CANONICAL__3 = cNorm_2efst___24a1(Vvar__0___24Anonymous__3200)
            & c_24__case__Norm_2etm_242929___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cNorm_2efst___24a1(c_24__fix__3546__v__CANONICAL__0___24a3(Vv__CANONICAL__2,Vv__CANONICAL__4,Vvar__0___24Anonymous__3200)) )
        | ? [Vvar__0___24Anonymous__3224] :
            ( cNorm_2etm___24t(Vvar__0___24Anonymous__3224)
            & Vv__CANONICAL__3 = cNorm_2esnd___24a1(Vvar__0___24Anonymous__3224)
            & c_24__case__Norm_2etm_242929___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cNorm_2esnd___24a1(c_24__fix__3546__v__CANONICAL__0___24a3(Vv__CANONICAL__2,Vv__CANONICAL__4,Vvar__0___24Anonymous__3224)) )
        | ( Vv__CANONICAL__3 = cNorm_2etru
          & c_24__case__Norm_2etm_242929___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cNorm_2etru )
        | ( Vv__CANONICAL__3 = cNorm_2efls
          & c_24__case__Norm_2etm_242929___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cNorm_2efls )
        | ? [Vvar__0___24Anonymous__3248] :
            ( cNorm_2etm___24t(Vvar__0___24Anonymous__3248)
            & ? [Vvar__1___24Anonymous__3249] :
                ( cNorm_2etm___24t(Vvar__1___24Anonymous__3249)
                & ? [Vvar__2___24Anonymous__3250] :
                    ( cNorm_2etm___24t(Vvar__2___24Anonymous__3250)
                    & Vv__CANONICAL__3 = cNorm_2etest___24a3(Vvar__0___24Anonymous__3248,Vvar__1___24Anonymous__3249,Vvar__2___24Anonymous__3250)
                    & c_24__case__Norm_2etm_242929___24a5(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4) = cNorm_2etest___24a3(c_24__fix__3546__v__CANONICAL__0___24a3(Vv__CANONICAL__2,Vv__CANONICAL__4,Vvar__0___24Anonymous__3248),c_24__fix__3546__v__CANONICAL__0___24a3(Vv__CANONICAL__2,Vv__CANONICAL__4,Vvar__1___24Anonymous__3249),c_24__fix__3546__v__CANONICAL__0___24a3(Vv__CANONICAL__2,Vv__CANONICAL__4,Vvar__2___24Anonymous__3250)) ) ) ) ) ) ).

fof('$_def_$_let_var_6_p_32780_32783',axiom,
    ! [V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__32779] : c_24__let__var__6__p__32780__32783___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__32779) = cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__32779) ).

fof('$_def_$_let_var_6_p_32782_32784',axiom,
    ! [V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__32781] : c_24__let__var__6__p__32782__32784___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__32781) = cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__32781) ).

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__31142] :
                  ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__31142)
                  & V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__31142)
                  & ( cCoq_2eArith_2eEqNat_2eeq__nat___24a2(V1__n,V2__m)
                  <=> p(c_24False) ) ) ) ) )
        | ? [Vvar__0___24Anonymous__31143] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__31143)
            & ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
             => ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__31143)
                & ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
                    & ( cCoq_2eArith_2eEqNat_2eeq__nat___24a2(V1__n,V2__m)
                    <=> p(c_24False) ) )
                  | ? [Vvar__0___24Anonymous__31146] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__31146)
                      & V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__31146)
                      & ( cCoq_2eArith_2eEqNat_2eeq__nat___24a2(V1__n,V2__m)
                      <=> cCoq_2eArith_2eEqNat_2eeq__nat___24a2(Vvar__0___24Anonymous__31143,Vvar__0___24Anonymous__31146) ) ) ) ) ) ) ) ) ).

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

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

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

fof('$_def_Coq.Arith.PeanoNat.Nat.eqf',axiom,
    ! [V0__f,V1__g] :
      ( cCoq_2eArith_2ePeanoNat_2eNat_2eeqf___24a2(V0__f,V1__g)
    <=> ! [V2__n] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
         => happ(V0__f,V2__n) = happ(V1__g,V2__n) ) ) ).

fof('$_def_Coq.Arith.PeanoNat.Nat.le',axiom,
    cCoq_2eArith_2ePeanoNat_2eNat_2ele = cCoq_2eInit_2ePeano_2ele ).

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

fof('$_def_Coq.Arith.PeanoNat.Nat.recursion',axiom,
    ! [V0__A] : cCoq_2eArith_2ePeanoNat_2eNat_2erecursion___24a1(V0__A) = cCoq_2eInit_2eDatatypes_2enat__rect___24a1(c_24__lam__44570___24a1(V0__A)) ).

fof('$_def_Coq.Arith.Plus.tail_plus',axiom,
    ! [V1__n,V2__m] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
     => ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
          & cCoq_2eArith_2ePlus_2etail__plus___24a2(V1__n,V2__m) = V2__m )
        | ? [Vvar__0___24Anonymous__36434] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__36434)
            & V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__36434)
            & cCoq_2eArith_2ePlus_2etail__plus___24a2(V1__n,V2__m) = cCoq_2eArith_2ePlus_2etail__plus___24a2(Vvar__0___24Anonymous__36434,cCoq_2eInit_2eDatatypes_2eS___24a1(V2__m)) ) ) ) ).

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

fof('$_def_Coq.Bool.Bool.Is_true',axiom,
    ! [V0__b] :
      ( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
     => ( ( V0__b = cCoq_2eInit_2eDatatypes_2etrue
          & ( cCoq_2eBool_2eBool_2eIs__true___24a1(V0__b)
          <=> p(c_24True) ) )
        | ( V0__b = cCoq_2eInit_2eDatatypes_2efalse
          & ( cCoq_2eBool_2eBool_2eIs__true___24a1(V0__b)
          <=> p(c_24False) ) ) ) ) ).

fof('$_def_Coq.Bool.Bool.eqb',axiom,
    ! [V0__b1,V1__b2] :
      ( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b1)
     => ( ( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__b2)
         => ( V0__b1 = cCoq_2eInit_2eDatatypes_2etrue
            & ( ( V1__b2 = cCoq_2eInit_2eDatatypes_2etrue
                & cCoq_2eBool_2eBool_2eeqb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2etrue )
              | ( V1__b2 = cCoq_2eInit_2eDatatypes_2efalse
                & cCoq_2eBool_2eBool_2eeqb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) )
        | ( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__b2)
         => ( V0__b1 = cCoq_2eInit_2eDatatypes_2efalse
            & ( ( V1__b2 = cCoq_2eInit_2eDatatypes_2etrue
                & cCoq_2eBool_2eBool_2eeqb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2efalse )
              | ( V1__b2 = cCoq_2eInit_2eDatatypes_2efalse
                & cCoq_2eBool_2eBool_2eeqb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) ) ) ).

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

fof('$_def_Coq.Bool.Bvector.Bvector',axiom,
    cCoq_2eBool_2eBvector_2eBvector = cCoq_2eVectors_2eVectorDef_2et___24a1(cCoq_2eInit_2eDatatypes_2ebool) ).

fof('$_def_Coq.Bool.Zerob.zerob',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => ( ( V0__n = cCoq_2eInit_2eDatatypes_2eO
          & cCoq_2eBool_2eZerob_2ezerob___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2etrue )
        | ? [Vvar__0___24Anonymous__44097] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__44097)
            & V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__44097)
            & cCoq_2eBool_2eZerob_2ezerob___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ).

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

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

fof('$_def_Coq.FSets.FSetPositive.PositiveSet.elt',axiom,
    ! [Vvar__7348] :
      ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vvar__7348)
    <=> cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__7348) ) ).

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

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

fof('$_def_Coq.FSets.FSetPositive.PositiveSet.mem',axiom,
    ! [V1__i,V2__m] :
      ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(V2__m)
     => ( ( V2__m = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf
          & cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V1__i,V2__m) = cCoq_2eInit_2eDatatypes_2efalse )
        | ? [Vvar__0___24Anonymous__30015] :
            ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__0___24Anonymous__30015)
            & ? [Vvar__1___24Anonymous__30016] :
                ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__30016)
                & ? [Vvar__2___24Anonymous__30017] :
                    ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__2___24Anonymous__30017)
                    & ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V1__i)
                     => ( V2__m = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__30015,Vvar__1___24Anonymous__30016,Vvar__2___24Anonymous__30017)
                        & ( ? [Vvar__0___24Anonymous__30030] :
                              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30030)
                              & V1__i = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__30030)
                              & cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V1__i,V2__m) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(Vvar__0___24Anonymous__30030,Vvar__2___24Anonymous__30017) )
                          | ? [Vvar__0___24Anonymous__30031] :
                              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30031)
                              & V1__i = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__30031)
                              & cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V1__i,V2__m) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(Vvar__0___24Anonymous__30031,Vvar__0___24Anonymous__30015) )
                          | ( V1__i = cCoq_2eNumbers_2eBinNums_2exH
                            & cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V1__i,V2__m) = Vvar__1___24Anonymous__30016 ) ) ) ) ) ) ) ) ) ).

fof('$_def_Coq.FSets.FSetPositive.PositiveSet.t',axiom,
    ! [Vvar__7349] :
      ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__7349)
    <=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__7349) ) ).

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

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

fof('$_def_Coq.Init.Datatypes.ID',axiom,
    ! [Vvar__31105] :
      ( cCoq_2eInit_2eDatatypes_2eID___24t(Vvar__31105)
    <=> ! [V0__A] :
          ( cType___24t(V0__A)
         => ! [V1___24Anonymous] :
              ( t(V1___24Anonymous,V0__A)
             => t(happ(happ(Vvar__31105,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__7482] :
              ( t(Vvar__1___24Anonymous__7482,V0__A)
              & ? [Vvar__2___24Anonymous__7483] :
                  ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__7483)
                  & V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__7482,Vvar__2___24Anonymous__7483)
                  & cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,V2__l,V3__m) = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__7482,cCoq_2eInit_2eDatatypes_2eapp___24a3(V0__A,Vvar__2___24Anonymous__7483,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__35328] :
              ( t(Vvar__2___24Anonymous__35328,V0__A)
              & ? [Vvar__3___24Anonymous__35329] :
                  ( t(Vvar__3___24Anonymous__35329,V1__B)
                  & V2__p = cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V1__B,Vvar__2___24Anonymous__35328,Vvar__3___24Anonymous__35329)
                  & cCoq_2eInit_2eDatatypes_2efst___24a3(V0__A,V1__B,V2__p) = Vvar__2___24Anonymous__35328 ) ) ) ) ) ).

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

fof('$_def_Coq.Init.Datatypes.implb',axiom,
    ! [V0__b1,V1__b2] :
      ( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b1)
     => ( ( V0__b1 = cCoq_2eInit_2eDatatypes_2etrue
          & cCoq_2eInit_2eDatatypes_2eimplb___24a2(V0__b1,V1__b2) = V1__b2 )
        | ( V0__b1 = cCoq_2eInit_2eDatatypes_2efalse
          & cCoq_2eInit_2eDatatypes_2eimplb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ).

fof('$_def_Coq.Init.Datatypes.length',axiom,
    ! [V0__A,V2__l] :
      ( cType___24t(V0__A)
     => ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
       => ( ( V2__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
            & cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__l) = cCoq_2eInit_2eDatatypes_2eO )
          | ? [Vvar__1___24Anonymous__23766] :
              ( t(Vvar__1___24Anonymous__23766,V0__A)
              & ? [Vvar__2___24Anonymous__23767] :
                  ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__23767)
                  & V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__23766,Vvar__2___24Anonymous__23767)
                  & cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,V2__l) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2elength___24a2(V0__A,Vvar__2___24Anonymous__23767)) ) ) ) ) ) ).

fof('$_def_Coq.Init.Datatypes.nat_rect',axiom,
    ! [V0__P,V1__f,V2__f,V4__n] :
      ( c_24__type__35299___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__35297] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__35297)
              & V4__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__35297)
              & cCoq_2eInit_2eDatatypes_2enat__rect___24a4(V0__P,V1__f,V2__f,V4__n) = happ(happ(V2__f,Vvar__0___24Anonymous__35297),cCoq_2eInit_2eDatatypes_2enat__rect___24a4(V0__P,V1__f,V2__f,Vvar__0___24Anonymous__35297)) ) ) ) ) ).

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

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

fof('$_def_Coq.Init.Datatypes.snd',axiom,
    ! [V0__A,V1__B,V2__p] :
      ( cType___24t(V0__A)
     => ( cType___24t(V1__B)
       => ( cCoq_2eInit_2eDatatypes_2eprod___24t(V0__A,V1__B,V2__p)
         => ? [Vvar__2___24Anonymous__35340] :
              ( t(Vvar__2___24Anonymous__35340,V0__A)
              & ? [Vvar__3___24Anonymous__35341] :
                  ( t(Vvar__3___24Anonymous__35341,V1__B)
                  & V2__p = cCoq_2eInit_2eDatatypes_2epair___24a4(V0__A,V1__B,Vvar__2___24Anonymous__35340,Vvar__3___24Anonymous__35341)
                  & cCoq_2eInit_2eDatatypes_2esnd___24a3(V0__A,V1__B,V2__p) = Vvar__3___24Anonymous__35341 ) ) ) ) ) ).

fof('$_def_Coq.Init.Datatypes.xorb',axiom,
    ! [V0__b1,V1__b2] :
      ( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b1)
     => ( ( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__b2)
         => ( V0__b1 = cCoq_2eInit_2eDatatypes_2etrue
            & ( ( V1__b2 = cCoq_2eInit_2eDatatypes_2etrue
                & cCoq_2eInit_2eDatatypes_2exorb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2efalse )
              | ( V1__b2 = cCoq_2eInit_2eDatatypes_2efalse
                & cCoq_2eInit_2eDatatypes_2exorb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) )
        | ( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__b2)
         => ( V0__b1 = cCoq_2eInit_2eDatatypes_2efalse
            & ( ( V1__b2 = cCoq_2eInit_2eDatatypes_2etrue
                & cCoq_2eInit_2eDatatypes_2exorb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2etrue )
              | ( V1__b2 = cCoq_2eInit_2eDatatypes_2efalse
                & cCoq_2eInit_2eDatatypes_2exorb___24a2(V0__b1,V1__b2) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ).

fof('$_def_Coq.Init.Decimal.int_of_int',axiom,
    ! [V0__i] : cCoq_2eInit_2eDecimal_2eint__of__int___24a1(V0__i) = V0__i ).

fof('$_def_Coq.Init.Decimal.nzhead',axiom,
    ! [V1__d] :
      ( cCoq_2eInit_2eDecimal_2euint___24t(V1__d)
     => ( ( V1__d = cCoq_2eInit_2eDecimal_2eNil
          & cCoq_2eInit_2eDecimal_2enzhead___24a1(V1__d) = V1__d )
        | ? [Vvar__0___24Anonymous__35351] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__35351)
            & V1__d = cCoq_2eInit_2eDecimal_2eD0___24a1(Vvar__0___24Anonymous__35351)
            & cCoq_2eInit_2eDecimal_2enzhead___24a1(V1__d) = cCoq_2eInit_2eDecimal_2enzhead___24a1(Vvar__0___24Anonymous__35351) )
        | ? [Vvar__0___24Anonymous__35352] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__35352)
            & V1__d = cCoq_2eInit_2eDecimal_2eD1___24a1(Vvar__0___24Anonymous__35352)
            & cCoq_2eInit_2eDecimal_2enzhead___24a1(V1__d) = V1__d )
        | ? [Vvar__0___24Anonymous__35353] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__35353)
            & V1__d = cCoq_2eInit_2eDecimal_2eD2___24a1(Vvar__0___24Anonymous__35353)
            & cCoq_2eInit_2eDecimal_2enzhead___24a1(V1__d) = V1__d )
        | ? [Vvar__0___24Anonymous__35354] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__35354)
            & V1__d = cCoq_2eInit_2eDecimal_2eD3___24a1(Vvar__0___24Anonymous__35354)
            & cCoq_2eInit_2eDecimal_2enzhead___24a1(V1__d) = V1__d )
        | ? [Vvar__0___24Anonymous__35355] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__35355)
            & V1__d = cCoq_2eInit_2eDecimal_2eD4___24a1(Vvar__0___24Anonymous__35355)
            & cCoq_2eInit_2eDecimal_2enzhead___24a1(V1__d) = V1__d )
        | ? [Vvar__0___24Anonymous__35356] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__35356)
            & V1__d = cCoq_2eInit_2eDecimal_2eD5___24a1(Vvar__0___24Anonymous__35356)
            & cCoq_2eInit_2eDecimal_2enzhead___24a1(V1__d) = V1__d )
        | ? [Vvar__0___24Anonymous__35357] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__35357)
            & V1__d = cCoq_2eInit_2eDecimal_2eD6___24a1(Vvar__0___24Anonymous__35357)
            & cCoq_2eInit_2eDecimal_2enzhead___24a1(V1__d) = V1__d )
        | ? [Vvar__0___24Anonymous__35358] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__35358)
            & V1__d = cCoq_2eInit_2eDecimal_2eD7___24a1(Vvar__0___24Anonymous__35358)
            & cCoq_2eInit_2eDecimal_2enzhead___24a1(V1__d) = V1__d )
        | ? [Vvar__0___24Anonymous__35359] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__35359)
            & V1__d = cCoq_2eInit_2eDecimal_2eD8___24a1(Vvar__0___24Anonymous__35359)
            & cCoq_2eInit_2eDecimal_2enzhead___24a1(V1__d) = V1__d )
        | ? [Vvar__0___24Anonymous__35360] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__35360)
            & V1__d = cCoq_2eInit_2eDecimal_2eD9___24a1(Vvar__0___24Anonymous__35360)
            & cCoq_2eInit_2eDecimal_2enzhead___24a1(V1__d) = V1__d ) ) ) ).

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

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

fof('$_def_Coq.Init.Nat.add',axiom,
    ! [V1__n,V2__m] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
     => ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
          & cCoq_2eInit_2eNat_2eadd___24a2(V1__n,V2__m) = V2__m )
        | ? [Vvar__0___24Anonymous__7] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__7)
            & V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__7)
            & cCoq_2eInit_2eNat_2eadd___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2eadd___24a2(Vvar__0___24Anonymous__7,V2__m)) ) ) ) ).

fof('$_def_Coq.Init.Nat.compare',axiom,
    ! [V1__n,V2__m] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
     => ( ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
         => ( V1__n = cCoq_2eInit_2eDatatypes_2eO
            & ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
                & cCoq_2eInit_2eNat_2ecompare___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eEq )
              | ? [Vvar__0___24Anonymous__25829] :
                  ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__25829)
                  & V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__25829)
                  & cCoq_2eInit_2eNat_2ecompare___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eLt ) ) ) )
        | ? [Vvar__0___24Anonymous__25830] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__25830)
            & ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
             => ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__25830)
                & ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
                    & cCoq_2eInit_2eNat_2ecompare___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eGt )
                  | ? [Vvar__0___24Anonymous__25833] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__25833)
                      & V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__25833)
                      & cCoq_2eInit_2eNat_2ecompare___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2ecompare___24a2(Vvar__0___24Anonymous__25830,Vvar__0___24Anonymous__25833) ) ) ) ) ) ) ) ).

fof('$_def_Coq.Init.Nat.div2',axiom,
    ! [V1__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
     => ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
          & cCoq_2eInit_2eNat_2ediv2___24a1(V1__n) = cCoq_2eInit_2eDatatypes_2eO )
        | ? [Vvar__0___24Anonymous__35882] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__35882)
            & ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__35882)
             => ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__35882)
                & ( ( Vvar__0___24Anonymous__35882 = cCoq_2eInit_2eDatatypes_2eO
                    & cCoq_2eInit_2eNat_2ediv2___24a1(V1__n) = cCoq_2eInit_2eDatatypes_2eO )
                  | ? [Vvar__0___24Anonymous__35885] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__35885)
                      & Vvar__0___24Anonymous__35882 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__35885)
                      & cCoq_2eInit_2eNat_2ediv2___24a1(V1__n) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2ediv2___24a1(Vvar__0___24Anonymous__35885)) ) ) ) ) ) ) ) ).

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

fof('$_def_Coq.Init.Nat.eqb',axiom,
    ! [V1__n,V2__m] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
     => ( ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
         => ( V1__n = cCoq_2eInit_2eDatatypes_2eO
            & ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
                & cCoq_2eInit_2eNat_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2etrue )
              | ? [Vvar__0___24Anonymous__35846] :
                  ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__35846)
                  & V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__35846)
                  & cCoq_2eInit_2eNat_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) )
        | ? [Vvar__0___24Anonymous__35847] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__35847)
            & ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
             => ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__35847)
                & ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
                    & cCoq_2eInit_2eNat_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse )
                  | ? [Vvar__0___24Anonymous__35850] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__35850)
                      & V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__35850)
                      & cCoq_2eInit_2eNat_2eeqb___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2eeqb___24a2(Vvar__0___24Anonymous__35847,Vvar__0___24Anonymous__35850) ) ) ) ) ) ) ) ).

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__35859] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__35859)
            & ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__35859)
             => ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__35859)
                & ( ( Vvar__0___24Anonymous__35859 = cCoq_2eInit_2eDatatypes_2eO
                    & cCoq_2eInit_2eNat_2eeven___24a1(V1__n) = cCoq_2eInit_2eDatatypes_2efalse )
                  | ? [Vvar__0___24Anonymous__35862] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__35862)
                      & Vvar__0___24Anonymous__35859 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__35862)
                      & cCoq_2eInit_2eNat_2eeven___24a1(V1__n) = cCoq_2eInit_2eNat_2eeven___24a1(Vvar__0___24Anonymous__35862) ) ) ) ) ) ) ) ).

fof('$_def_Coq.Init.Nat.leb',axiom,
    ! [V1__n,V2__m] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
     => ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
          & cCoq_2eInit_2eNat_2eleb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2etrue )
        | ? [Vvar__0___24Anonymous__25821] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__25821)
            & ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
             => ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__25821)
                & ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
                    & cCoq_2eInit_2eNat_2eleb___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse )
                  | ? [Vvar__0___24Anonymous__25824] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__25824)
                      & V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__25824)
                      & cCoq_2eInit_2eNat_2eleb___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2eleb___24a2(Vvar__0___24Anonymous__25821,Vvar__0___24Anonymous__25824) ) ) ) ) ) ) ) ).

fof('$_def_Coq.Init.Nat.log2_iter',axiom,
    ! [V1__k,V2__p,V3__q,V4__r] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__k)
     => ( ( V1__k = cCoq_2eInit_2eDatatypes_2eO
          & cCoq_2eInit_2eNat_2elog2__iter___24a4(V1__k,V2__p,V3__q,V4__r) = V2__p )
        | ? [Vvar__0___24Anonymous__35869] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__35869)
            & ( cCoq_2eInit_2eDatatypes_2enat___24t(V4__r)
             => ( V1__k = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__35869)
                & ( ( V4__r = cCoq_2eInit_2eDatatypes_2eO
                    & cCoq_2eInit_2eNat_2elog2__iter___24a4(V1__k,V2__p,V3__q,V4__r) = cCoq_2eInit_2eNat_2elog2__iter___24a4(Vvar__0___24Anonymous__35869,cCoq_2eInit_2eDatatypes_2eS___24a1(V2__p),cCoq_2eInit_2eDatatypes_2eS___24a1(V3__q),V3__q) )
                  | ? [Vvar__0___24Anonymous__35872] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__35872)
                      & V4__r = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__35872)
                      & cCoq_2eInit_2eNat_2elog2__iter___24a4(V1__k,V2__p,V3__q,V4__r) = cCoq_2eInit_2eNat_2elog2__iter___24a4(Vvar__0___24Anonymous__35869,V2__p,cCoq_2eInit_2eDatatypes_2eS___24a1(V3__q),Vvar__0___24Anonymous__35872) ) ) ) ) ) ) ) ).

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__32438] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__32438)
            & ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
             => ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__32438)
                & ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
                    & cCoq_2eInit_2eNat_2emax___24a2(V1__n,V2__m) = V1__n )
                  | ? [Vvar__0___24Anonymous__32441] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__32441)
                      & V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__32441)
                      & cCoq_2eInit_2eNat_2emax___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2emax___24a2(Vvar__0___24Anonymous__32438,Vvar__0___24Anonymous__32441)) ) ) ) ) ) ) ) ).

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__35853] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__35853)
            & ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
             => ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__35853)
                & ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
                    & cCoq_2eInit_2eNat_2emin___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eO )
                  | ? [Vvar__0___24Anonymous__35856] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__35856)
                      & V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__35856)
                      & cCoq_2eInit_2eNat_2emin___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2emin___24a2(Vvar__0___24Anonymous__35853,Vvar__0___24Anonymous__35856)) ) ) ) ) ) ) ) ).

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__5496] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__5496)
            & V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__5496)
            & cCoq_2eInit_2eNat_2emul___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2eadd___24a2(V2__m,cCoq_2eInit_2eNat_2emul___24a2(Vvar__0___24Anonymous__5496,V2__m)) ) ) ) ).

fof('$_def_Coq.Init.Nat.pow',axiom,
    ! [V1__n,V2__m] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
     => ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
          & cCoq_2eInit_2eNat_2epow___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO) )
        | ? [Vvar__0___24Anonymous__5499] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__5499)
            & V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__5499)
            & cCoq_2eInit_2eNat_2epow___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2emul___24a2(V1__n,cCoq_2eInit_2eNat_2epow___24a2(V1__n,Vvar__0___24Anonymous__5499)) ) ) ) ).

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__32436] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__32436)
            & V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__32436)
            & cCoq_2eInit_2eNat_2epred___24a1(V0__n) = Vvar__0___24Anonymous__32436 ) ) ) ).

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

fof('$_def_Coq.Init.Nat.sub',axiom,
    ! [V1__n,V2__m] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
     => ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
          & cCoq_2eInit_2eNat_2esub___24a2(V1__n,V2__m) = V1__n )
        | ? [Vvar__0___24Anonymous__30894] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__30894)
            & ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
             => ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__30894)
                & ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
                    & cCoq_2eInit_2eNat_2esub___24a2(V1__n,V2__m) = V1__n )
                  | ? [Vvar__0___24Anonymous__30897] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__30897)
                      & V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__30897)
                      & cCoq_2eInit_2eNat_2esub___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2esub___24a2(Vvar__0___24Anonymous__30894,Vvar__0___24Anonymous__30897) ) ) ) ) ) ) ) ).

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

fof('$_def_Coq.Init.Nat.t',axiom,
    ! [Vvar__32435] :
      ( cCoq_2eInit_2eNat_2et___24t(Vvar__32435)
    <=> cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__32435) ) ).

fof('$_def_Coq.Init.Nat.tail_add',axiom,
    ! [V1__n,V2__m] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
     => ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
          & cCoq_2eInit_2eNat_2etail__add___24a2(V1__n,V2__m) = V2__m )
        | ? [Vvar__0___24Anonymous__35866] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__35866)
            & V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__35866)
            & cCoq_2eInit_2eNat_2etail__add___24a2(V1__n,V2__m) = cCoq_2eInit_2eNat_2etail__add___24a2(Vvar__0___24Anonymous__35866,cCoq_2eInit_2eDatatypes_2eS___24a1(V2__m)) ) ) ) ).

fof('$_def_Coq.Init.Nat.testbit',axiom,
    ! [V1__a,V2__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
     => ( ( V2__n = cCoq_2eInit_2eDatatypes_2eO
          & cCoq_2eInit_2eNat_2etestbit___24a2(V1__a,V2__n) = cCoq_2eInit_2eNat_2eodd___24a1(V1__a) )
        | ? [Vvar__0___24Anonymous__35887] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__35887)
            & V2__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__35887)
            & cCoq_2eInit_2eNat_2etestbit___24a2(V1__a,V2__n) = cCoq_2eInit_2eNat_2etestbit___24a2(cCoq_2eInit_2eNat_2ediv2___24a1(V1__a),Vvar__0___24Anonymous__35887) ) ) ) ).

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__32635] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__32635)
            & V0__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__32635)
            & ( cCoq_2eInit_2ePeano_2eIsSucc___24a1(V0__n)
            <=> p(c_24True) ) ) ) ) ).

fof('$_def_Coq.Init.Peano.ge',axiom,
    ! [V0__n,V1__m] :
      ( cCoq_2eInit_2ePeano_2ege___24a2(V0__n,V1__m)
    <=> cCoq_2eInit_2ePeano_2ele___24a2(V1__m,V0__n) ) ).

fof('$_def_Coq.Init.Peano.gt',axiom,
    ! [V0__n,V1__m] :
      ( cCoq_2eInit_2ePeano_2egt___24a2(V0__n,V1__m)
    <=> cCoq_2eInit_2ePeano_2elt___24a2(V1__m,V0__n) ) ).

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

fof('$_def_Coq.Init.Specif.Exc',axiom,
    ! [V0__A] : cCoq_2eInit_2eSpecif_2eExc___24a1(V0__A) = cCoq_2eInit_2eDatatypes_2eoption___24a1(V0__A) ).

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

fof('$_def_Coq.Init.Specif.proj1_sig',axiom,
    ! [V0__A,V1__P,V2__e] :
      ( cType___24t(V0__A)
     => ( c_24__type__27836___24t(V0__A,V1__P,V1__P)
       => ( cCoq_2eInit_2eSpecif_2esig___24t(V0__A,V1__P,V2__e)
         => ? [Vvar__2__x__27830] :
              ( t(Vvar__2__x__27830,V0__A)
              & p(happ(V1__P,Vvar__2__x__27830))
              & V2__e = cCoq_2eInit_2eSpecif_2eexist___24a3(V0__A,V1__P,Vvar__2__x__27830)
              & cCoq_2eInit_2eSpecif_2eproj1__sig___24a3(V0__A,V1__P,V2__e) = Vvar__2__x__27830 ) ) ) ) ).

fof('$_def_Coq.Init.Specif.projT1',axiom,
    ! [V0__A,V1__P,V2__x] :
      ( cType___24t(V0__A)
     => ( c_24__type__27860___24t(V0__A,V1__P,V1__P)
       => ( cCoq_2eInit_2eSpecif_2esigT___24t(V0__A,V1__P,V2__x)
         => ? [Vvar__2__x__27854] :
              ( t(Vvar__2__x__27854,V0__A)
              & ? [Vvar__3___24Anonymous__27855] :
                  ( t(Vvar__3___24Anonymous__27855,happ(V1__P,Vvar__2__x__27854))
                  & V2__x = cCoq_2eInit_2eSpecif_2eexistT___24a4(V0__A,V1__P,Vvar__2__x__27854,Vvar__3___24Anonymous__27855)
                  & cCoq_2eInit_2eSpecif_2eprojT1___24a3(V0__A,V1__P,V2__x) = Vvar__2__x__27854 ) ) ) ) ) ).

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

fof('$_def_Coq.Lists.List.In',axiom,
    ! [V0__A,V2__a,V3__l] :
      ( cType___24t(V0__A)
     => ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
       => ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
            & ( cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__a,V3__l)
            <=> p(c_24False) ) )
          | ? [Vvar__1___24Anonymous__35573] :
              ( t(Vvar__1___24Anonymous__35573,V0__A)
              & ? [Vvar__2___24Anonymous__35574] :
                  ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__35574)
                  & V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__35573,Vvar__2___24Anonymous__35574)
                  & ( cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__a,V3__l)
                  <=> ( Vvar__1___24Anonymous__35573 = V2__a
                      | cCoq_2eLists_2eList_2eIn___24a3(V0__A,V2__a,Vvar__2___24Anonymous__35574) ) ) ) ) ) ) ) ).

fof('$_def_Coq.Lists.List.fold_left',axiom,
    ! [V0__A,V1__B,V2__f,V4__l,V5__a0] :
      ( cType___24t(V0__A)
     => ( cType___24t(V1__B)
       => ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,V4__l)
         => ( ( V4__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V1__B)
              & cCoq_2eLists_2eList_2efold__left___24a5(V0__A,V1__B,V2__f,V4__l,V5__a0) = V5__a0 )
            | ? [Vvar__1___24Anonymous__35634] :
                ( t(Vvar__1___24Anonymous__35634,V1__B)
                & ? [Vvar__2___24Anonymous__35635] :
                    ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,Vvar__2___24Anonymous__35635)
                    & V4__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__B,Vvar__1___24Anonymous__35634,Vvar__2___24Anonymous__35635)
                    & cCoq_2eLists_2eList_2efold__left___24a5(V0__A,V1__B,V2__f,V4__l,V5__a0) = cCoq_2eLists_2eList_2efold__left___24a5(V0__A,V1__B,V2__f,Vvar__2___24Anonymous__35635,happ(happ(V2__f,V5__a0),Vvar__1___24Anonymous__35634)) ) ) ) ) ) ) ).

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__35663] :
                ( t(Vvar__1___24Anonymous__35663,V1__B)
                & ? [Vvar__2___24Anonymous__35664] :
                    ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__B,Vvar__2___24Anonymous__35664)
                    & V5__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__B,Vvar__1___24Anonymous__35663,Vvar__2___24Anonymous__35664)
                    & cCoq_2eLists_2eList_2efold__right___24a5(V0__A,V1__B,V2__f,V3__a0,V5__l) = happ(happ(V2__f,Vvar__1___24Anonymous__35663),cCoq_2eLists_2eList_2efold__right___24a5(V0__A,V1__B,V2__f,V3__a0,Vvar__2___24Anonymous__35664)) ) ) ) ) ) ) ).

fof('$_def_Coq.Lists.List.hd',axiom,
    ! [V0__A,V1__default,V2__l] :
      ( cType___24t(V0__A)
     => ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
       => ( ( V2__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
            & cCoq_2eLists_2eList_2ehd___24a3(V0__A,V1__default,V2__l) = V1__default )
          | ? [Vvar__1___24Anonymous__35561] :
              ( t(Vvar__1___24Anonymous__35561,V0__A)
              & ? [Vvar__2___24Anonymous__35562] :
                  ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__35562)
                  & V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__35561,Vvar__2___24Anonymous__35562)
                  & cCoq_2eLists_2eList_2ehd___24a3(V0__A,V1__default,V2__l) = Vvar__1___24Anonymous__35561 ) ) ) ) ) ).

fof('$_def_Coq.Lists.List.last',axiom,
    ! [V0__A,V2__l,V3__d] :
      ( cType___24t(V0__A)
     => ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V2__l)
       => ( ( V2__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
            & cCoq_2eLists_2eList_2elast___24a3(V0__A,V2__l,V3__d) = V3__d )
          | ? [Vvar__1___24Anonymous__35610] :
              ( t(Vvar__1___24Anonymous__35610,V0__A)
              & ? [Vvar__2___24Anonymous__35611] :
                  ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__35611)
                  & ( cType___24t(V0__A)
                   => ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__35611)
                     => ( V2__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__35610,Vvar__2___24Anonymous__35611)
                        & ( ( Vvar__2___24Anonymous__35611 = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
                            & cCoq_2eLists_2eList_2elast___24a3(V0__A,V2__l,V3__d) = Vvar__1___24Anonymous__35610 )
                          | ? [Vvar__1___24Anonymous__35622] :
                              ( t(Vvar__1___24Anonymous__35622,V0__A)
                              & ? [Vvar__2___24Anonymous__35623] :
                                  ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__35623)
                                  & Vvar__2___24Anonymous__35611 = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__35622,Vvar__2___24Anonymous__35623)
                                  & cCoq_2eLists_2eList_2elast___24a3(V0__A,V2__l,V3__d) = cCoq_2eLists_2eList_2elast___24a3(V0__A,Vvar__2___24Anonymous__35611,V3__d) ) ) ) ) ) ) ) ) ) ) ) ).

fof('$_def_Coq.Lists.List.nth',axiom,
    ! [V0__A,V2__n,V3__l,V4__default] :
      ( cType___24t(V0__A)
     => ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
       => ( ( cType___24t(V0__A)
           => ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
             => ( V2__n = cCoq_2eInit_2eDatatypes_2eO
                & ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V0__A)
                    & cCoq_2eLists_2eList_2enth___24a4(V0__A,V2__n,V3__l,V4__default) = V4__default )
                  | ? [Vvar__1___24Anonymous__35585] :
                      ( t(Vvar__1___24Anonymous__35585,V0__A)
                      & ? [Vvar__2___24Anonymous__35586] :
                          ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__35586)
                          & V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__35585,Vvar__2___24Anonymous__35586)
                          & cCoq_2eLists_2eList_2enth___24a4(V0__A,V2__n,V3__l,V4__default) = Vvar__1___24Anonymous__35585 ) ) ) ) ) )
          | ? [Vvar__0___24Anonymous__35588] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__35588)
              & ( cType___24t(V0__A)
               => ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,V3__l)
                 => ( V2__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__35588)
                    & ( ( 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__35595] :
                          ( t(Vvar__1___24Anonymous__35595,V0__A)
                          & ? [Vvar__2___24Anonymous__35596] :
                              ( cCoq_2eInit_2eDatatypes_2elist___24t(V0__A,Vvar__2___24Anonymous__35596)
                              & V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V0__A,Vvar__1___24Anonymous__35595,Vvar__2___24Anonymous__35596)
                              & cCoq_2eLists_2eList_2enth___24a4(V0__A,V2__n,V3__l,V4__default) = cCoq_2eLists_2eList_2enth___24a4(V0__A,Vvar__0___24Anonymous__35588,Vvar__2___24Anonymous__35596,V4__default) ) ) ) ) ) ) ) ) ) ) ).

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

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

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

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

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

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

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

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

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

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

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

fof('$_def_Coq.NArith.BinNat.N.recursion',axiom,
    ! [V0__A] : cCoq_2eNArith_2eBinNat_2eN_2erecursion___24a1(V0__A) = cCoq_2eNArith_2eBinNat_2eN_2epeano__rect___24a1(c_24__lam__44548___24a1(V0__A)) ).

fof('$_def_Coq.NArith.BinNatDef.N.add',axiom,
    ! [V0__n,V1__m] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
     => ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
          & cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m) = V1__m )
        | ? [Vvar__0___24Anonymous__29678] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29678)
            & ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
             => ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__29678)
                & ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
                    & cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m) = V0__n )
                  | ? [Vvar__0___24Anonymous__29681] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29681)
                      & V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__29681)
                      & cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__29678,Vvar__0___24Anonymous__29681)) ) ) ) ) ) ) ) ).

fof('$_def_Coq.NArith.BinNatDef.N.div2',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
     => ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
          & cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eN0 )
        | ? [Vvar__0___24Anonymous__44529] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__44529)
            & ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__44529)
             => ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__44529)
                & ( ? [Vvar__0___24Anonymous__44533] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__44533)
                      & Vvar__0___24Anonymous__44529 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__44533)
                      & cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__44533) )
                  | ? [Vvar__0___24Anonymous__44534] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__44534)
                      & Vvar__0___24Anonymous__44529 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__44534)
                      & cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__44534) )
                  | ( Vvar__0___24Anonymous__44529 = cCoq_2eNumbers_2eBinNums_2exH
                    & cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eN0 ) ) ) ) ) ) ) ).

fof('$_def_Coq.NArith.BinNatDef.N.even',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
     => ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
          & cCoq_2eNArith_2eBinNatDef_2eN_2eeven___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2etrue )
        | ? [Vvar__0___24Anonymous__44535] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__44535)
            & ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__44535)
             => ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__44535)
                & ( ? [Vvar__0___24Anonymous__44539] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__44539)
                      & Vvar__0___24Anonymous__44535 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__44539)
                      & cCoq_2eNArith_2eBinNatDef_2eN_2eeven___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2efalse )
                  | ? [Vvar__0___24Anonymous__44540] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__44540)
                      & Vvar__0___24Anonymous__44535 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__44540)
                      & cCoq_2eNArith_2eBinNatDef_2eN_2eeven___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2etrue )
                  | ( Vvar__0___24Anonymous__44535 = cCoq_2eNumbers_2eBinNums_2exH
                    & cCoq_2eNArith_2eBinNatDef_2eN_2eeven___24a1(V0__n) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) ).

fof('$_def_Coq.NArith.BinNatDef.N.lxor',axiom,
    ! [V0__n,V1__m] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
     => ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
          & cCoq_2eNArith_2eBinNatDef_2eN_2elxor___24a2(V0__n,V1__m) = V1__m )
        | ? [Vvar__0___24Anonymous__44541] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__44541)
            & ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
             => ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__44541)
                & ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
                    & cCoq_2eNArith_2eBinNatDef_2eN_2elxor___24a2(V0__n,V1__m) = V0__n )
                  | ? [Vvar__0___24Anonymous__44544] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__44544)
                      & V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__44544)
                      & cCoq_2eNArith_2eBinNatDef_2eN_2elxor___24a2(V0__n,V1__m) = cCoq_2ePArith_2eBinPosDef_2ePos_2elxor___24a2(Vvar__0___24Anonymous__44541,Vvar__0___24Anonymous__44544) ) ) ) ) ) ) ) ).

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

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

fof('$_def_Coq.NArith.BinNatDef.N.mul',axiom,
    ! [V0__n,V1__m] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
     => ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
          & cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eN0 )
        | ? [Vvar__0___24Anonymous__29695] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29695)
            & ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
             => ( V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__29695)
                & ( ( V1__m = cCoq_2eNumbers_2eBinNums_2eN0
                    & cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eN0 )
                  | ? [Vvar__0___24Anonymous__29698] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29698)
                      & V1__m = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__29698)
                      & cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V1__m) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__29695,Vvar__0___24Anonymous__29698)) ) ) ) ) ) ) ) ).

fof('$_def_Coq.NArith.BinNatDef.N.pred',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
     => ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
          & cCoq_2eNArith_2eBinNatDef_2eN_2epred___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eN0 )
        | ? [Vvar__0___24Anonymous__29677] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29677)
            & V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__29677)
            & cCoq_2eNArith_2eBinNatDef_2eN_2epred___24a1(V0__n) = cCoq_2ePArith_2eBinPosDef_2ePos_2epred__N___24a1(Vvar__0___24Anonymous__29677) ) ) ) ).

fof('$_def_Coq.NArith.BinNatDef.N.succ',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
     => ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
          & cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2eNumbers_2eBinNums_2exH) )
        | ? [Vvar__0___24Anonymous__29674] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29674)
            & V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__29674)
            & cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__29674)) ) ) ) ).

fof('$_def_Coq.NArith.BinNatDef.N.t',axiom,
    ! [Vvar__35095] :
      ( cCoq_2eNArith_2eBinNatDef_2eN_2et___24t(Vvar__35095)
    <=> cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__35095) ) ).

fof('$_def_Coq.NArith.BinNatDef.N.testbit',axiom,
    ! [V0__a,V1__n] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
     => ( ( V0__a = cCoq_2eNumbers_2eBinNums_2eN0
          & cCoq_2eNArith_2eBinNatDef_2eN_2etestbit___24a2(V0__a,V1__n) = cCoq_2eInit_2eDatatypes_2efalse )
        | ? [Vvar__0___24Anonymous__29749] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29749)
            & V0__a = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__29749)
            & cCoq_2eNArith_2eBinNatDef_2eN_2etestbit___24a2(V0__a,V1__n) = cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit___24a2(Vvar__0___24Anonymous__29749,V1__n) ) ) ) ).

fof('$_def_Coq.NArith.BinNatDef.N.to_nat',axiom,
    ! [V0__a] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__a)
     => ( ( V0__a = cCoq_2eNumbers_2eBinNums_2eN0
          & cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat___24a1(V0__a) = cCoq_2eInit_2eDatatypes_2eO )
        | ? [Vvar__0___24Anonymous__44546] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__44546)
            & V0__a = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__44546)
            & cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat___24a1(V0__a) = cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(Vvar__0___24Anonymous__44546) ) ) ) ).

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

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

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

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

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

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

fof('$_def_Coq.PArith.BinPosDef.Pos.div2',axiom,
    ! [V0__p] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
     => ( ? [Vvar__0___24Anonymous__44601] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__44601)
            & V0__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__44601)
            & cCoq_2ePArith_2eBinPosDef_2ePos_2ediv2___24a1(V0__p) = Vvar__0___24Anonymous__44601 )
        | ? [Vvar__0___24Anonymous__44602] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__44602)
            & V0__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__44602)
            & cCoq_2ePArith_2eBinPosDef_2ePos_2ediv2___24a1(V0__p) = Vvar__0___24Anonymous__44602 )
        | ( V0__p = cCoq_2eNumbers_2eBinNums_2exH
          & cCoq_2ePArith_2eBinPosDef_2ePos_2ediv2___24a1(V0__p) = cCoq_2eNumbers_2eBinNums_2exH ) ) ) ).

fof('$_def_Coq.PArith.BinPosDef.Pos.eqb',axiom,
    ! [V1__p,V2__q] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p)
     => ( ? [Vvar__0___24Anonymous__44604] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__44604)
            & ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__q)
             => ( V1__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__44604)
                & ( ? [Vvar__0___24Anonymous__44608] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__44608)
                      & V2__q = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__44608)
                      & cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V1__p,V2__q) = cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(Vvar__0___24Anonymous__44604,Vvar__0___24Anonymous__44608) )
                  | ? [Vvar__0___24Anonymous__44609] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__44609)
                      & V2__q = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__44609)
                      & cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V1__p,V2__q) = cCoq_2eInit_2eDatatypes_2efalse )
                  | ( V2__q = cCoq_2eNumbers_2eBinNums_2exH
                    & cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V1__p,V2__q) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) )
        | ? [Vvar__0___24Anonymous__44610] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__44610)
            & ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__q)
             => ( V1__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__44610)
                & ( ? [Vvar__0___24Anonymous__44614] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__44614)
                      & V2__q = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__44614)
                      & cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V1__p,V2__q) = cCoq_2eInit_2eDatatypes_2efalse )
                  | ? [Vvar__0___24Anonymous__44615] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__44615)
                      & V2__q = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__44615)
                      & cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V1__p,V2__q) = cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(Vvar__0___24Anonymous__44610,Vvar__0___24Anonymous__44615) )
                  | ( V2__q = cCoq_2eNumbers_2eBinNums_2exH
                    & cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V1__p,V2__q) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) )
        | ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__q)
         => ( V1__p = cCoq_2eNumbers_2eBinNums_2exH
            & ( ? [Vvar__0___24Anonymous__44616] :
                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__44616)
                  & V2__q = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__44616)
                  & cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V1__p,V2__q) = cCoq_2eInit_2eDatatypes_2efalse )
              | ? [Vvar__0___24Anonymous__44617] :
                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__44617)
                  & V2__q = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__44617)
                  & cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V1__p,V2__q) = cCoq_2eInit_2eDatatypes_2efalse )
              | ( V2__q = cCoq_2eNumbers_2eBinNums_2exH
                & cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V1__p,V2__q) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) ) ) ).

fof('$_def_Coq.PArith.BinPosDef.Pos.iter',axiom,
    ! [V0__A,V1__f,V3__x,V4__n] :
      ( cType___24t(V0__A)
     => ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V4__n)
       => ( ? [Vvar__0___24Anonymous__35100] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35100)
              & V4__n = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__35100)
              & 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__35100),Vvar__0___24Anonymous__35100)) )
          | ? [Vvar__0___24Anonymous__35101] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35101)
              & V4__n = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__35101)
              & 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__35101),Vvar__0___24Anonymous__35101) )
          | ( 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__35113] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35113)
              & V3__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__35113)
              & 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__35113,happ(happ(V1__op,V4__a),V4__a))) )
          | ? [Vvar__0___24Anonymous__35114] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35114)
              & V3__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__35114)
              & 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__35114,happ(happ(V1__op,V4__a),V4__a)) )
          | ( V3__p = cCoq_2eNumbers_2eBinNums_2exH
            & cCoq_2ePArith_2eBinPosDef_2ePos_2eiter__op___24a4(V0__A,V1__op,V3__p,V4__a) = V4__a ) ) ) ) ).

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

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

fof('$_def_Coq.PArith.BinPosDef.Pos.mul',axiom,
    ! [V1__x,V2__y] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__x)
     => ( ? [Vvar__0___24Anonymous__29957] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29957)
            & V1__x = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__29957)
            & 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__29957,V2__y))) )
        | ? [Vvar__0___24Anonymous__29958] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29958)
            & V1__x = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__29958)
            & cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(V1__x,V2__y) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__29958,V2__y)) )
        | ( V1__x = cCoq_2eNumbers_2eBinNums_2exH
          & cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(V1__x,V2__y) = V2__y ) ) ) ).

fof('$_def_Coq.PArith.BinPosDef.Pos.of_nat',axiom,
    ! [V1__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
     => ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
          & cCoq_2ePArith_2eBinPosDef_2ePos_2eof__nat___24a1(V1__n) = cCoq_2eNumbers_2eBinNums_2exH )
        | ? [Vvar__0___24Anonymous__44650] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__44650)
            & ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__44650)
             => ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__44650)
                & ( ( Vvar__0___24Anonymous__44650 = cCoq_2eInit_2eDatatypes_2eO
                    & cCoq_2ePArith_2eBinPosDef_2ePos_2eof__nat___24a1(V1__n) = cCoq_2eNumbers_2eBinNums_2exH )
                  | ? [Vvar__0___24Anonymous__44653] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__44653)
                      & Vvar__0___24Anonymous__44650 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__44653)
                      & cCoq_2ePArith_2eBinPosDef_2ePos_2eof__nat___24a1(V1__n) = cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__nat___24a1(Vvar__0___24Anonymous__44650)) ) ) ) ) ) ) ) ).

fof('$_def_Coq.PArith.BinPosDef.Pos.of_succ_nat',axiom,
    ! [V1__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
     => ( ( V1__n = cCoq_2eInit_2eDatatypes_2eO
          & cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(V1__n) = cCoq_2eNumbers_2eBinNums_2exH )
        | ? [Vvar__0___24Anonymous__44657] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__44657)
            & V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__44657)
            & cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(V1__n) = cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(Vvar__0___24Anonymous__44657)) ) ) ) ).

fof('$_def_Coq.PArith.BinPosDef.Pos.size_nat',axiom,
    ! [V1__p] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p)
     => ( ? [Vvar__0___24Anonymous__29962] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29962)
            & V1__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__29962)
            & cCoq_2ePArith_2eBinPosDef_2ePos_2esize__nat___24a1(V1__p) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esize__nat___24a1(Vvar__0___24Anonymous__29962)) )
        | ? [Vvar__0___24Anonymous__29963] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29963)
            & V1__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__29963)
            & cCoq_2ePArith_2eBinPosDef_2ePos_2esize__nat___24a1(V1__p) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esize__nat___24a1(Vvar__0___24Anonymous__29963)) )
        | ( V1__p = cCoq_2eNumbers_2eBinNums_2exH
          & cCoq_2ePArith_2eBinPosDef_2ePos_2esize__nat___24a1(V1__p) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO) ) ) ) ).

fof('$_def_Coq.PArith.BinPosDef.Pos.sub',axiom,
    ! [V0__x,V1__y] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
     => ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__y)
       => ( ( cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask___24a2(V0__x,V1__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNul
            & cCoq_2ePArith_2eBinPosDef_2ePos_2esub___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2exH )
          | ? [Vvar__0___24Anonymous__29954] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29954)
              & cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask___24a2(V0__x,V1__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__29954)
              & cCoq_2ePArith_2eBinPosDef_2ePos_2esub___24a2(V0__x,V1__y) = Vvar__0___24Anonymous__29954 )
          | ( cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask___24a2(V0__x,V1__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNeg
            & cCoq_2ePArith_2eBinPosDef_2ePos_2esub___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2exH ) ) ) ) ).

fof('$_def_Coq.PArith.BinPosDef.Pos.succ',axiom,
    ! [V1__x] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__x)
     => ( ? [Vvar__0___24Anonymous__29920] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29920)
            & V1__x = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__29920)
            & cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(V1__x) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(Vvar__0___24Anonymous__29920)) )
        | ? [Vvar__0___24Anonymous__29921] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29921)
            & V1__x = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__29921)
            & cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(V1__x) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__29921) )
        | ( V1__x = cCoq_2eNumbers_2eBinNums_2exH
          & cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(V1__x) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ) ) ).

fof('$_def_Coq.PArith.BinPosDef.Pos.t',axiom,
    ! [Vvar__35098] :
      ( cCoq_2ePArith_2eBinPosDef_2ePos_2et___24t(Vvar__35098)
    <=> cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__35098) ) ).

fof('$_def_Coq.PArith.BinPosDef.Pos.testbit_nat',axiom,
    ! [V1__p] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p)
     => ( ? [Vvar__0___24Anonymous__44620] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__44620)
            & V1__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__44620)
            & cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat___24a1(V1__p) = c_24__lam__44633___24a1(Vvar__0___24Anonymous__44620) )
        | ? [Vvar__0___24Anonymous__44624] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__44624)
            & V1__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__44624)
            & cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat___24a1(V1__p) = c_24__lam__44640___24a1(Vvar__0___24Anonymous__44624) )
        | ( V1__p = cCoq_2eNumbers_2eBinNums_2exH
          & cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat___24a1(V1__p) = c_24__lam__44644 ) ) ) ).

fof('$_def_Coq.QArith.QArith_base.Qden',axiom,
    ! [V0__q] :
      ( cCoq_2eQArith_2eQArith__base_2eQ___24t(V0__q)
     => ? [Vvar__0__Qnum__9776] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__Qnum__9776)
          & ? [Vvar__1__Qden__9777] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__Qden__9777)
              & V0__q = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__9776,Vvar__1__Qden__9777)
              & cCoq_2eQArith_2eQArith__base_2eQden___24a1(V0__q) = Vvar__1__Qden__9777 ) ) ) ).

fof('$_def_Coq.QArith.QArith_base.Qnum',axiom,
    ! [V0__q] :
      ( cCoq_2eQArith_2eQArith__base_2eQ___24t(V0__q)
     => ? [Vvar__0__Qnum__9771] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__Qnum__9771)
          & ? [Vvar__1__Qden__9772] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__Qden__9772)
              & V0__q = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__9771,Vvar__1__Qden__9772)
              & cCoq_2eQArith_2eQArith__base_2eQnum___24a1(V0__q) = Vvar__0__Qnum__9771 ) ) ) ).

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

fof('$_def_Coq.Reals.Rdefinitions.IZR',axiom,
    ! [V0__z] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
     => ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
          & cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__z) = cCoq_2eReals_2eRdefinitions_2eR0 )
        | ? [Vvar__0___24Anonymous__26237] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__26237)
            & V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__26237)
            & cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__z) = cCoq_2eReals_2eRdefinitions_2eIPR___24a1(Vvar__0___24Anonymous__26237) )
        | ? [Vvar__0___24Anonymous__26238] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__26238)
            & V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__26238)
            & cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V0__z) = cCoq_2eReals_2eRdefinitions_2eRopp___24a1(cCoq_2eReals_2eRdefinitions_2eIPR___24a1(Vvar__0___24Anonymous__26238)) ) ) ) ).

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

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

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

fof('$_def_Coq.Relations.Relation_Definitions.relation',axiom,
    ! [V0__A] : cCoq_2eRelations_2eRelation__Definitions_2erelation___24a1(V0__A) = c_24__type__4775___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__4775___24a1(V0__U) ).

fof('$_def_Coq.Structures.GenericMinMax.gmax',axiom,
    ! [V0__A,V1__cmp,V2__x,V3__y] :
      ( cType___24t(V0__A)
     => ( c_24__type__35447___24t(V0__A,V1__cmp)
       => ( t(V2__x,V0__A)
         => ( t(V3__y,V0__A)
           => ( ( happ(happ(V1__cmp,V2__x),V3__y) = cCoq_2eInit_2eDatatypes_2eEq
                & cCoq_2eStructures_2eGenericMinMax_2egmax___24a4(V0__A,V1__cmp,V2__x,V3__y) = V2__x )
              | ( happ(happ(V1__cmp,V2__x),V3__y) = cCoq_2eInit_2eDatatypes_2eLt
                & cCoq_2eStructures_2eGenericMinMax_2egmax___24a4(V0__A,V1__cmp,V2__x,V3__y) = V3__y )
              | ( happ(happ(V1__cmp,V2__x),V3__y) = cCoq_2eInit_2eDatatypes_2eGt
                & cCoq_2eStructures_2eGenericMinMax_2egmax___24a4(V0__A,V1__cmp,V2__x,V3__y) = V2__x ) ) ) ) ) ) ).

fof('$_def_Coq.Structures.GenericMinMax.gmin',axiom,
    ! [V0__A,V1__cmp,V2__x,V3__y] :
      ( cType___24t(V0__A)
     => ( c_24__type__35447___24t(V0__A,V1__cmp)
       => ( t(V2__x,V0__A)
         => ( t(V3__y,V0__A)
           => ( ( happ(happ(V1__cmp,V2__x),V3__y) = cCoq_2eInit_2eDatatypes_2eEq
                & cCoq_2eStructures_2eGenericMinMax_2egmin___24a4(V0__A,V1__cmp,V2__x,V3__y) = V2__x )
              | ( happ(happ(V1__cmp,V2__x),V3__y) = cCoq_2eInit_2eDatatypes_2eLt
                & cCoq_2eStructures_2eGenericMinMax_2egmin___24a4(V0__A,V1__cmp,V2__x,V3__y) = V2__x )
              | ( happ(happ(V1__cmp,V2__x),V3__y) = cCoq_2eInit_2eDatatypes_2eGt
                & cCoq_2eStructures_2eGenericMinMax_2egmin___24a4(V0__A,V1__cmp,V2__x,V3__y) = V3__y ) ) ) ) ) ) ).

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

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

fof('$_def_Coq.Structures.OrderedTypeEx.N_as_OT.t',axiom,
    ! [Vvar__35096] :
      ( cCoq_2eStructures_2eOrderedTypeEx_2eN__as__OT_2et___24t(Vvar__35096)
    <=> cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__35096) ) ).

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__35097] :
      ( cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2et___24t(Vvar__35097)
    <=> cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__35097) ) ).

fof('$_def_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.bits_lt',axiom,
    ! [V1__p,V2__q] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p)
     => ( ? [Vvar__0___24Anonymous__35064] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35064)
            & ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__q)
             => ( V1__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__35064)
                & ( ? [Vvar__0___24Anonymous__35068] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35068)
                      & V2__q = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__35068)
                      & ( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(V1__p,V2__q)
                      <=> cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(Vvar__0___24Anonymous__35064,Vvar__0___24Anonymous__35068) ) )
                  | ? [Vvar__0___24Anonymous__35069] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35069)
                      & V2__q = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__35069)
                      & ( 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__35070] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35070)
            & ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V2__q)
             => ( V1__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__35070)
                & ( ? [Vvar__0___24Anonymous__35074] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35074)
                      & V2__q = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__35074)
                      & ( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(V1__p,V2__q)
                      <=> p(c_24True) ) )
                  | ? [Vvar__0___24Anonymous__35075] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35075)
                      & V2__q = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__35075)
                      & ( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(V1__p,V2__q)
                      <=> cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(Vvar__0___24Anonymous__35070,Vvar__0___24Anonymous__35075) ) )
                  | ( 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__35076] :
                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35076)
                  & V2__q = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__35076)
                  & ( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(V1__p,V2__q)
                  <=> p(c_24True) ) )
              | ? [Vvar__0___24Anonymous__35077] :
                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35077)
                  & V2__q = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__35077)
                  & ( 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__35062] :
      ( cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2et___24t(Vvar__35062)
    <=> cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__35062) ) ).

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

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

fof('$_def_Coq.Structures.OrderedTypeEx.Positive_as_OT.t',axiom,
    ! [Vvar__35201] :
      ( cCoq_2eStructures_2eOrderedTypeEx_2ePositive__as__OT_2et___24t(Vvar__35201)
    <=> cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__35201) ) ).

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

fof('$_def_Coq.Structures.OrderedTypeEx.String_as_OT.t',axiom,
    ! [Vvar__35202] :
      ( cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2et___24t(Vvar__35202)
    <=> cCoq_2eStrings_2eString_2estring___24t(Vvar__35202) ) ).

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

fof('$_def_Coq.Structures.OrderedTypeEx.Z_as_OT.lt',axiom,
    ! [V0__x,V1__y] :
      ( cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2elt___24a2(V0__x,V1__y)
    <=> p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V1__y)) ) ).

fof('$_def_Coq.Structures.OrderedTypeEx.Z_as_OT.t',axiom,
    ! [Vvar__35204] :
      ( cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2et___24t(Vvar__35204)
    <=> cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__35204) ) ).

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

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

fof('$_def_Coq.ZArith.BinInt.Z.divide',axiom,
    ! [V0__x,V1__y] :
      ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V0__x,V1__y)
    <=> ? [V2__z] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
          & V1__y = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V2__z,V0__x) ) ) ).

fof('$_def_Coq.ZArith.BinInt.Z.eq',axiom,
    cCoq_2eZArith_2eBinInt_2eZ_2eeq = c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eZ) ).

fof('$_def_Coq.ZArith.BinInt.Z.eqf',axiom,
    ! [V0__f,V1__g] :
      ( cCoq_2eZArith_2eBinInt_2eZ_2eeqf___24a2(V0__f,V1__g)
    <=> ! [V2__n] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__n)
         => happ(V0__f,V2__n) = happ(V1__g,V2__n) ) ) ).

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

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

fof('$_def_Coq.ZArith.BinInt.Z.lt',axiom,
    ! [V0__x,V1__y] :
      ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V1__y))
    <=> cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt ) ).

fof('$_def_Coq.ZArith.BinInt.Zne',axiom,
    ! [V0__x,V1__y] :
      ( cCoq_2eZArith_2eBinInt_2eZne___24a2(V0__x,V1__y)
    <=> V0__x != V1__y ) ).

fof('$_def_Coq.ZArith.BinIntDef.Z.abs',axiom,
    ! [V0__z] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
     => ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
          & cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZ0 )
        | ? [Vvar__0___24Anonymous__44996] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__44996)
            & V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__44996)
            & cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__44996) )
        | ? [Vvar__0___24Anonymous__44997] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__44997)
            & V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__44997)
            & cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__44997) ) ) ) ).

fof('$_def_Coq.ZArith.BinIntDef.Z.abs_N',axiom,
    ! [V0__z] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
     => ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
          & cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__N___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eN0 )
        | ? [Vvar__0___24Anonymous__45002] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__45002)
            & V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__45002)
            & cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__N___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__45002) )
        | ? [Vvar__0___24Anonymous__45003] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__45003)
            & V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__45003)
            & cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__N___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__45003) ) ) ) ).

fof('$_def_Coq.ZArith.BinIntDef.Z.abs_nat',axiom,
    ! [V0__z] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
     => ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
          & cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__nat___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2eO )
        | ? [Vvar__0___24Anonymous__44998] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__44998)
            & V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__44998)
            & cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__nat___24a1(V0__z) = cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(Vvar__0___24Anonymous__44998) )
        | ? [Vvar__0___24Anonymous__44999] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__44999)
            & V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__44999)
            & cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__nat___24a1(V0__z) = cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(Vvar__0___24Anonymous__44999) ) ) ) ).

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__7383] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__7383)
            & ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
             => ( V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__7383)
                & ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
                    & cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = V0__x )
                  | ? [Vvar__0___24Anonymous__7387] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__7387)
                      & V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__7387)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__7383,Vvar__0___24Anonymous__7387)) )
                  | ? [Vvar__0___24Anonymous__7388] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__7388)
                      & V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__7388)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(Vvar__0___24Anonymous__7383,Vvar__0___24Anonymous__7388) ) ) ) ) )
        | ? [Vvar__0___24Anonymous__7389] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__7389)
            & ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
             => ( V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__7389)
                & ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
                    & cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = V0__x )
                  | ? [Vvar__0___24Anonymous__7393] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__7393)
                      & V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__7393)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eZArith_2eBinIntDef_2eZ_2epos__sub___24a2(Vvar__0___24Anonymous__7393,Vvar__0___24Anonymous__7389) )
                  | ? [Vvar__0___24Anonymous__7394] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__7394)
                      & V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__7394)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0___24Anonymous__7389,Vvar__0___24Anonymous__7394)) ) ) ) ) ) ) ) ).

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__30571] :
                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30571)
                  & V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__30571)
                  & cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt )
              | ? [Vvar__0___24Anonymous__30572] :
                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30572)
                  & V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__30572)
                  & cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt ) ) ) )
        | ? [Vvar__0___24Anonymous__30573] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30573)
            & ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
             => ( V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__30573)
                & ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
                    & cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt )
                  | ? [Vvar__0___24Anonymous__30577] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30577)
                      & V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__30577)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__0___24Anonymous__30573,Vvar__0___24Anonymous__30577) )
                  | ? [Vvar__0___24Anonymous__30578] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30578)
                      & V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__30578)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eGt ) ) ) ) )
        | ? [Vvar__0___24Anonymous__30579] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30579)
            & ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
             => ( V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__30579)
                & ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
                    & cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt )
                  | ? [Vvar__0___24Anonymous__30583] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30583)
                      & V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__30583)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eLt )
                  | ? [Vvar__0___24Anonymous__30584] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30584)
                      & V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__30584)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2eCompOpp___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__0___24Anonymous__30579,Vvar__0___24Anonymous__30584)) ) ) ) ) ) ) ) ).

fof('$_def_Coq.ZArith.BinIntDef.Z.div',axiom,
    ! [V0__a,V1__b] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
     => ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
       => ? [Vvar__2___24Anonymous__15763] :
            ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2___24Anonymous__15763)
            & ? [Vvar__3___24Anonymous__15764] :
                ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3___24Anonymous__15764)
                & 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__15763,Vvar__3___24Anonymous__15764)
                & cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(V0__a,V1__b) = Vvar__2___24Anonymous__15763 ) ) ) ) ).

fof('$_def_Coq.ZArith.BinIntDef.Z.even',axiom,
    ! [V0__z] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
     => ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
          & cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2etrue )
        | ? [Vvar__0___24Anonymous__45010] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__45010)
            & ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__45010)
             => ( V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__45010)
                & ( ? [Vvar__0___24Anonymous__45014] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__45014)
                      & Vvar__0___24Anonymous__45010 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__45014)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2efalse )
                  | ? [Vvar__0___24Anonymous__45015] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__45015)
                      & Vvar__0___24Anonymous__45010 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__45015)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2etrue )
                  | ( Vvar__0___24Anonymous__45010 = cCoq_2eNumbers_2eBinNums_2exH
                    & cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) )
        | ? [Vvar__0___24Anonymous__45016] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__45016)
            & ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__45016)
             => ( V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__45016)
                & ( ? [Vvar__0___24Anonymous__45020] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__45020)
                      & Vvar__0___24Anonymous__45016 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__45020)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2efalse )
                  | ? [Vvar__0___24Anonymous__45021] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__45021)
                      & Vvar__0___24Anonymous__45016 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__45021)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2etrue )
                  | ( Vvar__0___24Anonymous__45016 = cCoq_2eNumbers_2eBinNums_2exH
                    & cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) ).

fof('$_def_Coq.ZArith.BinIntDef.Z.max',axiom,
    ! [V0__n,V1__m] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
       => ( ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2eEq
            & cCoq_2eZArith_2eBinIntDef_2eZ_2emax___24a2(V0__n,V1__m) = V0__n )
          | ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2eLt
            & cCoq_2eZArith_2eBinIntDef_2eZ_2emax___24a2(V0__n,V1__m) = V1__m )
          | ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2eGt
            & cCoq_2eZArith_2eBinIntDef_2eZ_2emax___24a2(V0__n,V1__m) = V0__n ) ) ) ) ).

fof('$_def_Coq.ZArith.BinIntDef.Z.min',axiom,
    ! [V0__n,V1__m] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
       => ( ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2eEq
            & cCoq_2eZArith_2eBinIntDef_2eZ_2emin___24a2(V0__n,V1__m) = V0__n )
          | ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2eLt
            & cCoq_2eZArith_2eBinIntDef_2eZ_2emin___24a2(V0__n,V1__m) = V0__n )
          | ( cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V0__n,V1__m) = cCoq_2eInit_2eDatatypes_2eGt
            & cCoq_2eZArith_2eBinIntDef_2eZ_2emin___24a2(V0__n,V1__m) = V1__m ) ) ) ) ).

fof('$_def_Coq.ZArith.BinIntDef.Z.modulo',axiom,
    ! [V0__a,V1__b] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__a)
     => ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__b)
       => ? [Vvar__2___24Anonymous__15771] :
            ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2___24Anonymous__15771)
            & ? [Vvar__3___24Anonymous__15772] :
                ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3___24Anonymous__15772)
                & 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__15771,Vvar__3___24Anonymous__15772)
                & cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(V0__a,V1__b) = Vvar__3___24Anonymous__15772 ) ) ) ) ).

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__15744] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__15744)
            & ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
             => ( V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__15744)
                & ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
                    & cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZ0 )
                  | ? [Vvar__0___24Anonymous__15748] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__15748)
                      & V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__15748)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__15744,Vvar__0___24Anonymous__15748)) )
                  | ? [Vvar__0___24Anonymous__15749] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__15749)
                      & V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__15749)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__15744,Vvar__0___24Anonymous__15749)) ) ) ) ) )
        | ? [Vvar__0___24Anonymous__15750] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__15750)
            & ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
             => ( V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__15750)
                & ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
                    & cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZ0 )
                  | ? [Vvar__0___24Anonymous__15754] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__15754)
                      & V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__15754)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__15750,Vvar__0___24Anonymous__15754)) )
                  | ? [Vvar__0___24Anonymous__15755] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__15755)
                      & V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__15755)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2emul___24a2(Vvar__0___24Anonymous__15750,Vvar__0___24Anonymous__15755)) ) ) ) ) ) ) ) ).

fof('$_def_Coq.ZArith.BinIntDef.Z.odd',axiom,
    ! [V0__z] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
     => ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
          & cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2efalse )
        | ? [Vvar__0___24Anonymous__45022] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__45022)
            & ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__45022)
             => ( V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__45022)
                & ( ? [Vvar__0___24Anonymous__45026] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__45026)
                      & Vvar__0___24Anonymous__45022 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__45026)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2etrue )
                  | ? [Vvar__0___24Anonymous__45027] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__45027)
                      & Vvar__0___24Anonymous__45022 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__45027)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2efalse )
                  | ( Vvar__0___24Anonymous__45022 = cCoq_2eNumbers_2eBinNums_2exH
                    & cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) )
        | ? [Vvar__0___24Anonymous__45028] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__45028)
            & ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__45028)
             => ( V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__45028)
                & ( ? [Vvar__0___24Anonymous__45032] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__45032)
                      & Vvar__0___24Anonymous__45028 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__45032)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2etrue )
                  | ? [Vvar__0___24Anonymous__45033] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__45033)
                      & Vvar__0___24Anonymous__45028 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__45033)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2efalse )
                  | ( Vvar__0___24Anonymous__45028 = cCoq_2eNumbers_2eBinNums_2exH
                    & cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2etrue ) ) ) ) ) ) ) ).

fof('$_def_Coq.ZArith.BinIntDef.Z.of_N',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
     => ( ( V0__n = cCoq_2eNumbers_2eBinNums_2eN0
          & cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eZ0 )
        | ? [Vvar__0___24Anonymous__30592] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30592)
            & V0__n = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__30592)
            & cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(V0__n) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__30592) ) ) ) ).

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__15742] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__15742)
            & V0__x = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__15742)
            & cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__15742) )
        | ? [Vvar__0___24Anonymous__15743] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__15743)
            & V0__x = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__15743)
            & cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V0__x) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__15743) ) ) ) ).

fof('$_def_Coq.ZArith.BinIntDef.Z.pow',axiom,
    ! [V0__x,V1__y] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
     => ( ( V1__y = cCoq_2eNumbers_2eBinNums_2eZ0
          & cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH) )
        | ? [Vvar__0___24Anonymous__30568] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30568)
            & V1__y = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__30568)
            & cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(V0__x,V1__y) = cCoq_2eZArith_2eBinIntDef_2eZ_2epow__pos___24a2(V0__x,Vvar__0___24Anonymous__30568) )
        | ? [Vvar__0___24Anonymous__30569] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30569)
            & V1__y = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__30569)
            & cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(V0__x,V1__y) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ).

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

fof('$_def_Coq.ZArith.BinIntDef.Z.sub',axiom,
    ! [V0__m,V1__n] : cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(V0__m,V1__n) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__m,cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(V1__n)) ).

fof('$_def_Coq.ZArith.BinIntDef.Z.succ',axiom,
    ! [V0__x] : cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(V0__x) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__x,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH)) ).

fof('$_def_Coq.ZArith.BinIntDef.Z.t',axiom,
    ! [Vvar__35203] :
      ( cCoq_2eZArith_2eBinIntDef_2eZ_2et___24t(Vvar__35203)
    <=> cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__35203) ) ).

fof('$_def_Coq.ZArith.BinIntDef.Z.to_N',axiom,
    ! [V0__z] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
     => ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
          & cCoq_2eZArith_2eBinIntDef_2eZ_2eto__N___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eN0 )
        | ? [Vvar__0___24Anonymous__45008] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__45008)
            & V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__45008)
            & cCoq_2eZArith_2eBinIntDef_2eZ_2eto__N___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__45008) )
        | ? [Vvar__0___24Anonymous__45009] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__45009)
            & V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__45009)
            & cCoq_2eZArith_2eBinIntDef_2eZ_2eto__N___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2eN0 ) ) ) ).

fof('$_def_Coq.ZArith.BinIntDef.Z.to_nat',axiom,
    ! [V0__z] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
     => ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
          & cCoq_2eZArith_2eBinIntDef_2eZ_2eto__nat___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2eO )
        | ? [Vvar__0___24Anonymous__45006] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__45006)
            & V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__45006)
            & cCoq_2eZArith_2eBinIntDef_2eZ_2eto__nat___24a1(V0__z) = cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(Vvar__0___24Anonymous__45006) )
        | ? [Vvar__0___24Anonymous__45007] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__45007)
            & V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__45007)
            & cCoq_2eZArith_2eBinIntDef_2eZ_2eto__nat___24a1(V0__z) = cCoq_2eInit_2eDatatypes_2eO ) ) ) ).

fof('$_def_Coq.ZArith.BinIntDef.Z.to_pos',axiom,
    ! [V0__z] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__z)
     => ( ( V0__z = cCoq_2eNumbers_2eBinNums_2eZ0
          & cCoq_2eZArith_2eBinIntDef_2eZ_2eto__pos___24a1(V0__z) = cCoq_2eNumbers_2eBinNums_2exH )
        | ? [Vvar__0___24Anonymous__30595] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30595)
            & V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__30595)
            & cCoq_2eZArith_2eBinIntDef_2eZ_2eto__pos___24a1(V0__z) = Vvar__0___24Anonymous__30595 )
        | ? [Vvar__0___24Anonymous__30596] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30596)
            & V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__30596)
            & 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__34788] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__34788)
            & ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__34788)
             => ( V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__34788)
                & ( ? [Vvar__0___24Anonymous__34792] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__34792)
                      & Vvar__0___24Anonymous__34788 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__34792)
                      & ( cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)
                      <=> p(c_24False) ) )
                  | ? [Vvar__0___24Anonymous__34793] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__34793)
                      & Vvar__0___24Anonymous__34788 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__34793)
                      & ( cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)
                      <=> p(c_24True) ) )
                  | ( Vvar__0___24Anonymous__34788 = cCoq_2eNumbers_2eBinNums_2exH
                    & ( cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)
                    <=> p(c_24False) ) ) ) ) ) )
        | ? [Vvar__0___24Anonymous__34794] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__34794)
            & ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__34794)
             => ( V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__34794)
                & ( ? [Vvar__0___24Anonymous__34798] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__34798)
                      & Vvar__0___24Anonymous__34794 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__34798)
                      & ( cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)
                      <=> p(c_24False) ) )
                  | ? [Vvar__0___24Anonymous__34799] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__34799)
                      & Vvar__0___24Anonymous__34794 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__34799)
                      & ( cCoq_2eZArith_2eZeven_2eZeven___24a1(V0__z)
                      <=> p(c_24True) ) )
                  | ( Vvar__0___24Anonymous__34794 = 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__34800] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__34800)
            & ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__34800)
             => ( V0__z = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__34800)
                & ( ? [Vvar__0___24Anonymous__34804] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__34804)
                      & Vvar__0___24Anonymous__34800 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__34804)
                      & ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
                      <=> p(c_24True) ) )
                  | ? [Vvar__0___24Anonymous__34805] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__34805)
                      & Vvar__0___24Anonymous__34800 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__34805)
                      & ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
                      <=> p(c_24False) ) )
                  | ( Vvar__0___24Anonymous__34800 = cCoq_2eNumbers_2eBinNums_2exH
                    & ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
                    <=> p(c_24True) ) ) ) ) ) )
        | ? [Vvar__0___24Anonymous__34806] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__34806)
            & ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__34806)
             => ( V0__z = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__34806)
                & ( ? [Vvar__0___24Anonymous__34810] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__34810)
                      & Vvar__0___24Anonymous__34806 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__34810)
                      & ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
                      <=> p(c_24True) ) )
                  | ? [Vvar__0___24Anonymous__34811] :
                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__34811)
                      & Vvar__0___24Anonymous__34806 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__34811)
                      & ( cCoq_2eZArith_2eZeven_2eZodd___24a1(V0__z)
                      <=> p(c_24False) ) )
                  | ( Vvar__0___24Anonymous__34806 = 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__34813] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__34813)
            & V1__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__34813)
            & ( cCoq_2eZArith_2eZlogarithm_2eIs__power___24a1(V1__p)
            <=> p(c_24False) ) )
        | ? [Vvar__0___24Anonymous__34814] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__34814)
            & V1__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__34814)
            & ( cCoq_2eZArith_2eZlogarithm_2eIs__power___24a1(V1__p)
            <=> cCoq_2eZArith_2eZlogarithm_2eIs__power___24a1(Vvar__0___24Anonymous__34814) ) )
        | ( V1__p = cCoq_2eNumbers_2eBinNums_2exH
          & ( cCoq_2eZArith_2eZlogarithm_2eIs__power___24a1(V1__p)
          <=> p(c_24True) ) ) ) ) ).

fof('$_def_Coq.ZArith.Zlogarithm.log_inf',axiom,
    ! [V1__p] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__p)
     => ( ? [Vvar__0___24Anonymous__29150] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29150)
            & V1__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__29150)
            & cCoq_2eZArith_2eZlogarithm_2elog__inf___24a1(V1__p) = cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(cCoq_2eZArith_2eZlogarithm_2elog__inf___24a1(Vvar__0___24Anonymous__29150)) )
        | ? [Vvar__0___24Anonymous__29151] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__29151)
            & V1__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__29151)
            & cCoq_2eZArith_2eZlogarithm_2elog__inf___24a1(V1__p) = cCoq_2eZArith_2eBinIntDef_2eZ_2esucc___24a1(cCoq_2eZArith_2eZlogarithm_2elog__inf___24a1(Vvar__0___24Anonymous__29151)) )
        | ( V1__p = cCoq_2eNumbers_2eBinNums_2exH
          & cCoq_2eZArith_2eZlogarithm_2elog__inf___24a1(V1__p) = cCoq_2eNumbers_2eBinNums_2eZ0 ) ) ) ).

fof('$_def_Coq.micromega.Env.Env',axiom,
    ! [V0__D] : cCoq_2emicromega_2eEnv_2eEnv___24a1(V0__D) = c_24__type__30799___24a1(V0__D) ).

fof('$_def_Coq.micromega.Refl.make_conj',axiom,
    ! [V1__A,V2__eval,V3__l] :
      ( cType___24t(V1__A)
     => ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,V3__l)
       => ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V1__A)
            & ( cCoq_2emicromega_2eRefl_2emake__conj___24a3(V1__A,V2__eval,V3__l)
            <=> p(c_24True) ) )
          | ? [Vvar__1___24Anonymous__36468] :
              ( t(Vvar__1___24Anonymous__36468,V1__A)
              & ? [Vvar__2___24Anonymous__36469] :
                  ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__36469)
                  & ( cType___24t(V1__A)
                   => ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__36469)
                     => ( V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__A,Vvar__1___24Anonymous__36468,Vvar__2___24Anonymous__36469)
                        & ( ( Vvar__2___24Anonymous__36469 = cCoq_2eInit_2eDatatypes_2enil___24a1(V1__A)
                            & ( cCoq_2emicromega_2eRefl_2emake__conj___24a3(V1__A,V2__eval,V3__l)
                            <=> p(happ(V2__eval,Vvar__1___24Anonymous__36468)) ) )
                          | ? [Vvar__1___24Anonymous__36480] :
                              ( t(Vvar__1___24Anonymous__36480,V1__A)
                              & ? [Vvar__2___24Anonymous__36481] :
                                  ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__36481)
                                  & Vvar__2___24Anonymous__36469 = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__A,Vvar__1___24Anonymous__36480,Vvar__2___24Anonymous__36481)
                                  & ( cCoq_2emicromega_2eRefl_2emake__conj___24a3(V1__A,V2__eval,V3__l)
                                  <=> ( p(happ(V2__eval,Vvar__1___24Anonymous__36468))
                                      & cCoq_2emicromega_2eRefl_2emake__conj___24a3(V1__A,V2__eval,Vvar__2___24Anonymous__36469) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('$_def_Coq.micromega.Refl.make_impl',axiom,
    ! [V1__A,V2__eval,V3__l,V4__goal] :
      ( cType___24t(V1__A)
     => ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,V3__l)
       => ( ( V3__l = cCoq_2eInit_2eDatatypes_2enil___24a1(V1__A)
            & ( cCoq_2emicromega_2eRefl_2emake__impl___24a4(V1__A,V2__eval,V3__l,V4__goal)
            <=> p(V4__goal) ) )
          | ? [Vvar__1___24Anonymous__36449] :
              ( t(Vvar__1___24Anonymous__36449,V1__A)
              & ? [Vvar__2___24Anonymous__36450] :
                  ( cCoq_2eInit_2eDatatypes_2elist___24t(V1__A,Vvar__2___24Anonymous__36450)
                  & V3__l = cCoq_2eInit_2eDatatypes_2econs___24a3(V1__A,Vvar__1___24Anonymous__36449,Vvar__2___24Anonymous__36450)
                  & ( cCoq_2emicromega_2eRefl_2emake__impl___24a4(V1__A,V2__eval,V3__l,V4__goal)
                  <=> ( p(happ(V2__eval,Vvar__1___24Anonymous__36449))
                     => cCoq_2emicromega_2eRefl_2emake__impl___24a4(V1__A,V2__eval,Vvar__2___24Anonymous__36450,V4__goal) ) ) ) ) ) ) ) ).

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

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

fof('$_def_Coq.micromega.RingMicromega.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__42274___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__42282___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__42290___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__42298___24a3(V0__R,V1__rO,V3__rle) ) ) ) ) ).

fof('$_def_Coq.micromega.RingMicromega.ge_bool',axiom,
    ! [V1__n,V2__m] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
     => ( ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
         => ( V1__n = cCoq_2eInit_2eDatatypes_2eO
            & ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
                & cCoq_2emicromega_2eRingMicromega_2ege__bool___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2etrue )
              | ? [Vvar__0___24Anonymous__42353] :
                  ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__42353)
                  & V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__42353)
                  & cCoq_2emicromega_2eRingMicromega_2ege__bool___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) )
        | ? [Vvar__0___24Anonymous__42354] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__42354)
            & ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
             => ( V1__n = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__42354)
                & ( ( V2__m = cCoq_2eInit_2eDatatypes_2eO
                    & cCoq_2emicromega_2eRingMicromega_2ege__bool___24a2(V1__n,V2__m) = cCoq_2eInit_2eDatatypes_2etrue )
                  | ? [Vvar__0___24Anonymous__42357] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__42357)
                      & V2__m = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__42357)
                      & cCoq_2emicromega_2eRingMicromega_2ege__bool___24a2(V1__n,V2__m) = cCoq_2emicromega_2eRingMicromega_2ege__bool___24a2(Vvar__0___24Anonymous__42354,Vvar__0___24Anonymous__42357) ) ) ) ) ) ) ) ).

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

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

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

fof('$_def_Coq.micromega.ZMicromega.ZWitness',axiom,
    ! [Vvar__29000] :
      ( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__29000)
    <=> cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(cCoq_2eNumbers_2eBinNums_2eZ,Vvar__29000) ) ).

fof('$_def_Coq.micromega.ZMicromega.coneMember',axiom,
    ! [Vvar__44096] :
      ( cCoq_2emicromega_2eZMicromega_2econeMember___24t(Vvar__44096)
    <=> cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__44096) ) ).

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

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

fof('$_def_Coq.omega.PreOmega.Zneg\'',axiom,
    cCoq_2eomega_2ePreOmega_2eZneg_27 = cCoq_2eNumbers_2eBinNums_2eZneg ).

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

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

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

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

fof('$_def_Coq.setoid_ring.InitialRing.Nword',axiom,
    ! [Vvar__35554] :
      ( cCoq_2esetoid__ring_2eInitialRing_2eNword___24t(Vvar__35554)
    <=> cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eNumbers_2eBinNums_2eN,Vvar__35554) ) ).

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__32389] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__32389)
              & ( cType___24t(V0__R)
               => ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__32389)
                 => ( V5__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__32389)
                    & ( ? [Vvar__0___24Anonymous__32393] :
                          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__32393)
                          & Vvar__0___24Anonymous__32389 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__32393)
                          & 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__32389))) )
                      | ? [Vvar__0___24Anonymous__32394] :
                          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__32394)
                          & Vvar__0___24Anonymous__32389 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__32394)
                          & 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__32389))) )
                      | ( Vvar__0___24Anonymous__32389 = 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__32395] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__32395)
              & ( cType___24t(V0__R)
               => ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__32395)
                 => ( V5__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__32395)
                    & ( ? [Vvar__0___24Anonymous__32399] :
                          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__32399)
                          & Vvar__0___24Anonymous__32395 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__32399)
                          & 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__32395)) )
                      | ? [Vvar__0___24Anonymous__32400] :
                          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__32400)
                          & Vvar__0___24Anonymous__32395 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__32400)
                          & 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__32395)) )
                      | ( Vvar__0___24Anonymous__32395 = 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__32356] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__32356)
              & V5__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__32356)
              & 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__32356))) )
          | ? [Vvar__0___24Anonymous__32357] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__32357)
              & V5__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__32357)
              & 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__32357)) )
          | ( V5__p = cCoq_2eNumbers_2eBinNums_2exH
            & cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1___24a5(V0__R,V1__rI,V2__radd,V3__rmul,V5__p) = V1__rI ) ) ) ) ).

fof('$_def_Coq.setoid_ring.Ring_polynom.Peq',axiom,
    ! [V0__C,V1__ceqb,V3__P,V4__P_27] :
      ( cType___24t(V0__C)
     => ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,V3__P)
       => ( ? [Vvar__1___24Anonymous__27229] :
              ( t(Vvar__1___24Anonymous__27229,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__27229)
                    & ( ? [Vvar__1___24Anonymous__27239] :
                          ( t(Vvar__1___24Anonymous__27239,V0__C)
                          & V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V0__C,Vvar__1___24Anonymous__27239)
                          & cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = happ(happ(V1__ceqb,Vvar__1___24Anonymous__27229),Vvar__1___24Anonymous__27239) )
                      | ? [Vvar__1___24Anonymous__27241] :
                          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__27241)
                          & ? [Vvar__2___24Anonymous__27242] :
                              ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__27242)
                              & V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V0__C,Vvar__1___24Anonymous__27241,Vvar__2___24Anonymous__27242)
                              & cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) )
                      | ? [Vvar__1___24Anonymous__27245] :
                          ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__27245)
                          & ? [Vvar__2___24Anonymous__27246] :
                              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__27246)
                              & ? [Vvar__3___24Anonymous__27247] :
                                  ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__27247)
                                  & V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V0__C,Vvar__1___24Anonymous__27245,Vvar__2___24Anonymous__27246,Vvar__3___24Anonymous__27247)
                                  & cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) )
          | ? [Vvar__1___24Anonymous__27252] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__27252)
              & ? [Vvar__2___24Anonymous__27253] :
                  ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__27253)
                  & ( 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__27252,Vvar__2___24Anonymous__27253)
                        & ( ? [Vvar__1___24Anonymous__27273] :
                              ( t(Vvar__1___24Anonymous__27273,V0__C)
                              & V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V0__C,Vvar__1___24Anonymous__27273)
                              & cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse )
                          | ? [Vvar__1___24Anonymous__27275] :
                              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__27275)
                              & ? [Vvar__2___24Anonymous__27276] :
                                  ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__27276)
                                  & ( cType___24t(V0__C)
                                   => ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__27252)
                                     => ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__27275)
                                       => ( V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V0__C,Vvar__1___24Anonymous__27275,Vvar__2___24Anonymous__27276)
                                          & ( ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__1___24Anonymous__27252,Vvar__1___24Anonymous__27275) = 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__27253,Vvar__2___24Anonymous__27276) )
                                            | ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__1___24Anonymous__27252,Vvar__1___24Anonymous__27275) = 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__27252,Vvar__1___24Anonymous__27275) = 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__27281] :
                              ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__27281)
                              & ? [Vvar__2___24Anonymous__27282] :
                                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__27282)
                                  & ? [Vvar__3___24Anonymous__27283] :
                                      ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__27283)
                                      & V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V0__C,Vvar__1___24Anonymous__27281,Vvar__2___24Anonymous__27282,Vvar__3___24Anonymous__27283)
                                      & cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) ) )
          | ? [Vvar__1___24Anonymous__27288] :
              ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__27288)
              & ? [Vvar__2___24Anonymous__27289] :
                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__27289)
                  & ? [Vvar__3___24Anonymous__27290] :
                      ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__27290)
                      & ( 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__27288,Vvar__2___24Anonymous__27289,Vvar__3___24Anonymous__27290)
                            & ( ? [Vvar__1___24Anonymous__27323] :
                                  ( t(Vvar__1___24Anonymous__27323,V0__C)
                                  & V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V0__C,Vvar__1___24Anonymous__27323)
                                  & cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse )
                              | ? [Vvar__1___24Anonymous__27325] :
                                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__27325)
                                  & ? [Vvar__2___24Anonymous__27326] :
                                      ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__2___24Anonymous__27326)
                                      & V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V0__C,Vvar__1___24Anonymous__27325,Vvar__2___24Anonymous__27326)
                                      & cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) )
                              | ? [Vvar__1___24Anonymous__27329] :
                                  ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__27329)
                                  & ? [Vvar__2___24Anonymous__27330] :
                                      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__27330)
                                      & ? [Vvar__3___24Anonymous__27331] :
                                          ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__3___24Anonymous__27331)
                                          & ( cType___24t(V0__C)
                                           => ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__27289)
                                             => ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__27330)
                                               => ( V4__P_27 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V0__C,Vvar__1___24Anonymous__27329,Vvar__2___24Anonymous__27330,Vvar__3___24Anonymous__27331)
                                                  & ( ( cType___24t(V0__C)
                                                     => ( c_24__type__9314___24t(V0__C,V1__ceqb)
                                                       => ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__27288)
                                                         => ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V0__C,Vvar__1___24Anonymous__27329)
                                                           => ( cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(Vvar__2___24Anonymous__27289,Vvar__2___24Anonymous__27330) = cCoq_2eInit_2eDatatypes_2eEq
                                                              & ( ( cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,Vvar__1___24Anonymous__27288,Vvar__1___24Anonymous__27329) = 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__27290,Vvar__3___24Anonymous__27331) )
                                                                | ( cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,Vvar__1___24Anonymous__27288,Vvar__1___24Anonymous__27329) = 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__27289,Vvar__2___24Anonymous__27330) = 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__27289,Vvar__2___24Anonymous__27330) = cCoq_2eInit_2eDatatypes_2eGt
                                                      & cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V0__C,V1__ceqb,V3__P,V4__P_27) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('$_def_Coq.setoid_ring.Ring_polynom.mkmult_pow',axiom,
    ! [V0__R,V1__rmul,V3__r,V4__x,V5__p] :
      ( cType___24t(V0__R)
     => ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V5__p)
       => ( ? [Vvar__0___24Anonymous__32758] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__32758)
              & V5__p = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__32758)
              & 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__32758),V4__x,Vvar__0___24Anonymous__32758) )
          | ? [Vvar__0___24Anonymous__32759] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__32759)
              & V5__p = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__32759)
              & 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__32759),V4__x,Vvar__0___24Anonymous__32759) )
          | ( V5__p = cCoq_2eNumbers_2eBinNums_2exH
            & cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow___24a5(V0__R,V1__rmul,V3__r,V4__x,V5__p) = happ(happ(V1__rmul,V3__r),V4__x) ) ) ) ) ).

fof('$_def_Coq.setoid_ring.Ring_tac.ring_subst_niter',axiom,
    cCoq_2esetoid__ring_2eRing__tac_2ering__subst__niter = cCoq_2eInit_2eNat_2emul___24a2(cCoq_2eInit_2eNat_2emul___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)))))))))),cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO))))))))))),cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO))))))))))) ).

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

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

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

fof('$_def_Coq.setoid_ring.Ring_theory.id_phi_N',axiom,
    ! [V0__x] : cCoq_2esetoid__ring_2eRing__theory_2eid__phi__N___24a1(V0__x) = V0__x ).

fof('$_def_Coq.setoid_ring.Ring_theory.pow_N',axiom,
    ! [V0__R,V1__rI,V2__rmul,V3__x,V4__p] :
      ( cType___24t(V0__R)
     => ( cCoq_2eNumbers_2eBinNums_2eN___24t(V4__p)
       => ( ( V4__p = cCoq_2eNumbers_2eBinNums_2eN0
            & cCoq_2esetoid__ring_2eRing__theory_2epow__N___24a5(V0__R,V1__rI,V2__rmul,V3__x,V4__p) = V1__rI )
          | ? [Vvar__0___24Anonymous__11431] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__11431)
              & V4__p = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__11431)
              & 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__11431) ) ) ) ) ).

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__32779] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__32779)
              & V4__i = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__32779)
              & 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__32780__32783___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__32779)),c_24__let__var__6__p__32780__32783___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__32779))) )
          | ? [Vvar__0___24Anonymous__32781] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__32781)
              & V4__i = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__32781)
              & 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__32782__32784___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__32781)),c_24__let__var__6__p__32782__32784___24a4(V0__R,V1__rmul,V3__x,Vvar__0___24Anonymous__32781)) )
          | ( 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_Norm.subst',axiom,
    ! [V1__x,V2__s,V3__t] :
      ( cNorm_2etm___24t(V3__t)
     => ( ? [Vvar__0___24Anonymous__4545] :
            ( cCoq_2eStrings_2eString_2estring___24t(Vvar__0___24Anonymous__4545)
            & ( cCoq_2eStrings_2eString_2estring___24t(V1__x)
             => ( cCoq_2eStrings_2eString_2estring___24t(Vvar__0___24Anonymous__4545)
               => ( V3__t = cNorm_2evar___24a1(Vvar__0___24Anonymous__4545)
                  & ( ( cPLF_2eMaps_2eeqb__string___24a2(V1__x,Vvar__0___24Anonymous__4545) = cCoq_2eInit_2eDatatypes_2etrue
                      & cNorm_2esubst___24a3(V1__x,V2__s,V3__t) = V2__s )
                    | ( cPLF_2eMaps_2eeqb__string___24a2(V1__x,Vvar__0___24Anonymous__4545) = cCoq_2eInit_2eDatatypes_2efalse
                      & cNorm_2esubst___24a3(V1__x,V2__s,V3__t) = V3__t ) ) ) ) ) )
        | ? [Vvar__0___24Anonymous__4547] :
            ( cNorm_2etm___24t(Vvar__0___24Anonymous__4547)
            & ? [Vvar__1___24Anonymous__4548] :
                ( cNorm_2etm___24t(Vvar__1___24Anonymous__4548)
                & V3__t = cNorm_2eapp___24a2(Vvar__0___24Anonymous__4547,Vvar__1___24Anonymous__4548)
                & cNorm_2esubst___24a3(V1__x,V2__s,V3__t) = cNorm_2eapp___24a2(cNorm_2esubst___24a3(V1__x,V2__s,Vvar__0___24Anonymous__4547),cNorm_2esubst___24a3(V1__x,V2__s,Vvar__1___24Anonymous__4548)) ) )
        | ? [Vvar__0___24Anonymous__4550] :
            ( cCoq_2eStrings_2eString_2estring___24t(Vvar__0___24Anonymous__4550)
            & ? [Vvar__1___24Anonymous__4551] :
                ( cNorm_2ety___24t(Vvar__1___24Anonymous__4551)
                & ? [Vvar__2___24Anonymous__4552] :
                    ( cNorm_2etm___24t(Vvar__2___24Anonymous__4552)
                    & V3__t = cNorm_2eabs___24a3(Vvar__0___24Anonymous__4550,Vvar__1___24Anonymous__4551,Vvar__2___24Anonymous__4552)
                    & cNorm_2esubst___24a3(V1__x,V2__s,V3__t) = cNorm_2eabs___24a3(Vvar__0___24Anonymous__4550,Vvar__1___24Anonymous__4551,c_24__case__Coq_2eInit_2eDatatypes_2ebool_244574___24a4(V1__x,V2__s,Vvar__0___24Anonymous__4550,Vvar__2___24Anonymous__4552)) ) ) )
        | ? [Vvar__0___24Anonymous__4559] :
            ( cNorm_2etm___24t(Vvar__0___24Anonymous__4559)
            & ? [Vvar__1___24Anonymous__4560] :
                ( cNorm_2etm___24t(Vvar__1___24Anonymous__4560)
                & V3__t = cNorm_2epair___24a2(Vvar__0___24Anonymous__4559,Vvar__1___24Anonymous__4560)
                & cNorm_2esubst___24a3(V1__x,V2__s,V3__t) = cNorm_2epair___24a2(cNorm_2esubst___24a3(V1__x,V2__s,Vvar__0___24Anonymous__4559),cNorm_2esubst___24a3(V1__x,V2__s,Vvar__1___24Anonymous__4560)) ) )
        | ? [Vvar__0___24Anonymous__4562] :
            ( cNorm_2etm___24t(Vvar__0___24Anonymous__4562)
            & V3__t = cNorm_2efst___24a1(Vvar__0___24Anonymous__4562)
            & cNorm_2esubst___24a3(V1__x,V2__s,V3__t) = cNorm_2efst___24a1(cNorm_2esubst___24a3(V1__x,V2__s,Vvar__0___24Anonymous__4562)) )
        | ? [Vvar__0___24Anonymous__4563] :
            ( cNorm_2etm___24t(Vvar__0___24Anonymous__4563)
            & V3__t = cNorm_2esnd___24a1(Vvar__0___24Anonymous__4563)
            & cNorm_2esubst___24a3(V1__x,V2__s,V3__t) = cNorm_2esnd___24a1(cNorm_2esubst___24a3(V1__x,V2__s,Vvar__0___24Anonymous__4563)) )
        | ( V3__t = cNorm_2etru
          & cNorm_2esubst___24a3(V1__x,V2__s,V3__t) = cNorm_2etru )
        | ( V3__t = cNorm_2efls
          & cNorm_2esubst___24a3(V1__x,V2__s,V3__t) = cNorm_2efls )
        | ? [Vvar__0___24Anonymous__4564] :
            ( cNorm_2etm___24t(Vvar__0___24Anonymous__4564)
            & ? [Vvar__1___24Anonymous__4565] :
                ( cNorm_2etm___24t(Vvar__1___24Anonymous__4565)
                & ? [Vvar__2___24Anonymous__4566] :
                    ( cNorm_2etm___24t(Vvar__2___24Anonymous__4566)
                    & V3__t = cNorm_2etest___24a3(Vvar__0___24Anonymous__4564,Vvar__1___24Anonymous__4565,Vvar__2___24Anonymous__4566)
                    & cNorm_2esubst___24a3(V1__x,V2__s,V3__t) = cNorm_2etest___24a3(cNorm_2esubst___24a3(V1__x,V2__s,Vvar__0___24Anonymous__4564),cNorm_2esubst___24a3(V1__x,V2__s,Vvar__1___24Anonymous__4565),cNorm_2esubst___24a3(V1__x,V2__s,Vvar__2___24Anonymous__4566)) ) ) ) ) ) ).

fof('$_def_PLF.Imp.state',axiom,
    ! [Vvar__25432] :
      ( cPLF_2eImp_2estate___24t(Vvar__25432)
    <=> cPLF_2eMaps_2etotal__map___24t(cCoq_2eInit_2eDatatypes_2enat,Vvar__25432) ) ).

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__4765___24a2(V0__x,V1__y),c_24__prop__4766___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__4767___24a2(V0__x,V1__y),c_24__prop__4768___24a2(V0__x,V1__y))
            & cPLF_2eMaps_2eeqb__string___24a2(V0__x,V1__y) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ).

fof('$_def_PLF.Maps.total_map',axiom,
    ! [V0__A] : cPLF_2eMaps_2etotal__map___24a1(V0__A) = c_24__type__32433___24a1(V0__A) ).

fof('$_def_PLF.Smallstep.normal_form',axiom,
    ! [V0__X,V1__R,V2__t] :
      ( cPLF_2eSmallstep_2enormal__form___24a3(V0__X,V1__R,V2__t)
    <=> ~ ? [V3__t_27] :
            ( t(V3__t_27,V0__X)
            & p(happ(happ(V1__R,V2__t),V3__t_27)) ) ) ).

fof('$_def_PLF.Smallstep.normalizing',axiom,
    ! [V0__X,V1__R] :
      ( cPLF_2eSmallstep_2enormalizing___24a2(V0__X,V1__R)
    <=> ! [V2__t] :
          ( t(V2__t,V0__X)
         => ? [V3__t_27] :
              ( t(V3__t_27,V0__X)
              & cPLF_2eSmallstep_2emulti___24a4(V0__X,V1__R,V2__t,V3__t_27)
              & cPLF_2eSmallstep_2enormal__form___24a3(V0__X,V1__R,V3__t_27) ) ) ) ).

fof('$_def_PLF.Smallstep.relation',axiom,
    ! [V0__X] : cPLF_2eSmallstep_2erelation___24a1(V0__X) = c_24__type__4775___24a1(V0__X) ).

fof('$_def_PLF.Smallstep.stack',axiom,
    ! [Vvar__43745] :
      ( cPLF_2eSmallstep_2estack___24t(Vvar__43745)
    <=> cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2eInit_2eDatatypes_2enat,Vvar__43745) ) ).

fof('$_def_PLF.Smallstep.step_normal_form',axiom,
    cPLF_2eSmallstep_2estep__normal__form = cPLF_2eSmallstep_2enormal__form___24a2(cPLF_2eSmallstep_2etm,cPLF_2eSmallstep_2estep) ).

fof('$_discrim_Coq.Bool.Bool.ReflectT$Coq.Bool.Bool.ReflectF',axiom,
    ! [Vvar__0__P__31083,Vvar__1___24Anonymous__31084,Vvar__0__P__31085,Vvar__1___24Anonymous__31086] : cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__31083) != cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__31085) ).

fof('$_discrim_Coq.FSets.FSetPositive.PositiveSet.Leaf$Coq.FSets.FSetPositive.PositiveSet.Node',axiom,
    ! [Vvar__0___24Anonymous__30005,Vvar__1___24Anonymous__30006,Vvar__2___24Anonymous__30007] : cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf != cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__30005,Vvar__1___24Anonymous__30006,Vvar__2___24Anonymous__30007) ).

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__23833,Vvar__1__Plt__23834,Vvar__2__Pgt__23835,Vvar__3___24Anonymous__23836,Vvar__0__Peq__23837,Vvar__1__Plt__23838,Vvar__2__Pgt__23839,Vvar__3___24Anonymous__23840] : cCoq_2eInit_2eDatatypes_2eCompEqT___24a3(Vvar__0__Peq__23833,Vvar__1__Plt__23834,Vvar__2__Pgt__23835) != cCoq_2eInit_2eDatatypes_2eCompLtT___24a3(Vvar__0__Peq__23837,Vvar__1__Plt__23838,Vvar__2__Pgt__23839) ).

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__7433,Vvar__1___24Anonymous__7434,Vvar__0__A__7435] : cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__7433,Vvar__1___24Anonymous__7434) != cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__7435) ).

fof('$_discrim_Coq.Init.Datatypes.inl$Coq.Init.Datatypes.inr',axiom,
    ! [Vvar__0__A__23718,Vvar__1__B__23719,Vvar__2___24Anonymous__23720,Vvar__0__A__23721,Vvar__1__B__23722,Vvar__2___24Anonymous__23723] : cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__23718,Vvar__1__B__23719,Vvar__2___24Anonymous__23720) != cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__23721,Vvar__1__B__23722,Vvar__2___24Anonymous__23723) ).

fof('$_discrim_Coq.Init.Datatypes.nil$Coq.Init.Datatypes.cons',axiom,
    ! [Vvar__0__A__7466,Vvar__0__A__7467,Vvar__1___24Anonymous__7468,Vvar__2___24Anonymous__7469] : cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__7466) != cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__7467,Vvar__1___24Anonymous__7468,Vvar__2___24Anonymous__7469) ).

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__31121,Vvar__1__f__31122,Vvar__0__i__31123,Vvar__1__f__31124,Vvar__2__e__31125] : cCoq_2eInit_2eDecimal_2eDecimal___24a2(Vvar__0__i__31121,Vvar__1__f__31122) != cCoq_2eInit_2eDecimal_2eDecimalExp___24a3(Vvar__0__i__31123,Vvar__1__f__31124,Vvar__2__e__31125) ).

fof('$_discrim_Coq.Init.Decimal.Nil$Coq.Init.Decimal.D0',axiom,
    ! [Vvar__0___24Anonymous__24073] : cCoq_2eInit_2eDecimal_2eNil != cCoq_2eInit_2eDecimal_2eD0___24a1(Vvar__0___24Anonymous__24073) ).

fof('$_discrim_Coq.Init.Decimal.Pos$Coq.Init.Decimal.Neg',axiom,
    ! [Vvar__0__d__31109,Vvar__0__d__31110] : cCoq_2eInit_2eDecimal_2ePos___24a1(Vvar__0__d__31109) != cCoq_2eInit_2eDecimal_2eNeg___24a1(Vvar__0__d__31110) ).

fof('$_discrim_Coq.Init.Specif.inleft$Coq.Init.Specif.inright',axiom,
    ! [Vvar__0__A__30912,Vvar__1__B__30913,Vvar__2___24Anonymous__30914,Vvar__0__A__30915,Vvar__1__B__30916,Vvar__2___24Anonymous__30917] : cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__30912,Vvar__1__B__30913,Vvar__2___24Anonymous__30914) != cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__30915,Vvar__1__B__30916) ).

fof('$_discrim_Coq.Init.Specif.left$Coq.Init.Specif.right',axiom,
    ! [Vvar__0__A__7150,Vvar__1__B__7151,Vvar__2___24Anonymous__7152,Vvar__0__A__7153,Vvar__1__B__7154,Vvar__2___24Anonymous__7155] : cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__7150,Vvar__1__B__7151) != cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__7153,Vvar__1__B__7154) ).

fof('$_discrim_Coq.Numbers.BinNums.N0$Coq.Numbers.BinNums.Npos',axiom,
    ! [Vvar__0___24Anonymous__7412] : cCoq_2eNumbers_2eBinNums_2eN0 != cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__7412) ).

fof('$_discrim_Coq.Numbers.BinNums.Z0$Coq.Numbers.BinNums.Zpos',axiom,
    ! [Vvar__0___24Anonymous__7421] : cCoq_2eNumbers_2eBinNums_2eZ0 != cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__7421) ).

fof('$_discrim_Coq.Numbers.BinNums.xI$Coq.Numbers.BinNums.xO',axiom,
    ! [Vvar__0___24Anonymous__5486,Vvar__0___24Anonymous__5487] : cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__5486) != cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__5487) ).

fof('$_discrim_Coq.PArith.BinPos.Pos.PeanoOne$Coq.PArith.BinPos.Pos.PeanoSucc',axiom,
    ! [Vvar__0__p__35186,Vvar__1___24Anonymous__35187] : cCoq_2ePArith_2eBinPos_2ePos_2ePeanoOne != cCoq_2ePArith_2eBinPos_2ePos_2ePeanoSucc___24a2(Vvar__0__p__35186,Vvar__1___24Anonymous__35187) ).

fof('$_discrim_Coq.PArith.BinPosDef.Pos.IsNul$Coq.PArith.BinPosDef.Pos.IsPos',axiom,
    ! [Vvar__0___24Anonymous__30985] : cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNul != cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__30985) ).

fof('$_discrim_Coq.Reals.Rfunctions.ZintNull$Coq.Reals.Rfunctions.ZintPos',axiom,
    ! [Vvar__0__x__32735,Vvar__1___24Anonymous__32736,Vvar__0__x__32737,Vvar__1__n__32738,Vvar__2___24Anonymous__32739] : cCoq_2eReals_2eRfunctions_2eZintNull___24a1(Vvar__0__x__32735) != cCoq_2eReals_2eRfunctions_2eZintPos___24a2(Vvar__0__x__32737,Vvar__1__n__32738) ).

fof('$_discrim_Coq.Strings.String.EmptyString$Coq.Strings.String.String',axiom,
    ! [Vvar__0___24Anonymous__130,Vvar__1___24Anonymous__131] : cCoq_2eStrings_2eString_2eEmptyString != cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__130,Vvar__1___24Anonymous__131) ).

fof('$_discrim_Coq.Structures.OrderedType.LT$Coq.Structures.OrderedType.EQ',axiom,
    ! [Vvar__0__X__32587,Vvar__1__lt__32588,Vvar__2__eq__32589,Vvar__3__x__32590,Vvar__4__y__32591,Vvar__5___24Anonymous__32592,Vvar__0__X__32593,Vvar__1__lt__32594,Vvar__2__eq__32595,Vvar__3__x__32596,Vvar__4__y__32597,Vvar__5___24Anonymous__32598] : cCoq_2eStructures_2eOrderedType_2eLT___24a5(Vvar__0__X__32587,Vvar__1__lt__32588,Vvar__2__eq__32589,Vvar__3__x__32590,Vvar__4__y__32591) != cCoq_2eStructures_2eOrderedType_2eEQ___24a5(Vvar__0__X__32593,Vvar__1__lt__32594,Vvar__2__eq__32595,Vvar__3__x__32596,Vvar__4__y__32597) ).

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__24998,Vvar__0__n__24999,Vvar__1___24Anonymous__25000] : cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__24998) != cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__24999,Vvar__1___24Anonymous__25000) ).

fof('$_discrim_Coq.Vectors.VectorDef.nil$Coq.Vectors.VectorDef.cons',axiom,
    ! [Vvar__0__A__28939,Vvar__0__A__28940,Vvar__1__h__28941,Vvar__2__n__28942,Vvar__3___24Anonymous__28943] : cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__28939) != cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__28940,Vvar__1__h__28941,Vvar__2__n__28942,Vvar__3___24Anonymous__28943) ).

fof('$_discrim_Coq.micromega.EnvRing.PEc$Coq.micromega.EnvRing.PEX',axiom,
    ! [Vvar__0__C__24225,Vvar__1___24Anonymous__24226,Vvar__0__C__24227,Vvar__1___24Anonymous__24228] : cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__24225,Vvar__1___24Anonymous__24226) != cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__24227,Vvar__1___24Anonymous__24228) ).

fof('$_discrim_Coq.micromega.EnvRing.Pc$Coq.micromega.EnvRing.Pinj',axiom,
    ! [Vvar__0__C__30825,Vvar__1___24Anonymous__30826,Vvar__0__C__30827,Vvar__1___24Anonymous__30828,Vvar__2___24Anonymous__30829] : cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__30825,Vvar__1___24Anonymous__30826) != cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__30827,Vvar__1___24Anonymous__30828,Vvar__2___24Anonymous__30829) ).

fof('$_discrim_Coq.micromega.EnvRing.mon0$Coq.micromega.EnvRing.zmon',axiom,
    ! [Vvar__0___24Anonymous__30859,Vvar__1___24Anonymous__30860] : cCoq_2emicromega_2eEnvRing_2emon0 != cCoq_2emicromega_2eEnvRing_2ezmon___24a2(Vvar__0___24Anonymous__30859,Vvar__1___24Anonymous__30860) ).

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__27069,Vvar__1___24Anonymous__27070,Vvar__0__C__27071,Vvar__1___24Anonymous__27072] : cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(Vvar__0__C__27069,Vvar__1___24Anonymous__27070) != cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(Vvar__0__C__27071,Vvar__1___24Anonymous__27072) ).

fof('$_discrim_Coq.micromega.Tauto.TT$Coq.micromega.Tauto.FF',axiom,
    ! [Vvar__0__TA__28321,Vvar__1__TX__28322,Vvar__2__AA__28323,Vvar__3__AF__28324,Vvar__0__TA__28325,Vvar__1__TX__28326,Vvar__2__AA__28327,Vvar__3__AF__28328] : cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__28321,Vvar__1__TX__28322,Vvar__2__AA__28323,Vvar__3__AF__28324) != cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__28325,Vvar__1__TX__28326,Vvar__2__AA__28327,Vvar__3__AF__28328) ).

fof('$_discrim_Coq.micromega.VarMap.Empty$Coq.micromega.VarMap.Elt',axiom,
    ! [Vvar__0__A__34771,Vvar__0__A__34772,Vvar__1___24Anonymous__34773] : cCoq_2emicromega_2eVarMap_2eEmpty___24a1(Vvar__0__A__34771) != cCoq_2emicromega_2eVarMap_2eElt___24a2(Vvar__0__A__34772,Vvar__1___24Anonymous__34773) ).

fof('$_discrim_Coq.micromega.ZMicromega.DoneProof$Coq.micromega.ZMicromega.RatProof',axiom,
    ! [Vvar__0___24Anonymous__29028,Vvar__1___24Anonymous__29029] : cCoq_2emicromega_2eZMicromega_2eDoneProof != cCoq_2emicromega_2eZMicromega_2eRatProof___24a2(Vvar__0___24Anonymous__29028,Vvar__1___24Anonymous__29029) ).

fof('$_discrim_Coq.setoid_ring.Field_theory.FEO$Coq.setoid_ring.Field_theory.FEI',axiom,
    ! [Vvar__0__C__8594,Vvar__0__C__8595] : cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__8594) != cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__8595) ).

fof('$_discrim_Coq.setoid_ring.Ring_polynom.PEO$Coq.setoid_ring.Ring_polynom.PEI',axiom,
    ! [Vvar__0__C__10033,Vvar__0__C__10034] : cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__10033) != cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__10034) ).

fof('$_discrim_Coq.setoid_ring.Ring_polynom.Pc$Coq.setoid_ring.Ring_polynom.Pinj',axiom,
    ! [Vvar__0__C__9809,Vvar__1___24Anonymous__9810,Vvar__0__C__9811,Vvar__1___24Anonymous__9812,Vvar__2___24Anonymous__9813] : cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__9809,Vvar__1___24Anonymous__9810) != cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__9811,Vvar__1___24Anonymous__9812,Vvar__2___24Anonymous__9813) ).

fof('$_discrim_Coq.setoid_ring.Ring_polynom.mon0$Coq.setoid_ring.Ring_polynom.zmon',axiom,
    ! [Vvar__0___24Anonymous__9843,Vvar__1___24Anonymous__9844] : cCoq_2esetoid__ring_2eRing__polynom_2emon0 != cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__9843,Vvar__1___24Anonymous__9844) ).

fof('$_discrim_Coq.setoid_ring.Ring_theory.Abstract$Coq.setoid_ring.Ring_theory.Computational',axiom,
    ! [Vvar__0__R__34448,Vvar__1__req__34449,Vvar__2__reqb__34450,Vvar__3___24Anonymous__34451] : cCoq_2esetoid__ring_2eRing__theory_2eAbstract != cCoq_2esetoid__ring_2eRing__theory_2eComputational___24a3(Vvar__0__R__34448,Vvar__1__req__34449,Vvar__2__reqb__34450) ).

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

fof('$_discrim_Norm.Bool$Norm.Arrow',axiom,
    ! [Vvar__0___24Anonymous__4746,Vvar__1___24Anonymous__4747] : cNorm_2eBool != cNorm_2eArrow___24a2(Vvar__0___24Anonymous__4746,Vvar__1___24Anonymous__4747) ).

fof('$_discrim_Norm.var$Norm.app',axiom,
    ! [Vvar__0___24Anonymous__4695,Vvar__0___24Anonymous__4696,Vvar__1___24Anonymous__4697] : cNorm_2evar___24a1(Vvar__0___24Anonymous__4695) != cNorm_2eapp___24a2(Vvar__0___24Anonymous__4696,Vvar__1___24Anonymous__4697) ).

fof('$_discrim_PLF.Imp.AExp.ANum$PLF.Imp.AExp.APlus',axiom,
    ! [Vvar__0__n__29220,Vvar__0__a1__29221,Vvar__1__a2__29222] : cPLF_2eImp_2eAExp_2eANum___24a1(Vvar__0__n__29220) != cPLF_2eImp_2eAExp_2eAPlus___24a2(Vvar__0__a1__29221,Vvar__1__a2__29222) ).

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__25472,Vvar__0__x__25473] : cPLF_2eImp_2eANum___24a1(Vvar__0__n__25472) != cPLF_2eImp_2eAId___24a1(Vvar__0__x__25473) ).

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__25596,Vvar__1__a__25597] : cPLF_2eImp_2eCSkip != cPLF_2eImp_2eCAss___24a2(Vvar__0__x__25596,Vvar__1__a__25597) ).

fof('$_discrim_PLF.Imp.SPush$PLF.Imp.SLoad',axiom,
    ! [Vvar__0__n__32349,Vvar__0__x__32350] : cPLF_2eImp_2eSPush___24a1(Vvar__0__n__32349) != cPLF_2eImp_2eSLoad___24a1(Vvar__0__x__32350) ).

fof('$_discrim_PLF.Imp.aevalR_division.ANum$PLF.Imp.aevalR_division.APlus',axiom,
    ! [Vvar__0__n__30774,Vvar__0__a1__30775,Vvar__1__a2__30776] : cPLF_2eImp_2eaevalR__division_2eANum___24a1(Vvar__0__n__30774) != cPLF_2eImp_2eaevalR__division_2eAPlus___24a2(Vvar__0__a1__30775,Vvar__1__a2__30776) ).

fof('$_discrim_PLF.Imp.aevalR_extended.AAny$PLF.Imp.aevalR_extended.ANum',axiom,
    ! [Vvar__0__n__35240] : cPLF_2eImp_2eaevalR__extended_2eAAny != cPLF_2eImp_2eaevalR__extended_2eANum___24a1(Vvar__0__n__35240) ).

fof('$_discrim_PLF.Smallstep.C$PLF.Smallstep.P',axiom,
    ! [Vvar__0___24Anonymous__15,Vvar__0___24Anonymous__16,Vvar__1___24Anonymous__17] : cPLF_2eSmallstep_2eC___24a1(Vvar__0___24Anonymous__15) != cPLF_2eSmallstep_2eP___24a2(Vvar__0___24Anonymous__16,Vvar__1___24Anonymous__17) ).

fof('$_discrim_PLF.Smallstep.CImp.CSkip$PLF.Smallstep.CImp.CAss',axiom,
    ! [Vvar__0___24Anonymous__29355,Vvar__1___24Anonymous__29356] : cPLF_2eSmallstep_2eCImp_2eCSkip != cPLF_2eSmallstep_2eCImp_2eCAss___24a2(Vvar__0___24Anonymous__29355,Vvar__1___24Anonymous__29356) ).

fof('$_discrim_PLF.Smallstep.Combined.C$PLF.Smallstep.Combined.P',axiom,
    ! [Vvar__0___24Anonymous__35047,Vvar__0___24Anonymous__35048,Vvar__1___24Anonymous__35049] : cPLF_2eSmallstep_2eCombined_2eC___24a1(Vvar__0___24Anonymous__35047) != cPLF_2eSmallstep_2eCombined_2eP___24a2(Vvar__0___24Anonymous__35048,Vvar__1___24Anonymous__35049) ).

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

fof('$_fix_120_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__120__v__CANONICAL__0___24a2(Vv__CANONICAL__1,Vv__CANONICAL__2) = Vv__CANONICAL__2 )
        | ? [Vvar__0___24Anonymous__121] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__121)
            & Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__121)
            & c_24__fix__120__v__CANONICAL__0___24a2(Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eDatatypes_2eS___24a1(c_24__fix__120__v__CANONICAL__0___24a2(Vvar__0___24Anonymous__121,Vv__CANONICAL__2)) ) ) ) ).

fof('$_fix_26837_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__26837__v__CANONICAL__1___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vv__CANONICAL__3 )
          | ? [Vvar__1___24Anonymous__26841] :
              ( t(Vvar__1___24Anonymous__26841,Vv__CANONICAL__0)
              & ? [Vvar__2___24Anonymous__26842] :
                  ( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vvar__2___24Anonymous__26842)
                  & Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__26841,Vvar__2___24Anonymous__26842)
                  & c_24__fix__26837__v__CANONICAL__1___24a3(Vv__CANONICAL__0,Vv__CANONICAL__2,Vv__CANONICAL__3) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vv__CANONICAL__0,Vvar__1___24Anonymous__26841,c_24__fix__26837__v__CANONICAL__1___24a3(Vv__CANONICAL__0,Vvar__2___24Anonymous__26842,Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_fix_35183_v_CANONICAL_0',axiom,
    ! [Vv__CANONICAL__1] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
     => ( ? [Vvar__0___24Anonymous__35184] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35184)
            & Vv__CANONICAL__1 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__35184)
            & c_24__fix__35183__v__CANONICAL__0___24a1(Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2exO___24a1(c_24__fix__35183__v__CANONICAL__0___24a1(Vvar__0___24Anonymous__35184)) )
        | ? [Vvar__0___24Anonymous__35185] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35185)
            & Vv__CANONICAL__1 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__35185)
            & c_24__fix__35183__v__CANONICAL__0___24a1(Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__35185) )
        | ( Vv__CANONICAL__1 = cCoq_2eNumbers_2eBinNums_2exH
          & c_24__fix__35183__v__CANONICAL__0___24a1(Vv__CANONICAL__1) = cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2eNumbers_2eBinNums_2exH) ) ) ) ).

fof('$_fix_3546_v_CANONICAL_0',axiom,
    ! [Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
      ( cNorm_2etm___24t(Vv__CANONICAL__3)
     => ( ? [Vvar__0___24Anonymous__3547] :
            ( cCoq_2eStrings_2eString_2estring___24t(Vvar__0___24Anonymous__3547)
            & ( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__1)
             => ( cCoq_2eStrings_2eString_2estring___24t(Vvar__0___24Anonymous__3547)
               => ( Vv__CANONICAL__3 = cNorm_2evar___24a1(Vvar__0___24Anonymous__3547)
                  & ( ( cPLF_2eMaps_2eeqb__string___24a2(Vv__CANONICAL__1,Vvar__0___24Anonymous__3547) = cCoq_2eInit_2eDatatypes_2etrue
                      & c_24__fix__3546__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__3547) = cCoq_2eInit_2eDatatypes_2efalse
                      & c_24__fix__3546__v__CANONICAL__0___24a3(Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = Vv__CANONICAL__3 ) ) ) ) ) )
        | ? [Vvar__0___24Anonymous__3549] :
            ( cNorm_2etm___24t(Vvar__0___24Anonymous__3549)
            & ? [Vvar__1___24Anonymous__3550] :
                ( cNorm_2etm___24t(Vvar__1___24Anonymous__3550)
                & Vv__CANONICAL__3 = cNorm_2eapp___24a2(Vvar__0___24Anonymous__3549,Vvar__1___24Anonymous__3550)
                & c_24__fix__3546__v__CANONICAL__0___24a3(Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cNorm_2eapp___24a2(c_24__fix__3546__v__CANONICAL__0___24a3(Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__0___24Anonymous__3549),c_24__fix__3546__v__CANONICAL__0___24a3(Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__1___24Anonymous__3550)) ) )
        | ? [Vvar__0___24Anonymous__3552] :
            ( cCoq_2eStrings_2eString_2estring___24t(Vvar__0___24Anonymous__3552)
            & ? [Vvar__1___24Anonymous__3553] :
                ( cNorm_2ety___24t(Vvar__1___24Anonymous__3553)
                & ? [Vvar__2___24Anonymous__3554] :
                    ( cNorm_2etm___24t(Vvar__2___24Anonymous__3554)
                    & Vv__CANONICAL__3 = cNorm_2eabs___24a3(Vvar__0___24Anonymous__3552,Vvar__1___24Anonymous__3553,Vvar__2___24Anonymous__3554)
                    & c_24__fix__3546__v__CANONICAL__0___24a3(Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cNorm_2eabs___24a3(Vvar__0___24Anonymous__3552,Vvar__1___24Anonymous__3553,c_24__case__Coq_2eInit_2eDatatypes_2ebool_243576___24a4(Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__0___24Anonymous__3552,Vvar__2___24Anonymous__3554)) ) ) )
        | ? [Vvar__0___24Anonymous__3561] :
            ( cNorm_2etm___24t(Vvar__0___24Anonymous__3561)
            & ? [Vvar__1___24Anonymous__3562] :
                ( cNorm_2etm___24t(Vvar__1___24Anonymous__3562)
                & Vv__CANONICAL__3 = cNorm_2epair___24a2(Vvar__0___24Anonymous__3561,Vvar__1___24Anonymous__3562)
                & c_24__fix__3546__v__CANONICAL__0___24a3(Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cNorm_2epair___24a2(c_24__fix__3546__v__CANONICAL__0___24a3(Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__0___24Anonymous__3561),c_24__fix__3546__v__CANONICAL__0___24a3(Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__1___24Anonymous__3562)) ) )
        | ? [Vvar__0___24Anonymous__3564] :
            ( cNorm_2etm___24t(Vvar__0___24Anonymous__3564)
            & Vv__CANONICAL__3 = cNorm_2efst___24a1(Vvar__0___24Anonymous__3564)
            & c_24__fix__3546__v__CANONICAL__0___24a3(Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cNorm_2efst___24a1(c_24__fix__3546__v__CANONICAL__0___24a3(Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__0___24Anonymous__3564)) )
        | ? [Vvar__0___24Anonymous__3565] :
            ( cNorm_2etm___24t(Vvar__0___24Anonymous__3565)
            & Vv__CANONICAL__3 = cNorm_2esnd___24a1(Vvar__0___24Anonymous__3565)
            & c_24__fix__3546__v__CANONICAL__0___24a3(Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cNorm_2esnd___24a1(c_24__fix__3546__v__CANONICAL__0___24a3(Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__0___24Anonymous__3565)) )
        | ( Vv__CANONICAL__3 = cNorm_2etru
          & c_24__fix__3546__v__CANONICAL__0___24a3(Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cNorm_2etru )
        | ( Vv__CANONICAL__3 = cNorm_2efls
          & c_24__fix__3546__v__CANONICAL__0___24a3(Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cNorm_2efls )
        | ? [Vvar__0___24Anonymous__3566] :
            ( cNorm_2etm___24t(Vvar__0___24Anonymous__3566)
            & ? [Vvar__1___24Anonymous__3567] :
                ( cNorm_2etm___24t(Vvar__1___24Anonymous__3567)
                & ? [Vvar__2___24Anonymous__3568] :
                    ( cNorm_2etm___24t(Vvar__2___24Anonymous__3568)
                    & Vv__CANONICAL__3 = cNorm_2etest___24a3(Vvar__0___24Anonymous__3566,Vvar__1___24Anonymous__3567,Vvar__2___24Anonymous__3568)
                    & c_24__fix__3546__v__CANONICAL__0___24a3(Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = cNorm_2etest___24a3(c_24__fix__3546__v__CANONICAL__0___24a3(Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__0___24Anonymous__3566),c_24__fix__3546__v__CANONICAL__0___24a3(Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__1___24Anonymous__3567),c_24__fix__3546__v__CANONICAL__0___24a3(Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__2___24Anonymous__3568)) ) ) ) ) ) ).

fof('$_fix_42920_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__42920__v__CANONICAL__0___24a2(Vv__CANONICAL__1,Vv__CANONICAL__2) = Vv__CANONICAL__1 )
        | ? [Vvar__0___24Anonymous__42921] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__42921)
            & ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
             => ( Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__42921)
                & ( ( Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2eO
                    & c_24__fix__42920__v__CANONICAL__0___24a2(Vv__CANONICAL__1,Vv__CANONICAL__2) = Vv__CANONICAL__1 )
                  | ? [Vvar__0___24Anonymous__42924] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__42924)
                      & Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__42924)
                      & c_24__fix__42920__v__CANONICAL__0___24a2(Vv__CANONICAL__1,Vv__CANONICAL__2) = c_24__fix__42920__v__CANONICAL__0___24a2(Vvar__0___24Anonymous__42921,Vvar__0___24Anonymous__42924) ) ) ) ) ) ) ) ).

fof('$_fix_43006_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__43006__v__CANONICAL__0___24a2(Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eDatatypes_2eO )
        | ? [Vvar__0___24Anonymous__43007] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__43007)
            & Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__43007)
            & c_24__fix__43006__v__CANONICAL__0___24a2(Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eNat_2eadd___24a2(Vv__CANONICAL__2,c_24__fix__43006__v__CANONICAL__0___24a2(Vvar__0___24Anonymous__43007,Vv__CANONICAL__2)) ) ) ) ).

fof('$_fix_43374_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__43374__v__CANONICAL__0___24a2(Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eDatatypes_2etrue )
              | ? [Vvar__0___24Anonymous__43375] :
                  ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__43375)
                  & Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__43375)
                  & c_24__fix__43374__v__CANONICAL__0___24a2(Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) )
        | ? [Vvar__0___24Anonymous__43376] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__43376)
            & ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
             => ( Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__43376)
                & ( ( Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2eO
                    & c_24__fix__43374__v__CANONICAL__0___24a2(Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eDatatypes_2efalse )
                  | ? [Vvar__0___24Anonymous__43379] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__43379)
                      & Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__43379)
                      & c_24__fix__43374__v__CANONICAL__0___24a2(Vv__CANONICAL__1,Vv__CANONICAL__2) = c_24__fix__43374__v__CANONICAL__0___24a2(Vvar__0___24Anonymous__43376,Vvar__0___24Anonymous__43379) ) ) ) ) ) ) ) ).

fof('$_fix_43676_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__43676__v__CANONICAL__0___24a2(Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eDatatypes_2etrue )
        | ? [Vvar__0___24Anonymous__43677] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__43677)
            & ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
             => ( Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__43677)
                & ( ( Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2eO
                    & c_24__fix__43676__v__CANONICAL__0___24a2(Vv__CANONICAL__1,Vv__CANONICAL__2) = cCoq_2eInit_2eDatatypes_2efalse )
                  | ? [Vvar__0___24Anonymous__43680] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__43680)
                      & Vv__CANONICAL__2 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__43680)
                      & c_24__fix__43676__v__CANONICAL__0___24a2(Vv__CANONICAL__1,Vv__CANONICAL__2) = c_24__fix__43676__v__CANONICAL__0___24a2(Vvar__0___24Anonymous__43677,Vvar__0___24Anonymous__43680) ) ) ) ) ) ) ) ).

fof('$_inj_Coq.Bool.Bool.ReflectF',axiom,
    ! [Vvar__0__P__31091,Vvar__0__P__31092,Vvar__1___24Anonymous__31093,Vvar__1___24Anonymous__31094] :
      ( cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__31091) = cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__31092)
     => ( c_24Proof = c_24Proof
        & Vvar__0__P__31091 = Vvar__0__P__31092 ) ) ).

fof('$_inj_Coq.Bool.Bool.ReflectT',axiom,
    ! [Vvar__0__P__31087,Vvar__0__P__31088,Vvar__1___24Anonymous__31089,Vvar__1___24Anonymous__31090] :
      ( cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__31087) = cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__31088)
     => ( c_24Proof = c_24Proof
        & Vvar__0__P__31087 = Vvar__0__P__31088 ) ) ).

fof('$_inj_Coq.FSets.FSetPositive.PositiveSet.Node',axiom,
    ! [Vvar__0___24Anonymous__30008,Vvar__0___24Anonymous__30009,Vvar__1___24Anonymous__30010,Vvar__1___24Anonymous__30011,Vvar__2___24Anonymous__30012,Vvar__2___24Anonymous__30013] :
      ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__30008,Vvar__1___24Anonymous__30010,Vvar__2___24Anonymous__30012) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__30009,Vvar__1___24Anonymous__30011,Vvar__2___24Anonymous__30013)
     => ( Vvar__2___24Anonymous__30012 = Vvar__2___24Anonymous__30013
        & Vvar__1___24Anonymous__30010 = Vvar__1___24Anonymous__30011
        & Vvar__0___24Anonymous__30008 = Vvar__0___24Anonymous__30009 ) ) ).

fof('$_inj_Coq.Init.Datatypes.CompEqT',axiom,
    ! [Vvar__0__Peq__23841,Vvar__0__Peq__23842,Vvar__1__Plt__23843,Vvar__1__Plt__23844,Vvar__2__Pgt__23845,Vvar__2__Pgt__23846,Vvar__3___24Anonymous__23847,Vvar__3___24Anonymous__23848] :
      ( cCoq_2eInit_2eDatatypes_2eCompEqT___24a3(Vvar__0__Peq__23841,Vvar__1__Plt__23843,Vvar__2__Pgt__23845) = cCoq_2eInit_2eDatatypes_2eCompEqT___24a3(Vvar__0__Peq__23842,Vvar__1__Plt__23844,Vvar__2__Pgt__23846)
     => ( c_24Proof = c_24Proof
        & Vvar__2__Pgt__23845 = Vvar__2__Pgt__23846
        & Vvar__1__Plt__23843 = Vvar__1__Plt__23844
        & Vvar__0__Peq__23841 = Vvar__0__Peq__23842 ) ) ).

fof('$_inj_Coq.Init.Datatypes.CompGtT',axiom,
    ! [Vvar__0__Peq__23857,Vvar__0__Peq__23858,Vvar__1__Plt__23859,Vvar__1__Plt__23860,Vvar__2__Pgt__23861,Vvar__2__Pgt__23862,Vvar__3___24Anonymous__23863,Vvar__3___24Anonymous__23864] :
      ( cCoq_2eInit_2eDatatypes_2eCompGtT___24a3(Vvar__0__Peq__23857,Vvar__1__Plt__23859,Vvar__2__Pgt__23861) = cCoq_2eInit_2eDatatypes_2eCompGtT___24a3(Vvar__0__Peq__23858,Vvar__1__Plt__23860,Vvar__2__Pgt__23862)
     => ( c_24Proof = c_24Proof
        & Vvar__2__Pgt__23861 = Vvar__2__Pgt__23862
        & Vvar__1__Plt__23859 = Vvar__1__Plt__23860
        & Vvar__0__Peq__23857 = Vvar__0__Peq__23858 ) ) ).

fof('$_inj_Coq.Init.Datatypes.CompLtT',axiom,
    ! [Vvar__0__Peq__23849,Vvar__0__Peq__23850,Vvar__1__Plt__23851,Vvar__1__Plt__23852,Vvar__2__Pgt__23853,Vvar__2__Pgt__23854,Vvar__3___24Anonymous__23855,Vvar__3___24Anonymous__23856] :
      ( cCoq_2eInit_2eDatatypes_2eCompLtT___24a3(Vvar__0__Peq__23849,Vvar__1__Plt__23851,Vvar__2__Pgt__23853) = cCoq_2eInit_2eDatatypes_2eCompLtT___24a3(Vvar__0__Peq__23850,Vvar__1__Plt__23852,Vvar__2__Pgt__23854)
     => ( c_24Proof = c_24Proof
        & Vvar__2__Pgt__23853 = Vvar__2__Pgt__23854
        & Vvar__1__Plt__23851 = Vvar__1__Plt__23852
        & Vvar__0__Peq__23849 = Vvar__0__Peq__23850 ) ) ).

fof('$_inj_Coq.Init.Datatypes.None',axiom,
    ! [Vvar__0__A__7440,Vvar__0__A__7441] :
      ( cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__7440) = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__7441)
     => Vvar__0__A__7440 = Vvar__0__A__7441 ) ).

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__7436,Vvar__0__A__7437,Vvar__1___24Anonymous__7438,Vvar__1___24Anonymous__7439] :
      ( cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__7436,Vvar__1___24Anonymous__7438) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__7437,Vvar__1___24Anonymous__7439)
     => ( Vvar__1___24Anonymous__7438 = Vvar__1___24Anonymous__7439
        & Vvar__0__A__7436 = Vvar__0__A__7437 ) ) ).

fof('$_inj_Coq.Init.Datatypes.cons',axiom,
    ! [Vvar__0__A__7472,Vvar__0__A__7473,Vvar__1___24Anonymous__7474,Vvar__1___24Anonymous__7475,Vvar__2___24Anonymous__7476,Vvar__2___24Anonymous__7477] :
      ( cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__7472,Vvar__1___24Anonymous__7474,Vvar__2___24Anonymous__7476) = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__7473,Vvar__1___24Anonymous__7475,Vvar__2___24Anonymous__7477)
     => ( Vvar__2___24Anonymous__7476 = Vvar__2___24Anonymous__7477
        & Vvar__1___24Anonymous__7474 = Vvar__1___24Anonymous__7475
        & Vvar__0__A__7472 = Vvar__0__A__7473 ) ) ).

fof('$_inj_Coq.Init.Datatypes.inl',axiom,
    ! [Vvar__0__A__23724,Vvar__0__A__23725,Vvar__1__B__23726,Vvar__1__B__23727,Vvar__2___24Anonymous__23728,Vvar__2___24Anonymous__23729] :
      ( cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__23724,Vvar__1__B__23726,Vvar__2___24Anonymous__23728) = cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__23725,Vvar__1__B__23727,Vvar__2___24Anonymous__23729)
     => ( Vvar__2___24Anonymous__23728 = Vvar__2___24Anonymous__23729
        & Vvar__1__B__23726 = Vvar__1__B__23727
        & Vvar__0__A__23724 = Vvar__0__A__23725 ) ) ).

fof('$_inj_Coq.Init.Datatypes.inr',axiom,
    ! [Vvar__0__A__23730,Vvar__0__A__23731,Vvar__1__B__23732,Vvar__1__B__23733,Vvar__2___24Anonymous__23734,Vvar__2___24Anonymous__23735] :
      ( cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__23730,Vvar__1__B__23732,Vvar__2___24Anonymous__23734) = cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__23731,Vvar__1__B__23733,Vvar__2___24Anonymous__23735)
     => ( Vvar__2___24Anonymous__23734 = Vvar__2___24Anonymous__23735
        & Vvar__1__B__23732 = Vvar__1__B__23733
        & Vvar__0__A__23730 = Vvar__0__A__23731 ) ) ).

fof('$_inj_Coq.Init.Datatypes.nil',axiom,
    ! [Vvar__0__A__7470,Vvar__0__A__7471] :
      ( cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__7470) = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__7471)
     => Vvar__0__A__7470 = Vvar__0__A__7471 ) ).

fof('$_inj_Coq.Init.Datatypes.pair',axiom,
    ! [Vvar__0__A__7452,Vvar__0__A__7453,Vvar__1__B__7454,Vvar__1__B__7455,Vvar__2___24Anonymous__7456,Vvar__2___24Anonymous__7457,Vvar__3___24Anonymous__7458,Vvar__3___24Anonymous__7459] :
      ( cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__7452,Vvar__1__B__7454,Vvar__2___24Anonymous__7456,Vvar__3___24Anonymous__7458) = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__7453,Vvar__1__B__7455,Vvar__2___24Anonymous__7457,Vvar__3___24Anonymous__7459)
     => ( Vvar__3___24Anonymous__7458 = Vvar__3___24Anonymous__7459
        & Vvar__2___24Anonymous__7456 = Vvar__2___24Anonymous__7457
        & Vvar__1__B__7454 = Vvar__1__B__7455
        & Vvar__0__A__7452 = Vvar__0__A__7453 ) ) ).

fof('$_inj_Coq.Init.Decimal.D0',axiom,
    ! [Vvar__0___24Anonymous__24074,Vvar__0___24Anonymous__24075] :
      ( cCoq_2eInit_2eDecimal_2eD0___24a1(Vvar__0___24Anonymous__24074) = cCoq_2eInit_2eDecimal_2eD0___24a1(Vvar__0___24Anonymous__24075)
     => Vvar__0___24Anonymous__24074 = Vvar__0___24Anonymous__24075 ) ).

fof('$_inj_Coq.Init.Decimal.D1',axiom,
    ! [Vvar__0___24Anonymous__24076,Vvar__0___24Anonymous__24077] :
      ( cCoq_2eInit_2eDecimal_2eD1___24a1(Vvar__0___24Anonymous__24076) = cCoq_2eInit_2eDecimal_2eD1___24a1(Vvar__0___24Anonymous__24077)
     => Vvar__0___24Anonymous__24076 = Vvar__0___24Anonymous__24077 ) ).

fof('$_inj_Coq.Init.Decimal.D2',axiom,
    ! [Vvar__0___24Anonymous__24078,Vvar__0___24Anonymous__24079] :
      ( cCoq_2eInit_2eDecimal_2eD2___24a1(Vvar__0___24Anonymous__24078) = cCoq_2eInit_2eDecimal_2eD2___24a1(Vvar__0___24Anonymous__24079)
     => Vvar__0___24Anonymous__24078 = Vvar__0___24Anonymous__24079 ) ).

fof('$_inj_Coq.Init.Decimal.D3',axiom,
    ! [Vvar__0___24Anonymous__24080,Vvar__0___24Anonymous__24081] :
      ( cCoq_2eInit_2eDecimal_2eD3___24a1(Vvar__0___24Anonymous__24080) = cCoq_2eInit_2eDecimal_2eD3___24a1(Vvar__0___24Anonymous__24081)
     => Vvar__0___24Anonymous__24080 = Vvar__0___24Anonymous__24081 ) ).

fof('$_inj_Coq.Init.Decimal.D4',axiom,
    ! [Vvar__0___24Anonymous__24082,Vvar__0___24Anonymous__24083] :
      ( cCoq_2eInit_2eDecimal_2eD4___24a1(Vvar__0___24Anonymous__24082) = cCoq_2eInit_2eDecimal_2eD4___24a1(Vvar__0___24Anonymous__24083)
     => Vvar__0___24Anonymous__24082 = Vvar__0___24Anonymous__24083 ) ).

fof('$_inj_Coq.Init.Decimal.D5',axiom,
    ! [Vvar__0___24Anonymous__24084,Vvar__0___24Anonymous__24085] :
      ( cCoq_2eInit_2eDecimal_2eD5___24a1(Vvar__0___24Anonymous__24084) = cCoq_2eInit_2eDecimal_2eD5___24a1(Vvar__0___24Anonymous__24085)
     => Vvar__0___24Anonymous__24084 = Vvar__0___24Anonymous__24085 ) ).

fof('$_inj_Coq.Init.Decimal.D6',axiom,
    ! [Vvar__0___24Anonymous__24086,Vvar__0___24Anonymous__24087] :
      ( cCoq_2eInit_2eDecimal_2eD6___24a1(Vvar__0___24Anonymous__24086) = cCoq_2eInit_2eDecimal_2eD6___24a1(Vvar__0___24Anonymous__24087)
     => Vvar__0___24Anonymous__24086 = Vvar__0___24Anonymous__24087 ) ).

fof('$_inj_Coq.Init.Decimal.D7',axiom,
    ! [Vvar__0___24Anonymous__24088,Vvar__0___24Anonymous__24089] :
      ( cCoq_2eInit_2eDecimal_2eD7___24a1(Vvar__0___24Anonymous__24088) = cCoq_2eInit_2eDecimal_2eD7___24a1(Vvar__0___24Anonymous__24089)
     => Vvar__0___24Anonymous__24088 = Vvar__0___24Anonymous__24089 ) ).

fof('$_inj_Coq.Init.Decimal.D8',axiom,
    ! [Vvar__0___24Anonymous__24090,Vvar__0___24Anonymous__24091] :
      ( cCoq_2eInit_2eDecimal_2eD8___24a1(Vvar__0___24Anonymous__24090) = cCoq_2eInit_2eDecimal_2eD8___24a1(Vvar__0___24Anonymous__24091)
     => Vvar__0___24Anonymous__24090 = Vvar__0___24Anonymous__24091 ) ).

fof('$_inj_Coq.Init.Decimal.D9',axiom,
    ! [Vvar__0___24Anonymous__24092,Vvar__0___24Anonymous__24093] :
      ( cCoq_2eInit_2eDecimal_2eD9___24a1(Vvar__0___24Anonymous__24092) = cCoq_2eInit_2eDecimal_2eD9___24a1(Vvar__0___24Anonymous__24093)
     => Vvar__0___24Anonymous__24092 = Vvar__0___24Anonymous__24093 ) ).

fof('$_inj_Coq.Init.Decimal.Decimal',axiom,
    ! [Vvar__0__i__31126,Vvar__0__i__31127,Vvar__1__f__31128,Vvar__1__f__31129] :
      ( cCoq_2eInit_2eDecimal_2eDecimal___24a2(Vvar__0__i__31126,Vvar__1__f__31128) = cCoq_2eInit_2eDecimal_2eDecimal___24a2(Vvar__0__i__31127,Vvar__1__f__31129)
     => ( Vvar__1__f__31128 = Vvar__1__f__31129
        & Vvar__0__i__31126 = Vvar__0__i__31127 ) ) ).

fof('$_inj_Coq.Init.Decimal.DecimalExp',axiom,
    ! [Vvar__0__i__31130,Vvar__0__i__31131,Vvar__1__f__31132,Vvar__1__f__31133,Vvar__2__e__31134,Vvar__2__e__31135] :
      ( cCoq_2eInit_2eDecimal_2eDecimalExp___24a3(Vvar__0__i__31130,Vvar__1__f__31132,Vvar__2__e__31134) = cCoq_2eInit_2eDecimal_2eDecimalExp___24a3(Vvar__0__i__31131,Vvar__1__f__31133,Vvar__2__e__31135)
     => ( Vvar__2__e__31134 = Vvar__2__e__31135
        & Vvar__1__f__31132 = Vvar__1__f__31133
        & Vvar__0__i__31130 = Vvar__0__i__31131 ) ) ).

fof('$_inj_Coq.Init.Decimal.Neg',axiom,
    ! [Vvar__0__d__31113,Vvar__0__d__31114] :
      ( cCoq_2eInit_2eDecimal_2eNeg___24a1(Vvar__0__d__31113) = cCoq_2eInit_2eDecimal_2eNeg___24a1(Vvar__0__d__31114)
     => Vvar__0__d__31113 = Vvar__0__d__31114 ) ).

fof('$_inj_Coq.Init.Decimal.Pos',axiom,
    ! [Vvar__0__d__31111,Vvar__0__d__31112] :
      ( cCoq_2eInit_2eDecimal_2ePos___24a1(Vvar__0__d__31111) = cCoq_2eInit_2eDecimal_2ePos___24a1(Vvar__0__d__31112)
     => Vvar__0__d__31111 = Vvar__0__d__31112 ) ).

fof('$_inj_Coq.Init.Specif.exist',axiom,
    ! [Vvar__0__A__27775,Vvar__0__A__27776,Vvar__1__P__27777,Vvar__1__P__27778,Vvar__2__x__27779,Vvar__2__x__27780,Vvar__3___24Anonymous__27781,Vvar__3___24Anonymous__27782] :
      ( cCoq_2eInit_2eSpecif_2eexist___24a3(Vvar__0__A__27775,Vvar__1__P__27777,Vvar__2__x__27779) = cCoq_2eInit_2eSpecif_2eexist___24a3(Vvar__0__A__27776,Vvar__1__P__27778,Vvar__2__x__27780)
     => ( c_24Proof = c_24Proof
        & Vvar__2__x__27779 = Vvar__2__x__27780
        & Vvar__1__P__27777 = Vvar__1__P__27778
        & Vvar__0__A__27775 = Vvar__0__A__27776 ) ) ).

fof('$_inj_Coq.Init.Specif.exist2',axiom,
    ! [Vvar__0__A__34679,Vvar__0__A__34680,Vvar__1__P__34681,Vvar__1__P__34682,Vvar__2__Q__34683,Vvar__2__Q__34684,Vvar__3__x__34685,Vvar__3__x__34686,Vvar__4___24Anonymous__34687,Vvar__4___24Anonymous__34688,Vvar__5___24Anonymous__34689,Vvar__5___24Anonymous__34690] :
      ( cCoq_2eInit_2eSpecif_2eexist2___24a4(Vvar__0__A__34679,Vvar__1__P__34681,Vvar__2__Q__34683,Vvar__3__x__34685) = cCoq_2eInit_2eSpecif_2eexist2___24a4(Vvar__0__A__34680,Vvar__1__P__34682,Vvar__2__Q__34684,Vvar__3__x__34686)
     => ( c_24Proof = c_24Proof
        & c_24Proof = c_24Proof
        & Vvar__3__x__34685 = Vvar__3__x__34686
        & Vvar__2__Q__34683 = Vvar__2__Q__34684
        & Vvar__1__P__34681 = Vvar__1__P__34682
        & Vvar__0__A__34679 = Vvar__0__A__34680 ) ) ).

fof('$_inj_Coq.Init.Specif.existT',axiom,
    ! [Vvar__0__A__27814,Vvar__0__A__27815,Vvar__1__P__27816,Vvar__1__P__27817,Vvar__2__x__27818,Vvar__2__x__27819,Vvar__3___24Anonymous__27820,Vvar__3___24Anonymous__27821] :
      ( cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__27814,Vvar__1__P__27816,Vvar__2__x__27818,Vvar__3___24Anonymous__27820) = cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__27815,Vvar__1__P__27817,Vvar__2__x__27819,Vvar__3___24Anonymous__27821)
     => ( Vvar__3___24Anonymous__27820 = Vvar__3___24Anonymous__27821
        & Vvar__2__x__27818 = Vvar__2__x__27819
        & Vvar__1__P__27816 = Vvar__1__P__27817
        & Vvar__0__A__27814 = Vvar__0__A__27815 ) ) ).

fof('$_inj_Coq.Init.Specif.existT2',axiom,
    ! [Vvar__0__A__34735,Vvar__0__A__34736,Vvar__1__P__34737,Vvar__1__P__34738,Vvar__2__Q__34739,Vvar__2__Q__34740,Vvar__3__x__34741,Vvar__3__x__34742,Vvar__4___24Anonymous__34743,Vvar__4___24Anonymous__34744,Vvar__5___24Anonymous__34745,Vvar__5___24Anonymous__34746] :
      ( cCoq_2eInit_2eSpecif_2eexistT2___24a6(Vvar__0__A__34735,Vvar__1__P__34737,Vvar__2__Q__34739,Vvar__3__x__34741,Vvar__4___24Anonymous__34743,Vvar__5___24Anonymous__34745) = cCoq_2eInit_2eSpecif_2eexistT2___24a6(Vvar__0__A__34736,Vvar__1__P__34738,Vvar__2__Q__34740,Vvar__3__x__34742,Vvar__4___24Anonymous__34744,Vvar__5___24Anonymous__34746)
     => ( Vvar__5___24Anonymous__34745 = Vvar__5___24Anonymous__34746
        & Vvar__4___24Anonymous__34743 = Vvar__4___24Anonymous__34744
        & Vvar__3__x__34741 = Vvar__3__x__34742
        & Vvar__2__Q__34739 = Vvar__2__Q__34740
        & Vvar__1__P__34737 = Vvar__1__P__34738
        & Vvar__0__A__34735 = Vvar__0__A__34736 ) ) ).

fof('$_inj_Coq.Init.Specif.inleft',axiom,
    ! [Vvar__0__A__30918,Vvar__0__A__30919,Vvar__1__B__30920,Vvar__1__B__30921,Vvar__2___24Anonymous__30922,Vvar__2___24Anonymous__30923] :
      ( cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__30918,Vvar__1__B__30920,Vvar__2___24Anonymous__30922) = cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__30919,Vvar__1__B__30921,Vvar__2___24Anonymous__30923)
     => ( Vvar__2___24Anonymous__30922 = Vvar__2___24Anonymous__30923
        & Vvar__1__B__30920 = Vvar__1__B__30921
        & Vvar__0__A__30918 = Vvar__0__A__30919 ) ) ).

fof('$_inj_Coq.Init.Specif.inright',axiom,
    ! [Vvar__0__A__30924,Vvar__0__A__30925,Vvar__1__B__30926,Vvar__1__B__30927,Vvar__2___24Anonymous__30928,Vvar__2___24Anonymous__30929] :
      ( cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__30924,Vvar__1__B__30926) = cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__30925,Vvar__1__B__30927)
     => ( c_24Proof = c_24Proof
        & Vvar__1__B__30926 = Vvar__1__B__30927
        & Vvar__0__A__30924 = Vvar__0__A__30925 ) ) ).

fof('$_inj_Coq.Init.Specif.left',axiom,
    ! [Vvar__0__A__7156,Vvar__0__A__7157,Vvar__1__B__7158,Vvar__1__B__7159,Vvar__2___24Anonymous__7160,Vvar__2___24Anonymous__7161] :
      ( cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__7156,Vvar__1__B__7158) = cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__7157,Vvar__1__B__7159)
     => ( c_24Proof = c_24Proof
        & Vvar__1__B__7158 = Vvar__1__B__7159
        & Vvar__0__A__7156 = Vvar__0__A__7157 ) ) ).

fof('$_inj_Coq.Init.Specif.right',axiom,
    ! [Vvar__0__A__7162,Vvar__0__A__7163,Vvar__1__B__7164,Vvar__1__B__7165,Vvar__2___24Anonymous__7166,Vvar__2___24Anonymous__7167] :
      ( cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__7162,Vvar__1__B__7164) = cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__7163,Vvar__1__B__7165)
     => ( c_24Proof = c_24Proof
        & Vvar__1__B__7164 = Vvar__1__B__7165
        & Vvar__0__A__7162 = Vvar__0__A__7163 ) ) ).

fof('$_inj_Coq.Numbers.BinNums.Npos',axiom,
    ! [Vvar__0___24Anonymous__7413,Vvar__0___24Anonymous__7414] :
      ( cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__7413) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__7414)
     => Vvar__0___24Anonymous__7413 = Vvar__0___24Anonymous__7414 ) ).

fof('$_inj_Coq.Numbers.BinNums.Zneg',axiom,
    ! [Vvar__0___24Anonymous__7424,Vvar__0___24Anonymous__7425] :
      ( cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__7424) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__7425)
     => Vvar__0___24Anonymous__7424 = Vvar__0___24Anonymous__7425 ) ).

fof('$_inj_Coq.Numbers.BinNums.Zpos',axiom,
    ! [Vvar__0___24Anonymous__7422,Vvar__0___24Anonymous__7423] :
      ( cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__7422) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__7423)
     => Vvar__0___24Anonymous__7422 = Vvar__0___24Anonymous__7423 ) ).

fof('$_inj_Coq.Numbers.BinNums.xI',axiom,
    ! [Vvar__0___24Anonymous__5488,Vvar__0___24Anonymous__5489] :
      ( cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__5488) = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__5489)
     => Vvar__0___24Anonymous__5488 = Vvar__0___24Anonymous__5489 ) ).

fof('$_inj_Coq.Numbers.BinNums.xO',axiom,
    ! [Vvar__0___24Anonymous__5490,Vvar__0___24Anonymous__5491] :
      ( cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__5490) = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__5491)
     => Vvar__0___24Anonymous__5490 = Vvar__0___24Anonymous__5491 ) ).

fof('$_inj_Coq.PArith.BinPos.Pos.PeanoSucc',axiom,
    ! [Vvar__0__p__35188,Vvar__0__p__35189,Vvar__1___24Anonymous__35190,Vvar__1___24Anonymous__35191] :
      ( cCoq_2ePArith_2eBinPos_2ePos_2ePeanoSucc___24a2(Vvar__0__p__35188,Vvar__1___24Anonymous__35190) = cCoq_2ePArith_2eBinPos_2ePos_2ePeanoSucc___24a2(Vvar__0__p__35189,Vvar__1___24Anonymous__35191)
     => ( Vvar__1___24Anonymous__35190 = Vvar__1___24Anonymous__35191
        & Vvar__0__p__35188 = Vvar__0__p__35189 ) ) ).

fof('$_inj_Coq.PArith.BinPosDef.Pos.IsPos',axiom,
    ! [Vvar__0___24Anonymous__30986,Vvar__0___24Anonymous__30987] :
      ( cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__30986) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__30987)
     => Vvar__0___24Anonymous__30986 = Vvar__0___24Anonymous__30987 ) ).

fof('$_inj_Coq.QArith.QArith_base.Qmake',axiom,
    ! [Vvar__0__Qnum__9767,Vvar__0__Qnum__9768,Vvar__1__Qden__9769,Vvar__1__Qden__9770] :
      ( cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__9767,Vvar__1__Qden__9769) = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__9768,Vvar__1__Qden__9770)
     => ( Vvar__1__Qden__9769 = Vvar__1__Qden__9770
        & Vvar__0__Qnum__9767 = Vvar__0__Qnum__9768 ) ) ).

fof('$_inj_Coq.Reals.RIneq.mknegreal',axiom,
    ! [Vvar__0__neg__32653,Vvar__0__neg__32654,Vvar__1__cond__neg__32655,Vvar__1__cond__neg__32656] :
      ( cCoq_2eReals_2eRIneq_2emknegreal___24a1(Vvar__0__neg__32653) = cCoq_2eReals_2eRIneq_2emknegreal___24a1(Vvar__0__neg__32654)
     => ( c_24Proof = c_24Proof
        & Vvar__0__neg__32653 = Vvar__0__neg__32654 ) ) ).

fof('$_inj_Coq.Reals.RIneq.mknonnegreal',axiom,
    ! [Vvar__0__nonneg__26019,Vvar__0__nonneg__26020,Vvar__1__cond__nonneg__26021,Vvar__1__cond__nonneg__26022] :
      ( cCoq_2eReals_2eRIneq_2emknonnegreal___24a1(Vvar__0__nonneg__26019) = cCoq_2eReals_2eRIneq_2emknonnegreal___24a1(Vvar__0__nonneg__26020)
     => ( c_24Proof = c_24Proof
        & Vvar__0__nonneg__26019 = Vvar__0__nonneg__26020 ) ) ).

fof('$_inj_Coq.Reals.RIneq.mknonposreal',axiom,
    ! [Vvar__0__nonpos__32646,Vvar__0__nonpos__32647,Vvar__1__cond__nonpos__32648,Vvar__1__cond__nonpos__32649] :
      ( cCoq_2eReals_2eRIneq_2emknonposreal___24a1(Vvar__0__nonpos__32646) = cCoq_2eReals_2eRIneq_2emknonposreal___24a1(Vvar__0__nonpos__32647)
     => ( c_24Proof = c_24Proof
        & Vvar__0__nonpos__32646 = Vvar__0__nonpos__32647 ) ) ).

fof('$_inj_Coq.Reals.RIneq.mknonzeroreal',axiom,
    ! [Vvar__0__nonzero__32660,Vvar__0__nonzero__32661,Vvar__1__cond__nonzero__32662,Vvar__1__cond__nonzero__32663] :
      ( cCoq_2eReals_2eRIneq_2emknonzeroreal___24a1(Vvar__0__nonzero__32660) = cCoq_2eReals_2eRIneq_2emknonzeroreal___24a1(Vvar__0__nonzero__32661)
     => ( c_24Proof = c_24Proof
        & Vvar__0__nonzero__32660 = Vvar__0__nonzero__32661 ) ) ).

fof('$_inj_Coq.Reals.RIneq.mkposreal',axiom,
    ! [Vvar__0__pos__32639,Vvar__0__pos__32640,Vvar__1__cond__pos__32641,Vvar__1__cond__pos__32642] :
      ( cCoq_2eReals_2eRIneq_2emkposreal___24a1(Vvar__0__pos__32639) = cCoq_2eReals_2eRIneq_2emkposreal___24a1(Vvar__0__pos__32640)
     => ( c_24Proof = c_24Proof
        & Vvar__0__pos__32639 = Vvar__0__pos__32640 ) ) ).

fof('$_inj_Coq.Reals.Rfunctions.ZintNeg',axiom,
    ! [Vvar__0__x__32750,Vvar__0__x__32751,Vvar__1__n__32752,Vvar__1__n__32753,Vvar__2___24Anonymous__32754,Vvar__2___24Anonymous__32755] :
      ( cCoq_2eReals_2eRfunctions_2eZintNeg___24a2(Vvar__0__x__32750,Vvar__1__n__32752) = cCoq_2eReals_2eRfunctions_2eZintNeg___24a2(Vvar__0__x__32751,Vvar__1__n__32753)
     => ( c_24Proof = c_24Proof
        & Vvar__1__n__32752 = Vvar__1__n__32753
        & Vvar__0__x__32750 = Vvar__0__x__32751 ) ) ).

fof('$_inj_Coq.Reals.Rfunctions.ZintNull',axiom,
    ! [Vvar__0__x__32740,Vvar__0__x__32741,Vvar__1___24Anonymous__32742,Vvar__1___24Anonymous__32743] :
      ( cCoq_2eReals_2eRfunctions_2eZintNull___24a1(Vvar__0__x__32740) = cCoq_2eReals_2eRfunctions_2eZintNull___24a1(Vvar__0__x__32741)
     => ( c_24Proof = c_24Proof
        & Vvar__0__x__32740 = Vvar__0__x__32741 ) ) ).

fof('$_inj_Coq.Reals.Rfunctions.ZintPos',axiom,
    ! [Vvar__0__x__32744,Vvar__0__x__32745,Vvar__1__n__32746,Vvar__1__n__32747,Vvar__2___24Anonymous__32748,Vvar__2___24Anonymous__32749] :
      ( cCoq_2eReals_2eRfunctions_2eZintPos___24a2(Vvar__0__x__32744,Vvar__1__n__32746) = cCoq_2eReals_2eRfunctions_2eZintPos___24a2(Vvar__0__x__32745,Vvar__1__n__32747)
     => ( c_24Proof = c_24Proof
        & Vvar__1__n__32746 = Vvar__1__n__32747
        & Vvar__0__x__32744 = Vvar__0__x__32745 ) ) ).

fof('$_inj_Coq.Strings.Ascii.Ascii',axiom,
    ! [Vvar__0___24Anonymous__15802,Vvar__0___24Anonymous__15803,Vvar__1___24Anonymous__15804,Vvar__1___24Anonymous__15805,Vvar__2___24Anonymous__15806,Vvar__2___24Anonymous__15807,Vvar__3___24Anonymous__15808,Vvar__3___24Anonymous__15809,Vvar__4___24Anonymous__15810,Vvar__4___24Anonymous__15811,Vvar__5___24Anonymous__15812,Vvar__5___24Anonymous__15813,Vvar__6___24Anonymous__15814,Vvar__6___24Anonymous__15815,Vvar__7___24Anonymous__15816,Vvar__7___24Anonymous__15817] :
      ( cCoq_2eStrings_2eAscii_2eAscii___24a8(Vvar__0___24Anonymous__15802,Vvar__1___24Anonymous__15804,Vvar__2___24Anonymous__15806,Vvar__3___24Anonymous__15808,Vvar__4___24Anonymous__15810,Vvar__5___24Anonymous__15812,Vvar__6___24Anonymous__15814,Vvar__7___24Anonymous__15816) = cCoq_2eStrings_2eAscii_2eAscii___24a8(Vvar__0___24Anonymous__15803,Vvar__1___24Anonymous__15805,Vvar__2___24Anonymous__15807,Vvar__3___24Anonymous__15809,Vvar__4___24Anonymous__15811,Vvar__5___24Anonymous__15813,Vvar__6___24Anonymous__15815,Vvar__7___24Anonymous__15817)
     => ( Vvar__7___24Anonymous__15816 = Vvar__7___24Anonymous__15817
        & Vvar__6___24Anonymous__15814 = Vvar__6___24Anonymous__15815
        & Vvar__5___24Anonymous__15812 = Vvar__5___24Anonymous__15813
        & Vvar__4___24Anonymous__15810 = Vvar__4___24Anonymous__15811
        & Vvar__3___24Anonymous__15808 = Vvar__3___24Anonymous__15809
        & Vvar__2___24Anonymous__15806 = Vvar__2___24Anonymous__15807
        & Vvar__1___24Anonymous__15804 = Vvar__1___24Anonymous__15805
        & Vvar__0___24Anonymous__15802 = Vvar__0___24Anonymous__15803 ) ) ).

fof('$_inj_Coq.Strings.String.String',axiom,
    ! [Vvar__0___24Anonymous__132,Vvar__0___24Anonymous__133,Vvar__1___24Anonymous__134,Vvar__1___24Anonymous__135] :
      ( cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__132,Vvar__1___24Anonymous__134) = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__133,Vvar__1___24Anonymous__135)
     => ( Vvar__1___24Anonymous__134 = Vvar__1___24Anonymous__135
        & Vvar__0___24Anonymous__132 = Vvar__0___24Anonymous__133 ) ) ).

fof('$_inj_Coq.Structures.OrderedType.EQ',axiom,
    ! [Vvar__0__X__32611,Vvar__0__X__32612,Vvar__1__lt__32613,Vvar__1__lt__32614,Vvar__2__eq__32615,Vvar__2__eq__32616,Vvar__3__x__32617,Vvar__3__x__32618,Vvar__4__y__32619,Vvar__4__y__32620,Vvar__5___24Anonymous__32621,Vvar__5___24Anonymous__32622] :
      ( cCoq_2eStructures_2eOrderedType_2eEQ___24a5(Vvar__0__X__32611,Vvar__1__lt__32613,Vvar__2__eq__32615,Vvar__3__x__32617,Vvar__4__y__32619) = cCoq_2eStructures_2eOrderedType_2eEQ___24a5(Vvar__0__X__32612,Vvar__1__lt__32614,Vvar__2__eq__32616,Vvar__3__x__32618,Vvar__4__y__32620)
     => ( c_24Proof = c_24Proof
        & Vvar__4__y__32619 = Vvar__4__y__32620
        & Vvar__3__x__32617 = Vvar__3__x__32618
        & Vvar__2__eq__32615 = Vvar__2__eq__32616
        & Vvar__1__lt__32613 = Vvar__1__lt__32614
        & Vvar__0__X__32611 = Vvar__0__X__32612 ) ) ).

fof('$_inj_Coq.Structures.OrderedType.GT',axiom,
    ! [Vvar__0__X__32623,Vvar__0__X__32624,Vvar__1__lt__32625,Vvar__1__lt__32626,Vvar__2__eq__32627,Vvar__2__eq__32628,Vvar__3__x__32629,Vvar__3__x__32630,Vvar__4__y__32631,Vvar__4__y__32632,Vvar__5___24Anonymous__32633,Vvar__5___24Anonymous__32634] :
      ( cCoq_2eStructures_2eOrderedType_2eGT___24a5(Vvar__0__X__32623,Vvar__1__lt__32625,Vvar__2__eq__32627,Vvar__3__x__32629,Vvar__4__y__32631) = cCoq_2eStructures_2eOrderedType_2eGT___24a5(Vvar__0__X__32624,Vvar__1__lt__32626,Vvar__2__eq__32628,Vvar__3__x__32630,Vvar__4__y__32632)
     => ( c_24Proof = c_24Proof
        & Vvar__4__y__32631 = Vvar__4__y__32632
        & Vvar__3__x__32629 = Vvar__3__x__32630
        & Vvar__2__eq__32627 = Vvar__2__eq__32628
        & Vvar__1__lt__32625 = Vvar__1__lt__32626
        & Vvar__0__X__32623 = Vvar__0__X__32624 ) ) ).

fof('$_inj_Coq.Structures.OrderedType.LT',axiom,
    ! [Vvar__0__X__32599,Vvar__0__X__32600,Vvar__1__lt__32601,Vvar__1__lt__32602,Vvar__2__eq__32603,Vvar__2__eq__32604,Vvar__3__x__32605,Vvar__3__x__32606,Vvar__4__y__32607,Vvar__4__y__32608,Vvar__5___24Anonymous__32609,Vvar__5___24Anonymous__32610] :
      ( cCoq_2eStructures_2eOrderedType_2eLT___24a5(Vvar__0__X__32599,Vvar__1__lt__32601,Vvar__2__eq__32603,Vvar__3__x__32605,Vvar__4__y__32607) = cCoq_2eStructures_2eOrderedType_2eLT___24a5(Vvar__0__X__32600,Vvar__1__lt__32602,Vvar__2__eq__32604,Vvar__3__x__32606,Vvar__4__y__32608)
     => ( c_24Proof = c_24Proof
        & Vvar__4__y__32607 = Vvar__4__y__32608
        & Vvar__3__x__32605 = Vvar__3__x__32606
        & Vvar__2__eq__32603 = Vvar__2__eq__32604
        & Vvar__1__lt__32601 = Vvar__1__lt__32602
        & Vvar__0__X__32599 = Vvar__0__X__32600 ) ) ).

fof('$_inj_Coq.Vectors.Fin.F1',axiom,
    ! [Vvar__0__n__25001,Vvar__0__n__25002] :
      ( cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__25001) = cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__25002)
     => Vvar__0__n__25001 = Vvar__0__n__25002 ) ).

fof('$_inj_Coq.Vectors.Fin.FS',axiom,
    ! [Vvar__0__n__25003,Vvar__0__n__25004,Vvar__1___24Anonymous__25005,Vvar__1___24Anonymous__25006] :
      ( cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__25003,Vvar__1___24Anonymous__25005) = cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__25004,Vvar__1___24Anonymous__25006)
     => ( Vvar__1___24Anonymous__25005 = Vvar__1___24Anonymous__25006
        & Vvar__0__n__25003 = Vvar__0__n__25004 ) ) ).

fof('$_inj_Coq.Vectors.VectorDef.cons',axiom,
    ! [Vvar__0__A__28946,Vvar__0__A__28947,Vvar__1__h__28948,Vvar__1__h__28949,Vvar__2__n__28950,Vvar__2__n__28951,Vvar__3___24Anonymous__28952,Vvar__3___24Anonymous__28953] :
      ( cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__28946,Vvar__1__h__28948,Vvar__2__n__28950,Vvar__3___24Anonymous__28952) = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__28947,Vvar__1__h__28949,Vvar__2__n__28951,Vvar__3___24Anonymous__28953)
     => ( Vvar__3___24Anonymous__28952 = Vvar__3___24Anonymous__28953
        & Vvar__2__n__28950 = Vvar__2__n__28951
        & Vvar__1__h__28948 = Vvar__1__h__28949
        & Vvar__0__A__28946 = Vvar__0__A__28947 ) ) ).

fof('$_inj_Coq.Vectors.VectorDef.nil',axiom,
    ! [Vvar__0__A__28944,Vvar__0__A__28945] :
      ( cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__28944) = cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__28945)
     => Vvar__0__A__28944 = Vvar__0__A__28945 ) ).

fof('$_inj_Coq.ZArith.Znumtheory.Euclid_intro',axiom,
    ! [Vvar__0__a__34826,Vvar__0__a__34827,Vvar__1__b__34828,Vvar__1__b__34829,Vvar__2__u__34830,Vvar__2__u__34831,Vvar__3__v__34832,Vvar__3__v__34833,Vvar__4__d__34834,Vvar__4__d__34835,Vvar__5___24Anonymous__34836,Vvar__5___24Anonymous__34837,Vvar__6___24Anonymous__34838,Vvar__6___24Anonymous__34839] :
      ( cCoq_2eZArith_2eZnumtheory_2eEuclid__intro___24a5(Vvar__0__a__34826,Vvar__1__b__34828,Vvar__2__u__34830,Vvar__3__v__34832,Vvar__4__d__34834) = cCoq_2eZArith_2eZnumtheory_2eEuclid__intro___24a5(Vvar__0__a__34827,Vvar__1__b__34829,Vvar__2__u__34831,Vvar__3__v__34833,Vvar__4__d__34835)
     => ( c_24Proof = c_24Proof
        & c_24Proof = c_24Proof
        & Vvar__4__d__34834 = Vvar__4__d__34835
        & Vvar__3__v__34832 = Vvar__3__v__34833
        & Vvar__2__u__34830 = Vvar__2__u__34831
        & Vvar__1__b__34828 = Vvar__1__b__34829
        & Vvar__0__a__34826 = Vvar__0__a__34827 ) ) ).

fof('$_inj_Coq.ZArith.Zpower.Zdiv_rest_proof',axiom,
    ! [Vvar__0__x__34874,Vvar__0__x__34875,Vvar__1__p__34876,Vvar__1__p__34877,Vvar__2__q__34878,Vvar__2__q__34879,Vvar__3__r__34880,Vvar__3__r__34881,Vvar__4___24Anonymous__34882,Vvar__4___24Anonymous__34883,Vvar__5___24Anonymous__34884,Vvar__5___24Anonymous__34885,Vvar__6___24Anonymous__34886,Vvar__6___24Anonymous__34887] :
      ( cCoq_2eZArith_2eZpower_2eZdiv__rest__proof___24a4(Vvar__0__x__34874,Vvar__1__p__34876,Vvar__2__q__34878,Vvar__3__r__34880) = cCoq_2eZArith_2eZpower_2eZdiv__rest__proof___24a4(Vvar__0__x__34875,Vvar__1__p__34877,Vvar__2__q__34879,Vvar__3__r__34881)
     => ( c_24Proof = c_24Proof
        & c_24Proof = c_24Proof
        & c_24Proof = c_24Proof
        & Vvar__3__r__34880 = Vvar__3__r__34881
        & Vvar__2__q__34878 = Vvar__2__q__34879
        & Vvar__1__p__34876 = Vvar__1__p__34877
        & Vvar__0__x__34874 = Vvar__0__x__34875 ) ) ).

fof('$_inj_Coq.micromega.EnvRing.PEX',axiom,
    ! [Vvar__0__C__24233,Vvar__0__C__24234,Vvar__1___24Anonymous__24235,Vvar__1___24Anonymous__24236] :
      ( cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__24233,Vvar__1___24Anonymous__24235) = cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__24234,Vvar__1___24Anonymous__24236)
     => ( Vvar__1___24Anonymous__24235 = Vvar__1___24Anonymous__24236
        & Vvar__0__C__24233 = Vvar__0__C__24234 ) ) ).

fof('$_inj_Coq.micromega.EnvRing.PEadd',axiom,
    ! [Vvar__0__C__24237,Vvar__0__C__24238,Vvar__1___24Anonymous__24239,Vvar__1___24Anonymous__24240,Vvar__2___24Anonymous__24241,Vvar__2___24Anonymous__24242] :
      ( cCoq_2emicromega_2eEnvRing_2ePEadd___24a3(Vvar__0__C__24237,Vvar__1___24Anonymous__24239,Vvar__2___24Anonymous__24241) = cCoq_2emicromega_2eEnvRing_2ePEadd___24a3(Vvar__0__C__24238,Vvar__1___24Anonymous__24240,Vvar__2___24Anonymous__24242)
     => ( Vvar__2___24Anonymous__24241 = Vvar__2___24Anonymous__24242
        & Vvar__1___24Anonymous__24239 = Vvar__1___24Anonymous__24240
        & Vvar__0__C__24237 = Vvar__0__C__24238 ) ) ).

fof('$_inj_Coq.micromega.EnvRing.PEc',axiom,
    ! [Vvar__0__C__24229,Vvar__0__C__24230,Vvar__1___24Anonymous__24231,Vvar__1___24Anonymous__24232] :
      ( cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__24229,Vvar__1___24Anonymous__24231) = cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__24230,Vvar__1___24Anonymous__24232)
     => ( Vvar__1___24Anonymous__24231 = Vvar__1___24Anonymous__24232
        & Vvar__0__C__24229 = Vvar__0__C__24230 ) ) ).

fof('$_inj_Coq.micromega.EnvRing.PEmul',axiom,
    ! [Vvar__0__C__24249,Vvar__0__C__24250,Vvar__1___24Anonymous__24251,Vvar__1___24Anonymous__24252,Vvar__2___24Anonymous__24253,Vvar__2___24Anonymous__24254] :
      ( cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(Vvar__0__C__24249,Vvar__1___24Anonymous__24251,Vvar__2___24Anonymous__24253) = cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(Vvar__0__C__24250,Vvar__1___24Anonymous__24252,Vvar__2___24Anonymous__24254)
     => ( Vvar__2___24Anonymous__24253 = Vvar__2___24Anonymous__24254
        & Vvar__1___24Anonymous__24251 = Vvar__1___24Anonymous__24252
        & Vvar__0__C__24249 = Vvar__0__C__24250 ) ) ).

fof('$_inj_Coq.micromega.EnvRing.PEopp',axiom,
    ! [Vvar__0__C__24255,Vvar__0__C__24256,Vvar__1___24Anonymous__24257,Vvar__1___24Anonymous__24258] :
      ( cCoq_2emicromega_2eEnvRing_2ePEopp___24a2(Vvar__0__C__24255,Vvar__1___24Anonymous__24257) = cCoq_2emicromega_2eEnvRing_2ePEopp___24a2(Vvar__0__C__24256,Vvar__1___24Anonymous__24258)
     => ( Vvar__1___24Anonymous__24257 = Vvar__1___24Anonymous__24258
        & Vvar__0__C__24255 = Vvar__0__C__24256 ) ) ).

fof('$_inj_Coq.micromega.EnvRing.PEpow',axiom,
    ! [Vvar__0__C__24259,Vvar__0__C__24260,Vvar__1___24Anonymous__24261,Vvar__1___24Anonymous__24262,Vvar__2___24Anonymous__24263,Vvar__2___24Anonymous__24264] :
      ( cCoq_2emicromega_2eEnvRing_2ePEpow___24a3(Vvar__0__C__24259,Vvar__1___24Anonymous__24261,Vvar__2___24Anonymous__24263) = cCoq_2emicromega_2eEnvRing_2ePEpow___24a3(Vvar__0__C__24260,Vvar__1___24Anonymous__24262,Vvar__2___24Anonymous__24264)
     => ( Vvar__2___24Anonymous__24263 = Vvar__2___24Anonymous__24264
        & Vvar__1___24Anonymous__24261 = Vvar__1___24Anonymous__24262
        & Vvar__0__C__24259 = Vvar__0__C__24260 ) ) ).

fof('$_inj_Coq.micromega.EnvRing.PEsub',axiom,
    ! [Vvar__0__C__24243,Vvar__0__C__24244,Vvar__1___24Anonymous__24245,Vvar__1___24Anonymous__24246,Vvar__2___24Anonymous__24247,Vvar__2___24Anonymous__24248] :
      ( cCoq_2emicromega_2eEnvRing_2ePEsub___24a3(Vvar__0__C__24243,Vvar__1___24Anonymous__24245,Vvar__2___24Anonymous__24247) = cCoq_2emicromega_2eEnvRing_2ePEsub___24a3(Vvar__0__C__24244,Vvar__1___24Anonymous__24246,Vvar__2___24Anonymous__24248)
     => ( Vvar__2___24Anonymous__24247 = Vvar__2___24Anonymous__24248
        & Vvar__1___24Anonymous__24245 = Vvar__1___24Anonymous__24246
        & Vvar__0__C__24243 = Vvar__0__C__24244 ) ) ).

fof('$_inj_Coq.micromega.EnvRing.PX',axiom,
    ! [Vvar__0__C__30840,Vvar__0__C__30841,Vvar__1___24Anonymous__30842,Vvar__1___24Anonymous__30843,Vvar__2___24Anonymous__30844,Vvar__2___24Anonymous__30845,Vvar__3___24Anonymous__30846,Vvar__3___24Anonymous__30847] :
      ( cCoq_2emicromega_2eEnvRing_2ePX___24a4(Vvar__0__C__30840,Vvar__1___24Anonymous__30842,Vvar__2___24Anonymous__30844,Vvar__3___24Anonymous__30846) = cCoq_2emicromega_2eEnvRing_2ePX___24a4(Vvar__0__C__30841,Vvar__1___24Anonymous__30843,Vvar__2___24Anonymous__30845,Vvar__3___24Anonymous__30847)
     => ( Vvar__3___24Anonymous__30846 = Vvar__3___24Anonymous__30847
        & Vvar__2___24Anonymous__30844 = Vvar__2___24Anonymous__30845
        & Vvar__1___24Anonymous__30842 = Vvar__1___24Anonymous__30843
        & Vvar__0__C__30840 = Vvar__0__C__30841 ) ) ).

fof('$_inj_Coq.micromega.EnvRing.Pc',axiom,
    ! [Vvar__0__C__30830,Vvar__0__C__30831,Vvar__1___24Anonymous__30832,Vvar__1___24Anonymous__30833] :
      ( cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__30830,Vvar__1___24Anonymous__30832) = cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__30831,Vvar__1___24Anonymous__30833)
     => ( Vvar__1___24Anonymous__30832 = Vvar__1___24Anonymous__30833
        & Vvar__0__C__30830 = Vvar__0__C__30831 ) ) ).

fof('$_inj_Coq.micromega.EnvRing.Pinj',axiom,
    ! [Vvar__0__C__30834,Vvar__0__C__30835,Vvar__1___24Anonymous__30836,Vvar__1___24Anonymous__30837,Vvar__2___24Anonymous__30838,Vvar__2___24Anonymous__30839] :
      ( cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__30834,Vvar__1___24Anonymous__30836,Vvar__2___24Anonymous__30838) = cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__30835,Vvar__1___24Anonymous__30837,Vvar__2___24Anonymous__30839)
     => ( Vvar__2___24Anonymous__30838 = Vvar__2___24Anonymous__30839
        & Vvar__1___24Anonymous__30836 = Vvar__1___24Anonymous__30837
        & Vvar__0__C__30834 = Vvar__0__C__30835 ) ) ).

fof('$_inj_Coq.micromega.EnvRing.vmon',axiom,
    ! [Vvar__0___24Anonymous__30865,Vvar__0___24Anonymous__30866,Vvar__1___24Anonymous__30867,Vvar__1___24Anonymous__30868] :
      ( cCoq_2emicromega_2eEnvRing_2evmon___24a2(Vvar__0___24Anonymous__30865,Vvar__1___24Anonymous__30867) = cCoq_2emicromega_2eEnvRing_2evmon___24a2(Vvar__0___24Anonymous__30866,Vvar__1___24Anonymous__30868)
     => ( Vvar__1___24Anonymous__30867 = Vvar__1___24Anonymous__30868
        & Vvar__0___24Anonymous__30865 = Vvar__0___24Anonymous__30866 ) ) ).

fof('$_inj_Coq.micromega.EnvRing.zmon',axiom,
    ! [Vvar__0___24Anonymous__30861,Vvar__0___24Anonymous__30862,Vvar__1___24Anonymous__30863,Vvar__1___24Anonymous__30864] :
      ( cCoq_2emicromega_2eEnvRing_2ezmon___24a2(Vvar__0___24Anonymous__30861,Vvar__1___24Anonymous__30863) = cCoq_2emicromega_2eEnvRing_2ezmon___24a2(Vvar__0___24Anonymous__30862,Vvar__1___24Anonymous__30864)
     => ( Vvar__1___24Anonymous__30863 = Vvar__1___24Anonymous__30864
        & Vvar__0___24Anonymous__30861 = Vvar__0___24Anonymous__30862 ) ) ).

fof('$_inj_Coq.micromega.RMicromega.CInv',axiom,
    ! [Vvar__0__r__26169,Vvar__0__r__26170] :
      ( cCoq_2emicromega_2eRMicromega_2eCInv___24a1(Vvar__0__r__26169) = cCoq_2emicromega_2eRMicromega_2eCInv___24a1(Vvar__0__r__26170)
     => Vvar__0__r__26169 = Vvar__0__r__26170 ) ).

fof('$_inj_Coq.micromega.RMicromega.CMinus',axiom,
    ! [Vvar__0__r1__26157,Vvar__0__r1__26158,Vvar__1__r2__26159,Vvar__1__r2__26160] :
      ( cCoq_2emicromega_2eRMicromega_2eCMinus___24a2(Vvar__0__r1__26157,Vvar__1__r2__26159) = cCoq_2emicromega_2eRMicromega_2eCMinus___24a2(Vvar__0__r1__26158,Vvar__1__r2__26160)
     => ( Vvar__1__r2__26159 = Vvar__1__r2__26160
        & Vvar__0__r1__26157 = Vvar__0__r1__26158 ) ) ).

fof('$_inj_Coq.micromega.RMicromega.CMult',axiom,
    ! [Vvar__0__r1__26161,Vvar__0__r1__26162,Vvar__1__r2__26163,Vvar__1__r2__26164] :
      ( cCoq_2emicromega_2eRMicromega_2eCMult___24a2(Vvar__0__r1__26161,Vvar__1__r2__26163) = cCoq_2emicromega_2eRMicromega_2eCMult___24a2(Vvar__0__r1__26162,Vvar__1__r2__26164)
     => ( Vvar__1__r2__26163 = Vvar__1__r2__26164
        & Vvar__0__r1__26161 = Vvar__0__r1__26162 ) ) ).

fof('$_inj_Coq.micromega.RMicromega.COpp',axiom,
    ! [Vvar__0__r__26171,Vvar__0__r__26172] :
      ( cCoq_2emicromega_2eRMicromega_2eCOpp___24a1(Vvar__0__r__26171) = cCoq_2emicromega_2eRMicromega_2eCOpp___24a1(Vvar__0__r__26172)
     => Vvar__0__r__26171 = Vvar__0__r__26172 ) ).

fof('$_inj_Coq.micromega.RMicromega.CPlus',axiom,
    ! [Vvar__0__r1__26153,Vvar__0__r1__26154,Vvar__1__r2__26155,Vvar__1__r2__26156] :
      ( cCoq_2emicromega_2eRMicromega_2eCPlus___24a2(Vvar__0__r1__26153,Vvar__1__r2__26155) = cCoq_2emicromega_2eRMicromega_2eCPlus___24a2(Vvar__0__r1__26154,Vvar__1__r2__26156)
     => ( Vvar__1__r2__26155 = Vvar__1__r2__26156
        & Vvar__0__r1__26153 = Vvar__0__r1__26154 ) ) ).

fof('$_inj_Coq.micromega.RMicromega.CPow',axiom,
    ! [Vvar__0__r1__26165,Vvar__0__r1__26166,Vvar__1__z__26167,Vvar__1__z__26168] :
      ( cCoq_2emicromega_2eRMicromega_2eCPow___24a2(Vvar__0__r1__26165,Vvar__1__z__26167) = cCoq_2emicromega_2eRMicromega_2eCPow___24a2(Vvar__0__r1__26166,Vvar__1__z__26168)
     => ( Vvar__1__z__26167 = Vvar__1__z__26168
        & Vvar__0__r1__26165 = Vvar__0__r1__26166 ) ) ).

fof('$_inj_Coq.micromega.RMicromega.CQ',axiom,
    ! [Vvar__0__r__26149,Vvar__0__r__26150] :
      ( cCoq_2emicromega_2eRMicromega_2eCQ___24a1(Vvar__0__r__26149) = cCoq_2emicromega_2eRMicromega_2eCQ___24a1(Vvar__0__r__26150)
     => Vvar__0__r__26149 = Vvar__0__r__26150 ) ).

fof('$_inj_Coq.micromega.RMicromega.CZ',axiom,
    ! [Vvar__0__r__26151,Vvar__0__r__26152] :
      ( cCoq_2emicromega_2eRMicromega_2eCZ___24a1(Vvar__0__r__26151) = cCoq_2emicromega_2eRMicromega_2eCZ___24a1(Vvar__0__r__26152)
     => Vvar__0__r__26151 = Vvar__0__r__26152 ) ).

fof('$_inj_Coq.micromega.RingMicromega.Build_Formula',axiom,
    ! [Vvar__0__T__27218,Vvar__0__T__27219,Vvar__1__Flhs__27220,Vvar__1__Flhs__27221,Vvar__2__Fop__27222,Vvar__2__Fop__27223,Vvar__3__Frhs__27224,Vvar__3__Frhs__27225] :
      ( cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(Vvar__0__T__27218,Vvar__1__Flhs__27220,Vvar__2__Fop__27222,Vvar__3__Frhs__27224) = cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(Vvar__0__T__27219,Vvar__1__Flhs__27221,Vvar__2__Fop__27223,Vvar__3__Frhs__27225)
     => ( Vvar__3__Frhs__27224 = Vvar__3__Frhs__27225
        & Vvar__2__Fop__27222 = Vvar__2__Fop__27223
        & Vvar__1__Flhs__27220 = Vvar__1__Flhs__27221
        & Vvar__0__T__27218 = Vvar__0__T__27219 ) ) ).

fof('$_inj_Coq.micromega.RingMicromega.PsatzAdd',axiom,
    ! [Vvar__0__C__27093,Vvar__0__C__27094,Vvar__1___24Anonymous__27095,Vvar__1___24Anonymous__27096,Vvar__2___24Anonymous__27097,Vvar__2___24Anonymous__27098] :
      ( cCoq_2emicromega_2eRingMicromega_2ePsatzAdd___24a3(Vvar__0__C__27093,Vvar__1___24Anonymous__27095,Vvar__2___24Anonymous__27097) = cCoq_2emicromega_2eRingMicromega_2ePsatzAdd___24a3(Vvar__0__C__27094,Vvar__1___24Anonymous__27096,Vvar__2___24Anonymous__27098)
     => ( Vvar__2___24Anonymous__27097 = Vvar__2___24Anonymous__27098
        & Vvar__1___24Anonymous__27095 = Vvar__1___24Anonymous__27096
        & Vvar__0__C__27093 = Vvar__0__C__27094 ) ) ).

fof('$_inj_Coq.micromega.RingMicromega.PsatzC',axiom,
    ! [Vvar__0__C__27099,Vvar__0__C__27100,Vvar__1___24Anonymous__27101,Vvar__1___24Anonymous__27102] :
      ( cCoq_2emicromega_2eRingMicromega_2ePsatzC___24a2(Vvar__0__C__27099,Vvar__1___24Anonymous__27101) = cCoq_2emicromega_2eRingMicromega_2ePsatzC___24a2(Vvar__0__C__27100,Vvar__1___24Anonymous__27102)
     => ( Vvar__1___24Anonymous__27101 = Vvar__1___24Anonymous__27102
        & Vvar__0__C__27099 = Vvar__0__C__27100 ) ) ).

fof('$_inj_Coq.micromega.RingMicromega.PsatzIn',axiom,
    ! [Vvar__0__C__27073,Vvar__0__C__27074,Vvar__1___24Anonymous__27075,Vvar__1___24Anonymous__27076] :
      ( cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(Vvar__0__C__27073,Vvar__1___24Anonymous__27075) = cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(Vvar__0__C__27074,Vvar__1___24Anonymous__27076)
     => ( Vvar__1___24Anonymous__27075 = Vvar__1___24Anonymous__27076
        & Vvar__0__C__27073 = Vvar__0__C__27074 ) ) ).

fof('$_inj_Coq.micromega.RingMicromega.PsatzMulC',axiom,
    ! [Vvar__0__C__27081,Vvar__0__C__27082,Vvar__1___24Anonymous__27083,Vvar__1___24Anonymous__27084,Vvar__2___24Anonymous__27085,Vvar__2___24Anonymous__27086] :
      ( cCoq_2emicromega_2eRingMicromega_2ePsatzMulC___24a3(Vvar__0__C__27081,Vvar__1___24Anonymous__27083,Vvar__2___24Anonymous__27085) = cCoq_2emicromega_2eRingMicromega_2ePsatzMulC___24a3(Vvar__0__C__27082,Vvar__1___24Anonymous__27084,Vvar__2___24Anonymous__27086)
     => ( Vvar__2___24Anonymous__27085 = Vvar__2___24Anonymous__27086
        & Vvar__1___24Anonymous__27083 = Vvar__1___24Anonymous__27084
        & Vvar__0__C__27081 = Vvar__0__C__27082 ) ) ).

fof('$_inj_Coq.micromega.RingMicromega.PsatzMulE',axiom,
    ! [Vvar__0__C__27087,Vvar__0__C__27088,Vvar__1___24Anonymous__27089,Vvar__1___24Anonymous__27090,Vvar__2___24Anonymous__27091,Vvar__2___24Anonymous__27092] :
      ( cCoq_2emicromega_2eRingMicromega_2ePsatzMulE___24a3(Vvar__0__C__27087,Vvar__1___24Anonymous__27089,Vvar__2___24Anonymous__27091) = cCoq_2emicromega_2eRingMicromega_2ePsatzMulE___24a3(Vvar__0__C__27088,Vvar__1___24Anonymous__27090,Vvar__2___24Anonymous__27092)
     => ( Vvar__2___24Anonymous__27091 = Vvar__2___24Anonymous__27092
        & Vvar__1___24Anonymous__27089 = Vvar__1___24Anonymous__27090
        & Vvar__0__C__27087 = Vvar__0__C__27088 ) ) ).

fof('$_inj_Coq.micromega.RingMicromega.PsatzSquare',axiom,
    ! [Vvar__0__C__27077,Vvar__0__C__27078,Vvar__1___24Anonymous__27079,Vvar__1___24Anonymous__27080] :
      ( cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(Vvar__0__C__27077,Vvar__1___24Anonymous__27079) = cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(Vvar__0__C__27078,Vvar__1___24Anonymous__27080)
     => ( Vvar__1___24Anonymous__27079 = Vvar__1___24Anonymous__27080
        & Vvar__0__C__27077 = Vvar__0__C__27078 ) ) ).

fof('$_inj_Coq.micromega.RingMicromega.PsatzZ',axiom,
    ! [Vvar__0__C__27103,Vvar__0__C__27104] :
      ( cCoq_2emicromega_2eRingMicromega_2ePsatzZ___24a1(Vvar__0__C__27103) = cCoq_2emicromega_2eRingMicromega_2ePsatzZ___24a1(Vvar__0__C__27104)
     => Vvar__0__C__27103 = Vvar__0__C__27104 ) ).

fof('$_inj_Coq.micromega.Tauto.A',axiom,
    ! [Vvar__0__TA__28355,Vvar__0__TA__28356,Vvar__1__TX__28357,Vvar__1__TX__28358,Vvar__2__AA__28359,Vvar__2__AA__28360,Vvar__3__AF__28361,Vvar__3__AF__28362,Vvar__4___24Anonymous__28363,Vvar__4___24Anonymous__28364,Vvar__5___24Anonymous__28365,Vvar__5___24Anonymous__28366] :
      ( cCoq_2emicromega_2eTauto_2eA___24a6(Vvar__0__TA__28355,Vvar__1__TX__28357,Vvar__2__AA__28359,Vvar__3__AF__28361,Vvar__4___24Anonymous__28363,Vvar__5___24Anonymous__28365) = cCoq_2emicromega_2eTauto_2eA___24a6(Vvar__0__TA__28356,Vvar__1__TX__28358,Vvar__2__AA__28360,Vvar__3__AF__28362,Vvar__4___24Anonymous__28364,Vvar__5___24Anonymous__28366)
     => ( Vvar__5___24Anonymous__28365 = Vvar__5___24Anonymous__28366
        & Vvar__4___24Anonymous__28363 = Vvar__4___24Anonymous__28364
        & Vvar__3__AF__28361 = Vvar__3__AF__28362
        & Vvar__2__AA__28359 = Vvar__2__AA__28360
        & Vvar__1__TX__28357 = Vvar__1__TX__28358
        & Vvar__0__TA__28355 = Vvar__0__TA__28356 ) ) ).

fof('$_inj_Coq.micromega.Tauto.Cj',axiom,
    ! [Vvar__0__TA__28367,Vvar__0__TA__28368,Vvar__1__TX__28369,Vvar__1__TX__28370,Vvar__2__AA__28371,Vvar__2__AA__28372,Vvar__3__AF__28373,Vvar__3__AF__28374,Vvar__4___24Anonymous__28375,Vvar__4___24Anonymous__28376,Vvar__5___24Anonymous__28377,Vvar__5___24Anonymous__28378] :
      ( cCoq_2emicromega_2eTauto_2eCj___24a6(Vvar__0__TA__28367,Vvar__1__TX__28369,Vvar__2__AA__28371,Vvar__3__AF__28373,Vvar__4___24Anonymous__28375,Vvar__5___24Anonymous__28377) = cCoq_2emicromega_2eTauto_2eCj___24a6(Vvar__0__TA__28368,Vvar__1__TX__28370,Vvar__2__AA__28372,Vvar__3__AF__28374,Vvar__4___24Anonymous__28376,Vvar__5___24Anonymous__28378)
     => ( Vvar__5___24Anonymous__28377 = Vvar__5___24Anonymous__28378
        & Vvar__4___24Anonymous__28375 = Vvar__4___24Anonymous__28376
        & Vvar__3__AF__28373 = Vvar__3__AF__28374
        & Vvar__2__AA__28371 = Vvar__2__AA__28372
        & Vvar__1__TX__28369 = Vvar__1__TX__28370
        & Vvar__0__TA__28367 = Vvar__0__TA__28368 ) ) ).

fof('$_inj_Coq.micromega.Tauto.D',axiom,
    ! [Vvar__0__TA__28379,Vvar__0__TA__28380,Vvar__1__TX__28381,Vvar__1__TX__28382,Vvar__2__AA__28383,Vvar__2__AA__28384,Vvar__3__AF__28385,Vvar__3__AF__28386,Vvar__4___24Anonymous__28387,Vvar__4___24Anonymous__28388,Vvar__5___24Anonymous__28389,Vvar__5___24Anonymous__28390] :
      ( cCoq_2emicromega_2eTauto_2eD___24a6(Vvar__0__TA__28379,Vvar__1__TX__28381,Vvar__2__AA__28383,Vvar__3__AF__28385,Vvar__4___24Anonymous__28387,Vvar__5___24Anonymous__28389) = cCoq_2emicromega_2eTauto_2eD___24a6(Vvar__0__TA__28380,Vvar__1__TX__28382,Vvar__2__AA__28384,Vvar__3__AF__28386,Vvar__4___24Anonymous__28388,Vvar__5___24Anonymous__28390)
     => ( Vvar__5___24Anonymous__28389 = Vvar__5___24Anonymous__28390
        & Vvar__4___24Anonymous__28387 = Vvar__4___24Anonymous__28388
        & Vvar__3__AF__28385 = Vvar__3__AF__28386
        & Vvar__2__AA__28383 = Vvar__2__AA__28384
        & Vvar__1__TX__28381 = Vvar__1__TX__28382
        & Vvar__0__TA__28379 = Vvar__0__TA__28380 ) ) ).

fof('$_inj_Coq.micromega.Tauto.FF',axiom,
    ! [Vvar__0__TA__28337,Vvar__0__TA__28338,Vvar__1__TX__28339,Vvar__1__TX__28340,Vvar__2__AA__28341,Vvar__2__AA__28342,Vvar__3__AF__28343,Vvar__3__AF__28344] :
      ( cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__28337,Vvar__1__TX__28339,Vvar__2__AA__28341,Vvar__3__AF__28343) = cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__28338,Vvar__1__TX__28340,Vvar__2__AA__28342,Vvar__3__AF__28344)
     => ( Vvar__3__AF__28343 = Vvar__3__AF__28344
        & Vvar__2__AA__28341 = Vvar__2__AA__28342
        & Vvar__1__TX__28339 = Vvar__1__TX__28340
        & Vvar__0__TA__28337 = Vvar__0__TA__28338 ) ) ).

fof('$_inj_Coq.micromega.Tauto.I',axiom,
    ! [Vvar__0__TA__28401,Vvar__0__TA__28402,Vvar__1__TX__28403,Vvar__1__TX__28404,Vvar__2__AA__28405,Vvar__2__AA__28406,Vvar__3__AF__28407,Vvar__3__AF__28408,Vvar__4___24Anonymous__28409,Vvar__4___24Anonymous__28410,Vvar__5___24Anonymous__28411,Vvar__5___24Anonymous__28412,Vvar__6___24Anonymous__28413,Vvar__6___24Anonymous__28414] :
      ( cCoq_2emicromega_2eTauto_2eI___24a7(Vvar__0__TA__28401,Vvar__1__TX__28403,Vvar__2__AA__28405,Vvar__3__AF__28407,Vvar__4___24Anonymous__28409,Vvar__5___24Anonymous__28411,Vvar__6___24Anonymous__28413) = cCoq_2emicromega_2eTauto_2eI___24a7(Vvar__0__TA__28402,Vvar__1__TX__28404,Vvar__2__AA__28406,Vvar__3__AF__28408,Vvar__4___24Anonymous__28410,Vvar__5___24Anonymous__28412,Vvar__6___24Anonymous__28414)
     => ( Vvar__6___24Anonymous__28413 = Vvar__6___24Anonymous__28414
        & Vvar__5___24Anonymous__28411 = Vvar__5___24Anonymous__28412
        & Vvar__4___24Anonymous__28409 = Vvar__4___24Anonymous__28410
        & Vvar__3__AF__28407 = Vvar__3__AF__28408
        & Vvar__2__AA__28405 = Vvar__2__AA__28406
        & Vvar__1__TX__28403 = Vvar__1__TX__28404
        & Vvar__0__TA__28401 = Vvar__0__TA__28402 ) ) ).

fof('$_inj_Coq.micromega.Tauto.N',axiom,
    ! [Vvar__0__TA__28391,Vvar__0__TA__28392,Vvar__1__TX__28393,Vvar__1__TX__28394,Vvar__2__AA__28395,Vvar__2__AA__28396,Vvar__3__AF__28397,Vvar__3__AF__28398,Vvar__4___24Anonymous__28399,Vvar__4___24Anonymous__28400] :
      ( cCoq_2emicromega_2eTauto_2eN___24a5(Vvar__0__TA__28391,Vvar__1__TX__28393,Vvar__2__AA__28395,Vvar__3__AF__28397,Vvar__4___24Anonymous__28399) = cCoq_2emicromega_2eTauto_2eN___24a5(Vvar__0__TA__28392,Vvar__1__TX__28394,Vvar__2__AA__28396,Vvar__3__AF__28398,Vvar__4___24Anonymous__28400)
     => ( Vvar__4___24Anonymous__28399 = Vvar__4___24Anonymous__28400
        & Vvar__3__AF__28397 = Vvar__3__AF__28398
        & Vvar__2__AA__28395 = Vvar__2__AA__28396
        & Vvar__1__TX__28393 = Vvar__1__TX__28394
        & Vvar__0__TA__28391 = Vvar__0__TA__28392 ) ) ).

fof('$_inj_Coq.micromega.Tauto.TT',axiom,
    ! [Vvar__0__TA__28329,Vvar__0__TA__28330,Vvar__1__TX__28331,Vvar__1__TX__28332,Vvar__2__AA__28333,Vvar__2__AA__28334,Vvar__3__AF__28335,Vvar__3__AF__28336] :
      ( cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__28329,Vvar__1__TX__28331,Vvar__2__AA__28333,Vvar__3__AF__28335) = cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__28330,Vvar__1__TX__28332,Vvar__2__AA__28334,Vvar__3__AF__28336)
     => ( Vvar__3__AF__28335 = Vvar__3__AF__28336
        & Vvar__2__AA__28333 = Vvar__2__AA__28334
        & Vvar__1__TX__28331 = Vvar__1__TX__28332
        & Vvar__0__TA__28329 = Vvar__0__TA__28330 ) ) ).

fof('$_inj_Coq.micromega.Tauto.X',axiom,
    ! [Vvar__0__TA__28345,Vvar__0__TA__28346,Vvar__1__TX__28347,Vvar__1__TX__28348,Vvar__2__AA__28349,Vvar__2__AA__28350,Vvar__3__AF__28351,Vvar__3__AF__28352,Vvar__4___24Anonymous__28353,Vvar__4___24Anonymous__28354] :
      ( cCoq_2emicromega_2eTauto_2eX___24a5(Vvar__0__TA__28345,Vvar__1__TX__28347,Vvar__2__AA__28349,Vvar__3__AF__28351,Vvar__4___24Anonymous__28353) = cCoq_2emicromega_2eTauto_2eX___24a5(Vvar__0__TA__28346,Vvar__1__TX__28348,Vvar__2__AA__28350,Vvar__3__AF__28352,Vvar__4___24Anonymous__28354)
     => ( Vvar__4___24Anonymous__28353 = Vvar__4___24Anonymous__28354
        & Vvar__3__AF__28351 = Vvar__3__AF__28352
        & Vvar__2__AA__28349 = Vvar__2__AA__28350
        & Vvar__1__TX__28347 = Vvar__1__TX__28348
        & Vvar__0__TA__28345 = Vvar__0__TA__28346 ) ) ).

fof('$_inj_Coq.micromega.VarMap.Branch',axiom,
    ! [Vvar__0__A__34780,Vvar__0__A__34781,Vvar__1___24Anonymous__34782,Vvar__1___24Anonymous__34783,Vvar__2___24Anonymous__34784,Vvar__2___24Anonymous__34785,Vvar__3___24Anonymous__34786,Vvar__3___24Anonymous__34787] :
      ( cCoq_2emicromega_2eVarMap_2eBranch___24a4(Vvar__0__A__34780,Vvar__1___24Anonymous__34782,Vvar__2___24Anonymous__34784,Vvar__3___24Anonymous__34786) = cCoq_2emicromega_2eVarMap_2eBranch___24a4(Vvar__0__A__34781,Vvar__1___24Anonymous__34783,Vvar__2___24Anonymous__34785,Vvar__3___24Anonymous__34787)
     => ( Vvar__3___24Anonymous__34786 = Vvar__3___24Anonymous__34787
        & Vvar__2___24Anonymous__34784 = Vvar__2___24Anonymous__34785
        & Vvar__1___24Anonymous__34782 = Vvar__1___24Anonymous__34783
        & Vvar__0__A__34780 = Vvar__0__A__34781 ) ) ).

fof('$_inj_Coq.micromega.VarMap.Elt',axiom,
    ! [Vvar__0__A__34776,Vvar__0__A__34777,Vvar__1___24Anonymous__34778,Vvar__1___24Anonymous__34779] :
      ( cCoq_2emicromega_2eVarMap_2eElt___24a2(Vvar__0__A__34776,Vvar__1___24Anonymous__34778) = cCoq_2emicromega_2eVarMap_2eElt___24a2(Vvar__0__A__34777,Vvar__1___24Anonymous__34779)
     => ( Vvar__1___24Anonymous__34778 = Vvar__1___24Anonymous__34779
        & Vvar__0__A__34776 = Vvar__0__A__34777 ) ) ).

fof('$_inj_Coq.micromega.VarMap.Empty',axiom,
    ! [Vvar__0__A__34774,Vvar__0__A__34775] :
      ( cCoq_2emicromega_2eVarMap_2eEmpty___24a1(Vvar__0__A__34774) = cCoq_2emicromega_2eVarMap_2eEmpty___24a1(Vvar__0__A__34775)
     => Vvar__0__A__34774 = Vvar__0__A__34775 ) ).

fof('$_inj_Coq.micromega.ZMicromega.CutProof',axiom,
    ! [Vvar__0___24Anonymous__29034,Vvar__0___24Anonymous__29035,Vvar__1___24Anonymous__29036,Vvar__1___24Anonymous__29037] :
      ( cCoq_2emicromega_2eZMicromega_2eCutProof___24a2(Vvar__0___24Anonymous__29034,Vvar__1___24Anonymous__29036) = cCoq_2emicromega_2eZMicromega_2eCutProof___24a2(Vvar__0___24Anonymous__29035,Vvar__1___24Anonymous__29037)
     => ( Vvar__1___24Anonymous__29036 = Vvar__1___24Anonymous__29037
        & Vvar__0___24Anonymous__29034 = Vvar__0___24Anonymous__29035 ) ) ).

fof('$_inj_Coq.micromega.ZMicromega.EnumProof',axiom,
    ! [Vvar__0___24Anonymous__29038,Vvar__0___24Anonymous__29039,Vvar__1___24Anonymous__29040,Vvar__1___24Anonymous__29041,Vvar__2___24Anonymous__29042,Vvar__2___24Anonymous__29043] :
      ( cCoq_2emicromega_2eZMicromega_2eEnumProof___24a3(Vvar__0___24Anonymous__29038,Vvar__1___24Anonymous__29040,Vvar__2___24Anonymous__29042) = cCoq_2emicromega_2eZMicromega_2eEnumProof___24a3(Vvar__0___24Anonymous__29039,Vvar__1___24Anonymous__29041,Vvar__2___24Anonymous__29043)
     => ( Vvar__2___24Anonymous__29042 = Vvar__2___24Anonymous__29043
        & Vvar__1___24Anonymous__29040 = Vvar__1___24Anonymous__29041
        & Vvar__0___24Anonymous__29038 = Vvar__0___24Anonymous__29039 ) ) ).

fof('$_inj_Coq.micromega.ZMicromega.RatProof',axiom,
    ! [Vvar__0___24Anonymous__29030,Vvar__0___24Anonymous__29031,Vvar__1___24Anonymous__29032,Vvar__1___24Anonymous__29033] :
      ( cCoq_2emicromega_2eZMicromega_2eRatProof___24a2(Vvar__0___24Anonymous__29030,Vvar__1___24Anonymous__29032) = cCoq_2emicromega_2eZMicromega_2eRatProof___24a2(Vvar__0___24Anonymous__29031,Vvar__1___24Anonymous__29033)
     => ( Vvar__1___24Anonymous__29032 = Vvar__1___24Anonymous__29033
        & Vvar__0___24Anonymous__29030 = Vvar__0___24Anonymous__29031 ) ) ).

fof('$_inj_Coq.setoid_ring.Field_theory.FEI',axiom,
    ! [Vvar__0__C__8598,Vvar__0__C__8599] :
      ( cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__8598) = cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__8599)
     => Vvar__0__C__8598 = Vvar__0__C__8599 ) ).

fof('$_inj_Coq.setoid_ring.Field_theory.FEO',axiom,
    ! [Vvar__0__C__8596,Vvar__0__C__8597] :
      ( cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__8596) = cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__8597)
     => Vvar__0__C__8596 = Vvar__0__C__8597 ) ).

fof('$_inj_Coq.setoid_ring.Field_theory.FEX',axiom,
    ! [Vvar__0__C__8604,Vvar__0__C__8605,Vvar__1___24Anonymous__8606,Vvar__1___24Anonymous__8607] :
      ( cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(Vvar__0__C__8604,Vvar__1___24Anonymous__8606) = cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(Vvar__0__C__8605,Vvar__1___24Anonymous__8607)
     => ( Vvar__1___24Anonymous__8606 = Vvar__1___24Anonymous__8607
        & Vvar__0__C__8604 = Vvar__0__C__8605 ) ) ).

fof('$_inj_Coq.setoid_ring.Field_theory.FEadd',axiom,
    ! [Vvar__0__C__8608,Vvar__0__C__8609,Vvar__1___24Anonymous__8610,Vvar__1___24Anonymous__8611,Vvar__2___24Anonymous__8612,Vvar__2___24Anonymous__8613] :
      ( cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(Vvar__0__C__8608,Vvar__1___24Anonymous__8610,Vvar__2___24Anonymous__8612) = cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(Vvar__0__C__8609,Vvar__1___24Anonymous__8611,Vvar__2___24Anonymous__8613)
     => ( Vvar__2___24Anonymous__8612 = Vvar__2___24Anonymous__8613
        & Vvar__1___24Anonymous__8610 = Vvar__1___24Anonymous__8611
        & Vvar__0__C__8608 = Vvar__0__C__8609 ) ) ).

fof('$_inj_Coq.setoid_ring.Field_theory.FEc',axiom,
    ! [Vvar__0__C__8600,Vvar__0__C__8601,Vvar__1___24Anonymous__8602,Vvar__1___24Anonymous__8603] :
      ( cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(Vvar__0__C__8600,Vvar__1___24Anonymous__8602) = cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(Vvar__0__C__8601,Vvar__1___24Anonymous__8603)
     => ( Vvar__1___24Anonymous__8602 = Vvar__1___24Anonymous__8603
        & Vvar__0__C__8600 = Vvar__0__C__8601 ) ) ).

fof('$_inj_Coq.setoid_ring.Field_theory.FEdiv',axiom,
    ! [Vvar__0__C__8634,Vvar__0__C__8635,Vvar__1___24Anonymous__8636,Vvar__1___24Anonymous__8637,Vvar__2___24Anonymous__8638,Vvar__2___24Anonymous__8639] :
      ( cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(Vvar__0__C__8634,Vvar__1___24Anonymous__8636,Vvar__2___24Anonymous__8638) = cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(Vvar__0__C__8635,Vvar__1___24Anonymous__8637,Vvar__2___24Anonymous__8639)
     => ( Vvar__2___24Anonymous__8638 = Vvar__2___24Anonymous__8639
        & Vvar__1___24Anonymous__8636 = Vvar__1___24Anonymous__8637
        & Vvar__0__C__8634 = Vvar__0__C__8635 ) ) ).

fof('$_inj_Coq.setoid_ring.Field_theory.FEinv',axiom,
    ! [Vvar__0__C__8630,Vvar__0__C__8631,Vvar__1___24Anonymous__8632,Vvar__1___24Anonymous__8633] :
      ( cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(Vvar__0__C__8630,Vvar__1___24Anonymous__8632) = cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(Vvar__0__C__8631,Vvar__1___24Anonymous__8633)
     => ( Vvar__1___24Anonymous__8632 = Vvar__1___24Anonymous__8633
        & Vvar__0__C__8630 = Vvar__0__C__8631 ) ) ).

fof('$_inj_Coq.setoid_ring.Field_theory.FEmul',axiom,
    ! [Vvar__0__C__8620,Vvar__0__C__8621,Vvar__1___24Anonymous__8622,Vvar__1___24Anonymous__8623,Vvar__2___24Anonymous__8624,Vvar__2___24Anonymous__8625] :
      ( cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(Vvar__0__C__8620,Vvar__1___24Anonymous__8622,Vvar__2___24Anonymous__8624) = cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(Vvar__0__C__8621,Vvar__1___24Anonymous__8623,Vvar__2___24Anonymous__8625)
     => ( Vvar__2___24Anonymous__8624 = Vvar__2___24Anonymous__8625
        & Vvar__1___24Anonymous__8622 = Vvar__1___24Anonymous__8623
        & Vvar__0__C__8620 = Vvar__0__C__8621 ) ) ).

fof('$_inj_Coq.setoid_ring.Field_theory.FEopp',axiom,
    ! [Vvar__0__C__8626,Vvar__0__C__8627,Vvar__1___24Anonymous__8628,Vvar__1___24Anonymous__8629] :
      ( cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(Vvar__0__C__8626,Vvar__1___24Anonymous__8628) = cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(Vvar__0__C__8627,Vvar__1___24Anonymous__8629)
     => ( Vvar__1___24Anonymous__8628 = Vvar__1___24Anonymous__8629
        & Vvar__0__C__8626 = Vvar__0__C__8627 ) ) ).

fof('$_inj_Coq.setoid_ring.Field_theory.FEpow',axiom,
    ! [Vvar__0__C__8640,Vvar__0__C__8641,Vvar__1___24Anonymous__8642,Vvar__1___24Anonymous__8643,Vvar__2___24Anonymous__8644,Vvar__2___24Anonymous__8645] :
      ( cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(Vvar__0__C__8640,Vvar__1___24Anonymous__8642,Vvar__2___24Anonymous__8644) = cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(Vvar__0__C__8641,Vvar__1___24Anonymous__8643,Vvar__2___24Anonymous__8645)
     => ( Vvar__2___24Anonymous__8644 = Vvar__2___24Anonymous__8645
        & Vvar__1___24Anonymous__8642 = Vvar__1___24Anonymous__8643
        & Vvar__0__C__8640 = Vvar__0__C__8641 ) ) ).

fof('$_inj_Coq.setoid_ring.Field_theory.FEsub',axiom,
    ! [Vvar__0__C__8614,Vvar__0__C__8615,Vvar__1___24Anonymous__8616,Vvar__1___24Anonymous__8617,Vvar__2___24Anonymous__8618,Vvar__2___24Anonymous__8619] :
      ( cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(Vvar__0__C__8614,Vvar__1___24Anonymous__8616,Vvar__2___24Anonymous__8618) = cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(Vvar__0__C__8615,Vvar__1___24Anonymous__8617,Vvar__2___24Anonymous__8619)
     => ( Vvar__2___24Anonymous__8618 = Vvar__2___24Anonymous__8619
        & Vvar__1___24Anonymous__8616 = Vvar__1___24Anonymous__8617
        & Vvar__0__C__8614 = Vvar__0__C__8615 ) ) ).

fof('$_inj_Coq.setoid_ring.Field_theory.mk_linear',axiom,
    ! [Vvar__0__C__8943,Vvar__0__C__8944,Vvar__1__num__8945,Vvar__1__num__8946,Vvar__2__denum__8947,Vvar__2__denum__8948,Vvar__3__condition__8949,Vvar__3__condition__8950] :
      ( cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(Vvar__0__C__8943,Vvar__1__num__8945,Vvar__2__denum__8947,Vvar__3__condition__8949) = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(Vvar__0__C__8944,Vvar__1__num__8946,Vvar__2__denum__8948,Vvar__3__condition__8950)
     => ( Vvar__3__condition__8949 = Vvar__3__condition__8950
        & Vvar__2__denum__8947 = Vvar__2__denum__8948
        & Vvar__1__num__8945 = Vvar__1__num__8946
        & Vvar__0__C__8943 = Vvar__0__C__8944 ) ) ).

fof('$_inj_Coq.setoid_ring.Field_theory.mk_rsplit',axiom,
    ! [Vvar__0__C__9232,Vvar__0__C__9233,Vvar__1__rsplit__left__9234,Vvar__1__rsplit__left__9235,Vvar__2__rsplit__common__9236,Vvar__2__rsplit__common__9237,Vvar__3__rsplit__right__9238,Vvar__3__rsplit__right__9239] :
      ( cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(Vvar__0__C__9232,Vvar__1__rsplit__left__9234,Vvar__2__rsplit__common__9236,Vvar__3__rsplit__right__9238) = cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(Vvar__0__C__9233,Vvar__1__rsplit__left__9235,Vvar__2__rsplit__common__9237,Vvar__3__rsplit__right__9239)
     => ( Vvar__3__rsplit__right__9238 = Vvar__3__rsplit__right__9239
        & Vvar__2__rsplit__common__9236 = Vvar__2__rsplit__common__9237
        & Vvar__1__rsplit__left__9234 = Vvar__1__rsplit__left__9235
        & Vvar__0__C__9232 = Vvar__0__C__9233 ) ) ).

fof('$_inj_Coq.setoid_ring.InitialRing.mkhypo',axiom,
    ! [Vvar__0__hypo__type__32426,Vvar__0__hypo__type__32427,Vvar__1__hypo__proof__32428,Vvar__1__hypo__proof__32429] :
      ( cCoq_2esetoid__ring_2eInitialRing_2emkhypo___24a2(Vvar__0__hypo__type__32426,Vvar__1__hypo__proof__32428) = cCoq_2esetoid__ring_2eInitialRing_2emkhypo___24a2(Vvar__0__hypo__type__32427,Vvar__1__hypo__proof__32429)
     => ( Vvar__1__hypo__proof__32428 = Vvar__1__hypo__proof__32429
        & Vvar__0__hypo__type__32426 = Vvar__0__hypo__type__32427 ) ) ).

fof('$_inj_Coq.setoid_ring.Ring_polynom.PEI',axiom,
    ! [Vvar__0__C__10037,Vvar__0__C__10038] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__10037) = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__10038)
     => Vvar__0__C__10037 = Vvar__0__C__10038 ) ).

fof('$_inj_Coq.setoid_ring.Ring_polynom.PEO',axiom,
    ! [Vvar__0__C__10035,Vvar__0__C__10036] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__10035) = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__10036)
     => Vvar__0__C__10035 = Vvar__0__C__10036 ) ).

fof('$_inj_Coq.setoid_ring.Ring_polynom.PEX',axiom,
    ! [Vvar__0__C__10043,Vvar__0__C__10044,Vvar__1___24Anonymous__10045,Vvar__1___24Anonymous__10046] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(Vvar__0__C__10043,Vvar__1___24Anonymous__10045) = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(Vvar__0__C__10044,Vvar__1___24Anonymous__10046)
     => ( Vvar__1___24Anonymous__10045 = Vvar__1___24Anonymous__10046
        & Vvar__0__C__10043 = Vvar__0__C__10044 ) ) ).

fof('$_inj_Coq.setoid_ring.Ring_polynom.PEadd',axiom,
    ! [Vvar__0__C__10047,Vvar__0__C__10048,Vvar__1___24Anonymous__10049,Vvar__1___24Anonymous__10050,Vvar__2___24Anonymous__10051,Vvar__2___24Anonymous__10052] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(Vvar__0__C__10047,Vvar__1___24Anonymous__10049,Vvar__2___24Anonymous__10051) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(Vvar__0__C__10048,Vvar__1___24Anonymous__10050,Vvar__2___24Anonymous__10052)
     => ( Vvar__2___24Anonymous__10051 = Vvar__2___24Anonymous__10052
        & Vvar__1___24Anonymous__10049 = Vvar__1___24Anonymous__10050
        & Vvar__0__C__10047 = Vvar__0__C__10048 ) ) ).

fof('$_inj_Coq.setoid_ring.Ring_polynom.PEc',axiom,
    ! [Vvar__0__C__10039,Vvar__0__C__10040,Vvar__1___24Anonymous__10041,Vvar__1___24Anonymous__10042] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(Vvar__0__C__10039,Vvar__1___24Anonymous__10041) = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(Vvar__0__C__10040,Vvar__1___24Anonymous__10042)
     => ( Vvar__1___24Anonymous__10041 = Vvar__1___24Anonymous__10042
        & Vvar__0__C__10039 = Vvar__0__C__10040 ) ) ).

fof('$_inj_Coq.setoid_ring.Ring_polynom.PEmul',axiom,
    ! [Vvar__0__C__10059,Vvar__0__C__10060,Vvar__1___24Anonymous__10061,Vvar__1___24Anonymous__10062,Vvar__2___24Anonymous__10063,Vvar__2___24Anonymous__10064] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(Vvar__0__C__10059,Vvar__1___24Anonymous__10061,Vvar__2___24Anonymous__10063) = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(Vvar__0__C__10060,Vvar__1___24Anonymous__10062,Vvar__2___24Anonymous__10064)
     => ( Vvar__2___24Anonymous__10063 = Vvar__2___24Anonymous__10064
        & Vvar__1___24Anonymous__10061 = Vvar__1___24Anonymous__10062
        & Vvar__0__C__10059 = Vvar__0__C__10060 ) ) ).

fof('$_inj_Coq.setoid_ring.Ring_polynom.PEopp',axiom,
    ! [Vvar__0__C__10065,Vvar__0__C__10066,Vvar__1___24Anonymous__10067,Vvar__1___24Anonymous__10068] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(Vvar__0__C__10065,Vvar__1___24Anonymous__10067) = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(Vvar__0__C__10066,Vvar__1___24Anonymous__10068)
     => ( Vvar__1___24Anonymous__10067 = Vvar__1___24Anonymous__10068
        & Vvar__0__C__10065 = Vvar__0__C__10066 ) ) ).

fof('$_inj_Coq.setoid_ring.Ring_polynom.PEpow',axiom,
    ! [Vvar__0__C__10069,Vvar__0__C__10070,Vvar__1___24Anonymous__10071,Vvar__1___24Anonymous__10072,Vvar__2___24Anonymous__10073,Vvar__2___24Anonymous__10074] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(Vvar__0__C__10069,Vvar__1___24Anonymous__10071,Vvar__2___24Anonymous__10073) = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(Vvar__0__C__10070,Vvar__1___24Anonymous__10072,Vvar__2___24Anonymous__10074)
     => ( Vvar__2___24Anonymous__10073 = Vvar__2___24Anonymous__10074
        & Vvar__1___24Anonymous__10071 = Vvar__1___24Anonymous__10072
        & Vvar__0__C__10069 = Vvar__0__C__10070 ) ) ).

fof('$_inj_Coq.setoid_ring.Ring_polynom.PEsub',axiom,
    ! [Vvar__0__C__10053,Vvar__0__C__10054,Vvar__1___24Anonymous__10055,Vvar__1___24Anonymous__10056,Vvar__2___24Anonymous__10057,Vvar__2___24Anonymous__10058] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(Vvar__0__C__10053,Vvar__1___24Anonymous__10055,Vvar__2___24Anonymous__10057) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(Vvar__0__C__10054,Vvar__1___24Anonymous__10056,Vvar__2___24Anonymous__10058)
     => ( Vvar__2___24Anonymous__10057 = Vvar__2___24Anonymous__10058
        & Vvar__1___24Anonymous__10055 = Vvar__1___24Anonymous__10056
        & Vvar__0__C__10053 = Vvar__0__C__10054 ) ) ).

fof('$_inj_Coq.setoid_ring.Ring_polynom.PX',axiom,
    ! [Vvar__0__C__9824,Vvar__0__C__9825,Vvar__1___24Anonymous__9826,Vvar__1___24Anonymous__9827,Vvar__2___24Anonymous__9828,Vvar__2___24Anonymous__9829,Vvar__3___24Anonymous__9830,Vvar__3___24Anonymous__9831] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(Vvar__0__C__9824,Vvar__1___24Anonymous__9826,Vvar__2___24Anonymous__9828,Vvar__3___24Anonymous__9830) = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(Vvar__0__C__9825,Vvar__1___24Anonymous__9827,Vvar__2___24Anonymous__9829,Vvar__3___24Anonymous__9831)
     => ( Vvar__3___24Anonymous__9830 = Vvar__3___24Anonymous__9831
        & Vvar__2___24Anonymous__9828 = Vvar__2___24Anonymous__9829
        & Vvar__1___24Anonymous__9826 = Vvar__1___24Anonymous__9827
        & Vvar__0__C__9824 = Vvar__0__C__9825 ) ) ).

fof('$_inj_Coq.setoid_ring.Ring_polynom.Pc',axiom,
    ! [Vvar__0__C__9814,Vvar__0__C__9815,Vvar__1___24Anonymous__9816,Vvar__1___24Anonymous__9817] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__9814,Vvar__1___24Anonymous__9816) = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__9815,Vvar__1___24Anonymous__9817)
     => ( Vvar__1___24Anonymous__9816 = Vvar__1___24Anonymous__9817
        & Vvar__0__C__9814 = Vvar__0__C__9815 ) ) ).

fof('$_inj_Coq.setoid_ring.Ring_polynom.Pinj',axiom,
    ! [Vvar__0__C__9818,Vvar__0__C__9819,Vvar__1___24Anonymous__9820,Vvar__1___24Anonymous__9821,Vvar__2___24Anonymous__9822,Vvar__2___24Anonymous__9823] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__9818,Vvar__1___24Anonymous__9820,Vvar__2___24Anonymous__9822) = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__9819,Vvar__1___24Anonymous__9821,Vvar__2___24Anonymous__9823)
     => ( Vvar__2___24Anonymous__9822 = Vvar__2___24Anonymous__9823
        & Vvar__1___24Anonymous__9820 = Vvar__1___24Anonymous__9821
        & Vvar__0__C__9818 = Vvar__0__C__9819 ) ) ).

fof('$_inj_Coq.setoid_ring.Ring_polynom.vmon',axiom,
    ! [Vvar__0___24Anonymous__9849,Vvar__0___24Anonymous__9850,Vvar__1___24Anonymous__9851,Vvar__1___24Anonymous__9852] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(Vvar__0___24Anonymous__9849,Vvar__1___24Anonymous__9851) = cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(Vvar__0___24Anonymous__9850,Vvar__1___24Anonymous__9852)
     => ( Vvar__1___24Anonymous__9851 = Vvar__1___24Anonymous__9852
        & Vvar__0___24Anonymous__9849 = Vvar__0___24Anonymous__9850 ) ) ).

fof('$_inj_Coq.setoid_ring.Ring_polynom.zmon',axiom,
    ! [Vvar__0___24Anonymous__9845,Vvar__0___24Anonymous__9846,Vvar__1___24Anonymous__9847,Vvar__1___24Anonymous__9848] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__9845,Vvar__1___24Anonymous__9847) = cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__9846,Vvar__1___24Anonymous__9848)
     => ( Vvar__1___24Anonymous__9847 = Vvar__1___24Anonymous__9848
        & Vvar__0___24Anonymous__9845 = Vvar__0___24Anonymous__9846 ) ) ).

fof('$_inj_Coq.setoid_ring.Ring_theory.Computational',axiom,
    ! [Vvar__0__R__34452,Vvar__0__R__34453,Vvar__1__req__34454,Vvar__1__req__34455,Vvar__2__reqb__34456,Vvar__2__reqb__34457,Vvar__3___24Anonymous__34458,Vvar__3___24Anonymous__34459] :
      ( cCoq_2esetoid__ring_2eRing__theory_2eComputational___24a3(Vvar__0__R__34452,Vvar__1__req__34454,Vvar__2__reqb__34456) = cCoq_2esetoid__ring_2eRing__theory_2eComputational___24a3(Vvar__0__R__34453,Vvar__1__req__34455,Vvar__2__reqb__34457)
     => ( c_24Proof = c_24Proof
        & Vvar__2__reqb__34456 = Vvar__2__reqb__34457
        & Vvar__1__req__34454 = Vvar__1__req__34455
        & Vvar__0__R__34452 = Vvar__0__R__34453 ) ) ).

fof('$_inj_Coq.setoid_ring.Ring_theory.Morphism',axiom,
    ! [Vvar__0__R__34460,Vvar__0__R__34461,Vvar__1__rO__34462,Vvar__1__rO__34463,Vvar__2__rI__34464,Vvar__2__rI__34465,Vvar__3__radd__34466,Vvar__3__radd__34467,Vvar__4__rmul__34468,Vvar__4__rmul__34469,Vvar__5__rsub__34470,Vvar__5__rsub__34471,Vvar__6__ropp__34472,Vvar__6__ropp__34473,Vvar__7__req__34474,Vvar__7__req__34475,Vvar__8__C__34476,Vvar__8__C__34477,Vvar__9__cO__34478,Vvar__9__cO__34479,Vvar__10__cI__34480,Vvar__10__cI__34481,Vvar__11__cadd__34482,Vvar__11__cadd__34483,Vvar__12__cmul__34484,Vvar__12__cmul__34485,Vvar__13__csub__34486,Vvar__13__csub__34487,Vvar__14__copp__34488,Vvar__14__copp__34489,Vvar__15__ceqb__34490,Vvar__15__ceqb__34491,Vvar__16__phi__34492,Vvar__16__phi__34493,Vvar__17___24Anonymous__34494,Vvar__17___24Anonymous__34495] :
      ( cCoq_2esetoid__ring_2eRing__theory_2eMorphism___24a17(Vvar__0__R__34460,Vvar__1__rO__34462,Vvar__2__rI__34464,Vvar__3__radd__34466,Vvar__4__rmul__34468,Vvar__5__rsub__34470,Vvar__6__ropp__34472,Vvar__7__req__34474,Vvar__8__C__34476,Vvar__9__cO__34478,Vvar__10__cI__34480,Vvar__11__cadd__34482,Vvar__12__cmul__34484,Vvar__13__csub__34486,Vvar__14__copp__34488,Vvar__15__ceqb__34490,Vvar__16__phi__34492) = cCoq_2esetoid__ring_2eRing__theory_2eMorphism___24a17(Vvar__0__R__34461,Vvar__1__rO__34463,Vvar__2__rI__34465,Vvar__3__radd__34467,Vvar__4__rmul__34469,Vvar__5__rsub__34471,Vvar__6__ropp__34473,Vvar__7__req__34475,Vvar__8__C__34477,Vvar__9__cO__34479,Vvar__10__cI__34481,Vvar__11__cadd__34483,Vvar__12__cmul__34485,Vvar__13__csub__34487,Vvar__14__copp__34489,Vvar__15__ceqb__34491,Vvar__16__phi__34493)
     => ( c_24Proof = c_24Proof
        & Vvar__16__phi__34492 = Vvar__16__phi__34493
        & Vvar__15__ceqb__34490 = Vvar__15__ceqb__34491
        & Vvar__14__copp__34488 = Vvar__14__copp__34489
        & Vvar__13__csub__34486 = Vvar__13__csub__34487
        & Vvar__12__cmul__34484 = Vvar__12__cmul__34485
        & Vvar__11__cadd__34482 = Vvar__11__cadd__34483
        & Vvar__10__cI__34480 = Vvar__10__cI__34481
        & Vvar__9__cO__34478 = Vvar__9__cO__34479
        & Vvar__8__C__34476 = Vvar__8__C__34477
        & Vvar__7__req__34474 = Vvar__7__req__34475
        & Vvar__6__ropp__34472 = Vvar__6__ropp__34473
        & Vvar__5__rsub__34470 = Vvar__5__rsub__34471
        & Vvar__4__rmul__34468 = Vvar__4__rmul__34469
        & Vvar__3__radd__34466 = Vvar__3__radd__34467
        & Vvar__2__rI__34464 = Vvar__2__rI__34465
        & Vvar__1__rO__34462 = Vvar__1__rO__34463
        & Vvar__0__R__34460 = Vvar__0__R__34461 ) ) ).

fof('$_inj_Norm.Arrow',axiom,
    ! [Vvar__0___24Anonymous__4748,Vvar__0___24Anonymous__4749,Vvar__1___24Anonymous__4750,Vvar__1___24Anonymous__4751] :
      ( cNorm_2eArrow___24a2(Vvar__0___24Anonymous__4748,Vvar__1___24Anonymous__4750) = cNorm_2eArrow___24a2(Vvar__0___24Anonymous__4749,Vvar__1___24Anonymous__4751)
     => ( Vvar__1___24Anonymous__4750 = Vvar__1___24Anonymous__4751
        & Vvar__0___24Anonymous__4748 = Vvar__0___24Anonymous__4749 ) ) ).

fof('$_inj_Norm.Prod',axiom,
    ! [Vvar__0___24Anonymous__4752,Vvar__0___24Anonymous__4753,Vvar__1___24Anonymous__4754,Vvar__1___24Anonymous__4755] :
      ( cNorm_2eProd___24a2(Vvar__0___24Anonymous__4752,Vvar__1___24Anonymous__4754) = cNorm_2eProd___24a2(Vvar__0___24Anonymous__4753,Vvar__1___24Anonymous__4755)
     => ( Vvar__1___24Anonymous__4754 = Vvar__1___24Anonymous__4755
        & Vvar__0___24Anonymous__4752 = Vvar__0___24Anonymous__4753 ) ) ).

fof('$_inj_Norm.abs',axiom,
    ! [Vvar__0___24Anonymous__4704,Vvar__0___24Anonymous__4705,Vvar__1___24Anonymous__4706,Vvar__1___24Anonymous__4707,Vvar__2___24Anonymous__4708,Vvar__2___24Anonymous__4709] :
      ( cNorm_2eabs___24a3(Vvar__0___24Anonymous__4704,Vvar__1___24Anonymous__4706,Vvar__2___24Anonymous__4708) = cNorm_2eabs___24a3(Vvar__0___24Anonymous__4705,Vvar__1___24Anonymous__4707,Vvar__2___24Anonymous__4709)
     => ( Vvar__2___24Anonymous__4708 = Vvar__2___24Anonymous__4709
        & Vvar__1___24Anonymous__4706 = Vvar__1___24Anonymous__4707
        & Vvar__0___24Anonymous__4704 = Vvar__0___24Anonymous__4705 ) ) ).

fof('$_inj_Norm.app',axiom,
    ! [Vvar__0___24Anonymous__4700,Vvar__0___24Anonymous__4701,Vvar__1___24Anonymous__4702,Vvar__1___24Anonymous__4703] :
      ( cNorm_2eapp___24a2(Vvar__0___24Anonymous__4700,Vvar__1___24Anonymous__4702) = cNorm_2eapp___24a2(Vvar__0___24Anonymous__4701,Vvar__1___24Anonymous__4703)
     => ( Vvar__1___24Anonymous__4702 = Vvar__1___24Anonymous__4703
        & Vvar__0___24Anonymous__4700 = Vvar__0___24Anonymous__4701 ) ) ).

fof('$_inj_Norm.fst',axiom,
    ! [Vvar__0___24Anonymous__4714,Vvar__0___24Anonymous__4715] :
      ( cNorm_2efst___24a1(Vvar__0___24Anonymous__4714) = cNorm_2efst___24a1(Vvar__0___24Anonymous__4715)
     => Vvar__0___24Anonymous__4714 = Vvar__0___24Anonymous__4715 ) ).

fof('$_inj_Norm.pair',axiom,
    ! [Vvar__0___24Anonymous__4710,Vvar__0___24Anonymous__4711,Vvar__1___24Anonymous__4712,Vvar__1___24Anonymous__4713] :
      ( cNorm_2epair___24a2(Vvar__0___24Anonymous__4710,Vvar__1___24Anonymous__4712) = cNorm_2epair___24a2(Vvar__0___24Anonymous__4711,Vvar__1___24Anonymous__4713)
     => ( Vvar__1___24Anonymous__4712 = Vvar__1___24Anonymous__4713
        & Vvar__0___24Anonymous__4710 = Vvar__0___24Anonymous__4711 ) ) ).

fof('$_inj_Norm.snd',axiom,
    ! [Vvar__0___24Anonymous__4716,Vvar__0___24Anonymous__4717] :
      ( cNorm_2esnd___24a1(Vvar__0___24Anonymous__4716) = cNorm_2esnd___24a1(Vvar__0___24Anonymous__4717)
     => Vvar__0___24Anonymous__4716 = Vvar__0___24Anonymous__4717 ) ).

fof('$_inj_Norm.test',axiom,
    ! [Vvar__0___24Anonymous__4718,Vvar__0___24Anonymous__4719,Vvar__1___24Anonymous__4720,Vvar__1___24Anonymous__4721,Vvar__2___24Anonymous__4722,Vvar__2___24Anonymous__4723] :
      ( cNorm_2etest___24a3(Vvar__0___24Anonymous__4718,Vvar__1___24Anonymous__4720,Vvar__2___24Anonymous__4722) = cNorm_2etest___24a3(Vvar__0___24Anonymous__4719,Vvar__1___24Anonymous__4721,Vvar__2___24Anonymous__4723)
     => ( Vvar__2___24Anonymous__4722 = Vvar__2___24Anonymous__4723
        & Vvar__1___24Anonymous__4720 = Vvar__1___24Anonymous__4721
        & Vvar__0___24Anonymous__4718 = Vvar__0___24Anonymous__4719 ) ) ).

fof('$_inj_Norm.var',axiom,
    ! [Vvar__0___24Anonymous__4698,Vvar__0___24Anonymous__4699] :
      ( cNorm_2evar___24a1(Vvar__0___24Anonymous__4698) = cNorm_2evar___24a1(Vvar__0___24Anonymous__4699)
     => Vvar__0___24Anonymous__4698 = Vvar__0___24Anonymous__4699 ) ).

fof('$_inj_PLF.Imp.AExp.AMinus',axiom,
    ! [Vvar__0__a1__29229,Vvar__0__a1__29230,Vvar__1__a2__29231,Vvar__1__a2__29232] :
      ( cPLF_2eImp_2eAExp_2eAMinus___24a2(Vvar__0__a1__29229,Vvar__1__a2__29231) = cPLF_2eImp_2eAExp_2eAMinus___24a2(Vvar__0__a1__29230,Vvar__1__a2__29232)
     => ( Vvar__1__a2__29231 = Vvar__1__a2__29232
        & Vvar__0__a1__29229 = Vvar__0__a1__29230 ) ) ).

fof('$_inj_PLF.Imp.AExp.AMult',axiom,
    ! [Vvar__0__a1__29233,Vvar__0__a1__29234,Vvar__1__a2__29235,Vvar__1__a2__29236] :
      ( cPLF_2eImp_2eAExp_2eAMult___24a2(Vvar__0__a1__29233,Vvar__1__a2__29235) = cPLF_2eImp_2eAExp_2eAMult___24a2(Vvar__0__a1__29234,Vvar__1__a2__29236)
     => ( Vvar__1__a2__29235 = Vvar__1__a2__29236
        & Vvar__0__a1__29233 = Vvar__0__a1__29234 ) ) ).

fof('$_inj_PLF.Imp.AExp.ANum',axiom,
    ! [Vvar__0__n__29223,Vvar__0__n__29224] :
      ( cPLF_2eImp_2eAExp_2eANum___24a1(Vvar__0__n__29223) = cPLF_2eImp_2eAExp_2eANum___24a1(Vvar__0__n__29224)
     => Vvar__0__n__29223 = Vvar__0__n__29224 ) ).

fof('$_inj_PLF.Imp.AExp.APlus',axiom,
    ! [Vvar__0__a1__29225,Vvar__0__a1__29226,Vvar__1__a2__29227,Vvar__1__a2__29228] :
      ( cPLF_2eImp_2eAExp_2eAPlus___24a2(Vvar__0__a1__29225,Vvar__1__a2__29227) = cPLF_2eImp_2eAExp_2eAPlus___24a2(Vvar__0__a1__29226,Vvar__1__a2__29228)
     => ( Vvar__1__a2__29227 = Vvar__1__a2__29228
        & Vvar__0__a1__29225 = Vvar__0__a1__29226 ) ) ).

fof('$_inj_PLF.Imp.AExp.BAnd',axiom,
    ! [Vvar__0__b1__34941,Vvar__0__b1__34942,Vvar__1__b2__34943,Vvar__1__b2__34944] :
      ( cPLF_2eImp_2eAExp_2eBAnd___24a2(Vvar__0__b1__34941,Vvar__1__b2__34943) = cPLF_2eImp_2eAExp_2eBAnd___24a2(Vvar__0__b1__34942,Vvar__1__b2__34944)
     => ( Vvar__1__b2__34943 = Vvar__1__b2__34944
        & Vvar__0__b1__34941 = Vvar__0__b1__34942 ) ) ).

fof('$_inj_PLF.Imp.AExp.BEq',axiom,
    ! [Vvar__0__a1__34931,Vvar__0__a1__34932,Vvar__1__a2__34933,Vvar__1__a2__34934] :
      ( cPLF_2eImp_2eAExp_2eBEq___24a2(Vvar__0__a1__34931,Vvar__1__a2__34933) = cPLF_2eImp_2eAExp_2eBEq___24a2(Vvar__0__a1__34932,Vvar__1__a2__34934)
     => ( Vvar__1__a2__34933 = Vvar__1__a2__34934
        & Vvar__0__a1__34931 = Vvar__0__a1__34932 ) ) ).

fof('$_inj_PLF.Imp.AExp.BLe',axiom,
    ! [Vvar__0__a1__34935,Vvar__0__a1__34936,Vvar__1__a2__34937,Vvar__1__a2__34938] :
      ( cPLF_2eImp_2eAExp_2eBLe___24a2(Vvar__0__a1__34935,Vvar__1__a2__34937) = cPLF_2eImp_2eAExp_2eBLe___24a2(Vvar__0__a1__34936,Vvar__1__a2__34938)
     => ( Vvar__1__a2__34937 = Vvar__1__a2__34938
        & Vvar__0__a1__34935 = Vvar__0__a1__34936 ) ) ).

fof('$_inj_PLF.Imp.AExp.BNot',axiom,
    ! [Vvar__0__b__34939,Vvar__0__b__34940] :
      ( cPLF_2eImp_2eAExp_2eBNot___24a1(Vvar__0__b__34939) = cPLF_2eImp_2eAExp_2eBNot___24a1(Vvar__0__b__34940)
     => Vvar__0__b__34939 = Vvar__0__b__34940 ) ).

fof('$_inj_PLF.Imp.AId',axiom,
    ! [Vvar__0__x__25476,Vvar__0__x__25477] :
      ( cPLF_2eImp_2eAId___24a1(Vvar__0__x__25476) = cPLF_2eImp_2eAId___24a1(Vvar__0__x__25477)
     => Vvar__0__x__25476 = Vvar__0__x__25477 ) ).

fof('$_inj_PLF.Imp.AMinus',axiom,
    ! [Vvar__0__a1__25482,Vvar__0__a1__25483,Vvar__1__a2__25484,Vvar__1__a2__25485] :
      ( cPLF_2eImp_2eAMinus___24a2(Vvar__0__a1__25482,Vvar__1__a2__25484) = cPLF_2eImp_2eAMinus___24a2(Vvar__0__a1__25483,Vvar__1__a2__25485)
     => ( Vvar__1__a2__25484 = Vvar__1__a2__25485
        & Vvar__0__a1__25482 = Vvar__0__a1__25483 ) ) ).

fof('$_inj_PLF.Imp.AMult',axiom,
    ! [Vvar__0__a1__25486,Vvar__0__a1__25487,Vvar__1__a2__25488,Vvar__1__a2__25489] :
      ( cPLF_2eImp_2eAMult___24a2(Vvar__0__a1__25486,Vvar__1__a2__25488) = cPLF_2eImp_2eAMult___24a2(Vvar__0__a1__25487,Vvar__1__a2__25489)
     => ( Vvar__1__a2__25488 = Vvar__1__a2__25489
        & Vvar__0__a1__25486 = Vvar__0__a1__25487 ) ) ).

fof('$_inj_PLF.Imp.ANum',axiom,
    ! [Vvar__0__n__25474,Vvar__0__n__25475] :
      ( cPLF_2eImp_2eANum___24a1(Vvar__0__n__25474) = cPLF_2eImp_2eANum___24a1(Vvar__0__n__25475)
     => Vvar__0__n__25474 = Vvar__0__n__25475 ) ).

fof('$_inj_PLF.Imp.APlus',axiom,
    ! [Vvar__0__a1__25478,Vvar__0__a1__25479,Vvar__1__a2__25480,Vvar__1__a2__25481] :
      ( cPLF_2eImp_2eAPlus___24a2(Vvar__0__a1__25478,Vvar__1__a2__25480) = cPLF_2eImp_2eAPlus___24a2(Vvar__0__a1__25479,Vvar__1__a2__25481)
     => ( Vvar__1__a2__25480 = Vvar__1__a2__25481
        & Vvar__0__a1__25478 = Vvar__0__a1__25479 ) ) ).

fof('$_inj_PLF.Imp.BAnd',axiom,
    ! [Vvar__0__b1__25548,Vvar__0__b1__25549,Vvar__1__b2__25550,Vvar__1__b2__25551] :
      ( cPLF_2eImp_2eBAnd___24a2(Vvar__0__b1__25548,Vvar__1__b2__25550) = cPLF_2eImp_2eBAnd___24a2(Vvar__0__b1__25549,Vvar__1__b2__25551)
     => ( Vvar__1__b2__25550 = Vvar__1__b2__25551
        & Vvar__0__b1__25548 = Vvar__0__b1__25549 ) ) ).

fof('$_inj_PLF.Imp.BEq',axiom,
    ! [Vvar__0__a1__25538,Vvar__0__a1__25539,Vvar__1__a2__25540,Vvar__1__a2__25541] :
      ( cPLF_2eImp_2eBEq___24a2(Vvar__0__a1__25538,Vvar__1__a2__25540) = cPLF_2eImp_2eBEq___24a2(Vvar__0__a1__25539,Vvar__1__a2__25541)
     => ( Vvar__1__a2__25540 = Vvar__1__a2__25541
        & Vvar__0__a1__25538 = Vvar__0__a1__25539 ) ) ).

fof('$_inj_PLF.Imp.BLe',axiom,
    ! [Vvar__0__a1__25542,Vvar__0__a1__25543,Vvar__1__a2__25544,Vvar__1__a2__25545] :
      ( cPLF_2eImp_2eBLe___24a2(Vvar__0__a1__25542,Vvar__1__a2__25544) = cPLF_2eImp_2eBLe___24a2(Vvar__0__a1__25543,Vvar__1__a2__25545)
     => ( Vvar__1__a2__25544 = Vvar__1__a2__25545
        & Vvar__0__a1__25542 = Vvar__0__a1__25543 ) ) ).

fof('$_inj_PLF.Imp.BNot',axiom,
    ! [Vvar__0__b__25546,Vvar__0__b__25547] :
      ( cPLF_2eImp_2eBNot___24a1(Vvar__0__b__25546) = cPLF_2eImp_2eBNot___24a1(Vvar__0__b__25547)
     => Vvar__0__b__25546 = Vvar__0__b__25547 ) ).

fof('$_inj_PLF.Imp.BreakImp.CAss',axiom,
    ! [Vvar__0__x__35000,Vvar__0__x__35001,Vvar__1__a__35002,Vvar__1__a__35003] :
      ( cPLF_2eImp_2eBreakImp_2eCAss___24a2(Vvar__0__x__35000,Vvar__1__a__35002) = cPLF_2eImp_2eBreakImp_2eCAss___24a2(Vvar__0__x__35001,Vvar__1__a__35003)
     => ( Vvar__1__a__35002 = Vvar__1__a__35003
        & Vvar__0__x__35000 = Vvar__0__x__35001 ) ) ).

fof('$_inj_PLF.Imp.BreakImp.CIf',axiom,
    ! [Vvar__0__b__35008,Vvar__0__b__35009,Vvar__1__c1__35010,Vvar__1__c1__35011,Vvar__2__c2__35012,Vvar__2__c2__35013] :
      ( cPLF_2eImp_2eBreakImp_2eCIf___24a3(Vvar__0__b__35008,Vvar__1__c1__35010,Vvar__2__c2__35012) = cPLF_2eImp_2eBreakImp_2eCIf___24a3(Vvar__0__b__35009,Vvar__1__c1__35011,Vvar__2__c2__35013)
     => ( Vvar__2__c2__35012 = Vvar__2__c2__35013
        & Vvar__1__c1__35010 = Vvar__1__c1__35011
        & Vvar__0__b__35008 = Vvar__0__b__35009 ) ) ).

fof('$_inj_PLF.Imp.BreakImp.CSeq',axiom,
    ! [Vvar__0__c1__35004,Vvar__0__c1__35005,Vvar__1__c2__35006,Vvar__1__c2__35007] :
      ( cPLF_2eImp_2eBreakImp_2eCSeq___24a2(Vvar__0__c1__35004,Vvar__1__c2__35006) = cPLF_2eImp_2eBreakImp_2eCSeq___24a2(Vvar__0__c1__35005,Vvar__1__c2__35007)
     => ( Vvar__1__c2__35006 = Vvar__1__c2__35007
        & Vvar__0__c1__35004 = Vvar__0__c1__35005 ) ) ).

fof('$_inj_PLF.Imp.BreakImp.CWhile',axiom,
    ! [Vvar__0__b__35014,Vvar__0__b__35015,Vvar__1__c__35016,Vvar__1__c__35017] :
      ( cPLF_2eImp_2eBreakImp_2eCWhile___24a2(Vvar__0__b__35014,Vvar__1__c__35016) = cPLF_2eImp_2eBreakImp_2eCWhile___24a2(Vvar__0__b__35015,Vvar__1__c__35017)
     => ( Vvar__1__c__35016 = Vvar__1__c__35017
        & Vvar__0__b__35014 = Vvar__0__b__35015 ) ) ).

fof('$_inj_PLF.Imp.CAss',axiom,
    ! [Vvar__0__x__25598,Vvar__0__x__25599,Vvar__1__a__25600,Vvar__1__a__25601] :
      ( cPLF_2eImp_2eCAss___24a2(Vvar__0__x__25598,Vvar__1__a__25600) = cPLF_2eImp_2eCAss___24a2(Vvar__0__x__25599,Vvar__1__a__25601)
     => ( Vvar__1__a__25600 = Vvar__1__a__25601
        & Vvar__0__x__25598 = Vvar__0__x__25599 ) ) ).

fof('$_inj_PLF.Imp.CIf',axiom,
    ! [Vvar__0__b__25606,Vvar__0__b__25607,Vvar__1__c1__25608,Vvar__1__c1__25609,Vvar__2__c2__25610,Vvar__2__c2__25611] :
      ( cPLF_2eImp_2eCIf___24a3(Vvar__0__b__25606,Vvar__1__c1__25608,Vvar__2__c2__25610) = cPLF_2eImp_2eCIf___24a3(Vvar__0__b__25607,Vvar__1__c1__25609,Vvar__2__c2__25611)
     => ( Vvar__2__c2__25610 = Vvar__2__c2__25611
        & Vvar__1__c1__25608 = Vvar__1__c1__25609
        & Vvar__0__b__25606 = Vvar__0__b__25607 ) ) ).

fof('$_inj_PLF.Imp.CSeq',axiom,
    ! [Vvar__0__c1__25602,Vvar__0__c1__25603,Vvar__1__c2__25604,Vvar__1__c2__25605] :
      ( cPLF_2eImp_2eCSeq___24a2(Vvar__0__c1__25602,Vvar__1__c2__25604) = cPLF_2eImp_2eCSeq___24a2(Vvar__0__c1__25603,Vvar__1__c2__25605)
     => ( Vvar__1__c2__25604 = Vvar__1__c2__25605
        & Vvar__0__c1__25602 = Vvar__0__c1__25603 ) ) ).

fof('$_inj_PLF.Imp.CWhile',axiom,
    ! [Vvar__0__b__25612,Vvar__0__b__25613,Vvar__1__c__25614,Vvar__1__c__25615] :
      ( cPLF_2eImp_2eCWhile___24a2(Vvar__0__b__25612,Vvar__1__c__25614) = cPLF_2eImp_2eCWhile___24a2(Vvar__0__b__25613,Vvar__1__c__25615)
     => ( Vvar__1__c__25614 = Vvar__1__c__25615
        & Vvar__0__b__25612 = Vvar__0__b__25613 ) ) ).

fof('$_inj_PLF.Imp.SLoad',axiom,
    ! [Vvar__0__x__32353,Vvar__0__x__32354] :
      ( cPLF_2eImp_2eSLoad___24a1(Vvar__0__x__32353) = cPLF_2eImp_2eSLoad___24a1(Vvar__0__x__32354)
     => Vvar__0__x__32353 = Vvar__0__x__32354 ) ).

fof('$_inj_PLF.Imp.SPush',axiom,
    ! [Vvar__0__n__32351,Vvar__0__n__32352] :
      ( cPLF_2eImp_2eSPush___24a1(Vvar__0__n__32351) = cPLF_2eImp_2eSPush___24a1(Vvar__0__n__32352)
     => Vvar__0__n__32351 = Vvar__0__n__32352 ) ).

fof('$_inj_PLF.Imp.aevalR_division.ADiv',axiom,
    ! [Vvar__0__a1__30791,Vvar__0__a1__30792,Vvar__1__a2__30793,Vvar__1__a2__30794] :
      ( cPLF_2eImp_2eaevalR__division_2eADiv___24a2(Vvar__0__a1__30791,Vvar__1__a2__30793) = cPLF_2eImp_2eaevalR__division_2eADiv___24a2(Vvar__0__a1__30792,Vvar__1__a2__30794)
     => ( Vvar__1__a2__30793 = Vvar__1__a2__30794
        & Vvar__0__a1__30791 = Vvar__0__a1__30792 ) ) ).

fof('$_inj_PLF.Imp.aevalR_division.AMinus',axiom,
    ! [Vvar__0__a1__30783,Vvar__0__a1__30784,Vvar__1__a2__30785,Vvar__1__a2__30786] :
      ( cPLF_2eImp_2eaevalR__division_2eAMinus___24a2(Vvar__0__a1__30783,Vvar__1__a2__30785) = cPLF_2eImp_2eaevalR__division_2eAMinus___24a2(Vvar__0__a1__30784,Vvar__1__a2__30786)
     => ( Vvar__1__a2__30785 = Vvar__1__a2__30786
        & Vvar__0__a1__30783 = Vvar__0__a1__30784 ) ) ).

fof('$_inj_PLF.Imp.aevalR_division.AMult',axiom,
    ! [Vvar__0__a1__30787,Vvar__0__a1__30788,Vvar__1__a2__30789,Vvar__1__a2__30790] :
      ( cPLF_2eImp_2eaevalR__division_2eAMult___24a2(Vvar__0__a1__30787,Vvar__1__a2__30789) = cPLF_2eImp_2eaevalR__division_2eAMult___24a2(Vvar__0__a1__30788,Vvar__1__a2__30790)
     => ( Vvar__1__a2__30789 = Vvar__1__a2__30790
        & Vvar__0__a1__30787 = Vvar__0__a1__30788 ) ) ).

fof('$_inj_PLF.Imp.aevalR_division.ANum',axiom,
    ! [Vvar__0__n__30777,Vvar__0__n__30778] :
      ( cPLF_2eImp_2eaevalR__division_2eANum___24a1(Vvar__0__n__30777) = cPLF_2eImp_2eaevalR__division_2eANum___24a1(Vvar__0__n__30778)
     => Vvar__0__n__30777 = Vvar__0__n__30778 ) ).

fof('$_inj_PLF.Imp.aevalR_division.APlus',axiom,
    ! [Vvar__0__a1__30779,Vvar__0__a1__30780,Vvar__1__a2__30781,Vvar__1__a2__30782] :
      ( cPLF_2eImp_2eaevalR__division_2eAPlus___24a2(Vvar__0__a1__30779,Vvar__1__a2__30781) = cPLF_2eImp_2eaevalR__division_2eAPlus___24a2(Vvar__0__a1__30780,Vvar__1__a2__30782)
     => ( Vvar__1__a2__30781 = Vvar__1__a2__30782
        & Vvar__0__a1__30779 = Vvar__0__a1__30780 ) ) ).

fof('$_inj_PLF.Imp.aevalR_extended.AMinus',axiom,
    ! [Vvar__0__a1__35247,Vvar__0__a1__35248,Vvar__1__a2__35249,Vvar__1__a2__35250] :
      ( cPLF_2eImp_2eaevalR__extended_2eAMinus___24a2(Vvar__0__a1__35247,Vvar__1__a2__35249) = cPLF_2eImp_2eaevalR__extended_2eAMinus___24a2(Vvar__0__a1__35248,Vvar__1__a2__35250)
     => ( Vvar__1__a2__35249 = Vvar__1__a2__35250
        & Vvar__0__a1__35247 = Vvar__0__a1__35248 ) ) ).

fof('$_inj_PLF.Imp.aevalR_extended.AMult',axiom,
    ! [Vvar__0__a1__35251,Vvar__0__a1__35252,Vvar__1__a2__35253,Vvar__1__a2__35254] :
      ( cPLF_2eImp_2eaevalR__extended_2eAMult___24a2(Vvar__0__a1__35251,Vvar__1__a2__35253) = cPLF_2eImp_2eaevalR__extended_2eAMult___24a2(Vvar__0__a1__35252,Vvar__1__a2__35254)
     => ( Vvar__1__a2__35253 = Vvar__1__a2__35254
        & Vvar__0__a1__35251 = Vvar__0__a1__35252 ) ) ).

fof('$_inj_PLF.Imp.aevalR_extended.ANum',axiom,
    ! [Vvar__0__n__35241,Vvar__0__n__35242] :
      ( cPLF_2eImp_2eaevalR__extended_2eANum___24a1(Vvar__0__n__35241) = cPLF_2eImp_2eaevalR__extended_2eANum___24a1(Vvar__0__n__35242)
     => Vvar__0__n__35241 = Vvar__0__n__35242 ) ).

fof('$_inj_PLF.Imp.aevalR_extended.APlus',axiom,
    ! [Vvar__0__a1__35243,Vvar__0__a1__35244,Vvar__1__a2__35245,Vvar__1__a2__35246] :
      ( cPLF_2eImp_2eaevalR__extended_2eAPlus___24a2(Vvar__0__a1__35243,Vvar__1__a2__35245) = cPLF_2eImp_2eaevalR__extended_2eAPlus___24a2(Vvar__0__a1__35244,Vvar__1__a2__35246)
     => ( Vvar__1__a2__35245 = Vvar__1__a2__35246
        & Vvar__0__a1__35243 = Vvar__0__a1__35244 ) ) ).

fof('$_inj_PLF.Smallstep.C',axiom,
    ! [Vvar__0___24Anonymous__18,Vvar__0___24Anonymous__19] :
      ( cPLF_2eSmallstep_2eC___24a1(Vvar__0___24Anonymous__18) = cPLF_2eSmallstep_2eC___24a1(Vvar__0___24Anonymous__19)
     => Vvar__0___24Anonymous__18 = Vvar__0___24Anonymous__19 ) ).

fof('$_inj_PLF.Smallstep.CImp.CAss',axiom,
    ! [Vvar__0___24Anonymous__29357,Vvar__0___24Anonymous__29358,Vvar__1___24Anonymous__29359,Vvar__1___24Anonymous__29360] :
      ( cPLF_2eSmallstep_2eCImp_2eCAss___24a2(Vvar__0___24Anonymous__29357,Vvar__1___24Anonymous__29359) = cPLF_2eSmallstep_2eCImp_2eCAss___24a2(Vvar__0___24Anonymous__29358,Vvar__1___24Anonymous__29360)
     => ( Vvar__1___24Anonymous__29359 = Vvar__1___24Anonymous__29360
        & Vvar__0___24Anonymous__29357 = Vvar__0___24Anonymous__29358 ) ) ).

fof('$_inj_PLF.Smallstep.CImp.CIf',axiom,
    ! [Vvar__0___24Anonymous__29365,Vvar__0___24Anonymous__29366,Vvar__1___24Anonymous__29367,Vvar__1___24Anonymous__29368,Vvar__2___24Anonymous__29369,Vvar__2___24Anonymous__29370] :
      ( cPLF_2eSmallstep_2eCImp_2eCIf___24a3(Vvar__0___24Anonymous__29365,Vvar__1___24Anonymous__29367,Vvar__2___24Anonymous__29369) = cPLF_2eSmallstep_2eCImp_2eCIf___24a3(Vvar__0___24Anonymous__29366,Vvar__1___24Anonymous__29368,Vvar__2___24Anonymous__29370)
     => ( Vvar__2___24Anonymous__29369 = Vvar__2___24Anonymous__29370
        & Vvar__1___24Anonymous__29367 = Vvar__1___24Anonymous__29368
        & Vvar__0___24Anonymous__29365 = Vvar__0___24Anonymous__29366 ) ) ).

fof('$_inj_PLF.Smallstep.CImp.CPar',axiom,
    ! [Vvar__0___24Anonymous__29375,Vvar__0___24Anonymous__29376,Vvar__1___24Anonymous__29377,Vvar__1___24Anonymous__29378] :
      ( cPLF_2eSmallstep_2eCImp_2eCPar___24a2(Vvar__0___24Anonymous__29375,Vvar__1___24Anonymous__29377) = cPLF_2eSmallstep_2eCImp_2eCPar___24a2(Vvar__0___24Anonymous__29376,Vvar__1___24Anonymous__29378)
     => ( Vvar__1___24Anonymous__29377 = Vvar__1___24Anonymous__29378
        & Vvar__0___24Anonymous__29375 = Vvar__0___24Anonymous__29376 ) ) ).

fof('$_inj_PLF.Smallstep.CImp.CSeq',axiom,
    ! [Vvar__0___24Anonymous__29361,Vvar__0___24Anonymous__29362,Vvar__1___24Anonymous__29363,Vvar__1___24Anonymous__29364] :
      ( cPLF_2eSmallstep_2eCImp_2eCSeq___24a2(Vvar__0___24Anonymous__29361,Vvar__1___24Anonymous__29363) = cPLF_2eSmallstep_2eCImp_2eCSeq___24a2(Vvar__0___24Anonymous__29362,Vvar__1___24Anonymous__29364)
     => ( Vvar__1___24Anonymous__29363 = Vvar__1___24Anonymous__29364
        & Vvar__0___24Anonymous__29361 = Vvar__0___24Anonymous__29362 ) ) ).

fof('$_inj_PLF.Smallstep.CImp.CWhile',axiom,
    ! [Vvar__0___24Anonymous__29371,Vvar__0___24Anonymous__29372,Vvar__1___24Anonymous__29373,Vvar__1___24Anonymous__29374] :
      ( cPLF_2eSmallstep_2eCImp_2eCWhile___24a2(Vvar__0___24Anonymous__29371,Vvar__1___24Anonymous__29373) = cPLF_2eSmallstep_2eCImp_2eCWhile___24a2(Vvar__0___24Anonymous__29372,Vvar__1___24Anonymous__29374)
     => ( Vvar__1___24Anonymous__29373 = Vvar__1___24Anonymous__29374
        & Vvar__0___24Anonymous__29371 = Vvar__0___24Anonymous__29372 ) ) ).

fof('$_inj_PLF.Smallstep.Combined.C',axiom,
    ! [Vvar__0___24Anonymous__35050,Vvar__0___24Anonymous__35051] :
      ( cPLF_2eSmallstep_2eCombined_2eC___24a1(Vvar__0___24Anonymous__35050) = cPLF_2eSmallstep_2eCombined_2eC___24a1(Vvar__0___24Anonymous__35051)
     => Vvar__0___24Anonymous__35050 = Vvar__0___24Anonymous__35051 ) ).

fof('$_inj_PLF.Smallstep.Combined.P',axiom,
    ! [Vvar__0___24Anonymous__35052,Vvar__0___24Anonymous__35053,Vvar__1___24Anonymous__35054,Vvar__1___24Anonymous__35055] :
      ( cPLF_2eSmallstep_2eCombined_2eP___24a2(Vvar__0___24Anonymous__35052,Vvar__1___24Anonymous__35054) = cPLF_2eSmallstep_2eCombined_2eP___24a2(Vvar__0___24Anonymous__35053,Vvar__1___24Anonymous__35055)
     => ( Vvar__1___24Anonymous__35054 = Vvar__1___24Anonymous__35055
        & Vvar__0___24Anonymous__35052 = Vvar__0___24Anonymous__35053 ) ) ).

fof('$_inj_PLF.Smallstep.Combined.test',axiom,
    ! [Vvar__0___24Anonymous__35056,Vvar__0___24Anonymous__35057,Vvar__1___24Anonymous__35058,Vvar__1___24Anonymous__35059,Vvar__2___24Anonymous__35060,Vvar__2___24Anonymous__35061] :
      ( cPLF_2eSmallstep_2eCombined_2etest___24a3(Vvar__0___24Anonymous__35056,Vvar__1___24Anonymous__35058,Vvar__2___24Anonymous__35060) = cPLF_2eSmallstep_2eCombined_2etest___24a3(Vvar__0___24Anonymous__35057,Vvar__1___24Anonymous__35059,Vvar__2___24Anonymous__35061)
     => ( Vvar__2___24Anonymous__35060 = Vvar__2___24Anonymous__35061
        & Vvar__1___24Anonymous__35058 = Vvar__1___24Anonymous__35059
        & Vvar__0___24Anonymous__35056 = Vvar__0___24Anonymous__35057 ) ) ).

fof('$_inj_PLF.Smallstep.P',axiom,
    ! [Vvar__0___24Anonymous__20,Vvar__0___24Anonymous__21,Vvar__1___24Anonymous__22,Vvar__1___24Anonymous__23] :
      ( cPLF_2eSmallstep_2eP___24a2(Vvar__0___24Anonymous__20,Vvar__1___24Anonymous__22) = cPLF_2eSmallstep_2eP___24a2(Vvar__0___24Anonymous__21,Vvar__1___24Anonymous__23)
     => ( Vvar__1___24Anonymous__22 = Vvar__1___24Anonymous__23
        & Vvar__0___24Anonymous__20 = Vvar__0___24Anonymous__21 ) ) ).

fof('$_inj_PLF.Smallstep.Temp4.test',axiom,
    ! [Vvar__0___24Anonymous__30542,Vvar__0___24Anonymous__30543,Vvar__1___24Anonymous__30544,Vvar__1___24Anonymous__30545,Vvar__2___24Anonymous__30546,Vvar__2___24Anonymous__30547] :
      ( cPLF_2eSmallstep_2eTemp4_2etest___24a3(Vvar__0___24Anonymous__30542,Vvar__1___24Anonymous__30544,Vvar__2___24Anonymous__30546) = cPLF_2eSmallstep_2eTemp4_2etest___24a3(Vvar__0___24Anonymous__30543,Vvar__1___24Anonymous__30545,Vvar__2___24Anonymous__30547)
     => ( Vvar__2___24Anonymous__30546 = Vvar__2___24Anonymous__30547
        & Vvar__1___24Anonymous__30544 = Vvar__1___24Anonymous__30545
        & Vvar__0___24Anonymous__30542 = Vvar__0___24Anonymous__30543 ) ) ).

fof('$_inversion_Coq.Arith.Between.P_nth',axiom,
    ! [Vvar__0__P__31028,Vvar__1__Q__31030,Vvar__2__init__31033,Vvar__3___24Anonymous__31034,Vvar__4___24Anonymous__31035] :
      ( c_24__type__31061___24t(Vvar__0__P__31028,Vvar__1__Q__31030,Vvar__2__init__31033,Vvar__3___24Anonymous__31034,Vvar__4___24Anonymous__31035,Vvar__0__P__31028)
     => ( c_24__type__31069___24t(Vvar__0__P__31028,Vvar__1__Q__31030,Vvar__2__init__31033,Vvar__3___24Anonymous__31034,Vvar__4___24Anonymous__31035,Vvar__1__Q__31030)
       => ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__init__31033)
         => ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__3___24Anonymous__31034)
           => ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__4___24Anonymous__31035)
             => ( cCoq_2eArith_2eBetween_2eP__nth___24a5(Vvar__0__P__31028,Vvar__1__Q__31030,Vvar__2__init__31033,Vvar__3___24Anonymous__31034,Vvar__4___24Anonymous__31035)
               => ( ( Vvar__4___24Anonymous__31035 = cCoq_2eInit_2eDatatypes_2eO
                    & Vvar__3___24Anonymous__31034 = Vvar__2__init__31033 )
                  | ? [Vvar__3__k__31049] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__3__k__31049)
                      & ? [Vvar__4__l__31050] :
                          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__4__l__31050)
                          & ? [Vvar__5__n__31051] :
                              ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__5__n__31051)
                              & cCoq_2eArith_2eBetween_2eP__nth___24a5(Vvar__0__P__31028,Vvar__1__Q__31030,Vvar__2__init__31033,Vvar__3__k__31049,Vvar__5__n__31051)
                              & cCoq_2eArith_2eBetween_2ebetween___24a3(Vvar__0__P__31028,cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__3__k__31049),Vvar__4__l__31050)
                              & p(happ(Vvar__1__Q__31030,Vvar__4__l__31050))
                              & Vvar__4___24Anonymous__31035 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__5__n__31051)
                              & Vvar__3___24Anonymous__31034 = Vvar__4__l__31050 ) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Arith.Between.between',axiom,
    ! [Vvar__0__P__30988,Vvar__1__k__30990,Vvar__2___24Anonymous__30991] :
      ( c_24__type__31005___24t(Vvar__0__P__30988,Vvar__1__k__30990,Vvar__2___24Anonymous__30991,Vvar__0__P__30988)
     => ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__k__30990)
       => ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2___24Anonymous__30991)
         => ( cCoq_2eArith_2eBetween_2ebetween___24a3(Vvar__0__P__30988,Vvar__1__k__30990,Vvar__2___24Anonymous__30991)
           => ( Vvar__2___24Anonymous__30991 = Vvar__1__k__30990
              | ? [Vvar__2__l__30999] :
                  ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__l__30999)
                  & cCoq_2eArith_2eBetween_2ebetween___24a3(Vvar__0__P__30988,Vvar__1__k__30990,Vvar__2__l__30999)
                  & p(happ(Vvar__0__P__30988,Vvar__2__l__30999))
                  & Vvar__2___24Anonymous__30991 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__l__30999) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Arith.Between.exists_between',axiom,
    ! [Vvar__0__Q__31007,Vvar__1__k__31009,Vvar__2___24Anonymous__31010] :
      ( c_24__type__31026___24t(Vvar__0__Q__31007,Vvar__1__k__31009,Vvar__2___24Anonymous__31010,Vvar__0__Q__31007)
     => ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__k__31009)
       => ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2___24Anonymous__31010)
         => ( cCoq_2eArith_2eBetween_2eexists__between___24a3(Vvar__0__Q__31007,Vvar__1__k__31009,Vvar__2___24Anonymous__31010)
           => ( ? [Vvar__2__l__31015] :
                  ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__l__31015)
                  & cCoq_2eArith_2eBetween_2eexists__between___24a3(Vvar__0__Q__31007,Vvar__1__k__31009,Vvar__2__l__31015)
                  & Vvar__2___24Anonymous__31010 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__l__31015) )
              | ? [Vvar__2__l__31020] :
                  ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__l__31020)
                  & cCoq_2eInit_2ePeano_2ele___24a2(Vvar__1__k__31009,Vvar__2__l__31020)
                  & p(happ(Vvar__0__Q__31007,Vvar__2__l__31020))
                  & Vvar__2___24Anonymous__31010 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__l__31020) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Arith.Even.even',axiom,
    ! [Vvar__0___24Anonymous__31176] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__31176)
     => ( cCoq_2eArith_2eEven_2eeven___24a1(Vvar__0___24Anonymous__31176)
       => ( Vvar__0___24Anonymous__31176 = cCoq_2eInit_2eDatatypes_2eO
          | ? [Vvar__0__n__31178] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__31178)
              & cCoq_2eArith_2eEven_2eodd___24a1(Vvar__0__n__31178)
              & Vvar__0___24Anonymous__31176 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0__n__31178) ) ) ) ) ).

fof('$_inversion_Coq.Arith.Even.odd',axiom,
    ! [Vvar__0___24Anonymous__31180] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__31180)
     => ( cCoq_2eArith_2eEven_2eodd___24a1(Vvar__0___24Anonymous__31180)
       => ? [Vvar__0__n__31182] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__31182)
            & cCoq_2eArith_2eEven_2eeven___24a1(Vvar__0__n__31182)
            & Vvar__0___24Anonymous__31180 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0__n__31182) ) ) ) ).

fof('$_inversion_Coq.Bool.Bool.reflect',axiom,
    ! [Vvar__0__P__31073,Vvar__1___24Anonymous__31074,VX31075] :
      ( cProp___24t(Vvar__0__P__31073)
     => ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__31074)
       => ( cCoq_2eBool_2eBool_2ereflect___24t(Vvar__0__P__31073,Vvar__1___24Anonymous__31074,VX31075)
         => ( ( p(Vvar__0__P__31073)
              & Vvar__1___24Anonymous__31074 = cCoq_2eInit_2eDatatypes_2etrue
              & VX31075 = cCoq_2eBool_2eBool_2eReflectT___24a1(Vvar__0__P__31073) )
            | ( ~ p(Vvar__0__P__31073)
              & Vvar__1___24Anonymous__31074 = cCoq_2eInit_2eDatatypes_2efalse
              & VX31075 = cCoq_2eBool_2eBool_2eReflectF___24a1(Vvar__0__P__31073) ) ) ) ) ) ).

fof('$_inversion_Coq.FSets.FSetPositive.PositiveSet.ct',axiom,
    ! [Vvar__0___24Anonymous__35192,Vvar__1___24Anonymous__35193,Vvar__2___24Anonymous__35194] :
      ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__0___24Anonymous__35192)
     => ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__1___24Anonymous__35193)
       => ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__2___24Anonymous__35194)
         => ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2ect___24a3(Vvar__0___24Anonymous__35192,Vvar__1___24Anonymous__35193,Vvar__2___24Anonymous__35194)
           => ( ? [Vvar__0__x__35196] :
                  ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__0__x__35196)
                  & Vvar__2___24Anonymous__35194 = Vvar__0__x__35196
                  & Vvar__1___24Anonymous__35193 = Vvar__0__x__35196
                  & Vvar__0___24Anonymous__35192 = Vvar__0__x__35196 )
              | ? [Vvar__0__x__35197] :
                  ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__0__x__35197)
                  & Vvar__2___24Anonymous__35194 = Vvar__0__x__35197
                  & Vvar__1___24Anonymous__35193 = cCoq_2eInit_2eDatatypes_2eEq
                  & Vvar__0___24Anonymous__35192 = Vvar__0__x__35197 )
              | ? [Vvar__0__x__35198] :
                  ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__0__x__35198)
                  & Vvar__2___24Anonymous__35194 = Vvar__0__x__35198
                  & Vvar__1___24Anonymous__35193 = Vvar__0__x__35198
                  & Vvar__0___24Anonymous__35192 = cCoq_2eInit_2eDatatypes_2eEq )
              | ? [Vvar__0__x__35199] :
                  ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__0__x__35199)
                  & Vvar__2___24Anonymous__35194 = Vvar__0__x__35199
                  & Vvar__1___24Anonymous__35193 = cCoq_2eInit_2eDatatypes_2eLt
                  & Vvar__0___24Anonymous__35192 = cCoq_2eInit_2eDatatypes_2eGt )
              | ? [Vvar__0__x__35200] :
                  ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__0__x__35200)
                  & Vvar__2___24Anonymous__35194 = Vvar__0__x__35200
                  & Vvar__1___24Anonymous__35193 = cCoq_2eInit_2eDatatypes_2eGt
                  & Vvar__0___24Anonymous__35192 = cCoq_2eInit_2eDatatypes_2eLt ) ) ) ) ) ) ).

fof('$_inversion_Coq.FSets.FSetPositive.PositiveSet.tree',axiom,
    ! [VX30001] :
      ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(VX30001)
     => ( VX30001 = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf
        | ? [Vvar__0___24Anonymous__30002] :
            ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__0___24Anonymous__30002)
            & ? [Vvar__1___24Anonymous__30003] :
                ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__30003)
                & ? [Vvar__2___24Anonymous__30004] :
                    ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(Vvar__2___24Anonymous__30004)
                    & VX30001 = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(Vvar__0___24Anonymous__30002,Vvar__1___24Anonymous__30003,Vvar__2___24Anonymous__30004) ) ) ) ) ) ).

fof('$_inversion_Coq.Init.Byte.byte',axiom,
    ! [VX15826] :
      ( cCoq_2eInit_2eByte_2ebyte___24t(VX15826)
     => ( VX15826 = cCoq_2eInit_2eByte_2ex00
        | VX15826 = cCoq_2eInit_2eByte_2ex01
        | VX15826 = cCoq_2eInit_2eByte_2ex02
        | VX15826 = cCoq_2eInit_2eByte_2ex03
        | VX15826 = cCoq_2eInit_2eByte_2ex04
        | VX15826 = cCoq_2eInit_2eByte_2ex05
        | VX15826 = cCoq_2eInit_2eByte_2ex06
        | VX15826 = cCoq_2eInit_2eByte_2ex07
        | VX15826 = cCoq_2eInit_2eByte_2ex08
        | VX15826 = cCoq_2eInit_2eByte_2ex09
        | VX15826 = cCoq_2eInit_2eByte_2ex0a
        | VX15826 = cCoq_2eInit_2eByte_2ex0b
        | VX15826 = cCoq_2eInit_2eByte_2ex0c
        | VX15826 = cCoq_2eInit_2eByte_2ex0d
        | VX15826 = cCoq_2eInit_2eByte_2ex0e
        | VX15826 = cCoq_2eInit_2eByte_2ex0f
        | VX15826 = cCoq_2eInit_2eByte_2ex10
        | VX15826 = cCoq_2eInit_2eByte_2ex11
        | VX15826 = cCoq_2eInit_2eByte_2ex12
        | VX15826 = cCoq_2eInit_2eByte_2ex13
        | VX15826 = cCoq_2eInit_2eByte_2ex14
        | VX15826 = cCoq_2eInit_2eByte_2ex15
        | VX15826 = cCoq_2eInit_2eByte_2ex16
        | VX15826 = cCoq_2eInit_2eByte_2ex17
        | VX15826 = cCoq_2eInit_2eByte_2ex18
        | VX15826 = cCoq_2eInit_2eByte_2ex19
        | VX15826 = cCoq_2eInit_2eByte_2ex1a
        | VX15826 = cCoq_2eInit_2eByte_2ex1b
        | VX15826 = cCoq_2eInit_2eByte_2ex1c
        | VX15826 = cCoq_2eInit_2eByte_2ex1d
        | VX15826 = cCoq_2eInit_2eByte_2ex1e
        | VX15826 = cCoq_2eInit_2eByte_2ex1f
        | VX15826 = cCoq_2eInit_2eByte_2ex20
        | VX15826 = cCoq_2eInit_2eByte_2ex21
        | VX15826 = cCoq_2eInit_2eByte_2ex22
        | VX15826 = cCoq_2eInit_2eByte_2ex23
        | VX15826 = cCoq_2eInit_2eByte_2ex24
        | VX15826 = cCoq_2eInit_2eByte_2ex25
        | VX15826 = cCoq_2eInit_2eByte_2ex26
        | VX15826 = cCoq_2eInit_2eByte_2ex27
        | VX15826 = cCoq_2eInit_2eByte_2ex28
        | VX15826 = cCoq_2eInit_2eByte_2ex29
        | VX15826 = cCoq_2eInit_2eByte_2ex2a
        | VX15826 = cCoq_2eInit_2eByte_2ex2b
        | VX15826 = cCoq_2eInit_2eByte_2ex2c
        | VX15826 = cCoq_2eInit_2eByte_2ex2d
        | VX15826 = cCoq_2eInit_2eByte_2ex2e
        | VX15826 = cCoq_2eInit_2eByte_2ex2f
        | VX15826 = cCoq_2eInit_2eByte_2ex30
        | VX15826 = cCoq_2eInit_2eByte_2ex31
        | VX15826 = cCoq_2eInit_2eByte_2ex32
        | VX15826 = cCoq_2eInit_2eByte_2ex33
        | VX15826 = cCoq_2eInit_2eByte_2ex34
        | VX15826 = cCoq_2eInit_2eByte_2ex35
        | VX15826 = cCoq_2eInit_2eByte_2ex36
        | VX15826 = cCoq_2eInit_2eByte_2ex37
        | VX15826 = cCoq_2eInit_2eByte_2ex38
        | VX15826 = cCoq_2eInit_2eByte_2ex39
        | VX15826 = cCoq_2eInit_2eByte_2ex3a
        | VX15826 = cCoq_2eInit_2eByte_2ex3b
        | VX15826 = cCoq_2eInit_2eByte_2ex3c
        | VX15826 = cCoq_2eInit_2eByte_2ex3d
        | VX15826 = cCoq_2eInit_2eByte_2ex3e
        | VX15826 = cCoq_2eInit_2eByte_2ex3f
        | VX15826 = cCoq_2eInit_2eByte_2ex40
        | VX15826 = cCoq_2eInit_2eByte_2ex41
        | VX15826 = cCoq_2eInit_2eByte_2ex42
        | VX15826 = cCoq_2eInit_2eByte_2ex43
        | VX15826 = cCoq_2eInit_2eByte_2ex44
        | VX15826 = cCoq_2eInit_2eByte_2ex45
        | VX15826 = cCoq_2eInit_2eByte_2ex46
        | VX15826 = cCoq_2eInit_2eByte_2ex47
        | VX15826 = cCoq_2eInit_2eByte_2ex48
        | VX15826 = cCoq_2eInit_2eByte_2ex49
        | VX15826 = cCoq_2eInit_2eByte_2ex4a
        | VX15826 = cCoq_2eInit_2eByte_2ex4b
        | VX15826 = cCoq_2eInit_2eByte_2ex4c
        | VX15826 = cCoq_2eInit_2eByte_2ex4d
        | VX15826 = cCoq_2eInit_2eByte_2ex4e
        | VX15826 = cCoq_2eInit_2eByte_2ex4f
        | VX15826 = cCoq_2eInit_2eByte_2ex50
        | VX15826 = cCoq_2eInit_2eByte_2ex51
        | VX15826 = cCoq_2eInit_2eByte_2ex52
        | VX15826 = cCoq_2eInit_2eByte_2ex53
        | VX15826 = cCoq_2eInit_2eByte_2ex54
        | VX15826 = cCoq_2eInit_2eByte_2ex55
        | VX15826 = cCoq_2eInit_2eByte_2ex56
        | VX15826 = cCoq_2eInit_2eByte_2ex57
        | VX15826 = cCoq_2eInit_2eByte_2ex58
        | VX15826 = cCoq_2eInit_2eByte_2ex59
        | VX15826 = cCoq_2eInit_2eByte_2ex5a
        | VX15826 = cCoq_2eInit_2eByte_2ex5b
        | VX15826 = cCoq_2eInit_2eByte_2ex5c
        | VX15826 = cCoq_2eInit_2eByte_2ex5d
        | VX15826 = cCoq_2eInit_2eByte_2ex5e
        | VX15826 = cCoq_2eInit_2eByte_2ex5f
        | VX15826 = cCoq_2eInit_2eByte_2ex60
        | VX15826 = cCoq_2eInit_2eByte_2ex61
        | VX15826 = cCoq_2eInit_2eByte_2ex62
        | VX15826 = cCoq_2eInit_2eByte_2ex63
        | VX15826 = cCoq_2eInit_2eByte_2ex64
        | VX15826 = cCoq_2eInit_2eByte_2ex65
        | VX15826 = cCoq_2eInit_2eByte_2ex66
        | VX15826 = cCoq_2eInit_2eByte_2ex67
        | VX15826 = cCoq_2eInit_2eByte_2ex68
        | VX15826 = cCoq_2eInit_2eByte_2ex69
        | VX15826 = cCoq_2eInit_2eByte_2ex6a
        | VX15826 = cCoq_2eInit_2eByte_2ex6b
        | VX15826 = cCoq_2eInit_2eByte_2ex6c
        | VX15826 = cCoq_2eInit_2eByte_2ex6d
        | VX15826 = cCoq_2eInit_2eByte_2ex6e
        | VX15826 = cCoq_2eInit_2eByte_2ex6f
        | VX15826 = cCoq_2eInit_2eByte_2ex70
        | VX15826 = cCoq_2eInit_2eByte_2ex71
        | VX15826 = cCoq_2eInit_2eByte_2ex72
        | VX15826 = cCoq_2eInit_2eByte_2ex73
        | VX15826 = cCoq_2eInit_2eByte_2ex74
        | VX15826 = cCoq_2eInit_2eByte_2ex75
        | VX15826 = cCoq_2eInit_2eByte_2ex76
        | VX15826 = cCoq_2eInit_2eByte_2ex77
        | VX15826 = cCoq_2eInit_2eByte_2ex78
        | VX15826 = cCoq_2eInit_2eByte_2ex79
        | VX15826 = cCoq_2eInit_2eByte_2ex7a
        | VX15826 = cCoq_2eInit_2eByte_2ex7b
        | VX15826 = cCoq_2eInit_2eByte_2ex7c
        | VX15826 = cCoq_2eInit_2eByte_2ex7d
        | VX15826 = cCoq_2eInit_2eByte_2ex7e
        | VX15826 = cCoq_2eInit_2eByte_2ex7f
        | VX15826 = cCoq_2eInit_2eByte_2ex80
        | VX15826 = cCoq_2eInit_2eByte_2ex81
        | VX15826 = cCoq_2eInit_2eByte_2ex82
        | VX15826 = cCoq_2eInit_2eByte_2ex83
        | VX15826 = cCoq_2eInit_2eByte_2ex84
        | VX15826 = cCoq_2eInit_2eByte_2ex85
        | VX15826 = cCoq_2eInit_2eByte_2ex86
        | VX15826 = cCoq_2eInit_2eByte_2ex87
        | VX15826 = cCoq_2eInit_2eByte_2ex88
        | VX15826 = cCoq_2eInit_2eByte_2ex89
        | VX15826 = cCoq_2eInit_2eByte_2ex8a
        | VX15826 = cCoq_2eInit_2eByte_2ex8b
        | VX15826 = cCoq_2eInit_2eByte_2ex8c
        | VX15826 = cCoq_2eInit_2eByte_2ex8d
        | VX15826 = cCoq_2eInit_2eByte_2ex8e
        | VX15826 = cCoq_2eInit_2eByte_2ex8f
        | VX15826 = cCoq_2eInit_2eByte_2ex90
        | VX15826 = cCoq_2eInit_2eByte_2ex91
        | VX15826 = cCoq_2eInit_2eByte_2ex92
        | VX15826 = cCoq_2eInit_2eByte_2ex93
        | VX15826 = cCoq_2eInit_2eByte_2ex94
        | VX15826 = cCoq_2eInit_2eByte_2ex95
        | VX15826 = cCoq_2eInit_2eByte_2ex96
        | VX15826 = cCoq_2eInit_2eByte_2ex97
        | VX15826 = cCoq_2eInit_2eByte_2ex98
        | VX15826 = cCoq_2eInit_2eByte_2ex99
        | VX15826 = cCoq_2eInit_2eByte_2ex9a
        | VX15826 = cCoq_2eInit_2eByte_2ex9b
        | VX15826 = cCoq_2eInit_2eByte_2ex9c
        | VX15826 = cCoq_2eInit_2eByte_2ex9d
        | VX15826 = cCoq_2eInit_2eByte_2ex9e
        | VX15826 = cCoq_2eInit_2eByte_2ex9f
        | VX15826 = cCoq_2eInit_2eByte_2exa0
        | VX15826 = cCoq_2eInit_2eByte_2exa1
        | VX15826 = cCoq_2eInit_2eByte_2exa2
        | VX15826 = cCoq_2eInit_2eByte_2exa3
        | VX15826 = cCoq_2eInit_2eByte_2exa4
        | VX15826 = cCoq_2eInit_2eByte_2exa5
        | VX15826 = cCoq_2eInit_2eByte_2exa6
        | VX15826 = cCoq_2eInit_2eByte_2exa7
        | VX15826 = cCoq_2eInit_2eByte_2exa8
        | VX15826 = cCoq_2eInit_2eByte_2exa9
        | VX15826 = cCoq_2eInit_2eByte_2exaa
        | VX15826 = cCoq_2eInit_2eByte_2exab
        | VX15826 = cCoq_2eInit_2eByte_2exac
        | VX15826 = cCoq_2eInit_2eByte_2exad
        | VX15826 = cCoq_2eInit_2eByte_2exae
        | VX15826 = cCoq_2eInit_2eByte_2exaf
        | VX15826 = cCoq_2eInit_2eByte_2exb0
        | VX15826 = cCoq_2eInit_2eByte_2exb1
        | VX15826 = cCoq_2eInit_2eByte_2exb2
        | VX15826 = cCoq_2eInit_2eByte_2exb3
        | VX15826 = cCoq_2eInit_2eByte_2exb4
        | VX15826 = cCoq_2eInit_2eByte_2exb5
        | VX15826 = cCoq_2eInit_2eByte_2exb6
        | VX15826 = cCoq_2eInit_2eByte_2exb7
        | VX15826 = cCoq_2eInit_2eByte_2exb8
        | VX15826 = cCoq_2eInit_2eByte_2exb9
        | VX15826 = cCoq_2eInit_2eByte_2exba
        | VX15826 = cCoq_2eInit_2eByte_2exbb
        | VX15826 = cCoq_2eInit_2eByte_2exbc
        | VX15826 = cCoq_2eInit_2eByte_2exbd
        | VX15826 = cCoq_2eInit_2eByte_2exbe
        | VX15826 = cCoq_2eInit_2eByte_2exbf
        | VX15826 = cCoq_2eInit_2eByte_2exc0
        | VX15826 = cCoq_2eInit_2eByte_2exc1
        | VX15826 = cCoq_2eInit_2eByte_2exc2
        | VX15826 = cCoq_2eInit_2eByte_2exc3
        | VX15826 = cCoq_2eInit_2eByte_2exc4
        | VX15826 = cCoq_2eInit_2eByte_2exc5
        | VX15826 = cCoq_2eInit_2eByte_2exc6
        | VX15826 = cCoq_2eInit_2eByte_2exc7
        | VX15826 = cCoq_2eInit_2eByte_2exc8
        | VX15826 = cCoq_2eInit_2eByte_2exc9
        | VX15826 = cCoq_2eInit_2eByte_2exca
        | VX15826 = cCoq_2eInit_2eByte_2excb
        | VX15826 = cCoq_2eInit_2eByte_2excc
        | VX15826 = cCoq_2eInit_2eByte_2excd
        | VX15826 = cCoq_2eInit_2eByte_2exce
        | VX15826 = cCoq_2eInit_2eByte_2excf
        | VX15826 = cCoq_2eInit_2eByte_2exd0
        | VX15826 = cCoq_2eInit_2eByte_2exd1
        | VX15826 = cCoq_2eInit_2eByte_2exd2
        | VX15826 = cCoq_2eInit_2eByte_2exd3
        | VX15826 = cCoq_2eInit_2eByte_2exd4
        | VX15826 = cCoq_2eInit_2eByte_2exd5
        | VX15826 = cCoq_2eInit_2eByte_2exd6
        | VX15826 = cCoq_2eInit_2eByte_2exd7
        | VX15826 = cCoq_2eInit_2eByte_2exd8
        | VX15826 = cCoq_2eInit_2eByte_2exd9
        | VX15826 = cCoq_2eInit_2eByte_2exda
        | VX15826 = cCoq_2eInit_2eByte_2exdb
        | VX15826 = cCoq_2eInit_2eByte_2exdc
        | VX15826 = cCoq_2eInit_2eByte_2exdd
        | VX15826 = cCoq_2eInit_2eByte_2exde
        | VX15826 = cCoq_2eInit_2eByte_2exdf
        | VX15826 = cCoq_2eInit_2eByte_2exe0
        | VX15826 = cCoq_2eInit_2eByte_2exe1
        | VX15826 = cCoq_2eInit_2eByte_2exe2
        | VX15826 = cCoq_2eInit_2eByte_2exe3
        | VX15826 = cCoq_2eInit_2eByte_2exe4
        | VX15826 = cCoq_2eInit_2eByte_2exe5
        | VX15826 = cCoq_2eInit_2eByte_2exe6
        | VX15826 = cCoq_2eInit_2eByte_2exe7
        | VX15826 = cCoq_2eInit_2eByte_2exe8
        | VX15826 = cCoq_2eInit_2eByte_2exe9
        | VX15826 = cCoq_2eInit_2eByte_2exea
        | VX15826 = cCoq_2eInit_2eByte_2exeb
        | VX15826 = cCoq_2eInit_2eByte_2exec
        | VX15826 = cCoq_2eInit_2eByte_2exed
        | VX15826 = cCoq_2eInit_2eByte_2exee
        | VX15826 = cCoq_2eInit_2eByte_2exef
        | VX15826 = cCoq_2eInit_2eByte_2exf0
        | VX15826 = cCoq_2eInit_2eByte_2exf1
        | VX15826 = cCoq_2eInit_2eByte_2exf2
        | VX15826 = cCoq_2eInit_2eByte_2exf3
        | VX15826 = cCoq_2eInit_2eByte_2exf4
        | VX15826 = cCoq_2eInit_2eByte_2exf5
        | VX15826 = cCoq_2eInit_2eByte_2exf6
        | VX15826 = cCoq_2eInit_2eByte_2exf7
        | VX15826 = cCoq_2eInit_2eByte_2exf8
        | VX15826 = cCoq_2eInit_2eByte_2exf9
        | VX15826 = cCoq_2eInit_2eByte_2exfa
        | VX15826 = cCoq_2eInit_2eByte_2exfb
        | VX15826 = cCoq_2eInit_2eByte_2exfc
        | VX15826 = cCoq_2eInit_2eByte_2exfd
        | VX15826 = cCoq_2eInit_2eByte_2exfe
        | VX15826 = cCoq_2eInit_2eByte_2exff ) ) ).

fof('$_inversion_Coq.Init.Datatypes.BoolSpec',axiom,
    ! [Vvar__0__P__23689,Vvar__1__Q__23690,Vvar__2___24Anonymous__23691] :
      ( cProp___24t(Vvar__0__P__23689)
     => ( cProp___24t(Vvar__1__Q__23690)
       => ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__2___24Anonymous__23691)
         => ( cCoq_2eInit_2eDatatypes_2eBoolSpec___24a3(Vvar__0__P__23689,Vvar__1__Q__23690,Vvar__2___24Anonymous__23691)
           => ( ( p(Vvar__0__P__23689)
                & Vvar__2___24Anonymous__23691 = cCoq_2eInit_2eDatatypes_2etrue )
              | ( p(Vvar__1__Q__23690)
                & Vvar__2___24Anonymous__23691 = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ) ) ) ).

fof('$_inversion_Coq.Init.Datatypes.CompareSpec',axiom,
    ! [Vvar__0__Peq__23775,Vvar__1__Plt__23776,Vvar__2__Pgt__23777,Vvar__3___24Anonymous__23778] :
      ( cProp___24t(Vvar__0__Peq__23775)
     => ( cProp___24t(Vvar__1__Plt__23776)
       => ( cProp___24t(Vvar__2__Pgt__23777)
         => ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__3___24Anonymous__23778)
           => ( cCoq_2eInit_2eDatatypes_2eCompareSpec___24a4(Vvar__0__Peq__23775,Vvar__1__Plt__23776,Vvar__2__Pgt__23777,Vvar__3___24Anonymous__23778)
             => ( ( p(Vvar__0__Peq__23775)
                  & Vvar__3___24Anonymous__23778 = cCoq_2eInit_2eDatatypes_2eEq )
                | ( p(Vvar__1__Plt__23776)
                  & Vvar__3___24Anonymous__23778 = cCoq_2eInit_2eDatatypes_2eLt )
                | ( p(Vvar__2__Pgt__23777)
                  & Vvar__3___24Anonymous__23778 = cCoq_2eInit_2eDatatypes_2eGt ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Init.Datatypes.CompareSpecT',axiom,
    ! [Vvar__0__Peq__23792,Vvar__1__Plt__23793,Vvar__2__Pgt__23794,Vvar__3___24Anonymous__23795,VX23796] :
      ( cProp___24t(Vvar__0__Peq__23792)
     => ( cProp___24t(Vvar__1__Plt__23793)
       => ( cProp___24t(Vvar__2__Pgt__23794)
         => ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vvar__3___24Anonymous__23795)
           => ( cCoq_2eInit_2eDatatypes_2eCompareSpecT___24t(Vvar__0__Peq__23792,Vvar__1__Plt__23793,Vvar__2__Pgt__23794,Vvar__3___24Anonymous__23795,VX23796)
             => ( ( p(Vvar__0__Peq__23792)
                  & Vvar__3___24Anonymous__23795 = cCoq_2eInit_2eDatatypes_2eEq
                  & VX23796 = cCoq_2eInit_2eDatatypes_2eCompEqT___24a3(Vvar__0__Peq__23792,Vvar__1__Plt__23793,Vvar__2__Pgt__23794) )
                | ( p(Vvar__1__Plt__23793)
                  & Vvar__3___24Anonymous__23795 = cCoq_2eInit_2eDatatypes_2eLt
                  & VX23796 = cCoq_2eInit_2eDatatypes_2eCompLtT___24a3(Vvar__0__Peq__23792,Vvar__1__Plt__23793,Vvar__2__Pgt__23794) )
                | ( p(Vvar__2__Pgt__23794)
                  & Vvar__3___24Anonymous__23795 = cCoq_2eInit_2eDatatypes_2eGt
                  & VX23796 = cCoq_2eInit_2eDatatypes_2eCompGtT___24a3(Vvar__0__Peq__23792,Vvar__1__Plt__23793,Vvar__2__Pgt__23794) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Init.Datatypes.bool',axiom,
    ! [VX4756] :
      ( cCoq_2eInit_2eDatatypes_2ebool___24t(VX4756)
     => ( VX4756 = cCoq_2eInit_2eDatatypes_2etrue
        | VX4756 = cCoq_2eInit_2eDatatypes_2efalse ) ) ).

fof('$_inversion_Coq.Init.Datatypes.comparison',axiom,
    ! [VX23772] :
      ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(VX23772)
     => ( VX23772 = cCoq_2eInit_2eDatatypes_2eEq
        | VX23772 = cCoq_2eInit_2eDatatypes_2eLt
        | VX23772 = cCoq_2eInit_2eDatatypes_2eGt ) ) ).

fof('$_inversion_Coq.Init.Datatypes.eq_true',axiom,
    ! [Vvar__0___24Anonymous__31097] :
      ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__0___24Anonymous__31097)
     => ( cCoq_2eInit_2eDatatypes_2eeq__true___24a1(Vvar__0___24Anonymous__31097)
       => Vvar__0___24Anonymous__31097 = cCoq_2eInit_2eDatatypes_2etrue ) ) ).

fof('$_inversion_Coq.Init.Datatypes.identity',axiom,
    ! [Vvar__0__A__31099,Vvar__1__a__31100,Vvar__2___24Anonymous__31101] :
      ( cType___24t(Vvar__0__A__31099)
     => ( t(Vvar__1__a__31100,Vvar__0__A__31099)
       => ( t(Vvar__2___24Anonymous__31101,Vvar__0__A__31099)
         => ( cCoq_2eInit_2eDatatypes_2eidentity___24a3(Vvar__0__A__31099,Vvar__1__a__31100,Vvar__2___24Anonymous__31101)
           => Vvar__2___24Anonymous__31101 = Vvar__1__a__31100 ) ) ) ) ).

fof('$_inversion_Coq.Init.Datatypes.list',axiom,
    ! [Vvar__0__A__7460,VX7461] :
      ( cType___24t(Vvar__0__A__7460)
     => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__7460,VX7461)
       => ( VX7461 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__7460)
          | ? [Vvar__1___24Anonymous__7464] :
              ( t(Vvar__1___24Anonymous__7464,Vvar__0__A__7460)
              & ? [Vvar__2___24Anonymous__7465] :
                  ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__7460,Vvar__2___24Anonymous__7465)
                  & VX7461 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__7460,Vvar__1___24Anonymous__7464,Vvar__2___24Anonymous__7465) ) ) ) ) ) ).

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__7428,VX7429] :
      ( cType___24t(Vvar__0__A__7428)
     => ( cCoq_2eInit_2eDatatypes_2eoption___24t(Vvar__0__A__7428,VX7429)
       => ( ? [Vvar__1___24Anonymous__7431] :
              ( t(Vvar__1___24Anonymous__7431,Vvar__0__A__7428)
              & VX7429 = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__A__7428,Vvar__1___24Anonymous__7431) )
          | VX7429 = cCoq_2eInit_2eDatatypes_2eNone___24a1(Vvar__0__A__7428) ) ) ) ).

fof('$_inversion_Coq.Init.Datatypes.prod',axiom,
    ! [Vvar__0__A__7442,Vvar__1__B__7443,VX7444] :
      ( cType___24t(Vvar__0__A__7442)
     => ( cType___24t(Vvar__1__B__7443)
       => ( cCoq_2eInit_2eDatatypes_2eprod___24t(Vvar__0__A__7442,Vvar__1__B__7443,VX7444)
         => ? [Vvar__2___24Anonymous__7447] :
              ( t(Vvar__2___24Anonymous__7447,Vvar__0__A__7442)
              & ? [Vvar__3___24Anonymous__7448] :
                  ( t(Vvar__3___24Anonymous__7448,Vvar__1__B__7443)
                  & VX7444 = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__7442,Vvar__1__B__7443,Vvar__2___24Anonymous__7447,Vvar__3___24Anonymous__7448) ) ) ) ) ) ).

fof('$_inversion_Coq.Init.Datatypes.sum',axiom,
    ! [Vvar__0__A__23708,Vvar__1__B__23709,VX23710] :
      ( cType___24t(Vvar__0__A__23708)
     => ( cType___24t(Vvar__1__B__23709)
       => ( cCoq_2eInit_2eDatatypes_2esum___24t(Vvar__0__A__23708,Vvar__1__B__23709,VX23710)
         => ( ? [Vvar__2___24Anonymous__23713] :
                ( t(Vvar__2___24Anonymous__23713,Vvar__0__A__23708)
                & VX23710 = cCoq_2eInit_2eDatatypes_2einl___24a3(Vvar__0__A__23708,Vvar__1__B__23709,Vvar__2___24Anonymous__23713) )
            | ? [Vvar__2___24Anonymous__23716] :
                ( t(Vvar__2___24Anonymous__23716,Vvar__1__B__23709)
                & VX23710 = cCoq_2eInit_2eDatatypes_2einr___24a3(Vvar__0__A__23708,Vvar__1__B__23709,Vvar__2___24Anonymous__23716) ) ) ) ) ) ).

fof('$_inversion_Coq.Init.Datatypes.unit',axiom,
    ! [VX5492] :
      ( cCoq_2eInit_2eDatatypes_2eunit___24t(VX5492)
     => VX5492 = cCoq_2eInit_2eDatatypes_2ett ) ).

fof('$_inversion_Coq.Init.Decimal.decimal',axiom,
    ! [VX31115] :
      ( cCoq_2eInit_2eDecimal_2edecimal___24t(VX31115)
     => ( ? [Vvar__0__i__31116] :
            ( cCoq_2eInit_2eDecimal_2eint___24t(Vvar__0__i__31116)
            & ? [Vvar__1__f__31117] :
                ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__1__f__31117)
                & VX31115 = cCoq_2eInit_2eDecimal_2eDecimal___24a2(Vvar__0__i__31116,Vvar__1__f__31117) ) )
        | ? [Vvar__0__i__31118] :
            ( cCoq_2eInit_2eDecimal_2eint___24t(Vvar__0__i__31118)
            & ? [Vvar__1__f__31119] :
                ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__1__f__31119)
                & ? [Vvar__2__e__31120] :
                    ( cCoq_2eInit_2eDecimal_2eint___24t(Vvar__2__e__31120)
                    & VX31115 = cCoq_2eInit_2eDecimal_2eDecimalExp___24a3(Vvar__0__i__31118,Vvar__1__f__31119,Vvar__2__e__31120) ) ) ) ) ) ).

fof('$_inversion_Coq.Init.Decimal.int',axiom,
    ! [VX31106] :
      ( cCoq_2eInit_2eDecimal_2eint___24t(VX31106)
     => ( ? [Vvar__0__d__31107] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0__d__31107)
            & VX31106 = cCoq_2eInit_2eDecimal_2ePos___24a1(Vvar__0__d__31107) )
        | ? [Vvar__0__d__31108] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0__d__31108)
            & VX31106 = cCoq_2eInit_2eDecimal_2eNeg___24a1(Vvar__0__d__31108) ) ) ) ).

fof('$_inversion_Coq.Init.Decimal.uint',axiom,
    ! [VX23963] :
      ( cCoq_2eInit_2eDecimal_2euint___24t(VX23963)
     => ( VX23963 = cCoq_2eInit_2eDecimal_2eNil
        | ? [Vvar__0___24Anonymous__23964] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__23964)
            & VX23963 = cCoq_2eInit_2eDecimal_2eD0___24a1(Vvar__0___24Anonymous__23964) )
        | ? [Vvar__0___24Anonymous__23965] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__23965)
            & VX23963 = cCoq_2eInit_2eDecimal_2eD1___24a1(Vvar__0___24Anonymous__23965) )
        | ? [Vvar__0___24Anonymous__23966] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__23966)
            & VX23963 = cCoq_2eInit_2eDecimal_2eD2___24a1(Vvar__0___24Anonymous__23966) )
        | ? [Vvar__0___24Anonymous__23967] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__23967)
            & VX23963 = cCoq_2eInit_2eDecimal_2eD3___24a1(Vvar__0___24Anonymous__23967) )
        | ? [Vvar__0___24Anonymous__23968] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__23968)
            & VX23963 = cCoq_2eInit_2eDecimal_2eD4___24a1(Vvar__0___24Anonymous__23968) )
        | ? [Vvar__0___24Anonymous__23969] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__23969)
            & VX23963 = cCoq_2eInit_2eDecimal_2eD5___24a1(Vvar__0___24Anonymous__23969) )
        | ? [Vvar__0___24Anonymous__23970] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__23970)
            & VX23963 = cCoq_2eInit_2eDecimal_2eD6___24a1(Vvar__0___24Anonymous__23970) )
        | ? [Vvar__0___24Anonymous__23971] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__23971)
            & VX23963 = cCoq_2eInit_2eDecimal_2eD7___24a1(Vvar__0___24Anonymous__23971) )
        | ? [Vvar__0___24Anonymous__23972] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__23972)
            & VX23963 = cCoq_2eInit_2eDecimal_2eD8___24a1(Vvar__0___24Anonymous__23972) )
        | ? [Vvar__0___24Anonymous__23973] :
            ( cCoq_2eInit_2eDecimal_2euint___24t(Vvar__0___24Anonymous__23973)
            & VX23963 = cCoq_2eInit_2eDecimal_2eD9___24a1(Vvar__0___24Anonymous__23973) ) ) ) ).

fof('$_inversion_Coq.Init.Peano.le',axiom,
    ! [Vvar__0__n__6621,Vvar__1___24Anonymous__6622] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__6621)
     => ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__6622)
       => ( cCoq_2eInit_2ePeano_2ele___24a2(Vvar__0__n__6621,Vvar__1___24Anonymous__6622)
         => ( Vvar__1___24Anonymous__6622 = Vvar__0__n__6621
            | ? [Vvar__1__m__6626] :
                ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__m__6626)
                & cCoq_2eInit_2ePeano_2ele___24a2(Vvar__0__n__6621,Vvar__1__m__6626)
                & Vvar__1___24Anonymous__6622 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__1__m__6626) ) ) ) ) ) ).

fof('$_inversion_Coq.Init.Specif.sig',axiom,
    ! [Vvar__0__A__27754,Vvar__1__P__27755,VX27758] :
      ( cType___24t(Vvar__0__A__27754)
     => ( c_24__type__27768___24t(Vvar__0__A__27754,Vvar__1__P__27755,Vvar__1__P__27755)
       => ( cCoq_2eInit_2eSpecif_2esig___24t(Vvar__0__A__27754,Vvar__1__P__27755,VX27758)
         => ? [Vvar__2__x__27763] :
              ( t(Vvar__2__x__27763,Vvar__0__A__27754)
              & p(happ(Vvar__1__P__27755,Vvar__2__x__27763))
              & VX27758 = cCoq_2eInit_2eSpecif_2eexist___24a3(Vvar__0__A__27754,Vvar__1__P__27755,Vvar__2__x__27763) ) ) ) ) ).

fof('$_inversion_Coq.Init.Specif.sig2',axiom,
    ! [Vvar__0__A__34635,Vvar__1__P__34636,Vvar__2__Q__34639,VX34642] :
      ( cType___24t(Vvar__0__A__34635)
     => ( c_24__type__34659___24t(Vvar__0__A__34635,Vvar__1__P__34636,Vvar__2__Q__34639,Vvar__1__P__34636)
       => ( c_24__type__34667___24t(Vvar__0__A__34635,Vvar__1__P__34636,Vvar__2__Q__34639,Vvar__2__Q__34639)
         => ( cCoq_2eInit_2eSpecif_2esig2___24t(Vvar__0__A__34635,Vvar__1__P__34636,Vvar__2__Q__34639,VX34642)
           => ? [Vvar__3__x__34650] :
                ( t(Vvar__3__x__34650,Vvar__0__A__34635)
                & p(happ(Vvar__1__P__34636,Vvar__3__x__34650))
                & p(happ(Vvar__2__Q__34639,Vvar__3__x__34650))
                & VX34642 = cCoq_2eInit_2eSpecif_2eexist2___24a4(Vvar__0__A__34635,Vvar__1__P__34636,Vvar__2__Q__34639,Vvar__3__x__34650) ) ) ) ) ) ).

fof('$_inversion_Coq.Init.Specif.sigT',axiom,
    ! [Vvar__0__A__27793,Vvar__1__P__27794,VX27797] :
      ( cType___24t(Vvar__0__A__27793)
     => ( c_24__type__27807___24t(Vvar__0__A__27793,Vvar__1__P__27794,Vvar__1__P__27794)
       => ( cCoq_2eInit_2eSpecif_2esigT___24t(Vvar__0__A__27793,Vvar__1__P__27794,VX27797)
         => ? [Vvar__2__x__27802] :
              ( t(Vvar__2__x__27802,Vvar__0__A__27793)
              & ? [Vvar__3___24Anonymous__27803] :
                  ( t(Vvar__3___24Anonymous__27803,happ(Vvar__1__P__27794,Vvar__2__x__27802))
                  & VX27797 = cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__27793,Vvar__1__P__27794,Vvar__2__x__27802,Vvar__3___24Anonymous__27803) ) ) ) ) ) ).

fof('$_inversion_Coq.Init.Specif.sigT2',axiom,
    ! [Vvar__0__A__34691,Vvar__1__P__34692,Vvar__2__Q__34695,VX34698] :
      ( cType___24t(Vvar__0__A__34691)
     => ( c_24__type__34715___24t(Vvar__0__A__34691,Vvar__1__P__34692,Vvar__2__Q__34695,Vvar__1__P__34692)
       => ( c_24__type__34723___24t(Vvar__0__A__34691,Vvar__1__P__34692,Vvar__2__Q__34695,Vvar__2__Q__34695)
         => ( cCoq_2eInit_2eSpecif_2esigT2___24t(Vvar__0__A__34691,Vvar__1__P__34692,Vvar__2__Q__34695,VX34698)
           => ? [Vvar__3__x__34706] :
                ( t(Vvar__3__x__34706,Vvar__0__A__34691)
                & ? [Vvar__4___24Anonymous__34707] :
                    ( t(Vvar__4___24Anonymous__34707,happ(Vvar__1__P__34692,Vvar__3__x__34706))
                    & ? [Vvar__5___24Anonymous__34708] :
                        ( t(Vvar__5___24Anonymous__34708,happ(Vvar__2__Q__34695,Vvar__3__x__34706))
                        & VX34698 = cCoq_2eInit_2eSpecif_2eexistT2___24a6(Vvar__0__A__34691,Vvar__1__P__34692,Vvar__2__Q__34695,Vvar__3__x__34706,Vvar__4___24Anonymous__34707,Vvar__5___24Anonymous__34708) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Init.Specif.sumbool',axiom,
    ! [Vvar__0__A__7138,Vvar__1__B__7139,VX7140] :
      ( cProp___24t(Vvar__0__A__7138)
     => ( cProp___24t(Vvar__1__B__7139)
       => ( cCoq_2eInit_2eSpecif_2esumbool___24t(Vvar__0__A__7138,Vvar__1__B__7139,VX7140)
         => ( ( p(Vvar__0__A__7138)
              & VX7140 = cCoq_2eInit_2eSpecif_2eleft___24a2(Vvar__0__A__7138,Vvar__1__B__7139) )
            | ( p(Vvar__1__B__7139)
              & VX7140 = cCoq_2eInit_2eSpecif_2eright___24a2(Vvar__0__A__7138,Vvar__1__B__7139) ) ) ) ) ) ).

fof('$_inversion_Coq.Init.Specif.sumor',axiom,
    ! [Vvar__0__A__30900,Vvar__1__B__30901,VX30902] :
      ( cType___24t(Vvar__0__A__30900)
     => ( cProp___24t(Vvar__1__B__30901)
       => ( cCoq_2eInit_2eSpecif_2esumor___24t(Vvar__0__A__30900,Vvar__1__B__30901,VX30902)
         => ( ? [Vvar__2___24Anonymous__30905] :
                ( t(Vvar__2___24Anonymous__30905,Vvar__0__A__30900)
                & VX30902 = cCoq_2eInit_2eSpecif_2einleft___24a3(Vvar__0__A__30900,Vvar__1__B__30901,Vvar__2___24Anonymous__30905) )
            | ( p(Vvar__1__B__30901)
              & VX30902 = cCoq_2eInit_2eSpecif_2einright___24a2(Vvar__0__A__30900,Vvar__1__B__30901) ) ) ) ) ) ).

fof('$_inversion_Coq.Init.Wf.Acc',axiom,
    ! [Vvar__0__A__30930,Vvar__1__R__30931,Vvar__2__x__30936] :
      ( cType___24t(Vvar__0__A__30930)
     => ( c_24__type__30965___24t(Vvar__0__A__30930,Vvar__1__R__30931,Vvar__2__x__30936,Vvar__1__R__30931)
       => ( t(Vvar__2__x__30936,Vvar__0__A__30930)
         => ( cCoq_2eInit_2eWf_2eAcc___24a3(Vvar__0__A__30930,Vvar__1__R__30931,Vvar__2__x__30936)
           => ( ! [Vvar__var__var__var__var__3__y__30946__30948__30950__30952__30954] :
                  ( t(Vvar__var__var__var__var__3__y__30946__30948__30950__30952__30954,Vvar__0__A__30930)
                 => ( p(happ(happ(Vvar__1__R__30931,Vvar__var__var__var__var__3__y__30946__30948__30950__30952__30954),Vvar__2__x__30936))
                   => cCoq_2eInit_2eWf_2eAcc___24a3(Vvar__0__A__30930,Vvar__1__R__30931,Vvar__var__var__var__var__3__y__30946__30948__30950__30952__30954) ) )
              & p(c_24True) ) ) ) ) ) ).

fof('$_inversion_Coq.Lists.List.Add',axiom,
    ! [Vvar__0__A__35690,Vvar__1__a__35691,Vvar__2___24Anonymous__35692,Vvar__3___24Anonymous__35693] :
      ( cType___24t(Vvar__0__A__35690)
     => ( t(Vvar__1__a__35691,Vvar__0__A__35690)
       => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__35690,Vvar__2___24Anonymous__35692)
         => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__35690,Vvar__3___24Anonymous__35693)
           => ( cCoq_2eLists_2eList_2eAdd___24a4(Vvar__0__A__35690,Vvar__1__a__35691,Vvar__2___24Anonymous__35692,Vvar__3___24Anonymous__35693)
             => ( ? [Vvar__2__l__35697] :
                    ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__35690,Vvar__2__l__35697)
                    & Vvar__3___24Anonymous__35693 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__35690,Vvar__1__a__35691,Vvar__2__l__35697)
                    & Vvar__2___24Anonymous__35692 = Vvar__2__l__35697 )
                | ? [Vvar__2__x__35700] :
                    ( t(Vvar__2__x__35700,Vvar__0__A__35690)
                    & ? [Vvar__3__l__35701] :
                        ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__35690,Vvar__3__l__35701)
                        & ? [Vvar__4__l_27__35702] :
                            ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__35690,Vvar__4__l_27__35702)
                            & cCoq_2eLists_2eList_2eAdd___24a4(Vvar__0__A__35690,Vvar__1__a__35691,Vvar__3__l__35701,Vvar__4__l_27__35702)
                            & Vvar__3___24Anonymous__35693 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__35690,Vvar__2__x__35700,Vvar__4__l_27__35702)
                            & Vvar__2___24Anonymous__35692 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__35690,Vvar__2__x__35700,Vvar__3__l__35701) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Lists.List.Exists',axiom,
    ! [Vvar__0__A__35713,Vvar__1__P__35714,Vvar__2___24Anonymous__35717] :
      ( cType___24t(Vvar__0__A__35713)
     => ( c_24__type__35737___24t(Vvar__0__A__35713,Vvar__1__P__35714,Vvar__2___24Anonymous__35717,Vvar__1__P__35714)
       => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__35713,Vvar__2___24Anonymous__35717)
         => ( cCoq_2eLists_2eList_2eExists___24a3(Vvar__0__A__35713,Vvar__1__P__35714,Vvar__2___24Anonymous__35717)
           => ( ? [Vvar__2__x__35723] :
                  ( t(Vvar__2__x__35723,Vvar__0__A__35713)
                  & ? [Vvar__3__l__35724] :
                      ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__35713,Vvar__3__l__35724)
                      & p(happ(Vvar__1__P__35714,Vvar__2__x__35723))
                      & Vvar__2___24Anonymous__35717 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__35713,Vvar__2__x__35723,Vvar__3__l__35724) ) )
              | ? [Vvar__2__x__35730] :
                  ( t(Vvar__2__x__35730,Vvar__0__A__35713)
                  & ? [Vvar__3__l__35731] :
                      ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__35713,Vvar__3__l__35731)
                      & cCoq_2eLists_2eList_2eExists___24a3(Vvar__0__A__35713,Vvar__1__P__35714,Vvar__3__l__35731)
                      & Vvar__2___24Anonymous__35717 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__35713,Vvar__2__x__35730,Vvar__3__l__35731) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Lists.List.Forall',axiom,
    ! [Vvar__0__A__35739,Vvar__1__P__35740,Vvar__2___24Anonymous__35743] :
      ( cType___24t(Vvar__0__A__35739)
     => ( c_24__type__35761___24t(Vvar__0__A__35739,Vvar__1__P__35740,Vvar__2___24Anonymous__35743,Vvar__1__P__35740)
       => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__35739,Vvar__2___24Anonymous__35743)
         => ( cCoq_2eLists_2eList_2eForall___24a3(Vvar__0__A__35739,Vvar__1__P__35740,Vvar__2___24Anonymous__35743)
           => ( Vvar__2___24Anonymous__35743 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__35739)
              | ? [Vvar__2__x__35753] :
                  ( t(Vvar__2__x__35753,Vvar__0__A__35739)
                  & ? [Vvar__3__l__35754] :
                      ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__35739,Vvar__3__l__35754)
                      & p(happ(Vvar__1__P__35740,Vvar__2__x__35753))
                      & cCoq_2eLists_2eList_2eForall___24a3(Vvar__0__A__35739,Vvar__1__P__35740,Vvar__3__l__35754)
                      & Vvar__2___24Anonymous__35743 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__35739,Vvar__2__x__35753,Vvar__3__l__35754) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Lists.List.Forall2',axiom,
    ! [Vvar__0__A__35763,Vvar__1__B__35764,Vvar__2__R__35765,Vvar__3___24Anonymous__35770,Vvar__4___24Anonymous__35771] :
      ( cType___24t(Vvar__0__A__35763)
     => ( cType___24t(Vvar__1__B__35764)
       => ( c_24__type__35808___24t(Vvar__0__A__35763,Vvar__1__B__35764,Vvar__2__R__35765,Vvar__3___24Anonymous__35770,Vvar__4___24Anonymous__35771,Vvar__2__R__35765)
         => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__35763,Vvar__3___24Anonymous__35770)
           => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__1__B__35764,Vvar__4___24Anonymous__35771)
             => ( cCoq_2eLists_2eList_2eForall2___24a5(Vvar__0__A__35763,Vvar__1__B__35764,Vvar__2__R__35765,Vvar__3___24Anonymous__35770,Vvar__4___24Anonymous__35771)
               => ( ( Vvar__4___24Anonymous__35771 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__1__B__35764)
                    & Vvar__3___24Anonymous__35770 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__35763) )
                  | ? [Vvar__3__x__35787] :
                      ( t(Vvar__3__x__35787,Vvar__0__A__35763)
                      & ? [Vvar__4__y__35788] :
                          ( t(Vvar__4__y__35788,Vvar__1__B__35764)
                          & ? [Vvar__5__l__35789] :
                              ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__35763,Vvar__5__l__35789)
                              & ? [Vvar__6__l_27__35790] :
                                  ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__1__B__35764,Vvar__6__l_27__35790)
                                  & p(happ(happ(Vvar__2__R__35765,Vvar__3__x__35787),Vvar__4__y__35788))
                                  & cCoq_2eLists_2eList_2eForall2___24a5(Vvar__0__A__35763,Vvar__1__B__35764,Vvar__2__R__35765,Vvar__5__l__35789,Vvar__6__l_27__35790)
                                  & Vvar__4___24Anonymous__35771 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__1__B__35764,Vvar__4__y__35788,Vvar__6__l_27__35790)
                                  & Vvar__3___24Anonymous__35770 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__35763,Vvar__3__x__35787,Vvar__5__l__35789) ) ) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Lists.List.ForallOrdPairs',axiom,
    ! [Vvar__0__A__35810,Vvar__1__R__35811,Vvar__2___24Anonymous__35816] :
      ( cType___24t(Vvar__0__A__35810)
     => ( c_24__type__35843___24t(Vvar__0__A__35810,Vvar__1__R__35811,Vvar__2___24Anonymous__35816,Vvar__1__R__35811)
       => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__35810,Vvar__2___24Anonymous__35816)
         => ( cCoq_2eLists_2eList_2eForallOrdPairs___24a3(Vvar__0__A__35810,Vvar__1__R__35811,Vvar__2___24Anonymous__35816)
           => ( Vvar__2___24Anonymous__35816 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__35810)
              | ? [Vvar__2__a__35830] :
                  ( t(Vvar__2__a__35830,Vvar__0__A__35810)
                  & ? [Vvar__3__l__35831] :
                      ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__35810,Vvar__3__l__35831)
                      & cCoq_2eLists_2eList_2eForall___24a3(Vvar__0__A__35810,happ(Vvar__1__R__35811,Vvar__2__a__35830),Vvar__3__l__35831)
                      & cCoq_2eLists_2eList_2eForallOrdPairs___24a3(Vvar__0__A__35810,Vvar__1__R__35811,Vvar__3__l__35831)
                      & Vvar__2___24Anonymous__35816 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__35810,Vvar__2__a__35830,Vvar__3__l__35831) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Lists.List.NoDup',axiom,
    ! [Vvar__0__A__35704,Vvar__1___24Anonymous__35705] :
      ( cType___24t(Vvar__0__A__35704)
     => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__35704,Vvar__1___24Anonymous__35705)
       => ( cCoq_2eLists_2eList_2eNoDup___24a2(Vvar__0__A__35704,Vvar__1___24Anonymous__35705)
         => ( Vvar__1___24Anonymous__35705 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__35704)
            | ? [Vvar__1__x__35709] :
                ( t(Vvar__1__x__35709,Vvar__0__A__35704)
                & ? [Vvar__2__l__35710] :
                    ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__35704,Vvar__2__l__35710)
                    & ~ cCoq_2eLists_2eList_2eIn___24a3(Vvar__0__A__35704,Vvar__1__x__35709,Vvar__2__l__35710)
                    & cCoq_2eLists_2eList_2eNoDup___24a2(Vvar__0__A__35704,Vvar__2__l__35710)
                    & Vvar__1___24Anonymous__35705 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__35704,Vvar__1__x__35709,Vvar__2__l__35710) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Lists.SetoidList.InA',axiom,
    ! [Vvar__0__A__34496,Vvar__1__eqA__34497,Vvar__2__x__34502,Vvar__3___24Anonymous__34503] :
      ( cType___24t(Vvar__0__A__34496)
     => ( c_24__type__34536___24t(Vvar__0__A__34496,Vvar__1__eqA__34497,Vvar__2__x__34502,Vvar__3___24Anonymous__34503,Vvar__1__eqA__34497)
       => ( t(Vvar__2__x__34502,Vvar__0__A__34496)
         => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__34496,Vvar__3___24Anonymous__34503)
           => ( cCoq_2eLists_2eSetoidList_2eInA___24a4(Vvar__0__A__34496,Vvar__1__eqA__34497,Vvar__2__x__34502,Vvar__3___24Anonymous__34503)
             => ( ? [Vvar__3__y__34512] :
                    ( t(Vvar__3__y__34512,Vvar__0__A__34496)
                    & ? [Vvar__4__l__34513] :
                        ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__34496,Vvar__4__l__34513)
                        & p(happ(happ(Vvar__1__eqA__34497,Vvar__2__x__34502),Vvar__3__y__34512))
                        & Vvar__3___24Anonymous__34503 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__34496,Vvar__3__y__34512,Vvar__4__l__34513) ) )
                | ? [Vvar__3__y__34522] :
                    ( t(Vvar__3__y__34522,Vvar__0__A__34496)
                    & ? [Vvar__4__l__34523] :
                        ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__34496,Vvar__4__l__34523)
                        & cCoq_2eLists_2eSetoidList_2eInA___24a4(Vvar__0__A__34496,Vvar__1__eqA__34497,Vvar__2__x__34502,Vvar__4__l__34523)
                        & Vvar__3___24Anonymous__34503 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__34496,Vvar__3__y__34522,Vvar__4__l__34523) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Lists.SetoidList.NoDupA',axiom,
    ! [Vvar__0__A__42477,Vvar__1__eqA__42478,Vvar__2___24Anonymous__42483] :
      ( cType___24t(Vvar__0__A__42477)
     => ( c_24__type__42510___24t(Vvar__0__A__42477,Vvar__1__eqA__42478,Vvar__2___24Anonymous__42483,Vvar__1__eqA__42478)
       => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__42477,Vvar__2___24Anonymous__42483)
         => ( cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(Vvar__0__A__42477,Vvar__1__eqA__42478,Vvar__2___24Anonymous__42483)
           => ( Vvar__2___24Anonymous__42483 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__42477)
              | ? [Vvar__2__x__42497] :
                  ( t(Vvar__2__x__42497,Vvar__0__A__42477)
                  & ? [Vvar__3__l__42498] :
                      ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__42477,Vvar__3__l__42498)
                      & ~ cCoq_2eLists_2eSetoidList_2eInA___24a4(Vvar__0__A__42477,Vvar__1__eqA__42478,Vvar__2__x__42497,Vvar__3__l__42498)
                      & cCoq_2eLists_2eSetoidList_2eNoDupA___24a3(Vvar__0__A__42477,Vvar__1__eqA__42478,Vvar__3__l__42498)
                      & Vvar__2___24Anonymous__42483 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__42477,Vvar__2__x__42497,Vvar__3__l__42498) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Lists.SetoidList.eqlistA',axiom,
    ! [Vvar__0__A__42512,Vvar__1__eqA__42513,Vvar__2___24Anonymous__42518,Vvar__3___24Anonymous__42519] :
      ( cType___24t(Vvar__0__A__42512)
     => ( c_24__type__42550___24t(Vvar__0__A__42512,Vvar__1__eqA__42513,Vvar__2___24Anonymous__42518,Vvar__3___24Anonymous__42519,Vvar__1__eqA__42513)
       => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__42512,Vvar__2___24Anonymous__42518)
         => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__42512,Vvar__3___24Anonymous__42519)
           => ( cCoq_2eLists_2eSetoidList_2eeqlistA___24a4(Vvar__0__A__42512,Vvar__1__eqA__42513,Vvar__2___24Anonymous__42518,Vvar__3___24Anonymous__42519)
             => ( ( Vvar__3___24Anonymous__42519 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__42512)
                  & Vvar__2___24Anonymous__42518 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__42512) )
                | ? [Vvar__2__x__42533] :
                    ( t(Vvar__2__x__42533,Vvar__0__A__42512)
                    & ? [Vvar__3__x_27__42534] :
                        ( t(Vvar__3__x_27__42534,Vvar__0__A__42512)
                        & ? [Vvar__4__l__42535] :
                            ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__42512,Vvar__4__l__42535)
                            & ? [Vvar__5__l_27__42536] :
                                ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__42512,Vvar__5__l_27__42536)
                                & p(happ(happ(Vvar__1__eqA__42513,Vvar__2__x__42533),Vvar__3__x_27__42534))
                                & cCoq_2eLists_2eSetoidList_2eeqlistA___24a4(Vvar__0__A__42512,Vvar__1__eqA__42513,Vvar__4__l__42535,Vvar__5__l_27__42536)
                                & Vvar__3___24Anonymous__42519 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__42512,Vvar__3__x_27__42534,Vvar__5__l_27__42536)
                                & Vvar__2___24Anonymous__42518 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__42512,Vvar__2__x__42533,Vvar__4__l__42535) ) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Logic.EqdepFacts.eq_dep',axiom,
    ! [Vvar__0__U__30869,Vvar__1__P__30870,Vvar__2__p__30873,Vvar__3__x__30874,Vvar__4__q__30875,Vvar__5___24Anonymous__30876] :
      ( cType___24t(Vvar__0__U__30869)
     => ( c_24__type__30891___24t(Vvar__0__U__30869,Vvar__1__P__30870,Vvar__2__p__30873,Vvar__3__x__30874,Vvar__4__q__30875,Vvar__5___24Anonymous__30876,Vvar__1__P__30870)
       => ( t(Vvar__2__p__30873,Vvar__0__U__30869)
         => ( t(Vvar__3__x__30874,happ(Vvar__1__P__30870,Vvar__2__p__30873))
           => ( t(Vvar__4__q__30875,Vvar__0__U__30869)
             => ( t(Vvar__5___24Anonymous__30876,happ(Vvar__1__P__30870,Vvar__4__q__30875))
               => ( cCoq_2eLogic_2eEqdepFacts_2eeq__dep___24a6(Vvar__0__U__30869,Vvar__1__P__30870,Vvar__2__p__30873,Vvar__3__x__30874,Vvar__4__q__30875,Vvar__5___24Anonymous__30876)
                 => ( Vvar__5___24Anonymous__30876 = Vvar__3__x__30874
                    & Vvar__4__q__30875 = Vvar__2__p__30873 ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Logic.EqdepFacts.eq_dep1',axiom,
    ! [Vvar__0__U__31148,Vvar__1__P__31149,Vvar__2__p__31152,Vvar__3__x__31153,Vvar__4__q__31154,Vvar__5__y__31155] :
      ( cType___24t(Vvar__0__U__31148)
     => ( c_24__type__31174___24t(Vvar__0__U__31148,Vvar__1__P__31149,Vvar__2__p__31152,Vvar__3__x__31153,Vvar__4__q__31154,Vvar__5__y__31155,Vvar__1__P__31149)
       => ( t(Vvar__2__p__31152,Vvar__0__U__31148)
         => ( t(Vvar__3__x__31153,happ(Vvar__1__P__31149,Vvar__2__p__31152))
           => ( t(Vvar__4__q__31154,Vvar__0__U__31148)
             => ( t(Vvar__5__y__31155,happ(Vvar__1__P__31149,Vvar__4__q__31154))
               => ( cCoq_2eLogic_2eEqdepFacts_2eeq__dep1___24a6(Vvar__0__U__31148,Vvar__1__P__31149,Vvar__2__p__31152,Vvar__3__x__31153,Vvar__4__q__31154,Vvar__5__y__31155)
                 => ( Vvar__4__q__31154 = Vvar__2__p__31152
                    & Vvar__3__x__31153 = cCoq_2eInit_2eLogic_2eeq__rect___24a5(Vvar__0__U__31148,Vvar__4__q__31154,Vvar__1__P__31149,Vvar__5__y__31155,Vvar__2__p__31152)
                    & p(c_24True) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Numbers.BinNums.N',axiom,
    ! [VX7410] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(VX7410)
     => ( VX7410 = cCoq_2eNumbers_2eBinNums_2eN0
        | ? [Vvar__0___24Anonymous__7411] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__7411)
            & VX7410 = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(Vvar__0___24Anonymous__7411) ) ) ) ).

fof('$_inversion_Coq.Numbers.BinNums.Z',axiom,
    ! [VX7415] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(VX7415)
     => ( VX7415 = cCoq_2eNumbers_2eBinNums_2eZ0
        | ? [Vvar__0___24Anonymous__7416] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__7416)
            & VX7415 = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(Vvar__0___24Anonymous__7416) )
        | ? [Vvar__0___24Anonymous__7417] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__7417)
            & VX7415 = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(Vvar__0___24Anonymous__7417) ) ) ) ).

fof('$_inversion_Coq.Numbers.BinNums.positive',axiom,
    ! [VX5481] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(VX5481)
     => ( ? [Vvar__0___24Anonymous__5482] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__5482)
            & VX5481 = cCoq_2eNumbers_2eBinNums_2exI___24a1(Vvar__0___24Anonymous__5482) )
        | ? [Vvar__0___24Anonymous__5483] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__5483)
            & VX5481 = cCoq_2eNumbers_2eBinNums_2exO___24a1(Vvar__0___24Anonymous__5483) )
        | VX5481 = cCoq_2eNumbers_2eBinNums_2exH ) ) ).

fof('$_inversion_Coq.PArith.BinPos.Pos.PeanoView',axiom,
    ! [Vvar__0___24Anonymous__35129,VX35130] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__35129)
     => ( cCoq_2ePArith_2eBinPos_2ePos_2ePeanoView___24t(Vvar__0___24Anonymous__35129,VX35130)
       => ( ( Vvar__0___24Anonymous__35129 = cCoq_2eNumbers_2eBinNums_2exH
            & VX35130 = cCoq_2ePArith_2eBinPos_2ePos_2ePeanoOne )
          | ? [Vvar__0__p__35131] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0__p__35131)
              & ? [Vvar__1___24Anonymous__35132] :
                  ( cCoq_2ePArith_2eBinPos_2ePos_2ePeanoView___24t(Vvar__0__p__35131,Vvar__1___24Anonymous__35132)
                  & Vvar__0___24Anonymous__35129 = c_24__case__Coq_2eNumbers_2eBinNums_2epositive_2435167___24a2(Vvar__0___24Anonymous__35129,Vvar__0__p__35131)
                  & VX35130 = cCoq_2ePArith_2eBinPos_2ePos_2ePeanoSucc___24a2(Vvar__0__p__35131,Vvar__1___24Anonymous__35132) ) ) ) ) ) ).

fof('$_inversion_Coq.PArith.BinPos.Pos.SubMaskSpec',axiom,
    ! [Vvar__0__p__44659,Vvar__1__q__44660,Vvar__2___24Anonymous__44661] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0__p__44659)
     => ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__q__44660)
       => ( cCoq_2ePArith_2eBinPosDef_2ePos_2emask___24t(Vvar__2___24Anonymous__44661)
         => ( cCoq_2ePArith_2eBinPos_2ePos_2eSubMaskSpec___24a3(Vvar__0__p__44659,Vvar__1__q__44660,Vvar__2___24Anonymous__44661)
           => ( ( Vvar__0__p__44659 = Vvar__1__q__44660
                & Vvar__2___24Anonymous__44661 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNul )
              | ? [Vvar__2__r__44668] :
                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2__r__44668)
                  & cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__1__q__44660,Vvar__2__r__44668) = Vvar__0__p__44659
                  & Vvar__2___24Anonymous__44661 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__2__r__44668) )
              | ? [Vvar__2__r__44672] :
                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2__r__44672)
                  & cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0__p__44659,Vvar__2__r__44672) = Vvar__1__q__44660
                  & Vvar__2___24Anonymous__44661 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNeg ) ) ) ) ) ) ).

fof('$_inversion_Coq.PArith.BinPosDef.Pos.mask',axiom,
    ! [VX30982] :
      ( cCoq_2ePArith_2eBinPosDef_2ePos_2emask___24t(VX30982)
     => ( VX30982 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNul
        | ? [Vvar__0___24Anonymous__30983] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30983)
            & VX30982 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(Vvar__0___24Anonymous__30983) )
        | VX30982 = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNeg ) ) ).

fof('$_inversion_Coq.QArith.QArith_base.Q',axiom,
    ! [VX9764] :
      ( cCoq_2eQArith_2eQArith__base_2eQ___24t(VX9764)
     => ? [Vvar__0__Qnum__9765] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__Qnum__9765)
          & ? [Vvar__1__Qden__9766] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__Qden__9766)
              & VX9764 = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(Vvar__0__Qnum__9765,Vvar__1__Qden__9766) ) ) ) ).

fof('$_inversion_Coq.Reals.RIneq.negreal',axiom,
    ! [VX32650] :
      ( cCoq_2eReals_2eRIneq_2enegreal___24t(VX32650)
     => ? [Vvar__0__neg__32651] :
          ( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0__neg__32651)
          & cCoq_2eReals_2eRdefinitions_2eRlt___24a2(Vvar__0__neg__32651,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0))
          & VX32650 = cCoq_2eReals_2eRIneq_2emknegreal___24a1(Vvar__0__neg__32651) ) ) ).

fof('$_inversion_Coq.Reals.RIneq.nonnegreal',axiom,
    ! [VX26016] :
      ( cCoq_2eReals_2eRIneq_2enonnegreal___24t(VX26016)
     => ? [Vvar__0__nonneg__26017] :
          ( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0__nonneg__26017)
          & cCoq_2eReals_2eRdefinitions_2eRle___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),Vvar__0__nonneg__26017)
          & VX26016 = cCoq_2eReals_2eRIneq_2emknonnegreal___24a1(Vvar__0__nonneg__26017) ) ) ).

fof('$_inversion_Coq.Reals.RIneq.nonposreal',axiom,
    ! [VX32643] :
      ( cCoq_2eReals_2eRIneq_2enonposreal___24t(VX32643)
     => ? [Vvar__0__nonpos__32644] :
          ( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0__nonpos__32644)
          & cCoq_2eReals_2eRdefinitions_2eRle___24a2(Vvar__0__nonpos__32644,cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0))
          & VX32643 = cCoq_2eReals_2eRIneq_2emknonposreal___24a1(Vvar__0__nonpos__32644) ) ) ).

fof('$_inversion_Coq.Reals.RIneq.nonzeroreal',axiom,
    ! [VX32657] :
      ( cCoq_2eReals_2eRIneq_2enonzeroreal___24t(VX32657)
     => ? [Vvar__0__nonzero__32658] :
          ( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0__nonzero__32658)
          & Vvar__0__nonzero__32658 != cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0)
          & VX32657 = cCoq_2eReals_2eRIneq_2emknonzeroreal___24a1(Vvar__0__nonzero__32658) ) ) ).

fof('$_inversion_Coq.Reals.RIneq.posreal',axiom,
    ! [VX32636] :
      ( cCoq_2eReals_2eRIneq_2eposreal___24t(VX32636)
     => ? [Vvar__0__pos__32637] :
          ( cCoq_2eReals_2eRdefinitions_2eR___24t(Vvar__0__pos__32637)
          & cCoq_2eReals_2eRdefinitions_2eRlt___24a2(cCoq_2eReals_2eRdefinitions_2eIZR___24a1(cCoq_2eNumbers_2eBinNums_2eZ0),Vvar__0__pos__32637)
          & VX32636 = cCoq_2eReals_2eRIneq_2emkposreal___24a1(Vvar__0__pos__32637) ) ) ).

fof('$_inversion_Coq.Reals.Rfunctions.Z_spec',axiom,
    ! [Vvar__0__x__32667,Vvar__1___24Anonymous__32668,VX32669] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__x__32667)
     => ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__1___24Anonymous__32668)
       => ( cCoq_2eReals_2eRfunctions_2eZ__spec___24t(Vvar__0__x__32667,Vvar__1___24Anonymous__32668,VX32669)
         => ( ( Vvar__0__x__32667 = cCoq_2eNumbers_2eBinNums_2eZ0
              & Vvar__1___24Anonymous__32668 = cCoq_2eNumbers_2eBinNums_2eZ0
              & VX32669 = cCoq_2eReals_2eRfunctions_2eZintNull___24a1(Vvar__0__x__32667) )
            | ? [Vvar__1__n__32673] :
                ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__n__32673)
                & Vvar__0__x__32667 = cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(Vvar__1__n__32673)
                & Vvar__1___24Anonymous__32668 = c_24__case__Coq_2eInit_2eDatatypes_2enat_2432693___24a3(Vvar__0__x__32667,Vvar__1___24Anonymous__32668,Vvar__1__n__32673)
                & VX32669 = cCoq_2eReals_2eRfunctions_2eZintPos___24a2(Vvar__0__x__32667,Vvar__1__n__32673) )
            | ? [Vvar__1__n__32678] :
                ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__n__32678)
                & Vvar__0__x__32667 = cCoq_2eZArith_2eBinIntDef_2eZ_2eopp___24a1(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(Vvar__1__n__32678))
                & Vvar__1___24Anonymous__32668 = c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2432710___24a3(Vvar__0__x__32667,Vvar__1___24Anonymous__32668,Vvar__1__n__32678)
                & VX32669 = cCoq_2eReals_2eRfunctions_2eZintNeg___24a2(Vvar__0__x__32667,Vvar__1__n__32678) ) ) ) ) ) ).

fof('$_inversion_Coq.Relations.Relation_Definitions.PER',axiom,
    ! [Vvar__0__A__36505,Vvar__1__R__36506] :
      ( cType___24t(Vvar__0__A__36505)
     => ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__36505,Vvar__1__R__36506)
       => ( cCoq_2eRelations_2eRelation__Definitions_2ePER___24a2(Vvar__0__A__36505,Vvar__1__R__36506)
         => ( cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(Vvar__0__A__36505,Vvar__1__R__36506)
            & cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(Vvar__0__A__36505,Vvar__1__R__36506)
            & p(c_24True) ) ) ) ) ).

fof('$_inversion_Coq.Relations.Relation_Definitions.equivalence',axiom,
    ! [Vvar__0__A__26250,Vvar__1__R__26251] :
      ( cType___24t(Vvar__0__A__26250)
     => ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__26250,Vvar__1__R__26251)
       => ( cCoq_2eRelations_2eRelation__Definitions_2eequivalence___24a2(Vvar__0__A__26250,Vvar__1__R__26251)
         => ( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(Vvar__0__A__26250,Vvar__1__R__26251)
            & cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(Vvar__0__A__26250,Vvar__1__R__26251)
            & cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(Vvar__0__A__26250,Vvar__1__R__26251)
            & p(c_24True) ) ) ) ) ).

fof('$_inversion_Coq.Relations.Relation_Definitions.order',axiom,
    ! [Vvar__0__A__36497,Vvar__1__R__36498] :
      ( cType___24t(Vvar__0__A__36497)
     => ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__36497,Vvar__1__R__36498)
       => ( cCoq_2eRelations_2eRelation__Definitions_2eorder___24a2(Vvar__0__A__36497,Vvar__1__R__36498)
         => ( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(Vvar__0__A__36497,Vvar__1__R__36498)
            & cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(Vvar__0__A__36497,Vvar__1__R__36498)
            & cCoq_2eRelations_2eRelation__Definitions_2eantisymmetric___24a2(Vvar__0__A__36497,Vvar__1__R__36498)
            & p(c_24True) ) ) ) ) ).

fof('$_inversion_Coq.Relations.Relation_Definitions.preorder',axiom,
    ! [Vvar__0__A__36490,Vvar__1__R__36491] :
      ( cType___24t(Vvar__0__A__36490)
     => ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__36490,Vvar__1__R__36491)
       => ( cCoq_2eRelations_2eRelation__Definitions_2epreorder___24a2(Vvar__0__A__36490,Vvar__1__R__36491)
         => ( cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(Vvar__0__A__36490,Vvar__1__R__36491)
            & cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(Vvar__0__A__36490,Vvar__1__R__36491)
            & p(c_24True) ) ) ) ) ).

fof('$_inversion_Coq.Relations.Relation_Operators.Desc',axiom,
    ! [Vvar__0__A__26411,Vvar__1__leA__26412,Vvar__2___24Anonymous__26417] :
      ( cType___24t(Vvar__0__A__26411)
     => ( c_24__type__26507___24t(Vvar__0__A__26411,Vvar__1__leA__26412,Vvar__2___24Anonymous__26417,Vvar__1__leA__26412)
       => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__26411,Vvar__2___24Anonymous__26417)
         => ( cCoq_2eRelations_2eRelation__Operators_2eDesc___24a3(Vvar__0__A__26411,Vvar__1__leA__26412,Vvar__2___24Anonymous__26417)
           => ( Vvar__2___24Anonymous__26417 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__26411)
              | ? [Vvar__2__x__26431] :
                  ( t(Vvar__2__x__26431,Vvar__0__A__26411)
                  & Vvar__2___24Anonymous__26417 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__26411,Vvar__2__x__26431,cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__26411)) )
              | ? [Vvar__2__x__26438] :
                  ( t(Vvar__2__x__26438,Vvar__0__A__26411)
                  & ? [Vvar__3__y__26439] :
                      ( t(Vvar__3__y__26439,Vvar__0__A__26411)
                      & ? [Vvar__4__l__26440] :
                          ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__26411,Vvar__4__l__26440)
                          & cCoq_2eRelations_2eRelation__Operators_2eclos__refl___24a4(Vvar__0__A__26411,Vvar__1__leA__26412,Vvar__2__x__26438,Vvar__3__y__26439)
                          & cCoq_2eRelations_2eRelation__Operators_2eDesc___24a3(Vvar__0__A__26411,Vvar__1__leA__26412,cCoq_2eInit_2eDatatypes_2eapp___24a3(Vvar__0__A__26411,Vvar__4__l__26440,cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__26411,Vvar__3__y__26439,cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__26411))))
                          & Vvar__2___24Anonymous__26417 = c_24__case__Coq_2eInit_2eDatatypes_2elist_2426705___24a6(Vvar__0__A__26411,Vvar__1__leA__26412,Vvar__2___24Anonymous__26417,Vvar__2__x__26438,Vvar__3__y__26439,Vvar__4__l__26440) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Relations.Relation_Operators.Ltl',axiom,
    ! [Vvar__0__A__36923,Vvar__1__leA__36924,Vvar__2___24Anonymous__36929,Vvar__3___24Anonymous__36930] :
      ( cType___24t(Vvar__0__A__36923)
     => ( c_24__type__36972___24t(Vvar__0__A__36923,Vvar__1__leA__36924,Vvar__2___24Anonymous__36929,Vvar__3___24Anonymous__36930,Vvar__1__leA__36924)
       => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__36923,Vvar__2___24Anonymous__36929)
         => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__36923,Vvar__3___24Anonymous__36930)
           => ( cCoq_2eRelations_2eRelation__Operators_2eLtl___24a4(Vvar__0__A__36923,Vvar__1__leA__36924,Vvar__2___24Anonymous__36929,Vvar__3___24Anonymous__36930)
             => ( ? [Vvar__2__a__36938] :
                    ( t(Vvar__2__a__36938,Vvar__0__A__36923)
                    & ? [Vvar__3__x__36939] :
                        ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__36923,Vvar__3__x__36939)
                        & Vvar__3___24Anonymous__36930 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__36923,Vvar__2__a__36938,Vvar__3__x__36939)
                        & Vvar__2___24Anonymous__36929 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__36923) ) )
                | ? [Vvar__2__a__36946] :
                    ( t(Vvar__2__a__36946,Vvar__0__A__36923)
                    & ? [Vvar__3__b__36947] :
                        ( t(Vvar__3__b__36947,Vvar__0__A__36923)
                        & p(happ(happ(Vvar__1__leA__36924,Vvar__2__a__36946),Vvar__3__b__36947))
                        & ? [Vvar__5__x__36949] :
                            ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__36923,Vvar__5__x__36949)
                            & ? [Vvar__6__y__36950] :
                                ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__36923,Vvar__6__y__36950)
                                & Vvar__3___24Anonymous__36930 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__36923,Vvar__3__b__36947,Vvar__6__y__36950)
                                & Vvar__2___24Anonymous__36929 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__36923,Vvar__2__a__36946,Vvar__5__x__36949) ) ) ) )
                | ? [Vvar__2__a__36957] :
                    ( t(Vvar__2__a__36957,Vvar__0__A__36923)
                    & ? [Vvar__3__x__36958] :
                        ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__36923,Vvar__3__x__36958)
                        & ? [Vvar__4__y__36959] :
                            ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__36923,Vvar__4__y__36959)
                            & cCoq_2eRelations_2eRelation__Operators_2eLtl___24a4(Vvar__0__A__36923,Vvar__1__leA__36924,Vvar__3__x__36958,Vvar__4__y__36959)
                            & Vvar__3___24Anonymous__36930 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__36923,Vvar__2__a__36957,Vvar__4__y__36959)
                            & Vvar__2___24Anonymous__36929 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__36923,Vvar__2__a__36957,Vvar__3__x__36958) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Relations.Relation_Operators.clos_refl',axiom,
    ! [Vvar__0__A__36563,Vvar__1__R__36564,Vvar__2__x__36565,Vvar__3___24Anonymous__36566] :
      ( cType___24t(Vvar__0__A__36563)
     => ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__36563,Vvar__1__R__36564)
       => ( t(Vvar__2__x__36565,Vvar__0__A__36563)
         => ( t(Vvar__3___24Anonymous__36566,Vvar__0__A__36563)
           => ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl___24a4(Vvar__0__A__36563,Vvar__1__R__36564,Vvar__2__x__36565,Vvar__3___24Anonymous__36566)
             => ( ? [Vvar__3__y__36571] :
                    ( t(Vvar__3__y__36571,Vvar__0__A__36563)
                    & p(happ(happ(Vvar__1__R__36564,Vvar__2__x__36565),Vvar__3__y__36571))
                    & Vvar__3___24Anonymous__36566 = Vvar__3__y__36571 )
                | Vvar__3___24Anonymous__36566 = Vvar__2__x__36565 ) ) ) ) ) ) ).

fof('$_inversion_Coq.Relations.Relation_Operators.clos_refl_sym_trans_1n',axiom,
    ! [Vvar__0__A__36606,Vvar__1__R__36607,Vvar__2__x__36608,Vvar__3___24Anonymous__36609] :
      ( cType___24t(Vvar__0__A__36606)
     => ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__36606,Vvar__1__R__36607)
       => ( t(Vvar__2__x__36608,Vvar__0__A__36606)
         => ( t(Vvar__3___24Anonymous__36609,Vvar__0__A__36606)
           => ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__1n___24a4(Vvar__0__A__36606,Vvar__1__R__36607,Vvar__2__x__36608,Vvar__3___24Anonymous__36609)
             => ( Vvar__3___24Anonymous__36609 = Vvar__2__x__36608
                | ? [Vvar__3__y__36617] :
                    ( t(Vvar__3__y__36617,Vvar__0__A__36606)
                    & ? [Vvar__4__z__36618] :
                        ( t(Vvar__4__z__36618,Vvar__0__A__36606)
                        & ( p(happ(happ(Vvar__1__R__36607,Vvar__2__x__36608),Vvar__3__y__36617))
                          | p(happ(happ(Vvar__1__R__36607,Vvar__3__y__36617),Vvar__2__x__36608)) )
                        & cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__1n___24a4(Vvar__0__A__36606,Vvar__1__R__36607,Vvar__3__y__36617,Vvar__4__z__36618)
                        & Vvar__3___24Anonymous__36609 = Vvar__4__z__36618 ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Relations.Relation_Operators.clos_refl_sym_trans_n1',axiom,
    ! [Vvar__0__A__36621,Vvar__1__R__36622,Vvar__2__x__36623,Vvar__3___24Anonymous__36624] :
      ( cType___24t(Vvar__0__A__36621)
     => ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__36621,Vvar__1__R__36622)
       => ( t(Vvar__2__x__36623,Vvar__0__A__36621)
         => ( t(Vvar__3___24Anonymous__36624,Vvar__0__A__36621)
           => ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__n1___24a4(Vvar__0__A__36621,Vvar__1__R__36622,Vvar__2__x__36623,Vvar__3___24Anonymous__36624)
             => ( Vvar__3___24Anonymous__36624 = Vvar__2__x__36623
                | ? [Vvar__3__y__36632] :
                    ( t(Vvar__3__y__36632,Vvar__0__A__36621)
                    & ? [Vvar__4__z__36633] :
                        ( t(Vvar__4__z__36633,Vvar__0__A__36621)
                        & ( p(happ(happ(Vvar__1__R__36622,Vvar__3__y__36632),Vvar__4__z__36633))
                          | p(happ(happ(Vvar__1__R__36622,Vvar__4__z__36633),Vvar__3__y__36632)) )
                        & cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__n1___24a4(Vvar__0__A__36621,Vvar__1__R__36622,Vvar__2__x__36623,Vvar__3__y__36632)
                        & Vvar__3___24Anonymous__36624 = Vvar__4__z__36633 ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Relations.Relation_Operators.clos_refl_trans',axiom,
    ! [Vvar__0__A__26258,Vvar__1__R__26259,Vvar__2__x__26260,Vvar__3___24Anonymous__26261] :
      ( cType___24t(Vvar__0__A__26258)
     => ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__26258,Vvar__1__R__26259)
       => ( t(Vvar__2__x__26260,Vvar__0__A__26258)
         => ( t(Vvar__3___24Anonymous__26261,Vvar__0__A__26258)
           => ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(Vvar__0__A__26258,Vvar__1__R__26259,Vvar__2__x__26260,Vvar__3___24Anonymous__26261)
             => ( ? [Vvar__3__y__26266] :
                    ( t(Vvar__3__y__26266,Vvar__0__A__26258)
                    & p(happ(happ(Vvar__1__R__26259,Vvar__2__x__26260),Vvar__3__y__26266))
                    & Vvar__3___24Anonymous__26261 = Vvar__3__y__26266 )
                | Vvar__3___24Anonymous__26261 = Vvar__2__x__26260
                | ? [Vvar__3__y__26274] :
                    ( t(Vvar__3__y__26274,Vvar__0__A__26258)
                    & ? [Vvar__4__z__26275] :
                        ( t(Vvar__4__z__26275,Vvar__0__A__26258)
                        & cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(Vvar__0__A__26258,Vvar__1__R__26259,Vvar__2__x__26260,Vvar__3__y__26274)
                        & cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(Vvar__0__A__26258,Vvar__1__R__26259,Vvar__3__y__26274,Vvar__4__z__26275)
                        & Vvar__3___24Anonymous__26261 = Vvar__4__z__26275 ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Relations.Relation_Operators.clos_refl_trans_1n',axiom,
    ! [Vvar__0__A__36576,Vvar__1__R__36577,Vvar__2__x__36578,Vvar__3___24Anonymous__36579] :
      ( cType___24t(Vvar__0__A__36576)
     => ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__36576,Vvar__1__R__36577)
       => ( t(Vvar__2__x__36578,Vvar__0__A__36576)
         => ( t(Vvar__3___24Anonymous__36579,Vvar__0__A__36576)
           => ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__1n___24a4(Vvar__0__A__36576,Vvar__1__R__36577,Vvar__2__x__36578,Vvar__3___24Anonymous__36579)
             => ( Vvar__3___24Anonymous__36579 = Vvar__2__x__36578
                | ? [Vvar__3__y__36587] :
                    ( t(Vvar__3__y__36587,Vvar__0__A__36576)
                    & ? [Vvar__4__z__36588] :
                        ( t(Vvar__4__z__36588,Vvar__0__A__36576)
                        & p(happ(happ(Vvar__1__R__36577,Vvar__2__x__36578),Vvar__3__y__36587))
                        & cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__1n___24a4(Vvar__0__A__36576,Vvar__1__R__36577,Vvar__3__y__36587,Vvar__4__z__36588)
                        & Vvar__3___24Anonymous__36579 = Vvar__4__z__36588 ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Relations.Relation_Operators.clos_refl_trans_n1',axiom,
    ! [Vvar__0__A__36591,Vvar__1__R__36592,Vvar__2__x__36593,Vvar__3___24Anonymous__36594] :
      ( cType___24t(Vvar__0__A__36591)
     => ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__36591,Vvar__1__R__36592)
       => ( t(Vvar__2__x__36593,Vvar__0__A__36591)
         => ( t(Vvar__3___24Anonymous__36594,Vvar__0__A__36591)
           => ( cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__n1___24a4(Vvar__0__A__36591,Vvar__1__R__36592,Vvar__2__x__36593,Vvar__3___24Anonymous__36594)
             => ( Vvar__3___24Anonymous__36594 = Vvar__2__x__36593
                | ? [Vvar__3__y__36602] :
                    ( t(Vvar__3__y__36602,Vvar__0__A__36591)
                    & ? [Vvar__4__z__36603] :
                        ( t(Vvar__4__z__36603,Vvar__0__A__36591)
                        & p(happ(happ(Vvar__1__R__36592,Vvar__3__y__36602),Vvar__4__z__36603))
                        & cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__n1___24a4(Vvar__0__A__36591,Vvar__1__R__36592,Vvar__2__x__36593,Vvar__3__y__36602)
                        & Vvar__3___24Anonymous__36594 = Vvar__4__z__36603 ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Relations.Relation_Operators.clos_trans',axiom,
    ! [Vvar__0__A__36512,Vvar__1__R__36513,Vvar__2__x__36514,Vvar__3___24Anonymous__36515] :
      ( cType___24t(Vvar__0__A__36512)
     => ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__36512,Vvar__1__R__36513)
       => ( t(Vvar__2__x__36514,Vvar__0__A__36512)
         => ( t(Vvar__3___24Anonymous__36515,Vvar__0__A__36512)
           => ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(Vvar__0__A__36512,Vvar__1__R__36513,Vvar__2__x__36514,Vvar__3___24Anonymous__36515)
             => ( ? [Vvar__3__y__36520] :
                    ( t(Vvar__3__y__36520,Vvar__0__A__36512)
                    & p(happ(happ(Vvar__1__R__36513,Vvar__2__x__36514),Vvar__3__y__36520))
                    & Vvar__3___24Anonymous__36515 = Vvar__3__y__36520 )
                | ? [Vvar__3__y__36525] :
                    ( t(Vvar__3__y__36525,Vvar__0__A__36512)
                    & ? [Vvar__4__z__36526] :
                        ( t(Vvar__4__z__36526,Vvar__0__A__36512)
                        & cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(Vvar__0__A__36512,Vvar__1__R__36513,Vvar__2__x__36514,Vvar__3__y__36525)
                        & cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(Vvar__0__A__36512,Vvar__1__R__36513,Vvar__3__y__36525,Vvar__4__z__36526)
                        & Vvar__3___24Anonymous__36515 = Vvar__4__z__36526 ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Relations.Relation_Operators.clos_trans_1n',axiom,
    ! [Vvar__0__A__36529,Vvar__1__R__36530,Vvar__2__x__36531,Vvar__3___24Anonymous__36532] :
      ( cType___24t(Vvar__0__A__36529)
     => ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__36529,Vvar__1__R__36530)
       => ( t(Vvar__2__x__36531,Vvar__0__A__36529)
         => ( t(Vvar__3___24Anonymous__36532,Vvar__0__A__36529)
           => ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans__1n___24a4(Vvar__0__A__36529,Vvar__1__R__36530,Vvar__2__x__36531,Vvar__3___24Anonymous__36532)
             => ( ? [Vvar__3__y__36537] :
                    ( t(Vvar__3__y__36537,Vvar__0__A__36529)
                    & p(happ(happ(Vvar__1__R__36530,Vvar__2__x__36531),Vvar__3__y__36537))
                    & Vvar__3___24Anonymous__36532 = Vvar__3__y__36537 )
                | ? [Vvar__3__y__36542] :
                    ( t(Vvar__3__y__36542,Vvar__0__A__36529)
                    & ? [Vvar__4__z__36543] :
                        ( t(Vvar__4__z__36543,Vvar__0__A__36529)
                        & p(happ(happ(Vvar__1__R__36530,Vvar__2__x__36531),Vvar__3__y__36542))
                        & cCoq_2eRelations_2eRelation__Operators_2eclos__trans__1n___24a4(Vvar__0__A__36529,Vvar__1__R__36530,Vvar__3__y__36542,Vvar__4__z__36543)
                        & Vvar__3___24Anonymous__36532 = Vvar__4__z__36543 ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Relations.Relation_Operators.clos_trans_n1',axiom,
    ! [Vvar__0__A__36546,Vvar__1__R__36547,Vvar__2__x__36548,Vvar__3___24Anonymous__36549] :
      ( cType___24t(Vvar__0__A__36546)
     => ( cCoq_2eRelations_2eRelation__Definitions_2erelation___24t(Vvar__0__A__36546,Vvar__1__R__36547)
       => ( t(Vvar__2__x__36548,Vvar__0__A__36546)
         => ( t(Vvar__3___24Anonymous__36549,Vvar__0__A__36546)
           => ( cCoq_2eRelations_2eRelation__Operators_2eclos__trans__n1___24a4(Vvar__0__A__36546,Vvar__1__R__36547,Vvar__2__x__36548,Vvar__3___24Anonymous__36549)
             => ( ? [Vvar__3__y__36554] :
                    ( t(Vvar__3__y__36554,Vvar__0__A__36546)
                    & p(happ(happ(Vvar__1__R__36547,Vvar__2__x__36548),Vvar__3__y__36554))
                    & Vvar__3___24Anonymous__36549 = Vvar__3__y__36554 )
                | ? [Vvar__3__y__36559] :
                    ( t(Vvar__3__y__36559,Vvar__0__A__36546)
                    & ? [Vvar__4__z__36560] :
                        ( t(Vvar__4__z__36560,Vvar__0__A__36546)
                        & p(happ(happ(Vvar__1__R__36547,Vvar__3__y__36559),Vvar__4__z__36560))
                        & cCoq_2eRelations_2eRelation__Operators_2eclos__trans__n1___24a4(Vvar__0__A__36546,Vvar__1__R__36547,Vvar__2__x__36548,Vvar__3__y__36559)
                        & Vvar__3___24Anonymous__36549 = Vvar__4__z__36560 ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Relations.Relation_Operators.lexprod',axiom,
    ! [Vvar__0__A__36636,Vvar__1__B__36637,Vvar__2__leA__36640,Vvar__3__leB__36645,Vvar__4___24Anonymous__36652,Vvar__5___24Anonymous__36653] :
      ( cType___24t(Vvar__0__A__36636)
     => ( c_24__type__36716___24t(Vvar__0__A__36636,Vvar__1__B__36637,Vvar__2__leA__36640,Vvar__3__leB__36645,Vvar__4___24Anonymous__36652,Vvar__5___24Anonymous__36653,Vvar__1__B__36637)
       => ( c_24__type__36745___24t(Vvar__0__A__36636,Vvar__1__B__36637,Vvar__2__leA__36640,Vvar__3__leB__36645,Vvar__4___24Anonymous__36652,Vvar__5___24Anonymous__36653,Vvar__2__leA__36640)
         => ( c_24__type__36782___24t(Vvar__0__A__36636,Vvar__1__B__36637,Vvar__2__leA__36640,Vvar__3__leB__36645,Vvar__4___24Anonymous__36652,Vvar__5___24Anonymous__36653,Vvar__3__leB__36645)
           => ( cCoq_2eInit_2eSpecif_2esigT___24t(Vvar__0__A__36636,Vvar__1__B__36637,Vvar__4___24Anonymous__36652)
             => ( cCoq_2eInit_2eSpecif_2esigT___24t(Vvar__0__A__36636,Vvar__1__B__36637,Vvar__5___24Anonymous__36653)
               => ( cCoq_2eRelations_2eRelation__Operators_2elexprod___24a6(Vvar__0__A__36636,Vvar__1__B__36637,Vvar__2__leA__36640,Vvar__3__leB__36645,Vvar__4___24Anonymous__36652,Vvar__5___24Anonymous__36653)
                 => ( ? [Vvar__4__x__36671] :
                        ( t(Vvar__4__x__36671,Vvar__0__A__36636)
                        & ? [Vvar__5__x_27__36672] :
                            ( t(Vvar__5__x_27__36672,Vvar__0__A__36636)
                            & ? [Vvar__6__y__36673] :
                                ( t(Vvar__6__y__36673,happ(Vvar__1__B__36637,Vvar__4__x__36671))
                                & ? [Vvar__7__y_27__36674] :
                                    ( t(Vvar__7__y_27__36674,happ(Vvar__1__B__36637,Vvar__5__x_27__36672))
                                    & p(happ(happ(Vvar__2__leA__36640,Vvar__4__x__36671),Vvar__5__x_27__36672))
                                    & Vvar__5___24Anonymous__36653 = cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__36636,Vvar__1__B__36637,Vvar__5__x_27__36672,Vvar__7__y_27__36674)
                                    & Vvar__4___24Anonymous__36652 = cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__36636,Vvar__1__B__36637,Vvar__4__x__36671,Vvar__6__y__36673) ) ) ) )
                    | ? [Vvar__4__x__36692] :
                        ( t(Vvar__4__x__36692,Vvar__0__A__36636)
                        & ? [Vvar__5__y__36693] :
                            ( t(Vvar__5__y__36693,happ(Vvar__1__B__36637,Vvar__4__x__36692))
                            & ? [Vvar__6__y_27__36694] :
                                ( t(Vvar__6__y_27__36694,happ(Vvar__1__B__36637,Vvar__4__x__36692))
                                & p(happ(happ(happ(Vvar__3__leB__36645,Vvar__4__x__36692),Vvar__5__y__36693),Vvar__6__y_27__36694))
                                & Vvar__5___24Anonymous__36653 = cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__36636,Vvar__1__B__36637,Vvar__4__x__36692,Vvar__6__y_27__36694)
                                & Vvar__4___24Anonymous__36652 = cCoq_2eInit_2eSpecif_2eexistT___24a4(Vvar__0__A__36636,Vvar__1__B__36637,Vvar__4__x__36692,Vvar__5__y__36693) ) ) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Relations.Relation_Operators.swapprod',axiom,
    ! [Vvar__0__A__36881,Vvar__1__R__36882,Vvar__2___24Anonymous__36887,Vvar__3___24Anonymous__36888] :
      ( cType___24t(Vvar__0__A__36881)
     => ( c_24__type__36921___24t(Vvar__0__A__36881,Vvar__1__R__36882,Vvar__2___24Anonymous__36887,Vvar__3___24Anonymous__36888,Vvar__1__R__36882)
       => ( cCoq_2eInit_2eDatatypes_2eprod___24t(Vvar__0__A__36881,Vvar__0__A__36881,Vvar__2___24Anonymous__36887)
         => ( cCoq_2eInit_2eDatatypes_2eprod___24t(Vvar__0__A__36881,Vvar__0__A__36881,Vvar__3___24Anonymous__36888)
           => ( cCoq_2eRelations_2eRelation__Operators_2eswapprod___24a4(Vvar__0__A__36881,Vvar__1__R__36882,Vvar__2___24Anonymous__36887,Vvar__3___24Anonymous__36888)
             => ( ? [Vvar__2__x__36896] :
                    ( t(Vvar__2__x__36896,Vvar__0__A__36881)
                    & ? [Vvar__3__y__36897] :
                        ( t(Vvar__3__y__36897,Vvar__0__A__36881)
                        & ? [Vvar__4__p__36898] :
                            ( cCoq_2eInit_2eDatatypes_2eprod___24t(Vvar__0__A__36881,Vvar__0__A__36881,Vvar__4__p__36898)
                            & cCoq_2eRelations_2eRelation__Operators_2esymprod___24a6(Vvar__0__A__36881,Vvar__0__A__36881,Vvar__1__R__36882,Vvar__1__R__36882,cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__36881,Vvar__0__A__36881,Vvar__2__x__36896,Vvar__3__y__36897),Vvar__4__p__36898)
                            & Vvar__3___24Anonymous__36888 = Vvar__4__p__36898
                            & Vvar__2___24Anonymous__36887 = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__36881,Vvar__0__A__36881,Vvar__2__x__36896,Vvar__3__y__36897) ) ) )
                | ? [Vvar__2__x__36906] :
                    ( t(Vvar__2__x__36906,Vvar__0__A__36881)
                    & ? [Vvar__3__y__36907] :
                        ( t(Vvar__3__y__36907,Vvar__0__A__36881)
                        & ? [Vvar__4__p__36908] :
                            ( cCoq_2eInit_2eDatatypes_2eprod___24t(Vvar__0__A__36881,Vvar__0__A__36881,Vvar__4__p__36908)
                            & cCoq_2eRelations_2eRelation__Operators_2esymprod___24a6(Vvar__0__A__36881,Vvar__0__A__36881,Vvar__1__R__36882,Vvar__1__R__36882,cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__36881,Vvar__0__A__36881,Vvar__2__x__36906,Vvar__3__y__36907),Vvar__4__p__36908)
                            & Vvar__3___24Anonymous__36888 = Vvar__4__p__36908
                            & Vvar__2___24Anonymous__36887 = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__36881,Vvar__0__A__36881,Vvar__3__y__36907,Vvar__2__x__36906) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Relations.Relation_Operators.symprod',axiom,
    ! [Vvar__0__A__36784,Vvar__1__B__36785,Vvar__2__leA__36786,Vvar__3__leB__36791,Vvar__4___24Anonymous__36796,Vvar__5___24Anonymous__36797] :
      ( cType___24t(Vvar__0__A__36784)
     => ( cType___24t(Vvar__1__B__36785)
       => ( c_24__type__36854___24t(Vvar__0__A__36784,Vvar__1__B__36785,Vvar__2__leA__36786,Vvar__3__leB__36791,Vvar__4___24Anonymous__36796,Vvar__5___24Anonymous__36797,Vvar__2__leA__36786)
         => ( c_24__type__36879___24t(Vvar__0__A__36784,Vvar__1__B__36785,Vvar__2__leA__36786,Vvar__3__leB__36791,Vvar__4___24Anonymous__36796,Vvar__5___24Anonymous__36797,Vvar__3__leB__36791)
           => ( cCoq_2eInit_2eDatatypes_2eprod___24t(Vvar__0__A__36784,Vvar__1__B__36785,Vvar__4___24Anonymous__36796)
             => ( cCoq_2eInit_2eDatatypes_2eprod___24t(Vvar__0__A__36784,Vvar__1__B__36785,Vvar__5___24Anonymous__36797)
               => ( cCoq_2eRelations_2eRelation__Operators_2esymprod___24a6(Vvar__0__A__36784,Vvar__1__B__36785,Vvar__2__leA__36786,Vvar__3__leB__36791,Vvar__4___24Anonymous__36796,Vvar__5___24Anonymous__36797)
                 => ( ? [Vvar__4__x__36811] :
                        ( t(Vvar__4__x__36811,Vvar__0__A__36784)
                        & ? [Vvar__5__x_27__36812] :
                            ( t(Vvar__5__x_27__36812,Vvar__0__A__36784)
                            & p(happ(happ(Vvar__2__leA__36786,Vvar__4__x__36811),Vvar__5__x_27__36812))
                            & ? [Vvar__7__y__36814] :
                                ( t(Vvar__7__y__36814,Vvar__1__B__36785)
                                & Vvar__5___24Anonymous__36797 = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__36784,Vvar__1__B__36785,Vvar__5__x_27__36812,Vvar__7__y__36814)
                                & Vvar__4___24Anonymous__36796 = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__36784,Vvar__1__B__36785,Vvar__4__x__36811,Vvar__7__y__36814) ) ) )
                    | ? [Vvar__4__y__36827] :
                        ( t(Vvar__4__y__36827,Vvar__1__B__36785)
                        & ? [Vvar__5__y_27__36828] :
                            ( t(Vvar__5__y_27__36828,Vvar__1__B__36785)
                            & p(happ(happ(Vvar__3__leB__36791,Vvar__4__y__36827),Vvar__5__y_27__36828))
                            & ? [Vvar__7__x__36830] :
                                ( t(Vvar__7__x__36830,Vvar__0__A__36784)
                                & Vvar__5___24Anonymous__36797 = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__36784,Vvar__1__B__36785,Vvar__7__x__36830,Vvar__5__y_27__36828)
                                & Vvar__4___24Anonymous__36796 = cCoq_2eInit_2eDatatypes_2epair___24a4(Vvar__0__A__36784,Vvar__1__B__36785,Vvar__7__x__36830,Vvar__4__y__36827) ) ) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Sorting.Sorted.HdRel',axiom,
    ! [Vvar__0__A__27708,Vvar__1__R__27709,Vvar__2__a__27714,Vvar__3___24Anonymous__27715] :
      ( cType___24t(Vvar__0__A__27708)
     => ( c_24__type__27745___24t(Vvar__0__A__27708,Vvar__1__R__27709,Vvar__2__a__27714,Vvar__3___24Anonymous__27715,Vvar__1__R__27709)
       => ( t(Vvar__2__a__27714,Vvar__0__A__27708)
         => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__27708,Vvar__3___24Anonymous__27715)
           => ( cCoq_2eSorting_2eSorted_2eHdRel___24a4(Vvar__0__A__27708,Vvar__1__R__27709,Vvar__2__a__27714,Vvar__3___24Anonymous__27715)
             => ( Vvar__3___24Anonymous__27715 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__27708)
                | ? [Vvar__3__b__27731] :
                    ( t(Vvar__3__b__27731,Vvar__0__A__27708)
                    & ? [Vvar__4__l__27732] :
                        ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__27708,Vvar__4__l__27732)
                        & p(happ(happ(Vvar__1__R__27709,Vvar__2__a__27714),Vvar__3__b__27731))
                        & Vvar__3___24Anonymous__27715 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__27708,Vvar__3__b__27731,Vvar__4__l__27732) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Sorting.Sorted.LocallySorted',axiom,
    ! [Vvar__0__A__43746,Vvar__1__R__43747,Vvar__2___24Anonymous__43752] :
      ( cType___24t(Vvar__0__A__43746)
     => ( c_24__type__43787___24t(Vvar__0__A__43746,Vvar__1__R__43747,Vvar__2___24Anonymous__43752,Vvar__1__R__43747)
       => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__43746,Vvar__2___24Anonymous__43752)
         => ( cCoq_2eSorting_2eSorted_2eLocallySorted___24a3(Vvar__0__A__43746,Vvar__1__R__43747,Vvar__2___24Anonymous__43752)
           => ( Vvar__2___24Anonymous__43752 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__43746)
              | ? [Vvar__2__a__43766] :
                  ( t(Vvar__2__a__43766,Vvar__0__A__43746)
                  & Vvar__2___24Anonymous__43752 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__43746,Vvar__2__a__43766,cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__43746)) )
              | ? [Vvar__2__a__43773] :
                  ( t(Vvar__2__a__43773,Vvar__0__A__43746)
                  & ? [Vvar__3__b__43774] :
                      ( t(Vvar__3__b__43774,Vvar__0__A__43746)
                      & ? [Vvar__4__l__43775] :
                          ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__43746,Vvar__4__l__43775)
                          & cCoq_2eSorting_2eSorted_2eLocallySorted___24a3(Vvar__0__A__43746,Vvar__1__R__43747,cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__43746,Vvar__3__b__43774,Vvar__4__l__43775))
                          & p(happ(happ(Vvar__1__R__43747,Vvar__2__a__43773),Vvar__3__b__43774))
                          & Vvar__2___24Anonymous__43752 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__43746,Vvar__2__a__43773,cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__43746,Vvar__3__b__43774,Vvar__4__l__43775)) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Sorting.Sorted.Sorted',axiom,
    ! [Vvar__0__A__43789,Vvar__1__R__43790,Vvar__2___24Anonymous__43795] :
      ( cType___24t(Vvar__0__A__43789)
     => ( c_24__type__43822___24t(Vvar__0__A__43789,Vvar__1__R__43790,Vvar__2___24Anonymous__43795,Vvar__1__R__43790)
       => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__43789,Vvar__2___24Anonymous__43795)
         => ( cCoq_2eSorting_2eSorted_2eSorted___24a3(Vvar__0__A__43789,Vvar__1__R__43790,Vvar__2___24Anonymous__43795)
           => ( Vvar__2___24Anonymous__43795 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__43789)
              | ? [Vvar__2__a__43809] :
                  ( t(Vvar__2__a__43809,Vvar__0__A__43789)
                  & ? [Vvar__3__l__43810] :
                      ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__43789,Vvar__3__l__43810)
                      & cCoq_2eSorting_2eSorted_2eSorted___24a3(Vvar__0__A__43789,Vvar__1__R__43790,Vvar__3__l__43810)
                      & cCoq_2eSorting_2eSorted_2eHdRel___24a4(Vvar__0__A__43789,Vvar__1__R__43790,Vvar__2__a__43809,Vvar__3__l__43810)
                      & Vvar__2___24Anonymous__43795 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__43789,Vvar__2__a__43809,Vvar__3__l__43810) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Sorting.Sorted.StronglySorted',axiom,
    ! [Vvar__0__A__43824,Vvar__1__R__43825,Vvar__2___24Anonymous__43830] :
      ( cType___24t(Vvar__0__A__43824)
     => ( c_24__type__43857___24t(Vvar__0__A__43824,Vvar__1__R__43825,Vvar__2___24Anonymous__43830,Vvar__1__R__43825)
       => ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__43824,Vvar__2___24Anonymous__43830)
         => ( cCoq_2eSorting_2eSorted_2eStronglySorted___24a3(Vvar__0__A__43824,Vvar__1__R__43825,Vvar__2___24Anonymous__43830)
           => ( Vvar__2___24Anonymous__43830 = cCoq_2eInit_2eDatatypes_2enil___24a1(Vvar__0__A__43824)
              | ? [Vvar__2__a__43844] :
                  ( t(Vvar__2__a__43844,Vvar__0__A__43824)
                  & ? [Vvar__3__l__43845] :
                      ( cCoq_2eInit_2eDatatypes_2elist___24t(Vvar__0__A__43824,Vvar__3__l__43845)
                      & cCoq_2eSorting_2eSorted_2eStronglySorted___24a3(Vvar__0__A__43824,Vvar__1__R__43825,Vvar__3__l__43845)
                      & cCoq_2eLists_2eList_2eForall___24a3(Vvar__0__A__43824,happ(Vvar__1__R__43825,Vvar__2__a__43844),Vvar__3__l__43845)
                      & Vvar__2___24Anonymous__43830 = cCoq_2eInit_2eDatatypes_2econs___24a3(Vvar__0__A__43824,Vvar__2__a__43844,Vvar__3__l__43845) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Strings.Ascii.ascii',axiom,
    ! [VX15793] :
      ( cCoq_2eStrings_2eAscii_2eascii___24t(VX15793)
     => ? [Vvar__0___24Anonymous__15794] :
          ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__0___24Anonymous__15794)
          & ? [Vvar__1___24Anonymous__15795] :
              ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__1___24Anonymous__15795)
              & ? [Vvar__2___24Anonymous__15796] :
                  ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__2___24Anonymous__15796)
                  & ? [Vvar__3___24Anonymous__15797] :
                      ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__3___24Anonymous__15797)
                      & ? [Vvar__4___24Anonymous__15798] :
                          ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__4___24Anonymous__15798)
                          & ? [Vvar__5___24Anonymous__15799] :
                              ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__5___24Anonymous__15799)
                              & ? [Vvar__6___24Anonymous__15800] :
                                  ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__6___24Anonymous__15800)
                                  & ? [Vvar__7___24Anonymous__15801] :
                                      ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vvar__7___24Anonymous__15801)
                                      & VX15793 = cCoq_2eStrings_2eAscii_2eAscii___24a8(Vvar__0___24Anonymous__15794,Vvar__1___24Anonymous__15795,Vvar__2___24Anonymous__15796,Vvar__3___24Anonymous__15797,Vvar__4___24Anonymous__15798,Vvar__5___24Anonymous__15799,Vvar__6___24Anonymous__15800,Vvar__7___24Anonymous__15801) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Strings.String.string',axiom,
    ! [VX127] :
      ( cCoq_2eStrings_2eString_2estring___24t(VX127)
     => ( VX127 = cCoq_2eStrings_2eString_2eEmptyString
        | ? [Vvar__0___24Anonymous__128] :
            ( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__0___24Anonymous__128)
            & ? [Vvar__1___24Anonymous__129] :
                ( cCoq_2eStrings_2eString_2estring___24t(Vvar__1___24Anonymous__129)
                & VX127 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0___24Anonymous__128,Vvar__1___24Anonymous__129) ) ) ) ) ).

fof('$_inversion_Coq.Structures.OrderedType.Compare',axiom,
    ! [Vvar__0__X__32443,Vvar__1__lt__32444,Vvar__2__eq__32449,Vvar__3__x__32454,Vvar__4__y__32455,VX32456] :
      ( cType___24t(Vvar__0__X__32443)
     => ( c_24__type__32516___24t(Vvar__0__X__32443,Vvar__1__lt__32444,Vvar__2__eq__32449,Vvar__3__x__32454,Vvar__4__y__32455,Vvar__1__lt__32444)
       => ( c_24__type__32535___24t(Vvar__0__X__32443,Vvar__1__lt__32444,Vvar__2__eq__32449,Vvar__3__x__32454,Vvar__4__y__32455,Vvar__2__eq__32449)
         => ( t(Vvar__3__x__32454,Vvar__0__X__32443)
           => ( t(Vvar__4__y__32455,Vvar__0__X__32443)
             => ( cCoq_2eStructures_2eOrderedType_2eCompare___24t(Vvar__0__X__32443,Vvar__1__lt__32444,Vvar__2__eq__32449,Vvar__3__x__32454,Vvar__4__y__32455,VX32456)
               => ( ( p(happ(happ(Vvar__1__lt__32444,Vvar__3__x__32454),Vvar__4__y__32455))
                    & VX32456 = cCoq_2eStructures_2eOrderedType_2eLT___24a5(Vvar__0__X__32443,Vvar__1__lt__32444,Vvar__2__eq__32449,Vvar__3__x__32454,Vvar__4__y__32455) )
                  | ( p(happ(happ(Vvar__2__eq__32449,Vvar__3__x__32454),Vvar__4__y__32455))
                    & VX32456 = cCoq_2eStructures_2eOrderedType_2eEQ___24a5(Vvar__0__X__32443,Vvar__1__lt__32444,Vvar__2__eq__32449,Vvar__3__x__32454,Vvar__4__y__32455) )
                  | ( p(happ(happ(Vvar__1__lt__32444,Vvar__4__y__32455),Vvar__3__x__32454))
                    & VX32456 = cCoq_2eStructures_2eOrderedType_2eGT___24a5(Vvar__0__X__32443,Vvar__1__lt__32444,Vvar__2__eq__32449,Vvar__3__x__32454,Vvar__4__y__32455) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Structures.OrderedTypeEx.String_as_OT.lts',axiom,
    ! [Vvar__0___24Anonymous__30518,Vvar__1___24Anonymous__30519] :
      ( cCoq_2eStrings_2eString_2estring___24t(Vvar__0___24Anonymous__30518)
     => ( cCoq_2eStrings_2eString_2estring___24t(Vvar__1___24Anonymous__30519)
       => ( cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2elts___24a2(Vvar__0___24Anonymous__30518,Vvar__1___24Anonymous__30519)
         => ( ? [Vvar__0__a__30521] :
                ( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__0__a__30521)
                & ? [Vvar__1__s__30522] :
                    ( cCoq_2eStrings_2eString_2estring___24t(Vvar__1__s__30522)
                    & Vvar__1___24Anonymous__30519 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0__a__30521,Vvar__1__s__30522)
                    & Vvar__0___24Anonymous__30518 = cCoq_2eStrings_2eString_2eEmptyString ) )
            | ? [Vvar__0__a__30523] :
                ( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__0__a__30523)
                & ? [Vvar__1__s1__30524] :
                    ( cCoq_2eStrings_2eString_2estring___24t(Vvar__1__s1__30524)
                    & ? [Vvar__2__s2__30525] :
                        ( cCoq_2eStrings_2eString_2estring___24t(Vvar__2__s2__30525)
                        & cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2elts___24a2(Vvar__1__s1__30524,Vvar__2__s2__30525)
                        & Vvar__1___24Anonymous__30519 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0__a__30523,Vvar__2__s2__30525)
                        & Vvar__0___24Anonymous__30518 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0__a__30523,Vvar__1__s1__30524) ) ) )
            | ? [Vvar__0__a__30527] :
                ( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__0__a__30527)
                & ? [Vvar__1__b__30528] :
                    ( cCoq_2eStrings_2eAscii_2eascii___24t(Vvar__1__b__30528)
                    & ? [Vvar__2__s1__30529] :
                        ( cCoq_2eStrings_2eString_2estring___24t(Vvar__2__s1__30529)
                        & ? [Vvar__3__s2__30530] :
                            ( cCoq_2eStrings_2eString_2estring___24t(Vvar__3__s2__30530)
                            & cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eStrings_2eAscii_2enat__of__ascii___24a1(Vvar__0__a__30527),cCoq_2eStrings_2eAscii_2enat__of__ascii___24a1(Vvar__1__b__30528))
                            & Vvar__1___24Anonymous__30519 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__1__b__30528,Vvar__3__s2__30530)
                            & Vvar__0___24Anonymous__30518 = cCoq_2eStrings_2eString_2eString___24a2(Vvar__0__a__30527,Vvar__2__s1__30529) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Structures.OrdersTac.ord',axiom,
    ! [VX30899] :
      ( cCoq_2eStructures_2eOrdersTac_2eord___24t(VX30899)
     => ( VX30899 = cCoq_2eStructures_2eOrdersTac_2eOEQ
        | VX30899 = cCoq_2eStructures_2eOrdersTac_2eOLT
        | VX30899 = cCoq_2eStructures_2eOrdersTac_2eOLE ) ) ).

fof('$_inversion_Coq.Vectors.Fin.t',axiom,
    ! [Vvar__0___24Anonymous__24993,VX24994] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__24993)
     => ( cCoq_2eVectors_2eFin_2et___24t(Vvar__0___24Anonymous__24993,VX24994)
       => ( ? [Vvar__0__n__24995] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__24995)
              & Vvar__0___24Anonymous__24993 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0__n__24995)
              & VX24994 = cCoq_2eVectors_2eFin_2eF1___24a1(Vvar__0__n__24995) )
          | ? [Vvar__0__n__24996] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__24996)
              & ? [Vvar__1___24Anonymous__24997] :
                  ( cCoq_2eVectors_2eFin_2et___24t(Vvar__0__n__24996,Vvar__1___24Anonymous__24997)
                  & Vvar__0___24Anonymous__24993 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0__n__24996)
                  & VX24994 = cCoq_2eVectors_2eFin_2eFS___24a2(Vvar__0__n__24996,Vvar__1___24Anonymous__24997) ) ) ) ) ) ).

fof('$_inversion_Coq.Vectors.VectorDef.Forall',axiom,
    ! [Vvar__0__A__43919,Vvar__1__P__43920,Vvar__2__n__43923,Vvar__3__v__43924] :
      ( cType___24t(Vvar__0__A__43919)
     => ( c_24__type__43944___24t(Vvar__0__A__43919,Vvar__1__P__43920,Vvar__2__n__43923,Vvar__3__v__43924,Vvar__1__P__43920)
       => ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__43923)
         => ( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__43919,Vvar__2__n__43923,Vvar__3__v__43924)
           => ( cCoq_2eVectors_2eVectorDef_2eForall___24a4(Vvar__0__A__43919,Vvar__1__P__43920,Vvar__2__n__43923,Vvar__3__v__43924)
             => ( ( Vvar__3__v__43924 = cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__43919)
                  & Vvar__2__n__43923 = cCoq_2eInit_2eDatatypes_2eO )
                | ? [Vvar__2__n__43934] :
                    ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__43934)
                    & ? [Vvar__3__x__43935] :
                        ( t(Vvar__3__x__43935,Vvar__0__A__43919)
                        & ? [Vvar__4__v__43936] :
                            ( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__43919,Vvar__2__n__43934,Vvar__4__v__43936)
                            & p(happ(Vvar__1__P__43920,Vvar__3__x__43935))
                            & cCoq_2eVectors_2eVectorDef_2eForall___24a4(Vvar__0__A__43919,Vvar__1__P__43920,Vvar__2__n__43934,Vvar__4__v__43936)
                            & Vvar__3__v__43924 = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__43919,Vvar__3__x__43935,Vvar__2__n__43934,Vvar__4__v__43936)
                            & Vvar__2__n__43923 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__n__43934) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Vectors.VectorDef.Forall2',axiom,
    ! [Vvar__0__A__43946,Vvar__1__B__43947,Vvar__2__P__43948,Vvar__3__n__43953,Vvar__4___24Anonymous__43954,Vvar__5___24Anonymous__43955] :
      ( cType___24t(Vvar__0__A__43946)
     => ( cType___24t(Vvar__1__B__43947)
       => ( c_24__type__43995___24t(Vvar__0__A__43946,Vvar__1__B__43947,Vvar__2__P__43948,Vvar__3__n__43953,Vvar__4___24Anonymous__43954,Vvar__5___24Anonymous__43955,Vvar__2__P__43948)
         => ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__3__n__43953)
           => ( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__43946,Vvar__3__n__43953,Vvar__4___24Anonymous__43954)
             => ( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__1__B__43947,Vvar__3__n__43953,Vvar__5___24Anonymous__43955)
               => ( cCoq_2eVectors_2eVectorDef_2eForall2___24a6(Vvar__0__A__43946,Vvar__1__B__43947,Vvar__2__P__43948,Vvar__3__n__43953,Vvar__4___24Anonymous__43954,Vvar__5___24Anonymous__43955)
                 => ( ( Vvar__5___24Anonymous__43955 = cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__1__B__43947)
                      & Vvar__4___24Anonymous__43954 = cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__43946)
                      & Vvar__3__n__43953 = cCoq_2eInit_2eDatatypes_2eO )
                    | ? [Vvar__3__m__43971] :
                        ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__3__m__43971)
                        & ? [Vvar__4__x1__43972] :
                            ( t(Vvar__4__x1__43972,Vvar__0__A__43946)
                            & ? [Vvar__5__x2__43973] :
                                ( t(Vvar__5__x2__43973,Vvar__1__B__43947)
                                & ? [Vvar__6__v1__43974] :
                                    ( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__43946,Vvar__3__m__43971,Vvar__6__v1__43974)
                                    & ? [Vvar__7__v2__43975] :
                                        ( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__1__B__43947,Vvar__3__m__43971,Vvar__7__v2__43975)
                                        & p(happ(happ(Vvar__2__P__43948,Vvar__4__x1__43972),Vvar__5__x2__43973))
                                        & cCoq_2eVectors_2eVectorDef_2eForall2___24a6(Vvar__0__A__43946,Vvar__1__B__43947,Vvar__2__P__43948,Vvar__3__m__43971,Vvar__6__v1__43974,Vvar__7__v2__43975)
                                        & Vvar__5___24Anonymous__43955 = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__1__B__43947,Vvar__5__x2__43973,Vvar__3__m__43971,Vvar__7__v2__43975)
                                        & Vvar__4___24Anonymous__43954 = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__43946,Vvar__4__x1__43972,Vvar__3__m__43971,Vvar__6__v1__43974)
                                        & Vvar__3__n__43953 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__3__m__43971) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.Vectors.VectorDef.t',axiom,
    ! [Vvar__0__A__28928,Vvar__1___24Anonymous__28929,VX28930] :
      ( cType___24t(Vvar__0__A__28928)
     => ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__28929)
       => ( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__28928,Vvar__1___24Anonymous__28929,VX28930)
         => ( ( Vvar__1___24Anonymous__28929 = cCoq_2eInit_2eDatatypes_2eO
              & VX28930 = cCoq_2eVectors_2eVectorDef_2enil___24a1(Vvar__0__A__28928) )
            | ? [Vvar__1__h__28933] :
                ( t(Vvar__1__h__28933,Vvar__0__A__28928)
                & ? [Vvar__2__n__28934] :
                    ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__28934)
                    & ? [Vvar__3___24Anonymous__28935] :
                        ( cCoq_2eVectors_2eVectorDef_2et___24t(Vvar__0__A__28928,Vvar__2__n__28934,Vvar__3___24Anonymous__28935)
                        & Vvar__1___24Anonymous__28929 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__2__n__28934)
                        & VX28930 = cCoq_2eVectors_2eVectorDef_2econs___24a4(Vvar__0__A__28928,Vvar__1__h__28933,Vvar__2__n__28934,Vvar__3___24Anonymous__28935) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.ZArith.Znumtheory.Bezout',axiom,
    ! [Vvar__0__a__34840,Vvar__1__b__34841,Vvar__2__d__34842] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__a__34840)
     => ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__1__b__34841)
       => ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2__d__34842)
         => ( cCoq_2eZArith_2eZnumtheory_2eBezout___24a3(Vvar__0__a__34840,Vvar__1__b__34841,Vvar__2__d__34842)
           => ? [Vvar__3__u__34847] :
                ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3__u__34847)
                & ? [Vvar__4__v__34848] :
                    ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__4__v__34848)
                    & cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__3__u__34847,Vvar__0__a__34840),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__4__v__34848,Vvar__1__b__34841)) = Vvar__2__d__34842
                    & p(c_24True) ) ) ) ) ) ) ).

fof('$_inversion_Coq.ZArith.Znumtheory.Euclid',axiom,
    ! [Vvar__0__a__34815,Vvar__1__b__34816,VX34817] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__a__34815)
     => ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__1__b__34816)
       => ( cCoq_2eZArith_2eZnumtheory_2eEuclid___24t(Vvar__0__a__34815,Vvar__1__b__34816,VX34817)
         => ? [Vvar__2__u__34820] :
              ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2__u__34820)
              & ? [Vvar__3__v__34821] :
                  ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3__v__34821)
                  & ? [Vvar__4__d__34822] :
                      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__4__d__34822)
                      & cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__2__u__34820,Vvar__0__a__34815),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__3__v__34821,Vvar__1__b__34816)) = Vvar__4__d__34822
                      & cCoq_2eZArith_2eZnumtheory_2eZis__gcd___24a3(Vvar__0__a__34815,Vvar__1__b__34816,Vvar__4__d__34822)
                      & VX34817 = cCoq_2eZArith_2eZnumtheory_2eEuclid__intro___24a5(Vvar__0__a__34815,Vvar__1__b__34816,Vvar__2__u__34820,Vvar__3__v__34821,Vvar__4__d__34822) ) ) ) ) ) ) ).

fof('$_inversion_Coq.ZArith.Znumtheory.Zis_gcd',axiom,
    ! [Vvar__0__a__29155,Vvar__1__b__29156,Vvar__2__g__29157] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__a__29155)
     => ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__1__b__29156)
       => ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2__g__29157)
         => ( cCoq_2eZArith_2eZnumtheory_2eZis__gcd___24a3(Vvar__0__a__29155,Vvar__1__b__29156,Vvar__2__g__29157)
           => ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__2__g__29157,Vvar__0__a__29155)
              & cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__2__g__29157,Vvar__1__b__29156)
              & ! [Vvar__var__var__var__var__5__x__29165__29168__29171__29174__29177] :
                  ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__var__var__var__var__5__x__29165__29168__29171__29174__29177)
                 => ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__var__var__var__var__5__x__29165__29168__29171__29174__29177,Vvar__0__a__29155)
                   => ( cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__var__var__var__var__5__x__29165__29168__29171__29174__29177,Vvar__1__b__29156)
                     => cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(Vvar__var__var__var__var__5__x__29165__29168__29171__29174__29177,Vvar__2__g__29157) ) ) )
              & p(c_24True) ) ) ) ) ) ).

fof('$_inversion_Coq.ZArith.Znumtheory.prime',axiom,
    ! [Vvar__0__p__30969] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__p__30969)
     => ( cCoq_2eZArith_2eZnumtheory_2eprime___24a1(Vvar__0__p__30969)
       => ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),Vvar__0__p__30969))
          & ! [Vvar__var__var__2__n__30974__30976__30978] :
              ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__var__var__2__n__30974__30976__30978)
             => ( ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH),Vvar__var__var__2__n__30974__30976__30978))
                  & p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(Vvar__var__var__2__n__30974__30976__30978,Vvar__0__p__30969)) )
               => cCoq_2eZArith_2eZnumtheory_2erel__prime___24a2(Vvar__var__var__2__n__30974__30976__30978,Vvar__0__p__30969) ) )
          & p(c_24True) ) ) ) ).

fof('$_inversion_Coq.ZArith.Zpower.Zdiv_rest_proofs',axiom,
    ! [Vvar__0__x__34850,Vvar__1__p__34851,VX34852] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__x__34850)
     => ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__p__34851)
       => ( cCoq_2eZArith_2eZpower_2eZdiv__rest__proofs___24t(Vvar__0__x__34850,Vvar__1__p__34851,VX34852)
         => ? [Vvar__2__q__34855] :
              ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__2__q__34855)
              & ? [Vvar__3__r__34856] :
                  ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__3__r__34856)
                  & Vvar__0__x__34850 = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(Vvar__2__q__34855,cCoq_2eZArith_2eZpower_2etwo__power__pos___24a1(Vvar__1__p__34851)),Vvar__3__r__34856)
                  & p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,Vvar__3__r__34856))
                  & p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(Vvar__3__r__34856,cCoq_2eZArith_2eZpower_2etwo__power__pos___24a1(Vvar__1__p__34851)))
                  & VX34852 = cCoq_2eZArith_2eZpower_2eZdiv__rest__proof___24a4(Vvar__0__x__34850,Vvar__1__p__34851,Vvar__2__q__34855,Vvar__3__r__34856) ) ) ) ) ) ).

fof('$_inversion_Coq.micromega.DeclConstant.DeclaredConstant',axiom,
    ! [Vvar__0__T__24096,Vvar__1__F__24097] :
      ( cType___24t(Vvar__0__T__24096)
     => ( t(Vvar__1__F__24097,Vvar__0__T__24096)
       => ( cCoq_2emicromega_2eDeclConstant_2eDeclaredConstant___24a2(Vvar__0__T__24096,Vvar__1__F__24097)
         => p(c_24True) ) ) ) ).

fof('$_inversion_Coq.micromega.DeclConstant.GT',axiom,
    ! [Vvar__0__T__31136,Vvar__1__F__31137] :
      ( cType___24t(Vvar__0__T__31136)
     => ( t(Vvar__1__F__31137,Vvar__0__T__31136)
       => ( cCoq_2emicromega_2eDeclConstant_2eGT___24a2(Vvar__0__T__31136,Vvar__1__F__31137)
         => p(c_24True) ) ) ) ).

fof('$_inversion_Coq.micromega.EnvRing.Mon',axiom,
    ! [VX30848] :
      ( cCoq_2emicromega_2eEnvRing_2eMon___24t(VX30848)
     => ( VX30848 = cCoq_2emicromega_2eEnvRing_2emon0
        | ? [Vvar__0___24Anonymous__30849] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30849)
            & ? [Vvar__1___24Anonymous__30850] :
                ( cCoq_2emicromega_2eEnvRing_2eMon___24t(Vvar__1___24Anonymous__30850)
                & VX30848 = cCoq_2emicromega_2eEnvRing_2ezmon___24a2(Vvar__0___24Anonymous__30849,Vvar__1___24Anonymous__30850) ) )
        | ? [Vvar__0___24Anonymous__30851] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__30851)
            & ? [Vvar__1___24Anonymous__30852] :
                ( cCoq_2emicromega_2eEnvRing_2eMon___24t(Vvar__1___24Anonymous__30852)
                & VX30848 = cCoq_2emicromega_2eEnvRing_2evmon___24a2(Vvar__0___24Anonymous__30851,Vvar__1___24Anonymous__30852) ) ) ) ) ).

fof('$_inversion_Coq.micromega.EnvRing.PExpr',axiom,
    ! [Vvar__0__C__24101,VX24102] :
      ( cType___24t(Vvar__0__C__24101)
     => ( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__24101,VX24102)
       => ( ? [Vvar__1___24Anonymous__24104] :
              ( t(Vvar__1___24Anonymous__24104,Vvar__0__C__24101)
              & VX24102 = cCoq_2emicromega_2eEnvRing_2ePEc___24a2(Vvar__0__C__24101,Vvar__1___24Anonymous__24104) )
          | ? [Vvar__1___24Anonymous__24106] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__24106)
              & VX24102 = cCoq_2emicromega_2eEnvRing_2ePEX___24a2(Vvar__0__C__24101,Vvar__1___24Anonymous__24106) )
          | ? [Vvar__1___24Anonymous__24108] :
              ( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__24101,Vvar__1___24Anonymous__24108)
              & ? [Vvar__2___24Anonymous__24109] :
                  ( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__24101,Vvar__2___24Anonymous__24109)
                  & VX24102 = cCoq_2emicromega_2eEnvRing_2ePEadd___24a3(Vvar__0__C__24101,Vvar__1___24Anonymous__24108,Vvar__2___24Anonymous__24109) ) )
          | ? [Vvar__1___24Anonymous__24111] :
              ( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__24101,Vvar__1___24Anonymous__24111)
              & ? [Vvar__2___24Anonymous__24112] :
                  ( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__24101,Vvar__2___24Anonymous__24112)
                  & VX24102 = cCoq_2emicromega_2eEnvRing_2ePEsub___24a3(Vvar__0__C__24101,Vvar__1___24Anonymous__24111,Vvar__2___24Anonymous__24112) ) )
          | ? [Vvar__1___24Anonymous__24114] :
              ( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__24101,Vvar__1___24Anonymous__24114)
              & ? [Vvar__2___24Anonymous__24115] :
                  ( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__24101,Vvar__2___24Anonymous__24115)
                  & VX24102 = cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(Vvar__0__C__24101,Vvar__1___24Anonymous__24114,Vvar__2___24Anonymous__24115) ) )
          | ? [Vvar__1___24Anonymous__24117] :
              ( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__24101,Vvar__1___24Anonymous__24117)
              & VX24102 = cCoq_2emicromega_2eEnvRing_2ePEopp___24a2(Vvar__0__C__24101,Vvar__1___24Anonymous__24117) )
          | ? [Vvar__1___24Anonymous__24119] :
              ( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__C__24101,Vvar__1___24Anonymous__24119)
              & ? [Vvar__2___24Anonymous__24120] :
                  ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__24120)
                  & VX24102 = cCoq_2emicromega_2eEnvRing_2ePEpow___24a3(Vvar__0__C__24101,Vvar__1___24Anonymous__24119,Vvar__2___24Anonymous__24120) ) ) ) ) ) ).

fof('$_inversion_Coq.micromega.EnvRing.Pol',axiom,
    ! [Vvar__0__C__30801,VX30802] :
      ( cType___24t(Vvar__0__C__30801)
     => ( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__30801,VX30802)
       => ( ? [Vvar__1___24Anonymous__30804] :
              ( t(Vvar__1___24Anonymous__30804,Vvar__0__C__30801)
              & VX30802 = cCoq_2emicromega_2eEnvRing_2ePc___24a2(Vvar__0__C__30801,Vvar__1___24Anonymous__30804) )
          | ? [Vvar__1___24Anonymous__30806] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__30806)
              & ? [Vvar__2___24Anonymous__30807] :
                  ( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__30801,Vvar__2___24Anonymous__30807)
                  & VX30802 = cCoq_2emicromega_2eEnvRing_2ePinj___24a3(Vvar__0__C__30801,Vvar__1___24Anonymous__30806,Vvar__2___24Anonymous__30807) ) )
          | ? [Vvar__1___24Anonymous__30809] :
              ( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__30801,Vvar__1___24Anonymous__30809)
              & ? [Vvar__2___24Anonymous__30810] :
                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__30810)
                  & ? [Vvar__3___24Anonymous__30811] :
                      ( cCoq_2emicromega_2eEnvRing_2ePol___24t(Vvar__0__C__30801,Vvar__3___24Anonymous__30811)
                      & VX30802 = cCoq_2emicromega_2eEnvRing_2ePX___24a4(Vvar__0__C__30801,Vvar__1___24Anonymous__30809,Vvar__2___24Anonymous__30810,Vvar__3___24Anonymous__30811) ) ) ) ) ) ) ).

fof('$_inversion_Coq.micromega.OrderedRing.SOR',axiom,
    ! [Vvar__0__R__5501,Vvar__1__rO__5502,Vvar__2__rI__5503,Vvar__3__rplus__5504,Vvar__4__rtimes__5509,Vvar__5__rminus__5514,Vvar__6__ropp__5519,Vvar__7__req__5522,Vvar__8__rle__5527,Vvar__9__rlt__5532] :
      ( cType___24t(Vvar__0__R__5501)
     => ( t(Vvar__1__rO__5502,Vvar__0__R__5501)
       => ( t(Vvar__2__rI__5503,Vvar__0__R__5501)
         => ( c_24__type__5933___24t(Vvar__0__R__5501,Vvar__1__rO__5502,Vvar__2__rI__5503,Vvar__3__rplus__5504,Vvar__4__rtimes__5509,Vvar__5__rminus__5514,Vvar__6__ropp__5519,Vvar__7__req__5522,Vvar__8__rle__5527,Vvar__9__rlt__5532,Vvar__3__rplus__5504)
           => ( c_24__type__6034___24t(Vvar__0__R__5501,Vvar__1__rO__5502,Vvar__2__rI__5503,Vvar__3__rplus__5504,Vvar__4__rtimes__5509,Vvar__5__rminus__5514,Vvar__6__ropp__5519,Vvar__7__req__5522,Vvar__8__rle__5527,Vvar__9__rlt__5532,Vvar__4__rtimes__5509)
             => ( c_24__type__6135___24t(Vvar__0__R__5501,Vvar__1__rO__5502,Vvar__2__rI__5503,Vvar__3__rplus__5504,Vvar__4__rtimes__5509,Vvar__5__rminus__5514,Vvar__6__ropp__5519,Vvar__7__req__5522,Vvar__8__rle__5527,Vvar__9__rlt__5532,Vvar__5__rminus__5514)
               => ( c_24__type__6225___24t(Vvar__0__R__5501,Vvar__1__rO__5502,Vvar__2__rI__5503,Vvar__3__rplus__5504,Vvar__4__rtimes__5509,Vvar__5__rminus__5514,Vvar__6__ropp__5519,Vvar__7__req__5522,Vvar__8__rle__5527,Vvar__9__rlt__5532,Vvar__6__ropp__5519)
                 => ( c_24__type__6326___24t(Vvar__0__R__5501,Vvar__1__rO__5502,Vvar__2__rI__5503,Vvar__3__rplus__5504,Vvar__4__rtimes__5509,Vvar__5__rminus__5514,Vvar__6__ropp__5519,Vvar__7__req__5522,Vvar__8__rle__5527,Vvar__9__rlt__5532,Vvar__7__req__5522)
                   => ( c_24__type__6427___24t(Vvar__0__R__5501,Vvar__1__rO__5502,Vvar__2__rI__5503,Vvar__3__rplus__5504,Vvar__4__rtimes__5509,Vvar__5__rminus__5514,Vvar__6__ropp__5519,Vvar__7__req__5522,Vvar__8__rle__5527,Vvar__9__rlt__5532,Vvar__8__rle__5527)
                     => ( c_24__type__6528___24t(Vvar__0__R__5501,Vvar__1__rO__5502,Vvar__2__rI__5503,Vvar__3__rplus__5504,Vvar__4__rtimes__5509,Vvar__5__rminus__5514,Vvar__6__ropp__5519,Vvar__7__req__5522,Vvar__8__rle__5527,Vvar__9__rlt__5532,Vvar__9__rlt__5532)
                       => ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(Vvar__0__R__5501,Vvar__1__rO__5502,Vvar__2__rI__5503,Vvar__3__rplus__5504,Vvar__4__rtimes__5509,Vvar__5__rminus__5514,Vvar__6__ropp__5519,Vvar__7__req__5522,Vvar__8__rle__5527,Vvar__9__rlt__5532)
                         => ( cCoq_2eSetoids_2eSetoid_2eSetoid__Theory___24a2(Vvar__0__R__5501,Vvar__7__req__5522)
                            & ! [Vvar__var__var__var__var__11__x1__5576__5582__5687__5693__5699] :
                                ( t(Vvar__var__var__var__var__11__x1__5576__5582__5687__5693__5699,Vvar__0__R__5501)
                               => ! [Vvar__var__var__var__var__12__x2__5577__5583__5688__5694__5700] :
                                    ( t(Vvar__var__var__var__var__12__x2__5577__5583__5688__5694__5700,Vvar__0__R__5501)
                                   => ( p(happ(happ(Vvar__7__req__5522,Vvar__var__var__var__var__11__x1__5576__5582__5687__5693__5699),Vvar__var__var__var__var__12__x2__5577__5583__5688__5694__5700))
                                     => ! [Vvar__var__var__var__var__14__y1__5578__5584__5689__5695__5701] :
                                          ( t(Vvar__var__var__var__var__14__y1__5578__5584__5689__5695__5701,Vvar__0__R__5501)
                                         => ! [Vvar__var__var__var__var__15__y2__5579__5585__5690__5696__5702] :
                                              ( t(Vvar__var__var__var__var__15__y2__5579__5585__5690__5696__5702,Vvar__0__R__5501)
                                             => ( p(happ(happ(Vvar__7__req__5522,Vvar__var__var__var__var__14__y1__5578__5584__5689__5695__5701),Vvar__var__var__var__var__15__y2__5579__5585__5690__5696__5702))
                                               => p(happ(happ(Vvar__7__req__5522,happ(happ(Vvar__3__rplus__5504,Vvar__var__var__var__var__11__x1__5576__5582__5687__5693__5699),Vvar__var__var__var__var__14__y1__5578__5584__5689__5695__5701)),happ(happ(Vvar__3__rplus__5504,Vvar__var__var__var__var__12__x2__5577__5583__5688__5694__5700),Vvar__var__var__var__var__15__y2__5579__5585__5690__5696__5702))) ) ) ) ) ) )
                            & ! [Vvar__var__var__var__var__12__x1__5589__5595__5705__5711__5717] :
                                ( t(Vvar__var__var__var__var__12__x1__5589__5595__5705__5711__5717,Vvar__0__R__5501)
                               => ! [Vvar__var__var__var__var__13__x2__5590__5596__5706__5712__5718] :
                                    ( t(Vvar__var__var__var__var__13__x2__5590__5596__5706__5712__5718,Vvar__0__R__5501)
                                   => ( p(happ(happ(Vvar__7__req__5522,Vvar__var__var__var__var__12__x1__5589__5595__5705__5711__5717),Vvar__var__var__var__var__13__x2__5590__5596__5706__5712__5718))
                                     => ! [Vvar__var__var__var__var__15__y1__5591__5597__5707__5713__5719] :
                                          ( t(Vvar__var__var__var__var__15__y1__5591__5597__5707__5713__5719,Vvar__0__R__5501)
                                         => ! [Vvar__var__var__var__var__16__y2__5592__5598__5708__5714__5720] :
                                              ( t(Vvar__var__var__var__var__16__y2__5592__5598__5708__5714__5720,Vvar__0__R__5501)
                                             => ( p(happ(happ(Vvar__7__req__5522,Vvar__var__var__var__var__15__y1__5591__5597__5707__5713__5719),Vvar__var__var__var__var__16__y2__5592__5598__5708__5714__5720))
                                               => p(happ(happ(Vvar__7__req__5522,happ(happ(Vvar__4__rtimes__5509,Vvar__var__var__var__var__12__x1__5589__5595__5705__5711__5717),Vvar__var__var__var__var__15__y1__5591__5597__5707__5713__5719)),happ(happ(Vvar__4__rtimes__5509,Vvar__var__var__var__var__13__x2__5590__5596__5706__5712__5718),Vvar__var__var__var__var__16__y2__5592__5598__5708__5714__5720))) ) ) ) ) ) )
                            & ! [Vvar__var__var__var__var__13__x1__5602__5605__5723__5726__5729] :
                                ( t(Vvar__var__var__var__var__13__x1__5602__5605__5723__5726__5729,Vvar__0__R__5501)
                               => ! [Vvar__var__var__var__var__14__x2__5603__5606__5724__5727__5730] :
                                    ( t(Vvar__var__var__var__var__14__x2__5603__5606__5724__5727__5730,Vvar__0__R__5501)
                                   => ( p(happ(happ(Vvar__7__req__5522,Vvar__var__var__var__var__13__x1__5602__5605__5723__5726__5729),Vvar__var__var__var__var__14__x2__5603__5606__5724__5727__5730))
                                     => p(happ(happ(Vvar__7__req__5522,happ(Vvar__6__ropp__5519,Vvar__var__var__var__var__13__x1__5602__5605__5723__5726__5729)),happ(Vvar__6__ropp__5519,Vvar__var__var__var__var__14__x2__5603__5606__5724__5727__5730))) ) ) )
                            & ! [Vvar__var__var__var__var__14__x1__5609__5615__5732__5738__5744] :
                                ( t(Vvar__var__var__var__var__14__x1__5609__5615__5732__5738__5744,Vvar__0__R__5501)
                               => ! [Vvar__var__var__var__var__15__x2__5610__5616__5733__5739__5745] :
                                    ( t(Vvar__var__var__var__var__15__x2__5610__5616__5733__5739__5745,Vvar__0__R__5501)
                                   => ( p(happ(happ(Vvar__7__req__5522,Vvar__var__var__var__var__14__x1__5609__5615__5732__5738__5744),Vvar__var__var__var__var__15__x2__5610__5616__5733__5739__5745))
                                     => ! [Vvar__var__var__var__var__17__y1__5611__5617__5734__5740__5746] :
                                          ( t(Vvar__var__var__var__var__17__y1__5611__5617__5734__5740__5746,Vvar__0__R__5501)
                                         => ! [Vvar__var__var__var__var__18__y2__5612__5618__5735__5741__5747] :
                                              ( t(Vvar__var__var__var__var__18__y2__5612__5618__5735__5741__5747,Vvar__0__R__5501)
                                             => ( p(happ(happ(Vvar__7__req__5522,Vvar__var__var__var__var__17__y1__5611__5617__5734__5740__5746),Vvar__var__var__var__var__18__y2__5612__5618__5735__5741__5747))
                                               => ( p(happ(happ(Vvar__8__rle__5527,Vvar__var__var__var__var__14__x1__5609__5615__5732__5738__5744),Vvar__var__var__var__var__17__y1__5611__5617__5734__5740__5746))
                                                <=> p(happ(happ(Vvar__8__rle__5527,Vvar__var__var__var__var__15__x2__5610__5616__5733__5739__5745),Vvar__var__var__var__var__18__y2__5612__5618__5735__5741__5747)) ) ) ) ) ) ) )
                            & ! [Vvar__var__var__var__var__15__x1__5622__5628__5750__5756__5762] :
                                ( t(Vvar__var__var__var__var__15__x1__5622__5628__5750__5756__5762,Vvar__0__R__5501)
                               => ! [Vvar__var__var__var__var__16__x2__5623__5629__5751__5757__5763] :
                                    ( t(Vvar__var__var__var__var__16__x2__5623__5629__5751__5757__5763,Vvar__0__R__5501)
                                   => ( p(happ(happ(Vvar__7__req__5522,Vvar__var__var__var__var__15__x1__5622__5628__5750__5756__5762),Vvar__var__var__var__var__16__x2__5623__5629__5751__5757__5763))
                                     => ! [Vvar__var__var__var__var__18__y1__5624__5630__5752__5758__5764] :
                                          ( t(Vvar__var__var__var__var__18__y1__5624__5630__5752__5758__5764,Vvar__0__R__5501)
                                         => ! [Vvar__var__var__var__var__19__y2__5625__5631__5753__5759__5765] :
                                              ( t(Vvar__var__var__var__var__19__y2__5625__5631__5753__5759__5765,Vvar__0__R__5501)
                                             => ( p(happ(happ(Vvar__7__req__5522,Vvar__var__var__var__var__18__y1__5624__5630__5752__5758__5764),Vvar__var__var__var__var__19__y2__5625__5631__5753__5759__5765))
                                               => ( p(happ(happ(Vvar__9__rlt__5532,Vvar__var__var__var__var__15__x1__5622__5628__5750__5756__5762),Vvar__var__var__var__var__18__y1__5624__5630__5752__5758__5764))
                                                <=> p(happ(happ(Vvar__9__rlt__5532,Vvar__var__var__var__var__16__x2__5623__5629__5751__5757__5763),Vvar__var__var__var__var__19__y2__5625__5631__5753__5759__5765)) ) ) ) ) ) ) )
                            & cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(Vvar__0__R__5501,Vvar__1__rO__5502,Vvar__2__rI__5503,Vvar__3__rplus__5504,Vvar__4__rtimes__5509,Vvar__5__rminus__5514,Vvar__6__ropp__5519,Vvar__7__req__5522)
                            & ! [Vvar__var__var__var__17__n__5636__5637__5768__5769] :
                                ( t(Vvar__var__var__var__17__n__5636__5637__5768__5769,Vvar__0__R__5501)
                               => p(happ(happ(Vvar__8__rle__5527,Vvar__var__var__var__17__n__5636__5637__5768__5769),Vvar__var__var__var__17__n__5636__5637__5768__5769)) )
                            & ! [Vvar__var__var__var__var__18__n__5639__5643__5770__5774__5778] :
                                ( t(Vvar__var__var__var__var__18__n__5639__5643__5770__5774__5778,Vvar__0__R__5501)
                               => ! [Vvar__var__var__var__var__19__m__5640__5644__5771__5775__5779] :
                                    ( t(Vvar__var__var__var__var__19__m__5640__5644__5771__5775__5779,Vvar__0__R__5501)
                                   => ( p(happ(happ(Vvar__8__rle__5527,Vvar__var__var__var__var__18__n__5639__5643__5770__5774__5778),Vvar__var__var__var__var__19__m__5640__5644__5771__5775__5779))
                                     => ( p(happ(happ(Vvar__8__rle__5527,Vvar__var__var__var__var__19__m__5640__5644__5771__5775__5779),Vvar__var__var__var__var__18__n__5639__5643__5770__5774__5778))
                                       => p(happ(happ(Vvar__7__req__5522,Vvar__var__var__var__var__18__n__5639__5643__5770__5774__5778),Vvar__var__var__var__var__19__m__5640__5644__5771__5775__5779)) ) ) ) )
                            & ! [Vvar__var__var__var__19__n__5648__5653__5782__5787] :
                                ( t(Vvar__var__var__var__19__n__5648__5653__5782__5787,Vvar__0__R__5501)
                               => ! [Vvar__var__var__var__20__m__5649__5654__5783__5788] :
                                    ( t(Vvar__var__var__var__20__m__5649__5654__5783__5788,Vvar__0__R__5501)
                                   => ! [Vvar__var__var__var__21__p__5650__5655__5784__5789] :
                                        ( t(Vvar__var__var__var__21__p__5650__5655__5784__5789,Vvar__0__R__5501)
                                       => ( p(happ(happ(Vvar__8__rle__5527,Vvar__var__var__var__19__n__5648__5653__5782__5787),Vvar__var__var__var__20__m__5649__5654__5783__5788))
                                         => ( p(happ(happ(Vvar__8__rle__5527,Vvar__var__var__var__20__m__5649__5654__5783__5788),Vvar__var__var__var__21__p__5650__5655__5784__5789))
                                           => p(happ(happ(Vvar__8__rle__5527,Vvar__var__var__var__19__n__5648__5653__5782__5787),Vvar__var__var__var__21__p__5650__5655__5784__5789)) ) ) ) ) )
                            & ! [Vvar__var__var__var__var__var__20__n__5659__5661__5792__5794__5796__5798] :
                                ( t(Vvar__var__var__var__var__var__20__n__5659__5661__5792__5794__5796__5798,Vvar__0__R__5501)
                               => ! [Vvar__var__var__var__var__var__21__m__5660__5662__5793__5795__5797__5799] :
                                    ( t(Vvar__var__var__var__var__var__21__m__5660__5662__5793__5795__5797__5799,Vvar__0__R__5501)
                                   => ( p(happ(happ(Vvar__9__rlt__5532,Vvar__var__var__var__var__var__20__n__5659__5661__5792__5794__5796__5798),Vvar__var__var__var__var__var__21__m__5660__5662__5793__5795__5797__5799))
                                    <=> ( p(happ(happ(Vvar__8__rle__5527,Vvar__var__var__var__var__var__20__n__5659__5661__5792__5794__5796__5798),Vvar__var__var__var__var__var__21__m__5660__5662__5793__5795__5797__5799))
                                        & ~ p(happ(happ(Vvar__7__req__5522,Vvar__var__var__var__var__var__20__n__5659__5661__5792__5794__5796__5798),Vvar__var__var__var__var__var__21__m__5660__5662__5793__5795__5797__5799)) ) ) ) )
                            & ! [Vvar__var__var__var__var__21__n__5664__5666__5800__5802__5804] :
                                ( t(Vvar__var__var__var__var__21__n__5664__5666__5800__5802__5804,Vvar__0__R__5501)
                               => ! [Vvar__var__var__var__var__22__m__5665__5667__5801__5803__5805] :
                                    ( t(Vvar__var__var__var__var__22__m__5665__5667__5801__5803__5805,Vvar__0__R__5501)
                                   => ( p(happ(happ(Vvar__9__rlt__5532,Vvar__var__var__var__var__21__n__5664__5666__5800__5802__5804),Vvar__var__var__var__var__22__m__5665__5667__5801__5803__5805))
                                      | p(happ(happ(Vvar__7__req__5522,Vvar__var__var__var__var__21__n__5664__5666__5800__5802__5804),Vvar__var__var__var__var__22__m__5665__5667__5801__5803__5805))
                                      | p(happ(happ(Vvar__9__rlt__5532,Vvar__var__var__var__var__22__m__5665__5667__5801__5803__5805),Vvar__var__var__var__var__21__n__5664__5666__5800__5802__5804)) ) ) )
                            & ! [Vvar__var__var__var__var__22__n__5669__5673__5806__5810__5814] :
                                ( t(Vvar__var__var__var__var__22__n__5669__5673__5806__5810__5814,Vvar__0__R__5501)
                               => ! [Vvar__var__var__var__var__23__m__5670__5674__5807__5811__5815] :
                                    ( t(Vvar__var__var__var__var__23__m__5670__5674__5807__5811__5815,Vvar__0__R__5501)
                                   => ! [Vvar__var__var__var__var__24__p__5671__5675__5808__5812__5816] :
                                        ( t(Vvar__var__var__var__var__24__p__5671__5675__5808__5812__5816,Vvar__0__R__5501)
                                       => ( p(happ(happ(Vvar__8__rle__5527,Vvar__var__var__var__var__22__n__5669__5673__5806__5810__5814),Vvar__var__var__var__var__23__m__5670__5674__5807__5811__5815))
                                         => p(happ(happ(Vvar__8__rle__5527,happ(happ(Vvar__3__rplus__5504,Vvar__var__var__var__var__24__p__5671__5675__5808__5812__5816),Vvar__var__var__var__var__22__n__5669__5673__5806__5810__5814)),happ(happ(Vvar__3__rplus__5504,Vvar__var__var__var__var__24__p__5671__5675__5808__5812__5816),Vvar__var__var__var__var__23__m__5670__5674__5807__5811__5815))) ) ) ) )
                            & ! [Vvar__var__var__var__var__var__23__n__5678__5682__5818__5822__5826__5830] :
                                ( t(Vvar__var__var__var__var__var__23__n__5678__5682__5818__5822__5826__5830,Vvar__0__R__5501)
                               => ! [Vvar__var__var__var__var__var__24__m__5679__5683__5819__5823__5827__5831] :
                                    ( t(Vvar__var__var__var__var__var__24__m__5679__5683__5819__5823__5827__5831,Vvar__0__R__5501)
                                   => ( p(happ(happ(Vvar__9__rlt__5532,Vvar__1__rO__5502),Vvar__var__var__var__var__var__23__n__5678__5682__5818__5822__5826__5830))
                                     => ( p(happ(happ(Vvar__9__rlt__5532,Vvar__1__rO__5502),Vvar__var__var__var__var__var__24__m__5679__5683__5819__5823__5827__5831))
                                       => p(happ(happ(Vvar__9__rlt__5532,Vvar__1__rO__5502),happ(happ(Vvar__4__rtimes__5509,Vvar__var__var__var__var__var__23__n__5678__5682__5818__5822__5826__5830),Vvar__var__var__var__var__var__24__m__5679__5683__5819__5823__5827__5831))) ) ) ) )
                            & ~ p(happ(happ(Vvar__7__req__5522,Vvar__1__rO__5502),Vvar__2__rI__5503))
                            & p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.micromega.RMicromega.Rcst',axiom,
    ! [VX26028] :
      ( cCoq_2emicromega_2eRMicromega_2eRcst___24t(VX26028)
     => ( VX26028 = cCoq_2emicromega_2eRMicromega_2eC0
        | VX26028 = cCoq_2emicromega_2eRMicromega_2eC1
        | ? [Vvar__0__r__26029] :
            ( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vvar__0__r__26029)
            & VX26028 = cCoq_2emicromega_2eRMicromega_2eCQ___24a1(Vvar__0__r__26029) )
        | ? [Vvar__0__r__26030] :
            ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vvar__0__r__26030)
            & VX26028 = cCoq_2emicromega_2eRMicromega_2eCZ___24a1(Vvar__0__r__26030) )
        | ? [Vvar__0__r1__26031] :
            ( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r1__26031)
            & ? [Vvar__1__r2__26032] :
                ( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__1__r2__26032)
                & VX26028 = cCoq_2emicromega_2eRMicromega_2eCPlus___24a2(Vvar__0__r1__26031,Vvar__1__r2__26032) ) )
        | ? [Vvar__0__r1__26033] :
            ( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r1__26033)
            & ? [Vvar__1__r2__26034] :
                ( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__1__r2__26034)
                & VX26028 = cCoq_2emicromega_2eRMicromega_2eCMinus___24a2(Vvar__0__r1__26033,Vvar__1__r2__26034) ) )
        | ? [Vvar__0__r1__26035] :
            ( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r1__26035)
            & ? [Vvar__1__r2__26036] :
                ( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__1__r2__26036)
                & VX26028 = cCoq_2emicromega_2eRMicromega_2eCMult___24a2(Vvar__0__r1__26035,Vvar__1__r2__26036) ) )
        | ? [Vvar__0__r1__26037] :
            ( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r1__26037)
            & ? [Vvar__1__z__26038] :
                ( cCoq_2eInit_2eDatatypes_2esum___24t(cCoq_2eNumbers_2eBinNums_2eZ,cCoq_2eInit_2eDatatypes_2enat,Vvar__1__z__26038)
                & VX26028 = cCoq_2emicromega_2eRMicromega_2eCPow___24a2(Vvar__0__r1__26037,Vvar__1__z__26038) ) )
        | ? [Vvar__0__r__26039] :
            ( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r__26039)
            & VX26028 = cCoq_2emicromega_2eRMicromega_2eCInv___24a1(Vvar__0__r__26039) )
        | ? [Vvar__0__r__26040] :
            ( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vvar__0__r__26040)
            & VX26028 = cCoq_2emicromega_2eRMicromega_2eCOpp___24a1(Vvar__0__r__26040) ) ) ) ).

fof('$_inversion_Coq.micromega.RingMicromega.Formula',axiom,
    ! [Vvar__0__T__27212,VX27213] :
      ( cType___24t(Vvar__0__T__27212)
     => ( cCoq_2emicromega_2eRingMicromega_2eFormula___24t(Vvar__0__T__27212,VX27213)
       => ? [Vvar__1__Flhs__27215] :
            ( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__T__27212,Vvar__1__Flhs__27215)
            & ? [Vvar__2__Fop__27216] :
                ( cCoq_2emicromega_2eRingMicromega_2eOp2___24t(Vvar__2__Fop__27216)
                & ? [Vvar__3__Frhs__27217] :
                    ( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vvar__0__T__27212,Vvar__3__Frhs__27217)
                    & VX27213 = cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(Vvar__0__T__27212,Vvar__1__Flhs__27215,Vvar__2__Fop__27216,Vvar__3__Frhs__27217) ) ) ) ) ) ).

fof('$_inversion_Coq.micromega.RingMicromega.Op1',axiom,
    ! [VX32756] :
      ( cCoq_2emicromega_2eRingMicromega_2eOp1___24t(VX32756)
     => ( VX32756 = cCoq_2emicromega_2eRingMicromega_2eEqual
        | VX32756 = cCoq_2emicromega_2eRingMicromega_2eNonEqual
        | VX32756 = cCoq_2emicromega_2eRingMicromega_2eStrict
        | VX32756 = cCoq_2emicromega_2eRingMicromega_2eNonStrict ) ) ).

fof('$_inversion_Coq.micromega.RingMicromega.Op2',axiom,
    ! [VX27211] :
      ( cCoq_2emicromega_2eRingMicromega_2eOp2___24t(VX27211)
     => ( VX27211 = cCoq_2emicromega_2eRingMicromega_2eOpEq
        | VX27211 = cCoq_2emicromega_2eRingMicromega_2eOpNEq
        | VX27211 = cCoq_2emicromega_2eRingMicromega_2eOpLe
        | VX27211 = cCoq_2emicromega_2eRingMicromega_2eOpGe
        | VX27211 = cCoq_2emicromega_2eRingMicromega_2eOpLt
        | VX27211 = cCoq_2emicromega_2eRingMicromega_2eOpGt ) ) ).

fof('$_inversion_Coq.micromega.RingMicromega.Psatz',axiom,
    ! [Vvar__0__C__26959,VX26960] :
      ( cType___24t(Vvar__0__C__26959)
     => ( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__26959,VX26960)
       => ( ? [Vvar__1___24Anonymous__26962] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__26962)
              & VX26960 = cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(Vvar__0__C__26959,Vvar__1___24Anonymous__26962) )
          | ? [Vvar__1___24Anonymous__26964] :
              ( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(Vvar__0__C__26959,Vvar__1___24Anonymous__26964)
              & VX26960 = cCoq_2emicromega_2eRingMicromega_2ePsatzSquare___24a2(Vvar__0__C__26959,Vvar__1___24Anonymous__26964) )
          | ? [Vvar__1___24Anonymous__26966] :
              ( cCoq_2emicromega_2eRingMicromega_2ePolC___24t(Vvar__0__C__26959,Vvar__1___24Anonymous__26966)
              & ? [Vvar__2___24Anonymous__26967] :
                  ( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__26959,Vvar__2___24Anonymous__26967)
                  & VX26960 = cCoq_2emicromega_2eRingMicromega_2ePsatzMulC___24a3(Vvar__0__C__26959,Vvar__1___24Anonymous__26966,Vvar__2___24Anonymous__26967) ) )
          | ? [Vvar__1___24Anonymous__26969] :
              ( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__26959,Vvar__1___24Anonymous__26969)
              & ? [Vvar__2___24Anonymous__26970] :
                  ( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__26959,Vvar__2___24Anonymous__26970)
                  & VX26960 = cCoq_2emicromega_2eRingMicromega_2ePsatzMulE___24a3(Vvar__0__C__26959,Vvar__1___24Anonymous__26969,Vvar__2___24Anonymous__26970) ) )
          | ? [Vvar__1___24Anonymous__26972] :
              ( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__26959,Vvar__1___24Anonymous__26972)
              & ? [Vvar__2___24Anonymous__26973] :
                  ( cCoq_2emicromega_2eRingMicromega_2ePsatz___24t(Vvar__0__C__26959,Vvar__2___24Anonymous__26973)
                  & VX26960 = cCoq_2emicromega_2eRingMicromega_2ePsatzAdd___24a3(Vvar__0__C__26959,Vvar__1___24Anonymous__26972,Vvar__2___24Anonymous__26973) ) )
          | ? [Vvar__1___24Anonymous__26975] :
              ( t(Vvar__1___24Anonymous__26975,Vvar__0__C__26959)
              & VX26960 = cCoq_2emicromega_2eRingMicromega_2ePsatzC___24a2(Vvar__0__C__26959,Vvar__1___24Anonymous__26975) )
          | VX26960 = cCoq_2emicromega_2eRingMicromega_2ePsatzZ___24a1(Vvar__0__C__26959) ) ) ) ).

fof('$_inversion_Coq.micromega.RingMicromega.SORaddon',axiom,
    ! [Vvar__0__R__36974,Vvar__1__rO__36975,Vvar__2__rI__36976,Vvar__3__rplus__36977,Vvar__4__rtimes__36982,Vvar__5__rminus__36987,Vvar__6__ropp__36992,Vvar__7__req__36995,Vvar__8__rle__37000,Vvar__9__C__37005,Vvar__10__cO__37006,Vvar__11__cI__37007,Vvar__12__cplus__37008,Vvar__13__ctimes__37013,Vvar__14__cminus__37018,Vvar__15__copp__37023,Vvar__16__ceqb__37026,Vvar__17__cleb__37031,Vvar__18__phi__37036,Vvar__19__E__37039,Vvar__20__pow__phi__37040,Vvar__21__rpow__37043] :
      ( cType___24t(Vvar__0__R__36974)
     => ( t(Vvar__1__rO__36975,Vvar__0__R__36974)
       => ( t(Vvar__2__rI__36976,Vvar__0__R__36974)
         => ( c_24__type__37507___24t(Vvar__0__R__36974,Vvar__1__rO__36975,Vvar__2__rI__36976,Vvar__3__rplus__36977,Vvar__4__rtimes__36982,Vvar__5__rminus__36987,Vvar__6__ropp__36992,Vvar__7__req__36995,Vvar__8__rle__37000,Vvar__9__C__37005,Vvar__10__cO__37006,Vvar__11__cI__37007,Vvar__12__cplus__37008,Vvar__13__ctimes__37013,Vvar__14__cminus__37018,Vvar__15__copp__37023,Vvar__16__ceqb__37026,Vvar__17__cleb__37031,Vvar__18__phi__37036,Vvar__19__E__37039,Vvar__20__pow__phi__37040,Vvar__21__rpow__37043,Vvar__3__rplus__36977)
           => ( c_24__type__37853___24t(Vvar__0__R__36974,Vvar__1__rO__36975,Vvar__2__rI__36976,Vvar__3__rplus__36977,Vvar__4__rtimes__36982,Vvar__5__rminus__36987,Vvar__6__ropp__36992,Vvar__7__req__36995,Vvar__8__rle__37000,Vvar__9__C__37005,Vvar__10__cO__37006,Vvar__11__cI__37007,Vvar__12__cplus__37008,Vvar__13__ctimes__37013,Vvar__14__cminus__37018,Vvar__15__copp__37023,Vvar__16__ceqb__37026,Vvar__17__cleb__37031,Vvar__18__phi__37036,Vvar__19__E__37039,Vvar__20__pow__phi__37040,Vvar__21__rpow__37043,Vvar__4__rtimes__36982)
             => ( c_24__type__38199___24t(Vvar__0__R__36974,Vvar__1__rO__36975,Vvar__2__rI__36976,Vvar__3__rplus__36977,Vvar__4__rtimes__36982,Vvar__5__rminus__36987,Vvar__6__ropp__36992,Vvar__7__req__36995,Vvar__8__rle__37000,Vvar__9__C__37005,Vvar__10__cO__37006,Vvar__11__cI__37007,Vvar__12__cplus__37008,Vvar__13__ctimes__37013,Vvar__14__cminus__37018,Vvar__15__copp__37023,Vvar__16__ceqb__37026,Vvar__17__cleb__37031,Vvar__18__phi__37036,Vvar__19__E__37039,Vvar__20__pow__phi__37040,Vvar__21__rpow__37043,Vvar__5__rminus__36987)
               => ( c_24__type__38522___24t(Vvar__0__R__36974,Vvar__1__rO__36975,Vvar__2__rI__36976,Vvar__3__rplus__36977,Vvar__4__rtimes__36982,Vvar__5__rminus__36987,Vvar__6__ropp__36992,Vvar__7__req__36995,Vvar__8__rle__37000,Vvar__9__C__37005,Vvar__10__cO__37006,Vvar__11__cI__37007,Vvar__12__cplus__37008,Vvar__13__ctimes__37013,Vvar__14__cminus__37018,Vvar__15__copp__37023,Vvar__16__ceqb__37026,Vvar__17__cleb__37031,Vvar__18__phi__37036,Vvar__19__E__37039,Vvar__20__pow__phi__37040,Vvar__21__rpow__37043,Vvar__6__ropp__36992)
                 => ( c_24__type__38868___24t(Vvar__0__R__36974,Vvar__1__rO__36975,Vvar__2__rI__36976,Vvar__3__rplus__36977,Vvar__4__rtimes__36982,Vvar__5__rminus__36987,Vvar__6__ropp__36992,Vvar__7__req__36995,Vvar__8__rle__37000,Vvar__9__C__37005,Vvar__10__cO__37006,Vvar__11__cI__37007,Vvar__12__cplus__37008,Vvar__13__ctimes__37013,Vvar__14__cminus__37018,Vvar__15__copp__37023,Vvar__16__ceqb__37026,Vvar__17__cleb__37031,Vvar__18__phi__37036,Vvar__19__E__37039,Vvar__20__pow__phi__37040,Vvar__21__rpow__37043,Vvar__7__req__36995)
                   => ( c_24__type__39214___24t(Vvar__0__R__36974,Vvar__1__rO__36975,Vvar__2__rI__36976,Vvar__3__rplus__36977,Vvar__4__rtimes__36982,Vvar__5__rminus__36987,Vvar__6__ropp__36992,Vvar__7__req__36995,Vvar__8__rle__37000,Vvar__9__C__37005,Vvar__10__cO__37006,Vvar__11__cI__37007,Vvar__12__cplus__37008,Vvar__13__ctimes__37013,Vvar__14__cminus__37018,Vvar__15__copp__37023,Vvar__16__ceqb__37026,Vvar__17__cleb__37031,Vvar__18__phi__37036,Vvar__19__E__37039,Vvar__20__pow__phi__37040,Vvar__21__rpow__37043,Vvar__8__rle__37000)
                     => ( cType___24t(Vvar__9__C__37005)
                       => ( t(Vvar__10__cO__37006,Vvar__9__C__37005)
                         => ( t(Vvar__11__cI__37007,Vvar__9__C__37005)
                           => ( c_24__type__39560___24t(Vvar__0__R__36974,Vvar__1__rO__36975,Vvar__2__rI__36976,Vvar__3__rplus__36977,Vvar__4__rtimes__36982,Vvar__5__rminus__36987,Vvar__6__ropp__36992,Vvar__7__req__36995,Vvar__8__rle__37000,Vvar__9__C__37005,Vvar__10__cO__37006,Vvar__11__cI__37007,Vvar__12__cplus__37008,Vvar__13__ctimes__37013,Vvar__14__cminus__37018,Vvar__15__copp__37023,Vvar__16__ceqb__37026,Vvar__17__cleb__37031,Vvar__18__phi__37036,Vvar__19__E__37039,Vvar__20__pow__phi__37040,Vvar__21__rpow__37043,Vvar__12__cplus__37008)
                             => ( c_24__type__39906___24t(Vvar__0__R__36974,Vvar__1__rO__36975,Vvar__2__rI__36976,Vvar__3__rplus__36977,Vvar__4__rtimes__36982,Vvar__5__rminus__36987,Vvar__6__ropp__36992,Vvar__7__req__36995,Vvar__8__rle__37000,Vvar__9__C__37005,Vvar__10__cO__37006,Vvar__11__cI__37007,Vvar__12__cplus__37008,Vvar__13__ctimes__37013,Vvar__14__cminus__37018,Vvar__15__copp__37023,Vvar__16__ceqb__37026,Vvar__17__cleb__37031,Vvar__18__phi__37036,Vvar__19__E__37039,Vvar__20__pow__phi__37040,Vvar__21__rpow__37043,Vvar__13__ctimes__37013)
                               => ( c_24__type__40252___24t(Vvar__0__R__36974,Vvar__1__rO__36975,Vvar__2__rI__36976,Vvar__3__rplus__36977,Vvar__4__rtimes__36982,Vvar__5__rminus__36987,Vvar__6__ropp__36992,Vvar__7__req__36995,Vvar__8__rle__37000,Vvar__9__C__37005,Vvar__10__cO__37006,Vvar__11__cI__37007,Vvar__12__cplus__37008,Vvar__13__ctimes__37013,Vvar__14__cminus__37018,Vvar__15__copp__37023,Vvar__16__ceqb__37026,Vvar__17__cleb__37031,Vvar__18__phi__37036,Vvar__19__E__37039,Vvar__20__pow__phi__37040,Vvar__21__rpow__37043,Vvar__14__cminus__37018)
                                 => ( c_24__type__40575___24t(Vvar__0__R__36974,Vvar__1__rO__36975,Vvar__2__rI__36976,Vvar__3__rplus__36977,Vvar__4__rtimes__36982,Vvar__5__rminus__36987,Vvar__6__ropp__36992,Vvar__7__req__36995,Vvar__8__rle__37000,Vvar__9__C__37005,Vvar__10__cO__37006,Vvar__11__cI__37007,Vvar__12__cplus__37008,Vvar__13__ctimes__37013,Vvar__14__cminus__37018,Vvar__15__copp__37023,Vvar__16__ceqb__37026,Vvar__17__cleb__37031,Vvar__18__phi__37036,Vvar__19__E__37039,Vvar__20__pow__phi__37040,Vvar__21__rpow__37043,Vvar__15__copp__37023)
                                   => ( c_24__type__40921___24t(Vvar__0__R__36974,Vvar__1__rO__36975,Vvar__2__rI__36976,Vvar__3__rplus__36977,Vvar__4__rtimes__36982,Vvar__5__rminus__36987,Vvar__6__ropp__36992,Vvar__7__req__36995,Vvar__8__rle__37000,Vvar__9__C__37005,Vvar__10__cO__37006,Vvar__11__cI__37007,Vvar__12__cplus__37008,Vvar__13__ctimes__37013,Vvar__14__cminus__37018,Vvar__15__copp__37023,Vvar__16__ceqb__37026,Vvar__17__cleb__37031,Vvar__18__phi__37036,Vvar__19__E__37039,Vvar__20__pow__phi__37040,Vvar__21__rpow__37043,Vvar__16__ceqb__37026)
                                     => ( c_24__type__41267___24t(Vvar__0__R__36974,Vvar__1__rO__36975,Vvar__2__rI__36976,Vvar__3__rplus__36977,Vvar__4__rtimes__36982,Vvar__5__rminus__36987,Vvar__6__ropp__36992,Vvar__7__req__36995,Vvar__8__rle__37000,Vvar__9__C__37005,Vvar__10__cO__37006,Vvar__11__cI__37007,Vvar__12__cplus__37008,Vvar__13__ctimes__37013,Vvar__14__cminus__37018,Vvar__15__copp__37023,Vvar__16__ceqb__37026,Vvar__17__cleb__37031,Vvar__18__phi__37036,Vvar__19__E__37039,Vvar__20__pow__phi__37040,Vvar__21__rpow__37043,Vvar__17__cleb__37031)
                                       => ( c_24__type__41590___24t(Vvar__0__R__36974,Vvar__1__rO__36975,Vvar__2__rI__36976,Vvar__3__rplus__36977,Vvar__4__rtimes__36982,Vvar__5__rminus__36987,Vvar__6__ropp__36992,Vvar__7__req__36995,Vvar__8__rle__37000,Vvar__9__C__37005,Vvar__10__cO__37006,Vvar__11__cI__37007,Vvar__12__cplus__37008,Vvar__13__ctimes__37013,Vvar__14__cminus__37018,Vvar__15__copp__37023,Vvar__16__ceqb__37026,Vvar__17__cleb__37031,Vvar__18__phi__37036,Vvar__19__E__37039,Vvar__20__pow__phi__37040,Vvar__21__rpow__37043,Vvar__18__phi__37036)
                                         => ( cType___24t(Vvar__19__E__37039)
                                           => ( c_24__type__41913___24t(Vvar__0__R__36974,Vvar__1__rO__36975,Vvar__2__rI__36976,Vvar__3__rplus__36977,Vvar__4__rtimes__36982,Vvar__5__rminus__36987,Vvar__6__ropp__36992,Vvar__7__req__36995,Vvar__8__rle__37000,Vvar__9__C__37005,Vvar__10__cO__37006,Vvar__11__cI__37007,Vvar__12__cplus__37008,Vvar__13__ctimes__37013,Vvar__14__cminus__37018,Vvar__15__copp__37023,Vvar__16__ceqb__37026,Vvar__17__cleb__37031,Vvar__18__phi__37036,Vvar__19__E__37039,Vvar__20__pow__phi__37040,Vvar__21__rpow__37043,Vvar__20__pow__phi__37040)
                                             => ( c_24__type__42259___24t(Vvar__0__R__36974,Vvar__1__rO__36975,Vvar__2__rI__36976,Vvar__3__rplus__36977,Vvar__4__rtimes__36982,Vvar__5__rminus__36987,Vvar__6__ropp__36992,Vvar__7__req__36995,Vvar__8__rle__37000,Vvar__9__C__37005,Vvar__10__cO__37006,Vvar__11__cI__37007,Vvar__12__cplus__37008,Vvar__13__ctimes__37013,Vvar__14__cminus__37018,Vvar__15__copp__37023,Vvar__16__ceqb__37026,Vvar__17__cleb__37031,Vvar__18__phi__37036,Vvar__19__E__37039,Vvar__20__pow__phi__37040,Vvar__21__rpow__37043,Vvar__21__rpow__37043)
                                               => ( cCoq_2emicromega_2eRingMicromega_2eSORaddon___24a22(Vvar__0__R__36974,Vvar__1__rO__36975,Vvar__2__rI__36976,Vvar__3__rplus__36977,Vvar__4__rtimes__36982,Vvar__5__rminus__36987,Vvar__6__ropp__36992,Vvar__7__req__36995,Vvar__8__rle__37000,Vvar__9__C__37005,Vvar__10__cO__37006,Vvar__11__cI__37007,Vvar__12__cplus__37008,Vvar__13__ctimes__37013,Vvar__14__cminus__37018,Vvar__15__copp__37023,Vvar__16__ceqb__37026,Vvar__17__cleb__37031,Vvar__18__phi__37036,Vvar__19__E__37039,Vvar__20__pow__phi__37040,Vvar__21__rpow__37043)
                                                 => ( cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(Vvar__0__R__36974,Vvar__1__rO__36975,Vvar__2__rI__36976,Vvar__3__rplus__36977,Vvar__4__rtimes__36982,Vvar__5__rminus__36987,Vvar__6__ropp__36992,Vvar__7__req__36995,Vvar__9__C__37005,Vvar__10__cO__37006,Vvar__11__cI__37007,Vvar__12__cplus__37008,Vvar__13__ctimes__37013,Vvar__14__cminus__37018,Vvar__15__copp__37023,Vvar__16__ceqb__37026,Vvar__18__phi__37036)
                                                    & cCoq_2esetoid__ring_2eRing__theory_2epower__theory___24a7(Vvar__0__R__36974,Vvar__2__rI__36976,Vvar__4__rtimes__36982,Vvar__7__req__36995,Vvar__19__E__37039,Vvar__20__pow__phi__37040,Vvar__21__rpow__37043)
                                                    & ! [Vvar__var__var__var__var__var__24__x__37126__37129__37139__37142__37145__37148] :
                                                        ( t(Vvar__var__var__var__var__var__24__x__37126__37129__37139__37142__37145__37148,Vvar__9__C__37005)
                                                       => ! [Vvar__var__var__var__var__var__25__y__37127__37130__37140__37143__37146__37149] :
                                                            ( t(Vvar__var__var__var__var__var__25__y__37127__37130__37140__37143__37146__37149,Vvar__9__C__37005)
                                                           => ( happ(happ(Vvar__16__ceqb__37026,Vvar__var__var__var__var__var__24__x__37126__37129__37139__37142__37145__37148),Vvar__var__var__var__var__var__25__y__37127__37130__37140__37143__37146__37149) = cCoq_2eInit_2eDatatypes_2efalse
                                                             => ~ p(happ(happ(Vvar__7__req__36995,happ(Vvar__18__phi__37036,Vvar__var__var__var__var__var__24__x__37126__37129__37139__37142__37145__37148)),happ(Vvar__18__phi__37036,Vvar__var__var__var__var__var__25__y__37127__37130__37140__37143__37146__37149))) ) ) )
                                                    & ! [Vvar__var__var__var__var__var__25__x__37133__37136__37151__37154__37157__37160] :
                                                        ( t(Vvar__var__var__var__var__var__25__x__37133__37136__37151__37154__37157__37160,Vvar__9__C__37005)
                                                       => ! [Vvar__var__var__var__var__var__26__y__37134__37137__37152__37155__37158__37161] :
                                                            ( t(Vvar__var__var__var__var__var__26__y__37134__37137__37152__37155__37158__37161,Vvar__9__C__37005)
                                                           => ( happ(happ(Vvar__17__cleb__37031,Vvar__var__var__var__var__var__25__x__37133__37136__37151__37154__37157__37160),Vvar__var__var__var__var__var__26__y__37134__37137__37152__37155__37158__37161) = cCoq_2eInit_2eDatatypes_2etrue
                                                             => p(happ(happ(Vvar__8__rle__37000,happ(Vvar__18__phi__37036,Vvar__var__var__var__var__var__25__x__37133__37136__37151__37154__37157__37160)),happ(Vvar__18__phi__37036,Vvar__var__var__var__var__var__26__y__37134__37137__37152__37155__37158__37161))) ) ) )
                                                    & p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.micromega.Tauto.GFormula',axiom,
    ! [Vvar__0__TA__27972,Vvar__1__TX__27973,Vvar__2__AA__27974,Vvar__3__AF__27975,VX27976] :
      ( cType___24t(Vvar__0__TA__27972)
     => ( cType___24t(Vvar__1__TX__27973)
       => ( cType___24t(Vvar__2__AA__27974)
         => ( cType___24t(Vvar__3__AF__27975)
           => ( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__27972,Vvar__1__TX__27973,Vvar__2__AA__27974,Vvar__3__AF__27975,VX27976)
             => ( VX27976 = cCoq_2emicromega_2eTauto_2eTT___24a4(Vvar__0__TA__27972,Vvar__1__TX__27973,Vvar__2__AA__27974,Vvar__3__AF__27975)
                | VX27976 = cCoq_2emicromega_2eTauto_2eFF___24a4(Vvar__0__TA__27972,Vvar__1__TX__27973,Vvar__2__AA__27974,Vvar__3__AF__27975)
                | ? [Vvar__4___24Anonymous__27989] :
                    ( t(Vvar__4___24Anonymous__27989,Vvar__1__TX__27973)
                    & VX27976 = cCoq_2emicromega_2eTauto_2eX___24a5(Vvar__0__TA__27972,Vvar__1__TX__27973,Vvar__2__AA__27974,Vvar__3__AF__27975,Vvar__4___24Anonymous__27989) )
                | ? [Vvar__4___24Anonymous__27994] :
                    ( t(Vvar__4___24Anonymous__27994,Vvar__0__TA__27972)
                    & ? [Vvar__5___24Anonymous__27995] :
                        ( t(Vvar__5___24Anonymous__27995,Vvar__2__AA__27974)
                        & VX27976 = cCoq_2emicromega_2eTauto_2eA___24a6(Vvar__0__TA__27972,Vvar__1__TX__27973,Vvar__2__AA__27974,Vvar__3__AF__27975,Vvar__4___24Anonymous__27994,Vvar__5___24Anonymous__27995) ) )
                | ? [Vvar__4___24Anonymous__28000] :
                    ( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__27972,Vvar__1__TX__27973,Vvar__2__AA__27974,Vvar__3__AF__27975,Vvar__4___24Anonymous__28000)
                    & ? [Vvar__5___24Anonymous__28001] :
                        ( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__27972,Vvar__1__TX__27973,Vvar__2__AA__27974,Vvar__3__AF__27975,Vvar__5___24Anonymous__28001)
                        & VX27976 = cCoq_2emicromega_2eTauto_2eCj___24a6(Vvar__0__TA__27972,Vvar__1__TX__27973,Vvar__2__AA__27974,Vvar__3__AF__27975,Vvar__4___24Anonymous__28000,Vvar__5___24Anonymous__28001) ) )
                | ? [Vvar__4___24Anonymous__28006] :
                    ( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__27972,Vvar__1__TX__27973,Vvar__2__AA__27974,Vvar__3__AF__27975,Vvar__4___24Anonymous__28006)
                    & ? [Vvar__5___24Anonymous__28007] :
                        ( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__27972,Vvar__1__TX__27973,Vvar__2__AA__27974,Vvar__3__AF__27975,Vvar__5___24Anonymous__28007)
                        & VX27976 = cCoq_2emicromega_2eTauto_2eD___24a6(Vvar__0__TA__27972,Vvar__1__TX__27973,Vvar__2__AA__27974,Vvar__3__AF__27975,Vvar__4___24Anonymous__28006,Vvar__5___24Anonymous__28007) ) )
                | ? [Vvar__4___24Anonymous__28012] :
                    ( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__27972,Vvar__1__TX__27973,Vvar__2__AA__27974,Vvar__3__AF__27975,Vvar__4___24Anonymous__28012)
                    & VX27976 = cCoq_2emicromega_2eTauto_2eN___24a5(Vvar__0__TA__27972,Vvar__1__TX__27973,Vvar__2__AA__27974,Vvar__3__AF__27975,Vvar__4___24Anonymous__28012) )
                | ? [Vvar__4___24Anonymous__28017] :
                    ( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__27972,Vvar__1__TX__27973,Vvar__2__AA__27974,Vvar__3__AF__27975,Vvar__4___24Anonymous__28017)
                    & ? [Vvar__5___24Anonymous__28018] :
                        ( cCoq_2eInit_2eDatatypes_2eoption___24t(Vvar__3__AF__27975,Vvar__5___24Anonymous__28018)
                        & ? [Vvar__6___24Anonymous__28019] :
                            ( cCoq_2emicromega_2eTauto_2eGFormula___24t(Vvar__0__TA__27972,Vvar__1__TX__27973,Vvar__2__AA__27974,Vvar__3__AF__27975,Vvar__6___24Anonymous__28019)
                            & VX27976 = cCoq_2emicromega_2eTauto_2eI___24a7(Vvar__0__TA__27972,Vvar__1__TX__27973,Vvar__2__AA__27974,Vvar__3__AF__27975,Vvar__4___24Anonymous__28017,Vvar__5___24Anonymous__28018,Vvar__6___24Anonymous__28019) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.micromega.VarMap.t',axiom,
    ! [Vvar__0__A__34751,VX34752] :
      ( cType___24t(Vvar__0__A__34751)
     => ( cCoq_2emicromega_2eVarMap_2et___24t(Vvar__0__A__34751,VX34752)
       => ( VX34752 = cCoq_2emicromega_2eVarMap_2eEmpty___24a1(Vvar__0__A__34751)
          | ? [Vvar__1___24Anonymous__34755] :
              ( t(Vvar__1___24Anonymous__34755,Vvar__0__A__34751)
              & VX34752 = cCoq_2emicromega_2eVarMap_2eElt___24a2(Vvar__0__A__34751,Vvar__1___24Anonymous__34755) )
          | ? [Vvar__1___24Anonymous__34757] :
              ( cCoq_2emicromega_2eVarMap_2et___24t(Vvar__0__A__34751,Vvar__1___24Anonymous__34757)
              & ? [Vvar__2___24Anonymous__34758] :
                  ( t(Vvar__2___24Anonymous__34758,Vvar__0__A__34751)
                  & ? [Vvar__3___24Anonymous__34759] :
                      ( cCoq_2emicromega_2eVarMap_2et___24t(Vvar__0__A__34751,Vvar__3___24Anonymous__34759)
                      & VX34752 = cCoq_2emicromega_2eVarMap_2eBranch___24a4(Vvar__0__A__34751,Vvar__1___24Anonymous__34757,Vvar__2___24Anonymous__34758,Vvar__3___24Anonymous__34759) ) ) ) ) ) ) ).

fof('$_inversion_Coq.micromega.ZMicromega.Vars.Facts.MP.Dec.FSetDecideAuxiliary.FSet_Prop',axiom,
    ! [Vvar__0___24Anonymous__35079] :
      ( cProp___24t(Vvar__0___24Anonymous__35079)
     => ( cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__Prop___24a1(Vvar__0___24Anonymous__35079)
       => ( ? [Vvar__0__P__35081] :
              ( cProp___24t(Vvar__0__P__35081)
              & cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__35081)
              & Vvar__0___24Anonymous__35079 = Vvar__0__P__35081 )
          | ? [Vvar__0__s__35083] :
              ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__0__s__35083)
              & Vvar__0___24Anonymous__35079 = c_24__prop__35092___24a2(Vvar__0___24Anonymous__35079,Vvar__0__s__35083) )
          | ? [Vvar__0__s1__35085] :
              ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__0__s1__35085)
              & ? [Vvar__1__s2__35086] :
                  ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__1__s2__35086)
                  & Vvar__0___24Anonymous__35079 = c_24__prop__35093___24a3(Vvar__0___24Anonymous__35079,Vvar__0__s1__35085,Vvar__1__s2__35086) ) )
          | ? [Vvar__0__s1__35089] :
              ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__0__s1__35089)
              & ? [Vvar__1__s2__35090] :
                  ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__1__s2__35090)
                  & Vvar__0___24Anonymous__35079 = c_24__prop__35094___24a3(Vvar__0___24Anonymous__35079,Vvar__0__s1__35089,Vvar__1__s2__35090) ) ) ) ) ) ).

fof('$_inversion_Coq.micromega.ZMicromega.Vars.Facts.MP.Dec.FSetDecideAuxiliary.FSet_elt_Prop',axiom,
    ! [Vvar__0___24Anonymous__29524] :
      ( cProp___24t(Vvar__0___24Anonymous__29524)
     => ( cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0___24Anonymous__29524)
       => ( ? [Vvar__0__S__29526] :
              ( cType___24t(Vvar__0__S__29526)
              & ? [Vvar__1__x__29527] :
                  ( t(Vvar__1__x__29527,Vvar__0__S__29526)
                  & ? [Vvar__2__y__29528] :
                      ( t(Vvar__2__y__29528,Vvar__0__S__29526)
                      & Vvar__0___24Anonymous__29524 = c_24__prop__29548___24a4(Vvar__0___24Anonymous__29524,Vvar__0__S__29526,Vvar__1__x__29527,Vvar__2__y__29528) ) ) )
          | ? [Vvar__0__x__29529] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0__x__29529)
              & ? [Vvar__1__y__29530] :
                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1__y__29530)
                  & Vvar__0___24Anonymous__29524 = c_24__prop__29549___24a3(Vvar__0___24Anonymous__29524,Vvar__0__x__29529,Vvar__1__y__29530) ) )
          | ? [Vvar__0__x__29531] :
              ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vvar__0__x__29531)
              & ? [Vvar__1__s__29532] :
                  ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vvar__1__s__29532)
                  & Vvar__0___24Anonymous__29524 = c_24__prop__29550___24a3(Vvar__0___24Anonymous__29524,Vvar__0__x__29531,Vvar__1__s__29532) ) )
          | Vvar__0___24Anonymous__29524 = c_24True
          | Vvar__0___24Anonymous__29524 = c_24False
          | ? [Vvar__0__P__29533] :
              ( cProp___24t(Vvar__0__P__29533)
              & ? [Vvar__1__Q__29534] :
                  ( cProp___24t(Vvar__1__Q__29534)
                  & cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__29533)
                  & cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__1__Q__29534)
                  & Vvar__0___24Anonymous__29524 = c_24__prop__29551___24a3(Vvar__0___24Anonymous__29524,Vvar__0__P__29533,Vvar__1__Q__29534) ) )
          | ? [Vvar__0__P__29537] :
              ( cProp___24t(Vvar__0__P__29537)
              & ? [Vvar__1__Q__29538] :
                  ( cProp___24t(Vvar__1__Q__29538)
                  & cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__29537)
                  & cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__1__Q__29538)
                  & Vvar__0___24Anonymous__29524 = c_24__prop__29552___24a3(Vvar__0___24Anonymous__29524,Vvar__0__P__29537,Vvar__1__Q__29538) ) )
          | ? [Vvar__0__P__29541] :
              ( cProp___24t(Vvar__0__P__29541)
              & ? [Vvar__1__Q__29542] :
                  ( cProp___24t(Vvar__1__Q__29542)
                  & cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__29541)
                  & cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__1__Q__29542)
                  & Vvar__0___24Anonymous__29524 = c_24__prop__29553___24a3(Vvar__0___24Anonymous__29524,Vvar__0__P__29541,Vvar__1__Q__29542) ) )
          | ? [Vvar__0__P__29546] :
              ( cProp___24t(Vvar__0__P__29546)
              & cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(Vvar__0__P__29546)
              & Vvar__0___24Anonymous__29524 = c_24__prop__29554___24a2(Vvar__0___24Anonymous__29524,Vvar__0__P__29546) ) ) ) ) ).

fof('$_inversion_Coq.micromega.ZMicromega.ZArithProof',axiom,
    ! [VX29001] :
      ( cCoq_2emicromega_2eZMicromega_2eZArithProof___24t(VX29001)
     => ( VX29001 = cCoq_2emicromega_2eZMicromega_2eDoneProof
        | ? [Vvar__0___24Anonymous__29002] :
            ( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__0___24Anonymous__29002)
            & ? [Vvar__1___24Anonymous__29003] :
                ( cCoq_2emicromega_2eZMicromega_2eZArithProof___24t(Vvar__1___24Anonymous__29003)
                & VX29001 = cCoq_2emicromega_2eZMicromega_2eRatProof___24a2(Vvar__0___24Anonymous__29002,Vvar__1___24Anonymous__29003) ) )
        | ? [Vvar__0___24Anonymous__29004] :
            ( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__0___24Anonymous__29004)
            & ? [Vvar__1___24Anonymous__29005] :
                ( cCoq_2emicromega_2eZMicromega_2eZArithProof___24t(Vvar__1___24Anonymous__29005)
                & VX29001 = cCoq_2emicromega_2eZMicromega_2eCutProof___24a2(Vvar__0___24Anonymous__29004,Vvar__1___24Anonymous__29005) ) )
        | ? [Vvar__0___24Anonymous__29006] :
            ( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__0___24Anonymous__29006)
            & ? [Vvar__1___24Anonymous__29007] :
                ( cCoq_2emicromega_2eZMicromega_2eZWitness___24t(Vvar__1___24Anonymous__29007)
                & ? [Vvar__2___24Anonymous__29008] :
                    ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2emicromega_2eZMicromega_2eZArithProof,Vvar__2___24Anonymous__29008)
                    & VX29001 = cCoq_2emicromega_2eZMicromega_2eEnumProof___24a3(Vvar__0___24Anonymous__29006,Vvar__1___24Anonymous__29007,Vvar__2___24Anonymous__29008) ) ) ) ) ) ).

fof('$_inversion_Coq.micromega.ZMicromega.is_diff_env_elt',axiom,
    ! [Vvar__0__fr__29047,Vvar__1__env__29048,Vvar__2__env_27__29051,Vvar__3__x__29054] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0__fr__29047)
     => ( c_24__type__29075___24t(Vvar__0__fr__29047,Vvar__1__env__29048,Vvar__2__env_27__29051,Vvar__3__x__29054,Vvar__1__env__29048)
       => ( c_24__type__29084___24t(Vvar__0__fr__29047,Vvar__1__env__29048,Vvar__2__env_27__29051,Vvar__3__x__29054,Vvar__2__env_27__29051)
         => ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__3__x__29054)
           => ( cCoq_2emicromega_2eZMicromega_2eis__diff__env__elt___24a4(Vvar__0__fr__29047,Vvar__1__env__29048,Vvar__2__env_27__29051,Vvar__3__x__29054)
             => ( happ(Vvar__1__env__29048,Vvar__3__x__29054) = happ(Vvar__2__env_27__29051,Vvar__3__x__29054)
                & happ(Vvar__1__env__29048,Vvar__3__x__29054) = cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(happ(Vvar__2__env_27__29051,cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0__fr__29047,Vvar__3__x__29054))),happ(Vvar__2__env_27__29051,cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0__fr__29047,Vvar__3__x__29054))))
                & cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(happ(Vvar__2__env_27__29051,cCoq_2eNumbers_2eBinNums_2exO___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0__fr__29047,Vvar__3__x__29054))),cCoq_2eNumbers_2eBinNums_2eZ0)
                & cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(happ(Vvar__2__env_27__29051,cCoq_2eNumbers_2eBinNums_2exI___24a1(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(Vvar__0__fr__29047,Vvar__3__x__29054))),cCoq_2eNumbers_2eBinNums_2eZ0)
                & p(c_24True) ) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Field_theory.FExpr',axiom,
    ! [Vvar__0__C__8319,VX8320] :
      ( cType___24t(Vvar__0__C__8319)
     => ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__8319,VX8320)
       => ( VX8320 = cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(Vvar__0__C__8319)
          | VX8320 = cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(Vvar__0__C__8319)
          | ? [Vvar__1___24Anonymous__8324] :
              ( t(Vvar__1___24Anonymous__8324,Vvar__0__C__8319)
              & VX8320 = cCoq_2esetoid__ring_2eField__theory_2eFEc___24a2(Vvar__0__C__8319,Vvar__1___24Anonymous__8324) )
          | ? [Vvar__1___24Anonymous__8326] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__8326)
              & VX8320 = cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(Vvar__0__C__8319,Vvar__1___24Anonymous__8326) )
          | ? [Vvar__1___24Anonymous__8328] :
              ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__8319,Vvar__1___24Anonymous__8328)
              & ? [Vvar__2___24Anonymous__8329] :
                  ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__8319,Vvar__2___24Anonymous__8329)
                  & VX8320 = cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(Vvar__0__C__8319,Vvar__1___24Anonymous__8328,Vvar__2___24Anonymous__8329) ) )
          | ? [Vvar__1___24Anonymous__8331] :
              ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__8319,Vvar__1___24Anonymous__8331)
              & ? [Vvar__2___24Anonymous__8332] :
                  ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__8319,Vvar__2___24Anonymous__8332)
                  & VX8320 = cCoq_2esetoid__ring_2eField__theory_2eFEsub___24a3(Vvar__0__C__8319,Vvar__1___24Anonymous__8331,Vvar__2___24Anonymous__8332) ) )
          | ? [Vvar__1___24Anonymous__8334] :
              ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__8319,Vvar__1___24Anonymous__8334)
              & ? [Vvar__2___24Anonymous__8335] :
                  ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__8319,Vvar__2___24Anonymous__8335)
                  & VX8320 = cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(Vvar__0__C__8319,Vvar__1___24Anonymous__8334,Vvar__2___24Anonymous__8335) ) )
          | ? [Vvar__1___24Anonymous__8337] :
              ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__8319,Vvar__1___24Anonymous__8337)
              & VX8320 = cCoq_2esetoid__ring_2eField__theory_2eFEopp___24a2(Vvar__0__C__8319,Vvar__1___24Anonymous__8337) )
          | ? [Vvar__1___24Anonymous__8339] :
              ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__8319,Vvar__1___24Anonymous__8339)
              & VX8320 = cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(Vvar__0__C__8319,Vvar__1___24Anonymous__8339) )
          | ? [Vvar__1___24Anonymous__8341] :
              ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__8319,Vvar__1___24Anonymous__8341)
              & ? [Vvar__2___24Anonymous__8342] :
                  ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__8319,Vvar__2___24Anonymous__8342)
                  & VX8320 = cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(Vvar__0__C__8319,Vvar__1___24Anonymous__8341,Vvar__2___24Anonymous__8342) ) )
          | ? [Vvar__1___24Anonymous__8344] :
              ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vvar__0__C__8319,Vvar__1___24Anonymous__8344)
              & ? [Vvar__2___24Anonymous__8345] :
                  ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__8345)
                  & VX8320 = cCoq_2esetoid__ring_2eField__theory_2eFEpow___24a3(Vvar__0__C__8319,Vvar__1___24Anonymous__8344,Vvar__2___24Anonymous__8345) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Field_theory.almost_field_theory',axiom,
    ! [Vvar__0__R__7491,Vvar__1__rO__7492,Vvar__2__rI__7493,Vvar__3__radd__7494,Vvar__4__rmul__7499,Vvar__5__rsub__7504,Vvar__6__ropp__7509,Vvar__7__rdiv__7512,Vvar__8__rinv__7517,Vvar__9__req__7520] :
      ( cType___24t(Vvar__0__R__7491)
     => ( t(Vvar__1__rO__7492,Vvar__0__R__7491)
       => ( t(Vvar__2__rI__7493,Vvar__0__R__7491)
         => ( c_24__type__7685___24t(Vvar__0__R__7491,Vvar__1__rO__7492,Vvar__2__rI__7493,Vvar__3__radd__7494,Vvar__4__rmul__7499,Vvar__5__rsub__7504,Vvar__6__ropp__7509,Vvar__7__rdiv__7512,Vvar__8__rinv__7517,Vvar__9__req__7520,Vvar__3__radd__7494)
           => ( c_24__type__7778___24t(Vvar__0__R__7491,Vvar__1__rO__7492,Vvar__2__rI__7493,Vvar__3__radd__7494,Vvar__4__rmul__7499,Vvar__5__rsub__7504,Vvar__6__ropp__7509,Vvar__7__rdiv__7512,Vvar__8__rinv__7517,Vvar__9__req__7520,Vvar__4__rmul__7499)
             => ( c_24__type__7871___24t(Vvar__0__R__7491,Vvar__1__rO__7492,Vvar__2__rI__7493,Vvar__3__radd__7494,Vvar__4__rmul__7499,Vvar__5__rsub__7504,Vvar__6__ropp__7509,Vvar__7__rdiv__7512,Vvar__8__rinv__7517,Vvar__9__req__7520,Vvar__5__rsub__7504)
               => ( c_24__type__7953___24t(Vvar__0__R__7491,Vvar__1__rO__7492,Vvar__2__rI__7493,Vvar__3__radd__7494,Vvar__4__rmul__7499,Vvar__5__rsub__7504,Vvar__6__ropp__7509,Vvar__7__rdiv__7512,Vvar__8__rinv__7517,Vvar__9__req__7520,Vvar__6__ropp__7509)
                 => ( c_24__type__8046___24t(Vvar__0__R__7491,Vvar__1__rO__7492,Vvar__2__rI__7493,Vvar__3__radd__7494,Vvar__4__rmul__7499,Vvar__5__rsub__7504,Vvar__6__ropp__7509,Vvar__7__rdiv__7512,Vvar__8__rinv__7517,Vvar__9__req__7520,Vvar__7__rdiv__7512)
                   => ( c_24__type__8128___24t(Vvar__0__R__7491,Vvar__1__rO__7492,Vvar__2__rI__7493,Vvar__3__radd__7494,Vvar__4__rmul__7499,Vvar__5__rsub__7504,Vvar__6__ropp__7509,Vvar__7__rdiv__7512,Vvar__8__rinv__7517,Vvar__9__req__7520,Vvar__8__rinv__7517)
                     => ( c_24__type__8221___24t(Vvar__0__R__7491,Vvar__1__rO__7492,Vvar__2__rI__7493,Vvar__3__radd__7494,Vvar__4__rmul__7499,Vvar__5__rsub__7504,Vvar__6__ropp__7509,Vvar__7__rdiv__7512,Vvar__8__rinv__7517,Vvar__9__req__7520,Vvar__9__req__7520)
                       => ( cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(Vvar__0__R__7491,Vvar__1__rO__7492,Vvar__2__rI__7493,Vvar__3__radd__7494,Vvar__4__rmul__7499,Vvar__5__rsub__7504,Vvar__6__ropp__7509,Vvar__7__rdiv__7512,Vvar__8__rinv__7517,Vvar__9__req__7520)
                         => ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(Vvar__0__R__7491,Vvar__1__rO__7492,Vvar__2__rI__7493,Vvar__3__radd__7494,Vvar__4__rmul__7499,Vvar__5__rsub__7504,Vvar__6__ropp__7509,Vvar__9__req__7520)
                            & ~ p(happ(happ(Vvar__9__req__7520,Vvar__2__rI__7493),Vvar__1__rO__7492))
                            & ! [Vvar__var__var__var__var__var__var__12__p__7563__7565__7572__7574__7576__7578__7580] :
                                ( t(Vvar__var__var__var__var__var__var__12__p__7563__7565__7572__7574__7576__7578__7580,Vvar__0__R__7491)
                               => ! [Vvar__var__var__var__var__var__var__13__q__7564__7566__7573__7575__7577__7579__7581] :
                                    ( t(Vvar__var__var__var__var__var__var__13__q__7564__7566__7573__7575__7577__7579__7581,Vvar__0__R__7491)
                                   => p(happ(happ(Vvar__9__req__7520,happ(happ(Vvar__7__rdiv__7512,Vvar__var__var__var__var__var__var__12__p__7563__7565__7572__7574__7576__7578__7580),Vvar__var__var__var__var__var__var__13__q__7564__7566__7573__7575__7577__7579__7581)),happ(happ(Vvar__4__rmul__7499,Vvar__var__var__var__var__var__var__12__p__7563__7565__7572__7574__7576__7578__7580),happ(Vvar__8__rinv__7517,Vvar__var__var__var__var__var__var__13__q__7564__7566__7573__7575__7577__7579__7581)))) ) )
                            & ! [Vvar__var__var__var__var__var__var__var__13__p__7568__7570__7582__7584__7586__7588__7590__7592] :
                                ( t(Vvar__var__var__var__var__var__var__var__13__p__7568__7570__7582__7584__7586__7588__7590__7592,Vvar__0__R__7491)
                               => ( ~ p(happ(happ(Vvar__9__req__7520,Vvar__var__var__var__var__var__var__var__13__p__7568__7570__7582__7584__7586__7588__7590__7592),Vvar__1__rO__7492))
                                 => p(happ(happ(Vvar__9__req__7520,happ(happ(Vvar__4__rmul__7499,happ(Vvar__8__rinv__7517,Vvar__var__var__var__var__var__var__var__13__p__7568__7570__7582__7584__7586__7588__7590__7592)),Vvar__var__var__var__var__var__var__var__13__p__7568__7570__7582__7584__7586__7588__7590__7592)),Vvar__2__rI__7493)) ) )
                            & p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Field_theory.field_theory',axiom,
    ! [Vvar__0__R__31184,Vvar__1__rO__31185,Vvar__2__rI__31186,Vvar__3__radd__31187,Vvar__4__rmul__31192,Vvar__5__rsub__31197,Vvar__6__ropp__31202,Vvar__7__rdiv__31205,Vvar__8__rinv__31210,Vvar__9__req__31213] :
      ( cType___24t(Vvar__0__R__31184)
     => ( t(Vvar__1__rO__31185,Vvar__0__R__31184)
       => ( t(Vvar__2__rI__31186,Vvar__0__R__31184)
         => ( c_24__type__31378___24t(Vvar__0__R__31184,Vvar__1__rO__31185,Vvar__2__rI__31186,Vvar__3__radd__31187,Vvar__4__rmul__31192,Vvar__5__rsub__31197,Vvar__6__ropp__31202,Vvar__7__rdiv__31205,Vvar__8__rinv__31210,Vvar__9__req__31213,Vvar__3__radd__31187)
           => ( c_24__type__31471___24t(Vvar__0__R__31184,Vvar__1__rO__31185,Vvar__2__rI__31186,Vvar__3__radd__31187,Vvar__4__rmul__31192,Vvar__5__rsub__31197,Vvar__6__ropp__31202,Vvar__7__rdiv__31205,Vvar__8__rinv__31210,Vvar__9__req__31213,Vvar__4__rmul__31192)
             => ( c_24__type__31564___24t(Vvar__0__R__31184,Vvar__1__rO__31185,Vvar__2__rI__31186,Vvar__3__radd__31187,Vvar__4__rmul__31192,Vvar__5__rsub__31197,Vvar__6__ropp__31202,Vvar__7__rdiv__31205,Vvar__8__rinv__31210,Vvar__9__req__31213,Vvar__5__rsub__31197)
               => ( c_24__type__31646___24t(Vvar__0__R__31184,Vvar__1__rO__31185,Vvar__2__rI__31186,Vvar__3__radd__31187,Vvar__4__rmul__31192,Vvar__5__rsub__31197,Vvar__6__ropp__31202,Vvar__7__rdiv__31205,Vvar__8__rinv__31210,Vvar__9__req__31213,Vvar__6__ropp__31202)
                 => ( c_24__type__31739___24t(Vvar__0__R__31184,Vvar__1__rO__31185,Vvar__2__rI__31186,Vvar__3__radd__31187,Vvar__4__rmul__31192,Vvar__5__rsub__31197,Vvar__6__ropp__31202,Vvar__7__rdiv__31205,Vvar__8__rinv__31210,Vvar__9__req__31213,Vvar__7__rdiv__31205)
                   => ( c_24__type__31821___24t(Vvar__0__R__31184,Vvar__1__rO__31185,Vvar__2__rI__31186,Vvar__3__radd__31187,Vvar__4__rmul__31192,Vvar__5__rsub__31197,Vvar__6__ropp__31202,Vvar__7__rdiv__31205,Vvar__8__rinv__31210,Vvar__9__req__31213,Vvar__8__rinv__31210)
                     => ( c_24__type__31914___24t(Vvar__0__R__31184,Vvar__1__rO__31185,Vvar__2__rI__31186,Vvar__3__radd__31187,Vvar__4__rmul__31192,Vvar__5__rsub__31197,Vvar__6__ropp__31202,Vvar__7__rdiv__31205,Vvar__8__rinv__31210,Vvar__9__req__31213,Vvar__9__req__31213)
                       => ( cCoq_2esetoid__ring_2eField__theory_2efield__theory___24a10(Vvar__0__R__31184,Vvar__1__rO__31185,Vvar__2__rI__31186,Vvar__3__radd__31187,Vvar__4__rmul__31192,Vvar__5__rsub__31197,Vvar__6__ropp__31202,Vvar__7__rdiv__31205,Vvar__8__rinv__31210,Vvar__9__req__31213)
                         => ( cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(Vvar__0__R__31184,Vvar__1__rO__31185,Vvar__2__rI__31186,Vvar__3__radd__31187,Vvar__4__rmul__31192,Vvar__5__rsub__31197,Vvar__6__ropp__31202,Vvar__9__req__31213)
                            & ~ p(happ(happ(Vvar__9__req__31213,Vvar__2__rI__31186),Vvar__1__rO__31185))
                            & ! [Vvar__var__var__var__var__var__var__12__p__31256__31258__31265__31267__31269__31271__31273] :
                                ( t(Vvar__var__var__var__var__var__var__12__p__31256__31258__31265__31267__31269__31271__31273,Vvar__0__R__31184)
                               => ! [Vvar__var__var__var__var__var__var__13__q__31257__31259__31266__31268__31270__31272__31274] :
                                    ( t(Vvar__var__var__var__var__var__var__13__q__31257__31259__31266__31268__31270__31272__31274,Vvar__0__R__31184)
                                   => p(happ(happ(Vvar__9__req__31213,happ(happ(Vvar__7__rdiv__31205,Vvar__var__var__var__var__var__var__12__p__31256__31258__31265__31267__31269__31271__31273),Vvar__var__var__var__var__var__var__13__q__31257__31259__31266__31268__31270__31272__31274)),happ(happ(Vvar__4__rmul__31192,Vvar__var__var__var__var__var__var__12__p__31256__31258__31265__31267__31269__31271__31273),happ(Vvar__8__rinv__31210,Vvar__var__var__var__var__var__var__13__q__31257__31259__31266__31268__31270__31272__31274)))) ) )
                            & ! [Vvar__var__var__var__var__var__var__var__13__p__31261__31263__31275__31277__31279__31281__31283__31285] :
                                ( t(Vvar__var__var__var__var__var__var__var__13__p__31261__31263__31275__31277__31279__31281__31283__31285,Vvar__0__R__31184)
                               => ( ~ p(happ(happ(Vvar__9__req__31213,Vvar__var__var__var__var__var__var__var__13__p__31261__31263__31275__31277__31279__31281__31283__31285),Vvar__1__rO__31185))
                                 => p(happ(happ(Vvar__9__req__31213,happ(happ(Vvar__4__rmul__31192,happ(Vvar__8__rinv__31210,Vvar__var__var__var__var__var__var__var__13__p__31261__31263__31275__31277__31279__31281__31283__31285)),Vvar__var__var__var__var__var__var__var__13__p__31261__31263__31275__31277__31279__31281__31283__31285)),Vvar__2__rI__31186)) ) )
                            & p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Field_theory.linear',axiom,
    ! [Vvar__0__C__8937,VX8938] :
      ( cType___24t(Vvar__0__C__8937)
     => ( cCoq_2esetoid__ring_2eField__theory_2elinear___24t(Vvar__0__C__8937,VX8938)
       => ? [Vvar__1__num__8940] :
            ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__8937,Vvar__1__num__8940)
            & ? [Vvar__2__denum__8941] :
                ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__8937,Vvar__2__denum__8941)
                & ? [Vvar__3__condition__8942] :
                    ( cCoq_2eInit_2eDatatypes_2elist___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(Vvar__0__C__8937),Vvar__3__condition__8942)
                    & VX8938 = cCoq_2esetoid__ring_2eField__theory_2emk__linear___24a4(Vvar__0__C__8937,Vvar__1__num__8940,Vvar__2__denum__8941,Vvar__3__condition__8942) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Field_theory.rsplit',axiom,
    ! [Vvar__0__C__9226,VX9227] :
      ( cType___24t(Vvar__0__C__9226)
     => ( cCoq_2esetoid__ring_2eField__theory_2ersplit___24t(Vvar__0__C__9226,VX9227)
       => ? [Vvar__1__rsplit__left__9229] :
            ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__9226,Vvar__1__rsplit__left__9229)
            & ? [Vvar__2__rsplit__common__9230] :
                ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__9226,Vvar__2__rsplit__common__9230)
                & ? [Vvar__3__rsplit__right__9231] :
                    ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__9226,Vvar__3__rsplit__right__9231)
                    & VX9227 = cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(Vvar__0__C__9226,Vvar__1__rsplit__left__9229,Vvar__2__rsplit__common__9230,Vvar__3__rsplit__right__9231) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Field_theory.semi_field_theory',axiom,
    ! [Vvar__0__R__31920,Vvar__1__rO__31921,Vvar__2__rI__31922,Vvar__3__radd__31923,Vvar__4__rmul__31928,Vvar__5__rdiv__31933,Vvar__6__rinv__31938,Vvar__7__req__31941] :
      ( cType___24t(Vvar__0__R__31920)
     => ( t(Vvar__1__rO__31921,Vvar__0__R__31920)
       => ( t(Vvar__2__rI__31922,Vvar__0__R__31920)
         => ( c_24__type__32068___24t(Vvar__0__R__31920,Vvar__1__rO__31921,Vvar__2__rI__31922,Vvar__3__radd__31923,Vvar__4__rmul__31928,Vvar__5__rdiv__31933,Vvar__6__rinv__31938,Vvar__7__req__31941,Vvar__3__radd__31923)
           => ( c_24__type__32131___24t(Vvar__0__R__31920,Vvar__1__rO__31921,Vvar__2__rI__31922,Vvar__3__radd__31923,Vvar__4__rmul__31928,Vvar__5__rdiv__31933,Vvar__6__rinv__31938,Vvar__7__req__31941,Vvar__4__rmul__31928)
             => ( c_24__type__32194___24t(Vvar__0__R__31920,Vvar__1__rO__31921,Vvar__2__rI__31922,Vvar__3__radd__31923,Vvar__4__rmul__31928,Vvar__5__rdiv__31933,Vvar__6__rinv__31938,Vvar__7__req__31941,Vvar__5__rdiv__31933)
               => ( c_24__type__32248___24t(Vvar__0__R__31920,Vvar__1__rO__31921,Vvar__2__rI__31922,Vvar__3__radd__31923,Vvar__4__rmul__31928,Vvar__5__rdiv__31933,Vvar__6__rinv__31938,Vvar__7__req__31941,Vvar__6__rinv__31938)
                 => ( c_24__type__32311___24t(Vvar__0__R__31920,Vvar__1__rO__31921,Vvar__2__rI__31922,Vvar__3__radd__31923,Vvar__4__rmul__31928,Vvar__5__rdiv__31933,Vvar__6__rinv__31938,Vvar__7__req__31941,Vvar__7__req__31941)
                   => ( cCoq_2esetoid__ring_2eField__theory_2esemi__field__theory___24a8(Vvar__0__R__31920,Vvar__1__rO__31921,Vvar__2__rI__31922,Vvar__3__radd__31923,Vvar__4__rmul__31928,Vvar__5__rdiv__31933,Vvar__6__rinv__31938,Vvar__7__req__31941)
                     => ( cCoq_2esetoid__ring_2eRing__theory_2esemi__ring__theory___24a6(Vvar__0__R__31920,Vvar__1__rO__31921,Vvar__2__rI__31922,Vvar__3__radd__31923,Vvar__4__rmul__31928,Vvar__7__req__31941)
                        & ~ p(happ(happ(Vvar__7__req__31941,Vvar__2__rI__31922),Vvar__1__rO__31921))
                        & ! [Vvar__var__var__var__var__var__var__10__p__31976__31978__31985__31987__31989__31991__31993] :
                            ( t(Vvar__var__var__var__var__var__var__10__p__31976__31978__31985__31987__31989__31991__31993,Vvar__0__R__31920)
                           => ! [Vvar__var__var__var__var__var__var__11__q__31977__31979__31986__31988__31990__31992__31994] :
                                ( t(Vvar__var__var__var__var__var__var__11__q__31977__31979__31986__31988__31990__31992__31994,Vvar__0__R__31920)
                               => p(happ(happ(Vvar__7__req__31941,happ(happ(Vvar__5__rdiv__31933,Vvar__var__var__var__var__var__var__10__p__31976__31978__31985__31987__31989__31991__31993),Vvar__var__var__var__var__var__var__11__q__31977__31979__31986__31988__31990__31992__31994)),happ(happ(Vvar__4__rmul__31928,Vvar__var__var__var__var__var__var__10__p__31976__31978__31985__31987__31989__31991__31993),happ(Vvar__6__rinv__31938,Vvar__var__var__var__var__var__var__11__q__31977__31979__31986__31988__31990__31992__31994)))) ) )
                        & ! [Vvar__var__var__var__var__var__var__var__11__p__31981__31983__31995__31997__31999__32001__32003__32005] :
                            ( t(Vvar__var__var__var__var__var__var__var__11__p__31981__31983__31995__31997__31999__32001__32003__32005,Vvar__0__R__31920)
                           => ( ~ p(happ(happ(Vvar__7__req__31941,Vvar__var__var__var__var__var__var__var__11__p__31981__31983__31995__31997__31999__32001__32003__32005),Vvar__1__rO__31921))
                             => p(happ(happ(Vvar__7__req__31941,happ(happ(Vvar__4__rmul__31928,happ(Vvar__6__rinv__31938,Vvar__var__var__var__var__var__var__var__11__p__31981__31983__31995__31997__31999__32001__32003__32005)),Vvar__var__var__var__var__var__var__var__11__p__31981__31983__31995__31997__31999__32001__32003__32005)),Vvar__2__rI__31922)) ) )
                        & p(c_24True) ) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.InitialRing.hypo',axiom,
    ! [VX32423] :
      ( cCoq_2esetoid__ring_2eInitialRing_2ehypo___24t(VX32423)
     => ? [Vvar__0__hypo__type__32424] :
          ( cType___24t(Vvar__0__hypo__type__32424)
          & ? [Vvar__1__hypo__proof__32425] :
              ( t(Vvar__1__hypo__proof__32425,Vvar__0__hypo__type__32424)
              & VX32423 = cCoq_2esetoid__ring_2eInitialRing_2emkhypo___24a2(Vvar__0__hypo__type__32424,Vvar__1__hypo__proof__32425) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Ring_polynom.Mon',axiom,
    ! [VX9832] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(VX9832)
     => ( VX9832 = cCoq_2esetoid__ring_2eRing__polynom_2emon0
        | ? [Vvar__0___24Anonymous__9833] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__9833)
            & ? [Vvar__1___24Anonymous__9834] :
                ( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(Vvar__1___24Anonymous__9834)
                & VX9832 = cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(Vvar__0___24Anonymous__9833,Vvar__1___24Anonymous__9834) ) )
        | ? [Vvar__0___24Anonymous__9835] :
            ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__0___24Anonymous__9835)
            & ? [Vvar__1___24Anonymous__9836] :
                ( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(Vvar__1___24Anonymous__9836)
                & VX9832 = cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(Vvar__0___24Anonymous__9835,Vvar__1___24Anonymous__9836) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Ring_polynom.PExpr',axiom,
    ! [Vvar__0__C__9853,VX9854] :
      ( cType___24t(Vvar__0__C__9853)
     => ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__9853,VX9854)
       => ( VX9854 = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(Vvar__0__C__9853)
          | VX9854 = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(Vvar__0__C__9853)
          | ? [Vvar__1___24Anonymous__9858] :
              ( t(Vvar__1___24Anonymous__9858,Vvar__0__C__9853)
              & VX9854 = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(Vvar__0__C__9853,Vvar__1___24Anonymous__9858) )
          | ? [Vvar__1___24Anonymous__9860] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__9860)
              & VX9854 = cCoq_2esetoid__ring_2eRing__polynom_2ePEX___24a2(Vvar__0__C__9853,Vvar__1___24Anonymous__9860) )
          | ? [Vvar__1___24Anonymous__9862] :
              ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__9853,Vvar__1___24Anonymous__9862)
              & ? [Vvar__2___24Anonymous__9863] :
                  ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__9853,Vvar__2___24Anonymous__9863)
                  & VX9854 = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(Vvar__0__C__9853,Vvar__1___24Anonymous__9862,Vvar__2___24Anonymous__9863) ) )
          | ? [Vvar__1___24Anonymous__9865] :
              ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__9853,Vvar__1___24Anonymous__9865)
              & ? [Vvar__2___24Anonymous__9866] :
                  ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__9853,Vvar__2___24Anonymous__9866)
                  & VX9854 = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(Vvar__0__C__9853,Vvar__1___24Anonymous__9865,Vvar__2___24Anonymous__9866) ) )
          | ? [Vvar__1___24Anonymous__9868] :
              ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__9853,Vvar__1___24Anonymous__9868)
              & ? [Vvar__2___24Anonymous__9869] :
                  ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__9853,Vvar__2___24Anonymous__9869)
                  & VX9854 = cCoq_2esetoid__ring_2eRing__polynom_2ePEmul___24a3(Vvar__0__C__9853,Vvar__1___24Anonymous__9868,Vvar__2___24Anonymous__9869) ) )
          | ? [Vvar__1___24Anonymous__9871] :
              ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__9853,Vvar__1___24Anonymous__9871)
              & VX9854 = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(Vvar__0__C__9853,Vvar__1___24Anonymous__9871) )
          | ? [Vvar__1___24Anonymous__9873] :
              ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vvar__0__C__9853,Vvar__1___24Anonymous__9873)
              & ? [Vvar__2___24Anonymous__9874] :
                  ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__2___24Anonymous__9874)
                  & VX9854 = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(Vvar__0__C__9853,Vvar__1___24Anonymous__9873,Vvar__2___24Anonymous__9874) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Ring_polynom.Pol',axiom,
    ! [Vvar__0__C__9785,VX9786] :
      ( cType___24t(Vvar__0__C__9785)
     => ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__9785,VX9786)
       => ( ? [Vvar__1___24Anonymous__9788] :
              ( t(Vvar__1___24Anonymous__9788,Vvar__0__C__9785)
              & VX9786 = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(Vvar__0__C__9785,Vvar__1___24Anonymous__9788) )
          | ? [Vvar__1___24Anonymous__9790] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__1___24Anonymous__9790)
              & ? [Vvar__2___24Anonymous__9791] :
                  ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__9785,Vvar__2___24Anonymous__9791)
                  & VX9786 = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(Vvar__0__C__9785,Vvar__1___24Anonymous__9790,Vvar__2___24Anonymous__9791) ) )
          | ? [Vvar__1___24Anonymous__9793] :
              ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__9785,Vvar__1___24Anonymous__9793)
              & ? [Vvar__2___24Anonymous__9794] :
                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vvar__2___24Anonymous__9794)
                  & ? [Vvar__3___24Anonymous__9795] :
                      ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vvar__0__C__9785,Vvar__3___24Anonymous__9795)
                      & VX9786 = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(Vvar__0__C__9785,Vvar__1___24Anonymous__9793,Vvar__2___24Anonymous__9794,Vvar__3___24Anonymous__9795) ) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Ring_theory.almost_ring_theory',axiom,
    ! [Vvar__0__R__11452,Vvar__1__rO__11453,Vvar__2__rI__11454,Vvar__3__radd__11455,Vvar__4__rmul__11460,Vvar__5__rsub__11465,Vvar__6__ropp__11470,Vvar__7__req__11473] :
      ( cType___24t(Vvar__0__R__11452)
     => ( t(Vvar__1__rO__11453,Vvar__0__R__11452)
       => ( t(Vvar__2__rI__11454,Vvar__0__R__11452)
         => ( c_24__type__11701___24t(Vvar__0__R__11452,Vvar__1__rO__11453,Vvar__2__rI__11454,Vvar__3__radd__11455,Vvar__4__rmul__11460,Vvar__5__rsub__11465,Vvar__6__ropp__11470,Vvar__7__req__11473,Vvar__3__radd__11455)
           => ( c_24__type__11764___24t(Vvar__0__R__11452,Vvar__1__rO__11453,Vvar__2__rI__11454,Vvar__3__radd__11455,Vvar__4__rmul__11460,Vvar__5__rsub__11465,Vvar__6__ropp__11470,Vvar__7__req__11473,Vvar__4__rmul__11460)
             => ( c_24__type__11827___24t(Vvar__0__R__11452,Vvar__1__rO__11453,Vvar__2__rI__11454,Vvar__3__radd__11455,Vvar__4__rmul__11460,Vvar__5__rsub__11465,Vvar__6__ropp__11470,Vvar__7__req__11473,Vvar__5__rsub__11465)
               => ( c_24__type__11881___24t(Vvar__0__R__11452,Vvar__1__rO__11453,Vvar__2__rI__11454,Vvar__3__radd__11455,Vvar__4__rmul__11460,Vvar__5__rsub__11465,Vvar__6__ropp__11470,Vvar__7__req__11473,Vvar__6__ropp__11470)
                 => ( c_24__type__11944___24t(Vvar__0__R__11452,Vvar__1__rO__11453,Vvar__2__rI__11454,Vvar__3__radd__11455,Vvar__4__rmul__11460,Vvar__5__rsub__11465,Vvar__6__ropp__11470,Vvar__7__req__11473,Vvar__7__req__11473)
                   => ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(Vvar__0__R__11452,Vvar__1__rO__11453,Vvar__2__rI__11454,Vvar__3__radd__11455,Vvar__4__rmul__11460,Vvar__5__rsub__11465,Vvar__6__ropp__11470,Vvar__7__req__11473)
                     => ( ! [Vvar__var__var__var__var__var__8__x__11506__11507__11560__11561__11562__11563] :
                            ( t(Vvar__var__var__var__var__var__8__x__11506__11507__11560__11561__11562__11563,Vvar__0__R__11452)
                           => p(happ(happ(Vvar__7__req__11473,happ(happ(Vvar__3__radd__11455,Vvar__1__rO__11453),Vvar__var__var__var__var__var__8__x__11506__11507__11560__11561__11562__11563)),Vvar__var__var__var__var__var__8__x__11506__11507__11560__11561__11562__11563)) )
                        & ! [Vvar__var__var__var__var__9__x__11509__11511__11564__11566__11568] :
                            ( t(Vvar__var__var__var__var__9__x__11509__11511__11564__11566__11568,Vvar__0__R__11452)
                           => ! [Vvar__var__var__var__var__10__y__11510__11512__11565__11567__11569] :
                                ( t(Vvar__var__var__var__var__10__y__11510__11512__11565__11567__11569,Vvar__0__R__11452)
                               => p(happ(happ(Vvar__7__req__11473,happ(happ(Vvar__3__radd__11455,Vvar__var__var__var__var__9__x__11509__11511__11564__11566__11568),Vvar__var__var__var__var__10__y__11510__11512__11565__11567__11569)),happ(happ(Vvar__3__radd__11455,Vvar__var__var__var__var__10__y__11510__11512__11565__11567__11569),Vvar__var__var__var__var__9__x__11509__11511__11564__11566__11568))) ) )
                        & ! [Vvar__var__var__var__var__10__x__11514__11517__11570__11573__11576] :
                            ( t(Vvar__var__var__var__var__10__x__11514__11517__11570__11573__11576,Vvar__0__R__11452)
                           => ! [Vvar__var__var__var__var__11__y__11515__11518__11571__11574__11577] :
                                ( t(Vvar__var__var__var__var__11__y__11515__11518__11571__11574__11577,Vvar__0__R__11452)
                               => ! [Vvar__var__var__var__var__12__z__11516__11519__11572__11575__11578] :
                                    ( t(Vvar__var__var__var__var__12__z__11516__11519__11572__11575__11578,Vvar__0__R__11452)
                                   => p(happ(happ(Vvar__7__req__11473,happ(happ(Vvar__3__radd__11455,Vvar__var__var__var__var__10__x__11514__11517__11570__11573__11576),happ(happ(Vvar__3__radd__11455,Vvar__var__var__var__var__11__y__11515__11518__11571__11574__11577),Vvar__var__var__var__var__12__z__11516__11519__11572__11575__11578))),happ(happ(Vvar__3__radd__11455,happ(happ(Vvar__3__radd__11455,Vvar__var__var__var__var__10__x__11514__11517__11570__11573__11576),Vvar__var__var__var__var__11__y__11515__11518__11571__11574__11577)),Vvar__var__var__var__var__12__z__11516__11519__11572__11575__11578))) ) ) )
                        & ! [Vvar__var__var__var__var__var__11__x__11521__11522__11579__11580__11581__11582] :
                            ( t(Vvar__var__var__var__var__var__11__x__11521__11522__11579__11580__11581__11582,Vvar__0__R__11452)
                           => p(happ(happ(Vvar__7__req__11473,happ(happ(Vvar__4__rmul__11460,Vvar__2__rI__11454),Vvar__var__var__var__var__var__11__x__11521__11522__11579__11580__11581__11582)),Vvar__var__var__var__var__var__11__x__11521__11522__11579__11580__11581__11582)) )
                        & ! [Vvar__var__var__var__var__var__12__x__11524__11525__11583__11584__11585__11586] :
                            ( t(Vvar__var__var__var__var__var__12__x__11524__11525__11583__11584__11585__11586,Vvar__0__R__11452)
                           => p(happ(happ(Vvar__7__req__11473,happ(happ(Vvar__4__rmul__11460,Vvar__1__rO__11453),Vvar__var__var__var__var__var__12__x__11524__11525__11583__11584__11585__11586)),Vvar__1__rO__11453)) )
                        & ! [Vvar__var__var__var__var__13__x__11527__11529__11587__11589__11591] :
                            ( t(Vvar__var__var__var__var__13__x__11527__11529__11587__11589__11591,Vvar__0__R__11452)
                           => ! [Vvar__var__var__var__var__14__y__11528__11530__11588__11590__11592] :
                                ( t(Vvar__var__var__var__var__14__y__11528__11530__11588__11590__11592,Vvar__0__R__11452)
                               => p(happ(happ(Vvar__7__req__11473,happ(happ(Vvar__4__rmul__11460,Vvar__var__var__var__var__13__x__11527__11529__11587__11589__11591),Vvar__var__var__var__var__14__y__11528__11530__11588__11590__11592)),happ(happ(Vvar__4__rmul__11460,Vvar__var__var__var__var__14__y__11528__11530__11588__11590__11592),Vvar__var__var__var__var__13__x__11527__11529__11587__11589__11591))) ) )
                        & ! [Vvar__var__var__var__var__14__x__11532__11535__11593__11596__11599] :
                            ( t(Vvar__var__var__var__var__14__x__11532__11535__11593__11596__11599,Vvar__0__R__11452)
                           => ! [Vvar__var__var__var__var__15__y__11533__11536__11594__11597__11600] :
                                ( t(Vvar__var__var__var__var__15__y__11533__11536__11594__11597__11600,Vvar__0__R__11452)
                               => ! [Vvar__var__var__var__var__16__z__11534__11537__11595__11598__11601] :
                                    ( t(Vvar__var__var__var__var__16__z__11534__11537__11595__11598__11601,Vvar__0__R__11452)
                                   => p(happ(happ(Vvar__7__req__11473,happ(happ(Vvar__4__rmul__11460,Vvar__var__var__var__var__14__x__11532__11535__11593__11596__11599),happ(happ(Vvar__4__rmul__11460,Vvar__var__var__var__var__15__y__11533__11536__11594__11597__11600),Vvar__var__var__var__var__16__z__11534__11537__11595__11598__11601))),happ(happ(Vvar__4__rmul__11460,happ(happ(Vvar__4__rmul__11460,Vvar__var__var__var__var__14__x__11532__11535__11593__11596__11599),Vvar__var__var__var__var__15__y__11533__11536__11594__11597__11600)),Vvar__var__var__var__var__16__z__11534__11537__11595__11598__11601))) ) ) )
                        & ! [Vvar__var__var__var__var__var__15__x__11539__11542__11602__11605__11608__11611] :
                            ( t(Vvar__var__var__var__var__var__15__x__11539__11542__11602__11605__11608__11611,Vvar__0__R__11452)
                           => ! [Vvar__var__var__var__var__var__16__y__11540__11543__11603__11606__11609__11612] :
                                ( t(Vvar__var__var__var__var__var__16__y__11540__11543__11603__11606__11609__11612,Vvar__0__R__11452)
                               => ! [Vvar__var__var__var__var__var__17__z__11541__11544__11604__11607__11610__11613] :
                                    ( t(Vvar__var__var__var__var__var__17__z__11541__11544__11604__11607__11610__11613,Vvar__0__R__11452)
                                   => p(happ(happ(Vvar__7__req__11473,happ(happ(Vvar__4__rmul__11460,happ(happ(Vvar__3__radd__11455,Vvar__var__var__var__var__var__15__x__11539__11542__11602__11605__11608__11611),Vvar__var__var__var__var__var__16__y__11540__11543__11603__11606__11609__11612)),Vvar__var__var__var__var__var__17__z__11541__11544__11604__11607__11610__11613)),happ(happ(Vvar__3__radd__11455,happ(happ(Vvar__4__rmul__11460,Vvar__var__var__var__var__var__15__x__11539__11542__11602__11605__11608__11611),Vvar__var__var__var__var__var__17__z__11541__11544__11604__11607__11610__11613)),happ(happ(Vvar__4__rmul__11460,Vvar__var__var__var__var__var__16__y__11540__11543__11603__11606__11609__11612),Vvar__var__var__var__var__var__17__z__11541__11544__11604__11607__11610__11613)))) ) ) )
                        & ! [Vvar__var__var__var__var__var__16__x__11546__11548__11614__11616__11618__11620] :
                            ( t(Vvar__var__var__var__var__var__16__x__11546__11548__11614__11616__11618__11620,Vvar__0__R__11452)
                           => ! [Vvar__var__var__var__var__var__17__y__11547__11549__11615__11617__11619__11621] :
                                ( t(Vvar__var__var__var__var__var__17__y__11547__11549__11615__11617__11619__11621,Vvar__0__R__11452)
                               => p(happ(happ(Vvar__7__req__11473,happ(Vvar__6__ropp__11470,happ(happ(Vvar__4__rmul__11460,Vvar__var__var__var__var__var__16__x__11546__11548__11614__11616__11618__11620),Vvar__var__var__var__var__var__17__y__11547__11549__11615__11617__11619__11621))),happ(happ(Vvar__4__rmul__11460,happ(Vvar__6__ropp__11470,Vvar__var__var__var__var__var__16__x__11546__11548__11614__11616__11618__11620)),Vvar__var__var__var__var__var__17__y__11547__11549__11615__11617__11619__11621))) ) )
                        & ! [Vvar__var__var__var__var__var__17__x__11551__11553__11622__11624__11626__11628] :
                            ( t(Vvar__var__var__var__var__var__17__x__11551__11553__11622__11624__11626__11628,Vvar__0__R__11452)
                           => ! [Vvar__var__var__var__var__var__18__y__11552__11554__11623__11625__11627__11629] :
                                ( t(Vvar__var__var__var__var__var__18__y__11552__11554__11623__11625__11627__11629,Vvar__0__R__11452)
                               => p(happ(happ(Vvar__7__req__11473,happ(Vvar__6__ropp__11470,happ(happ(Vvar__3__radd__11455,Vvar__var__var__var__var__var__17__x__11551__11553__11622__11624__11626__11628),Vvar__var__var__var__var__var__18__y__11552__11554__11623__11625__11627__11629))),happ(happ(Vvar__3__radd__11455,happ(Vvar__6__ropp__11470,Vvar__var__var__var__var__var__17__x__11551__11553__11622__11624__11626__11628)),happ(Vvar__6__ropp__11470,Vvar__var__var__var__var__var__18__y__11552__11554__11623__11625__11627__11629)))) ) )
                        & ! [Vvar__var__var__var__var__var__var__18__x__11556__11558__11630__11632__11634__11636__11638] :
                            ( t(Vvar__var__var__var__var__var__var__18__x__11556__11558__11630__11632__11634__11636__11638,Vvar__0__R__11452)
                           => ! [Vvar__var__var__var__var__var__var__19__y__11557__11559__11631__11633__11635__11637__11639] :
                                ( t(Vvar__var__var__var__var__var__var__19__y__11557__11559__11631__11633__11635__11637__11639,Vvar__0__R__11452)
                               => p(happ(happ(Vvar__7__req__11473,happ(happ(Vvar__5__rsub__11465,Vvar__var__var__var__var__var__var__18__x__11556__11558__11630__11632__11634__11636__11638),Vvar__var__var__var__var__var__var__19__y__11557__11559__11631__11633__11635__11637__11639)),happ(happ(Vvar__3__radd__11455,Vvar__var__var__var__var__var__var__18__x__11556__11558__11630__11632__11634__11636__11638),happ(Vvar__6__ropp__11470,Vvar__var__var__var__var__var__var__19__y__11557__11559__11631__11633__11635__11637__11639)))) ) )
                        & p(c_24True) ) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Ring_theory.div_theory',axiom,
    ! [Vvar__0__R__15028,Vvar__1__req__15029,Vvar__2__C__15034,Vvar__3__cadd__15035,Vvar__4__cmul__15040,Vvar__5__phi__15045,Vvar__6__cdiv__15048] :
      ( cType___24t(Vvar__0__R__15028)
     => ( c_24__type__15168___24t(Vvar__0__R__15028,Vvar__1__req__15029,Vvar__2__C__15034,Vvar__3__cadd__15035,Vvar__4__cmul__15040,Vvar__5__phi__15045,Vvar__6__cdiv__15048,Vvar__1__req__15029)
       => ( cType___24t(Vvar__2__C__15034)
         => ( c_24__type__15218___24t(Vvar__0__R__15028,Vvar__1__req__15029,Vvar__2__C__15034,Vvar__3__cadd__15035,Vvar__4__cmul__15040,Vvar__5__phi__15045,Vvar__6__cdiv__15048,Vvar__3__cadd__15035)
           => ( c_24__type__15268___24t(Vvar__0__R__15028,Vvar__1__req__15029,Vvar__2__C__15034,Vvar__3__cadd__15035,Vvar__4__cmul__15040,Vvar__5__phi__15045,Vvar__6__cdiv__15048,Vvar__4__cmul__15040)
             => ( c_24__type__15310___24t(Vvar__0__R__15028,Vvar__1__req__15029,Vvar__2__C__15034,Vvar__3__cadd__15035,Vvar__4__cmul__15040,Vvar__5__phi__15045,Vvar__6__cdiv__15048,Vvar__5__phi__15045)
               => ( c_24__type__15360___24t(Vvar__0__R__15028,Vvar__1__req__15029,Vvar__2__C__15034,Vvar__3__cadd__15035,Vvar__4__cmul__15040,Vvar__5__phi__15045,Vvar__6__cdiv__15048,Vvar__6__cdiv__15048)
                 => ( cCoq_2esetoid__ring_2eRing__theory_2ediv__theory___24a7(Vvar__0__R__15028,Vvar__1__req__15029,Vvar__2__C__15034,Vvar__3__cadd__15035,Vvar__4__cmul__15040,Vvar__5__phi__15045,Vvar__6__cdiv__15048)
                   => ( ! [Vvar__var__var__var__var__var__var__var__7__a__15080__15085__15090__15095__15100__15105__15110__15115] :
                          ( t(Vvar__var__var__var__var__var__var__var__7__a__15080__15085__15090__15095__15100__15105__15110__15115,Vvar__2__C__15034)
                         => ! [Vvar__var__var__var__var__var__var__var__8__b__15081__15086__15091__15096__15101__15106__15111__15116] :
                              ( t(Vvar__var__var__var__var__var__var__var__8__b__15081__15086__15091__15096__15101__15106__15111__15116,Vvar__2__C__15034)
                             => c_24__case__Coq_2eInit_2eDatatypes_2eprod_2415423___24a9(Vvar__0__R__15028,Vvar__1__req__15029,Vvar__2__C__15034,Vvar__3__cadd__15035,Vvar__4__cmul__15040,Vvar__5__phi__15045,Vvar__6__cdiv__15048,Vvar__var__var__var__var__var__var__var__7__a__15080__15085__15090__15095__15100__15105__15110__15115,Vvar__var__var__var__var__var__var__var__8__b__15081__15086__15091__15096__15101__15106__15111__15116) ) )
                      & p(c_24True) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Ring_theory.power_theory',axiom,
    ! [Vvar__0__R__15443,Vvar__1__rI__15444,Vvar__2__rmul__15445,Vvar__3__req__15450,Vvar__4__Cpow__15455,Vvar__5__Cp__phi__15456,Vvar__6__rpow__15459] :
      ( cType___24t(Vvar__0__R__15443)
     => ( t(Vvar__1__rI__15444,Vvar__0__R__15443)
       => ( c_24__type__15545___24t(Vvar__0__R__15443,Vvar__1__rI__15444,Vvar__2__rmul__15445,Vvar__3__req__15450,Vvar__4__Cpow__15455,Vvar__5__Cp__phi__15456,Vvar__6__rpow__15459,Vvar__2__rmul__15445)
         => ( c_24__type__15589___24t(Vvar__0__R__15443,Vvar__1__rI__15444,Vvar__2__rmul__15445,Vvar__3__req__15450,Vvar__4__Cpow__15455,Vvar__5__Cp__phi__15456,Vvar__6__rpow__15459,Vvar__3__req__15450)
           => ( cType___24t(Vvar__4__Cpow__15455)
             => ( c_24__type__15625___24t(Vvar__0__R__15443,Vvar__1__rI__15444,Vvar__2__rmul__15445,Vvar__3__req__15450,Vvar__4__Cpow__15455,Vvar__5__Cp__phi__15456,Vvar__6__rpow__15459,Vvar__5__Cp__phi__15456)
               => ( c_24__type__15669___24t(Vvar__0__R__15443,Vvar__1__rI__15444,Vvar__2__rmul__15445,Vvar__3__req__15450,Vvar__4__Cpow__15455,Vvar__5__Cp__phi__15456,Vvar__6__rpow__15459,Vvar__6__rpow__15459)
                 => ( cCoq_2esetoid__ring_2eRing__theory_2epower__theory___24a7(Vvar__0__R__15443,Vvar__1__rI__15444,Vvar__2__rmul__15445,Vvar__3__req__15450,Vvar__4__Cpow__15455,Vvar__5__Cp__phi__15456,Vvar__6__rpow__15459)
                   => ( ! [Vvar__var__var__var__var__var__var__var__7__r__15487__15489__15491__15493__15495__15497__15499__15501] :
                          ( t(Vvar__var__var__var__var__var__var__var__7__r__15487__15489__15491__15493__15495__15497__15499__15501,Vvar__0__R__15443)
                         => ! [Vvar__var__var__var__var__var__var__var__8__n__15488__15490__15492__15494__15496__15498__15500__15502] :
                              ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vvar__var__var__var__var__var__var__var__8__n__15488__15490__15492__15494__15496__15498__15500__15502)
                             => p(happ(happ(Vvar__3__req__15450,happ(happ(Vvar__6__rpow__15459,Vvar__var__var__var__var__var__var__var__7__r__15487__15489__15491__15493__15495__15497__15499__15501),happ(Vvar__5__Cp__phi__15456,Vvar__var__var__var__var__var__var__var__8__n__15488__15490__15492__15494__15496__15498__15500__15502))),cCoq_2esetoid__ring_2eRing__theory_2epow__N___24a5(Vvar__0__R__15443,Vvar__1__rI__15444,Vvar__2__rmul__15445,Vvar__var__var__var__var__var__var__var__7__r__15487__15489__15491__15493__15495__15497__15499__15501,Vvar__var__var__var__var__var__var__var__8__n__15488__15490__15492__15494__15496__15498__15500__15502))) ) )
                      & p(c_24True) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Ring_theory.ring_eq_ext',axiom,
    ! [Vvar__0__R__12046,Vvar__1__radd__12047,Vvar__2__rmul__12052,Vvar__3__ropp__12057,Vvar__4__req__12060] :
      ( cType___24t(Vvar__0__R__12046)
     => ( c_24__type__12151___24t(Vvar__0__R__12046,Vvar__1__radd__12047,Vvar__2__rmul__12052,Vvar__3__ropp__12057,Vvar__4__req__12060,Vvar__1__radd__12047)
       => ( c_24__type__12181___24t(Vvar__0__R__12046,Vvar__1__radd__12047,Vvar__2__rmul__12052,Vvar__3__ropp__12057,Vvar__4__req__12060,Vvar__2__rmul__12052)
         => ( c_24__type__12205___24t(Vvar__0__R__12046,Vvar__1__radd__12047,Vvar__2__rmul__12052,Vvar__3__ropp__12057,Vvar__4__req__12060,Vvar__3__ropp__12057)
           => ( c_24__type__12235___24t(Vvar__0__R__12046,Vvar__1__radd__12047,Vvar__2__rmul__12052,Vvar__3__ropp__12057,Vvar__4__req__12060,Vvar__4__req__12060)
             => ( cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(Vvar__0__R__12046,Vvar__1__radd__12047,Vvar__2__rmul__12052,Vvar__3__ropp__12057,Vvar__4__req__12060)
               => ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__12265___24a5(Vvar__0__R__12046,Vvar__1__radd__12047,Vvar__2__rmul__12052,Vvar__3__ropp__12057,Vvar__4__req__12060),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__12046,c_24__type__12289___24a5(Vvar__0__R__12046,Vvar__1__radd__12047,Vvar__2__rmul__12052,Vvar__3__ropp__12057,Vvar__4__req__12060),Vvar__4__req__12060,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__12046,Vvar__0__R__12046,Vvar__4__req__12060,Vvar__4__req__12060)),Vvar__1__radd__12047)
                  & cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__12322___24a5(Vvar__0__R__12046,Vvar__1__radd__12047,Vvar__2__rmul__12052,Vvar__3__ropp__12057,Vvar__4__req__12060),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__12046,c_24__type__12346___24a5(Vvar__0__R__12046,Vvar__1__radd__12047,Vvar__2__rmul__12052,Vvar__3__ropp__12057,Vvar__4__req__12060),Vvar__4__req__12060,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__12046,Vvar__0__R__12046,Vvar__4__req__12060,Vvar__4__req__12060)),Vvar__2__rmul__12052)
                  & cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__12373___24a5(Vvar__0__R__12046,Vvar__1__radd__12047,Vvar__2__rmul__12052,Vvar__3__ropp__12057,Vvar__4__req__12060),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__12046,Vvar__0__R__12046,Vvar__4__req__12060,Vvar__4__req__12060),Vvar__3__ropp__12057)
                  & p(c_24True) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Ring_theory.ring_kind',axiom,
    ! [VX34287] :
      ( cCoq_2esetoid__ring_2eRing__theory_2ering__kind___24t(VX34287)
     => ( VX34287 = cCoq_2esetoid__ring_2eRing__theory_2eAbstract
        | ? [Vvar__0__R__34288] :
            ( cType___24t(Vvar__0__R__34288)
            & ? [Vvar__1__req__34289] :
                ( c_24__type__4775___24t(Vvar__0__R__34288,Vvar__1__req__34289)
                & ? [Vvar__2__reqb__34294] :
                    ( c_24__type__9314___24t(Vvar__0__R__34288,Vvar__2__reqb__34294)
                    & ! [Vvar__var__3__x__34300__34303] :
                        ( t(Vvar__var__3__x__34300__34303,Vvar__0__R__34288)
                       => ! [Vvar__var__4__y__34301__34304] :
                            ( t(Vvar__var__4__y__34301__34304,Vvar__0__R__34288)
                           => ( happ(happ(Vvar__2__reqb__34294,Vvar__var__3__x__34300__34303),Vvar__var__4__y__34301__34304) = cCoq_2eInit_2eDatatypes_2etrue
                             => p(happ(happ(Vvar__1__req__34289,Vvar__var__3__x__34300__34303),Vvar__var__4__y__34301__34304)) ) ) )
                    & VX34287 = cCoq_2esetoid__ring_2eRing__theory_2eComputational___24a3(Vvar__0__R__34288,Vvar__1__req__34289,Vvar__2__reqb__34294) ) ) )
        | ? [Vvar__0__R__34306] :
            ( cType___24t(Vvar__0__R__34306)
            & ? [Vvar__1__rO__34307] :
                ( t(Vvar__1__rO__34307,Vvar__0__R__34306)
                & ? [Vvar__2__rI__34308] :
                    ( t(Vvar__2__rI__34308,Vvar__0__R__34306)
                    & ? [Vvar__3__radd__34309] :
                        ( c_24__type__6582___24t(Vvar__0__R__34306,Vvar__3__radd__34309)
                        & ? [Vvar__4__rmul__34314] :
                            ( c_24__type__6582___24t(Vvar__0__R__34306,Vvar__4__rmul__34314)
                            & ? [Vvar__5__rsub__34319] :
                                ( c_24__type__6582___24t(Vvar__0__R__34306,Vvar__5__rsub__34319)
                                & ? [Vvar__6__ropp__34324] :
                                    ( c_24__type__6591___24t(Vvar__0__R__34306,Vvar__6__ropp__34324)
                                    & ? [Vvar__7__req__34327] :
                                        ( c_24__type__4775___24t(Vvar__0__R__34306,Vvar__7__req__34327)
                                        & ? [Vvar__8__C__34332] :
                                            ( cType___24t(Vvar__8__C__34332)
                                            & ? [Vvar__9__cO__34333] :
                                                ( t(Vvar__9__cO__34333,Vvar__8__C__34332)
                                                & ? [Vvar__10__cI__34334] :
                                                    ( t(Vvar__10__cI__34334,Vvar__8__C__34332)
                                                    & ? [Vvar__11__cadd__34335] :
                                                        ( c_24__type__9338___24t(Vvar__0__R__34306,Vvar__8__C__34332,Vvar__11__cadd__34335)
                                                        & ? [Vvar__12__cmul__34340] :
                                                            ( c_24__type__9338___24t(Vvar__0__R__34306,Vvar__8__C__34332,Vvar__12__cmul__34340)
                                                            & ? [Vvar__13__csub__34345] :
                                                                ( c_24__type__9338___24t(Vvar__0__R__34306,Vvar__8__C__34332,Vvar__13__csub__34345)
                                                                & ? [Vvar__14__copp__34350] :
                                                                    ( c_24__type__9352___24t(Vvar__0__R__34306,Vvar__8__C__34332,Vvar__14__copp__34350)
                                                                    & ? [Vvar__15__ceqb__34353] :
                                                                        ( c_24__type__9359___24t(Vvar__0__R__34306,Vvar__8__C__34332,Vvar__15__ceqb__34353)
                                                                        & ? [Vvar__16__phi__34358] :
                                                                            ( c_24__type__8921___24t(Vvar__0__R__34306,Vvar__8__C__34332,Vvar__16__phi__34358)
                                                                            & cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(Vvar__0__R__34306,Vvar__1__rO__34307,Vvar__2__rI__34308,Vvar__3__radd__34309,Vvar__4__rmul__34314,Vvar__5__rsub__34319,Vvar__6__ropp__34324,Vvar__7__req__34327,Vvar__8__C__34332,Vvar__9__cO__34333,Vvar__10__cI__34334,Vvar__11__cadd__34335,Vvar__12__cmul__34340,Vvar__13__csub__34345,Vvar__14__copp__34350,Vvar__15__ceqb__34353,Vvar__16__phi__34358)
                                                                            & VX34287 = cCoq_2esetoid__ring_2eRing__theory_2eMorphism___24a17(Vvar__0__R__34306,Vvar__1__rO__34307,Vvar__2__rI__34308,Vvar__3__radd__34309,Vvar__4__rmul__34314,Vvar__5__rsub__34319,Vvar__6__ropp__34324,Vvar__7__req__34327,Vvar__8__C__34332,Vvar__9__cO__34333,Vvar__10__cI__34334,Vvar__11__cadd__34335,Vvar__12__cmul__34340,Vvar__13__csub__34345,Vvar__14__copp__34350,Vvar__15__ceqb__34353,Vvar__16__phi__34358) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Ring_theory.ring_morph',axiom,
    ! [Vvar__0__R__12376,Vvar__1__rO__12377,Vvar__2__rI__12378,Vvar__3__radd__12379,Vvar__4__rmul__12384,Vvar__5__rsub__12389,Vvar__6__ropp__12394,Vvar__7__req__12397,Vvar__8__C__12402,Vvar__9__cO__12403,Vvar__10__cI__12404,Vvar__11__cadd__12405,Vvar__12__cmul__12410,Vvar__13__csub__12415,Vvar__14__copp__12420,Vvar__15__ceqb__12423,Vvar__16__phi__12428] :
      ( cType___24t(Vvar__0__R__12376)
     => ( t(Vvar__1__rO__12377,Vvar__0__R__12376)
       => ( t(Vvar__2__rI__12378,Vvar__0__R__12376)
         => ( c_24__type__12772___24t(Vvar__0__R__12376,Vvar__1__rO__12377,Vvar__2__rI__12378,Vvar__3__radd__12379,Vvar__4__rmul__12384,Vvar__5__rsub__12389,Vvar__6__ropp__12394,Vvar__7__req__12397,Vvar__8__C__12402,Vvar__9__cO__12403,Vvar__10__cI__12404,Vvar__11__cadd__12405,Vvar__12__cmul__12410,Vvar__13__csub__12415,Vvar__14__copp__12420,Vvar__15__ceqb__12423,Vvar__16__phi__12428,Vvar__3__radd__12379)
           => ( c_24__type__12985___24t(Vvar__0__R__12376,Vvar__1__rO__12377,Vvar__2__rI__12378,Vvar__3__radd__12379,Vvar__4__rmul__12384,Vvar__5__rsub__12389,Vvar__6__ropp__12394,Vvar__7__req__12397,Vvar__8__C__12402,Vvar__9__cO__12403,Vvar__10__cI__12404,Vvar__11__cadd__12405,Vvar__12__cmul__12410,Vvar__13__csub__12415,Vvar__14__copp__12420,Vvar__15__ceqb__12423,Vvar__16__phi__12428,Vvar__4__rmul__12384)
             => ( c_24__type__13198___24t(Vvar__0__R__12376,Vvar__1__rO__12377,Vvar__2__rI__12378,Vvar__3__radd__12379,Vvar__4__rmul__12384,Vvar__5__rsub__12389,Vvar__6__ropp__12394,Vvar__7__req__12397,Vvar__8__C__12402,Vvar__9__cO__12403,Vvar__10__cI__12404,Vvar__11__cadd__12405,Vvar__12__cmul__12410,Vvar__13__csub__12415,Vvar__14__copp__12420,Vvar__15__ceqb__12423,Vvar__16__phi__12428,Vvar__5__rsub__12389)
               => ( c_24__type__13393___24t(Vvar__0__R__12376,Vvar__1__rO__12377,Vvar__2__rI__12378,Vvar__3__radd__12379,Vvar__4__rmul__12384,Vvar__5__rsub__12389,Vvar__6__ropp__12394,Vvar__7__req__12397,Vvar__8__C__12402,Vvar__9__cO__12403,Vvar__10__cI__12404,Vvar__11__cadd__12405,Vvar__12__cmul__12410,Vvar__13__csub__12415,Vvar__14__copp__12420,Vvar__15__ceqb__12423,Vvar__16__phi__12428,Vvar__6__ropp__12394)
                 => ( c_24__type__13606___24t(Vvar__0__R__12376,Vvar__1__rO__12377,Vvar__2__rI__12378,Vvar__3__radd__12379,Vvar__4__rmul__12384,Vvar__5__rsub__12389,Vvar__6__ropp__12394,Vvar__7__req__12397,Vvar__8__C__12402,Vvar__9__cO__12403,Vvar__10__cI__12404,Vvar__11__cadd__12405,Vvar__12__cmul__12410,Vvar__13__csub__12415,Vvar__14__copp__12420,Vvar__15__ceqb__12423,Vvar__16__phi__12428,Vvar__7__req__12397)
                   => ( cType___24t(Vvar__8__C__12402)
                     => ( t(Vvar__9__cO__12403,Vvar__8__C__12402)
                       => ( t(Vvar__10__cI__12404,Vvar__8__C__12402)
                         => ( c_24__type__13819___24t(Vvar__0__R__12376,Vvar__1__rO__12377,Vvar__2__rI__12378,Vvar__3__radd__12379,Vvar__4__rmul__12384,Vvar__5__rsub__12389,Vvar__6__ropp__12394,Vvar__7__req__12397,Vvar__8__C__12402,Vvar__9__cO__12403,Vvar__10__cI__12404,Vvar__11__cadd__12405,Vvar__12__cmul__12410,Vvar__13__csub__12415,Vvar__14__copp__12420,Vvar__15__ceqb__12423,Vvar__16__phi__12428,Vvar__11__cadd__12405)
                           => ( c_24__type__14032___24t(Vvar__0__R__12376,Vvar__1__rO__12377,Vvar__2__rI__12378,Vvar__3__radd__12379,Vvar__4__rmul__12384,Vvar__5__rsub__12389,Vvar__6__ropp__12394,Vvar__7__req__12397,Vvar__8__C__12402,Vvar__9__cO__12403,Vvar__10__cI__12404,Vvar__11__cadd__12405,Vvar__12__cmul__12410,Vvar__13__csub__12415,Vvar__14__copp__12420,Vvar__15__ceqb__12423,Vvar__16__phi__12428,Vvar__12__cmul__12410)
                             => ( c_24__type__14245___24t(Vvar__0__R__12376,Vvar__1__rO__12377,Vvar__2__rI__12378,Vvar__3__radd__12379,Vvar__4__rmul__12384,Vvar__5__rsub__12389,Vvar__6__ropp__12394,Vvar__7__req__12397,Vvar__8__C__12402,Vvar__9__cO__12403,Vvar__10__cI__12404,Vvar__11__cadd__12405,Vvar__12__cmul__12410,Vvar__13__csub__12415,Vvar__14__copp__12420,Vvar__15__ceqb__12423,Vvar__16__phi__12428,Vvar__13__csub__12415)
                               => ( c_24__type__14440___24t(Vvar__0__R__12376,Vvar__1__rO__12377,Vvar__2__rI__12378,Vvar__3__radd__12379,Vvar__4__rmul__12384,Vvar__5__rsub__12389,Vvar__6__ropp__12394,Vvar__7__req__12397,Vvar__8__C__12402,Vvar__9__cO__12403,Vvar__10__cI__12404,Vvar__11__cadd__12405,Vvar__12__cmul__12410,Vvar__13__csub__12415,Vvar__14__copp__12420,Vvar__15__ceqb__12423,Vvar__16__phi__12428,Vvar__14__copp__12420)
                                 => ( c_24__type__14653___24t(Vvar__0__R__12376,Vvar__1__rO__12377,Vvar__2__rI__12378,Vvar__3__radd__12379,Vvar__4__rmul__12384,Vvar__5__rsub__12389,Vvar__6__ropp__12394,Vvar__7__req__12397,Vvar__8__C__12402,Vvar__9__cO__12403,Vvar__10__cI__12404,Vvar__11__cadd__12405,Vvar__12__cmul__12410,Vvar__13__csub__12415,Vvar__14__copp__12420,Vvar__15__ceqb__12423,Vvar__16__phi__12428,Vvar__15__ceqb__12423)
                                   => ( c_24__type__14848___24t(Vvar__0__R__12376,Vvar__1__rO__12377,Vvar__2__rI__12378,Vvar__3__radd__12379,Vvar__4__rmul__12384,Vvar__5__rsub__12389,Vvar__6__ropp__12394,Vvar__7__req__12397,Vvar__8__C__12402,Vvar__9__cO__12403,Vvar__10__cI__12404,Vvar__11__cadd__12405,Vvar__12__cmul__12410,Vvar__13__csub__12415,Vvar__14__copp__12420,Vvar__15__ceqb__12423,Vvar__16__phi__12428,Vvar__16__phi__12428)
                                     => ( cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(Vvar__0__R__12376,Vvar__1__rO__12377,Vvar__2__rI__12378,Vvar__3__radd__12379,Vvar__4__rmul__12384,Vvar__5__rsub__12389,Vvar__6__ropp__12394,Vvar__7__req__12397,Vvar__8__C__12402,Vvar__9__cO__12403,Vvar__10__cI__12404,Vvar__11__cadd__12405,Vvar__12__cmul__12410,Vvar__13__csub__12415,Vvar__14__copp__12420,Vvar__15__ceqb__12423,Vvar__16__phi__12428)
                                       => ( p(happ(happ(Vvar__7__req__12397,happ(Vvar__16__phi__12428,Vvar__9__cO__12403)),Vvar__1__rO__12377))
                                          & p(happ(happ(Vvar__7__req__12397,happ(Vvar__16__phi__12428,Vvar__10__cI__12404)),Vvar__2__rI__12378))
                                          & ! [Vvar__var__var__var__var__var__var__19__x__12490__12492__12514__12516__12518__12520__12522] :
                                              ( t(Vvar__var__var__var__var__var__var__19__x__12490__12492__12514__12516__12518__12520__12522,Vvar__8__C__12402)
                                             => ! [Vvar__var__var__var__var__var__var__20__y__12491__12493__12515__12517__12519__12521__12523] :
                                                  ( t(Vvar__var__var__var__var__var__var__20__y__12491__12493__12515__12517__12519__12521__12523,Vvar__8__C__12402)
                                                 => p(happ(happ(Vvar__7__req__12397,happ(Vvar__16__phi__12428,happ(happ(Vvar__11__cadd__12405,Vvar__var__var__var__var__var__var__19__x__12490__12492__12514__12516__12518__12520__12522),Vvar__var__var__var__var__var__var__20__y__12491__12493__12515__12517__12519__12521__12523))),happ(happ(Vvar__3__radd__12379,happ(Vvar__16__phi__12428,Vvar__var__var__var__var__var__var__19__x__12490__12492__12514__12516__12518__12520__12522)),happ(Vvar__16__phi__12428,Vvar__var__var__var__var__var__var__20__y__12491__12493__12515__12517__12519__12521__12523)))) ) )
                                          & ! [Vvar__var__var__var__var__var__var__20__x__12495__12497__12524__12526__12528__12530__12532] :
                                              ( t(Vvar__var__var__var__var__var__var__20__x__12495__12497__12524__12526__12528__12530__12532,Vvar__8__C__12402)
                                             => ! [Vvar__var__var__var__var__var__var__21__y__12496__12498__12525__12527__12529__12531__12533] :
                                                  ( t(Vvar__var__var__var__var__var__var__21__y__12496__12498__12525__12527__12529__12531__12533,Vvar__8__C__12402)
                                                 => p(happ(happ(Vvar__7__req__12397,happ(Vvar__16__phi__12428,happ(happ(Vvar__13__csub__12415,Vvar__var__var__var__var__var__var__20__x__12495__12497__12524__12526__12528__12530__12532),Vvar__var__var__var__var__var__var__21__y__12496__12498__12525__12527__12529__12531__12533))),happ(happ(Vvar__5__rsub__12389,happ(Vvar__16__phi__12428,Vvar__var__var__var__var__var__var__20__x__12495__12497__12524__12526__12528__12530__12532)),happ(Vvar__16__phi__12428,Vvar__var__var__var__var__var__var__21__y__12496__12498__12525__12527__12529__12531__12533)))) ) )
                                          & ! [Vvar__var__var__var__var__var__var__21__x__12500__12502__12534__12536__12538__12540__12542] :
                                              ( t(Vvar__var__var__var__var__var__var__21__x__12500__12502__12534__12536__12538__12540__12542,Vvar__8__C__12402)
                                             => ! [Vvar__var__var__var__var__var__var__22__y__12501__12503__12535__12537__12539__12541__12543] :
                                                  ( t(Vvar__var__var__var__var__var__var__22__y__12501__12503__12535__12537__12539__12541__12543,Vvar__8__C__12402)
                                                 => p(happ(happ(Vvar__7__req__12397,happ(Vvar__16__phi__12428,happ(happ(Vvar__12__cmul__12410,Vvar__var__var__var__var__var__var__21__x__12500__12502__12534__12536__12538__12540__12542),Vvar__var__var__var__var__var__var__22__y__12501__12503__12535__12537__12539__12541__12543))),happ(happ(Vvar__4__rmul__12384,happ(Vvar__16__phi__12428,Vvar__var__var__var__var__var__var__21__x__12500__12502__12534__12536__12538__12540__12542)),happ(Vvar__16__phi__12428,Vvar__var__var__var__var__var__var__22__y__12501__12503__12535__12537__12539__12541__12543)))) ) )
                                          & ! [Vvar__var__var__var__var__var__var__22__x__12505__12506__12544__12545__12546__12547__12548] :
                                              ( t(Vvar__var__var__var__var__var__var__22__x__12505__12506__12544__12545__12546__12547__12548,Vvar__8__C__12402)
                                             => p(happ(happ(Vvar__7__req__12397,happ(Vvar__16__phi__12428,happ(Vvar__14__copp__12420,Vvar__var__var__var__var__var__var__22__x__12505__12506__12544__12545__12546__12547__12548))),happ(Vvar__6__ropp__12394,happ(Vvar__16__phi__12428,Vvar__var__var__var__var__var__var__22__x__12505__12506__12544__12545__12546__12547__12548)))) )
                                          & ! [Vvar__var__var__var__var__var__23__x__12508__12511__12549__12552__12555__12558] :
                                              ( t(Vvar__var__var__var__var__var__23__x__12508__12511__12549__12552__12555__12558,Vvar__8__C__12402)
                                             => ! [Vvar__var__var__var__var__var__24__y__12509__12512__12550__12553__12556__12559] :
                                                  ( t(Vvar__var__var__var__var__var__24__y__12509__12512__12550__12553__12556__12559,Vvar__8__C__12402)
                                                 => ( happ(happ(Vvar__15__ceqb__12423,Vvar__var__var__var__var__var__23__x__12508__12511__12549__12552__12555__12558),Vvar__var__var__var__var__var__24__y__12509__12512__12550__12553__12556__12559) = cCoq_2eInit_2eDatatypes_2etrue
                                                   => p(happ(happ(Vvar__7__req__12397,happ(Vvar__16__phi__12428,Vvar__var__var__var__var__var__23__x__12508__12511__12549__12552__12555__12558)),happ(Vvar__16__phi__12428,Vvar__var__var__var__var__var__24__y__12509__12512__12550__12553__12556__12559))) ) ) )
                                          & p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Ring_theory.ring_theory',axiom,
    ! [Vvar__0__R__6631,Vvar__1__rO__6632,Vvar__2__rI__6633,Vvar__3__radd__6634,Vvar__4__rmul__6639,Vvar__5__rsub__6644,Vvar__6__ropp__6649,Vvar__7__req__6652] :
      ( cType___24t(Vvar__0__R__6631)
     => ( t(Vvar__1__rO__6632,Vvar__0__R__6631)
       => ( t(Vvar__2__rI__6633,Vvar__0__R__6631)
         => ( c_24__type__6855___24t(Vvar__0__R__6631,Vvar__1__rO__6632,Vvar__2__rI__6633,Vvar__3__radd__6634,Vvar__4__rmul__6639,Vvar__5__rsub__6644,Vvar__6__ropp__6649,Vvar__7__req__6652,Vvar__3__radd__6634)
           => ( c_24__type__6918___24t(Vvar__0__R__6631,Vvar__1__rO__6632,Vvar__2__rI__6633,Vvar__3__radd__6634,Vvar__4__rmul__6639,Vvar__5__rsub__6644,Vvar__6__ropp__6649,Vvar__7__req__6652,Vvar__4__rmul__6639)
             => ( c_24__type__6981___24t(Vvar__0__R__6631,Vvar__1__rO__6632,Vvar__2__rI__6633,Vvar__3__radd__6634,Vvar__4__rmul__6639,Vvar__5__rsub__6644,Vvar__6__ropp__6649,Vvar__7__req__6652,Vvar__5__rsub__6644)
               => ( c_24__type__7035___24t(Vvar__0__R__6631,Vvar__1__rO__6632,Vvar__2__rI__6633,Vvar__3__radd__6634,Vvar__4__rmul__6639,Vvar__5__rsub__6644,Vvar__6__ropp__6649,Vvar__7__req__6652,Vvar__6__ropp__6649)
                 => ( c_24__type__7098___24t(Vvar__0__R__6631,Vvar__1__rO__6632,Vvar__2__rI__6633,Vvar__3__radd__6634,Vvar__4__rmul__6639,Vvar__5__rsub__6644,Vvar__6__ropp__6649,Vvar__7__req__6652,Vvar__7__req__6652)
                   => ( cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(Vvar__0__R__6631,Vvar__1__rO__6632,Vvar__2__rI__6633,Vvar__3__radd__6634,Vvar__4__rmul__6639,Vvar__5__rsub__6644,Vvar__6__ropp__6649,Vvar__7__req__6652)
                     => ( ! [Vvar__var__var__var__var__var__8__x__6685__6686__6729__6730__6731__6732] :
                            ( t(Vvar__var__var__var__var__var__8__x__6685__6686__6729__6730__6731__6732,Vvar__0__R__6631)
                           => p(happ(happ(Vvar__7__req__6652,happ(happ(Vvar__3__radd__6634,Vvar__1__rO__6632),Vvar__var__var__var__var__var__8__x__6685__6686__6729__6730__6731__6732)),Vvar__var__var__var__var__var__8__x__6685__6686__6729__6730__6731__6732)) )
                        & ! [Vvar__var__var__var__var__9__x__6688__6690__6733__6735__6737] :
                            ( t(Vvar__var__var__var__var__9__x__6688__6690__6733__6735__6737,Vvar__0__R__6631)
                           => ! [Vvar__var__var__var__var__10__y__6689__6691__6734__6736__6738] :
                                ( t(Vvar__var__var__var__var__10__y__6689__6691__6734__6736__6738,Vvar__0__R__6631)
                               => p(happ(happ(Vvar__7__req__6652,happ(happ(Vvar__3__radd__6634,Vvar__var__var__var__var__9__x__6688__6690__6733__6735__6737),Vvar__var__var__var__var__10__y__6689__6691__6734__6736__6738)),happ(happ(Vvar__3__radd__6634,Vvar__var__var__var__var__10__y__6689__6691__6734__6736__6738),Vvar__var__var__var__var__9__x__6688__6690__6733__6735__6737))) ) )
                        & ! [Vvar__var__var__var__var__10__x__6693__6696__6739__6742__6745] :
                            ( t(Vvar__var__var__var__var__10__x__6693__6696__6739__6742__6745,Vvar__0__R__6631)
                           => ! [Vvar__var__var__var__var__11__y__6694__6697__6740__6743__6746] :
                                ( t(Vvar__var__var__var__var__11__y__6694__6697__6740__6743__6746,Vvar__0__R__6631)
                               => ! [Vvar__var__var__var__var__12__z__6695__6698__6741__6744__6747] :
                                    ( t(Vvar__var__var__var__var__12__z__6695__6698__6741__6744__6747,Vvar__0__R__6631)
                                   => p(happ(happ(Vvar__7__req__6652,happ(happ(Vvar__3__radd__6634,Vvar__var__var__var__var__10__x__6693__6696__6739__6742__6745),happ(happ(Vvar__3__radd__6634,Vvar__var__var__var__var__11__y__6694__6697__6740__6743__6746),Vvar__var__var__var__var__12__z__6695__6698__6741__6744__6747))),happ(happ(Vvar__3__radd__6634,happ(happ(Vvar__3__radd__6634,Vvar__var__var__var__var__10__x__6693__6696__6739__6742__6745),Vvar__var__var__var__var__11__y__6694__6697__6740__6743__6746)),Vvar__var__var__var__var__12__z__6695__6698__6741__6744__6747))) ) ) )
                        & ! [Vvar__var__var__var__var__var__11__x__6700__6701__6748__6749__6750__6751] :
                            ( t(Vvar__var__var__var__var__var__11__x__6700__6701__6748__6749__6750__6751,Vvar__0__R__6631)
                           => p(happ(happ(Vvar__7__req__6652,happ(happ(Vvar__4__rmul__6639,Vvar__2__rI__6633),Vvar__var__var__var__var__var__11__x__6700__6701__6748__6749__6750__6751)),Vvar__var__var__var__var__var__11__x__6700__6701__6748__6749__6750__6751)) )
                        & ! [Vvar__var__var__var__var__12__x__6703__6705__6752__6754__6756] :
                            ( t(Vvar__var__var__var__var__12__x__6703__6705__6752__6754__6756,Vvar__0__R__6631)
                           => ! [Vvar__var__var__var__var__13__y__6704__6706__6753__6755__6757] :
                                ( t(Vvar__var__var__var__var__13__y__6704__6706__6753__6755__6757,Vvar__0__R__6631)
                               => p(happ(happ(Vvar__7__req__6652,happ(happ(Vvar__4__rmul__6639,Vvar__var__var__var__var__12__x__6703__6705__6752__6754__6756),Vvar__var__var__var__var__13__y__6704__6706__6753__6755__6757)),happ(happ(Vvar__4__rmul__6639,Vvar__var__var__var__var__13__y__6704__6706__6753__6755__6757),Vvar__var__var__var__var__12__x__6703__6705__6752__6754__6756))) ) )
                        & ! [Vvar__var__var__var__var__13__x__6708__6711__6758__6761__6764] :
                            ( t(Vvar__var__var__var__var__13__x__6708__6711__6758__6761__6764,Vvar__0__R__6631)
                           => ! [Vvar__var__var__var__var__14__y__6709__6712__6759__6762__6765] :
                                ( t(Vvar__var__var__var__var__14__y__6709__6712__6759__6762__6765,Vvar__0__R__6631)
                               => ! [Vvar__var__var__var__var__15__z__6710__6713__6760__6763__6766] :
                                    ( t(Vvar__var__var__var__var__15__z__6710__6713__6760__6763__6766,Vvar__0__R__6631)
                                   => p(happ(happ(Vvar__7__req__6652,happ(happ(Vvar__4__rmul__6639,Vvar__var__var__var__var__13__x__6708__6711__6758__6761__6764),happ(happ(Vvar__4__rmul__6639,Vvar__var__var__var__var__14__y__6709__6712__6759__6762__6765),Vvar__var__var__var__var__15__z__6710__6713__6760__6763__6766))),happ(happ(Vvar__4__rmul__6639,happ(happ(Vvar__4__rmul__6639,Vvar__var__var__var__var__13__x__6708__6711__6758__6761__6764),Vvar__var__var__var__var__14__y__6709__6712__6759__6762__6765)),Vvar__var__var__var__var__15__z__6710__6713__6760__6763__6766))) ) ) )
                        & ! [Vvar__var__var__var__var__var__14__x__6715__6718__6767__6770__6773__6776] :
                            ( t(Vvar__var__var__var__var__var__14__x__6715__6718__6767__6770__6773__6776,Vvar__0__R__6631)
                           => ! [Vvar__var__var__var__var__var__15__y__6716__6719__6768__6771__6774__6777] :
                                ( t(Vvar__var__var__var__var__var__15__y__6716__6719__6768__6771__6774__6777,Vvar__0__R__6631)
                               => ! [Vvar__var__var__var__var__var__16__z__6717__6720__6769__6772__6775__6778] :
                                    ( t(Vvar__var__var__var__var__var__16__z__6717__6720__6769__6772__6775__6778,Vvar__0__R__6631)
                                   => p(happ(happ(Vvar__7__req__6652,happ(happ(Vvar__4__rmul__6639,happ(happ(Vvar__3__radd__6634,Vvar__var__var__var__var__var__14__x__6715__6718__6767__6770__6773__6776),Vvar__var__var__var__var__var__15__y__6716__6719__6768__6771__6774__6777)),Vvar__var__var__var__var__var__16__z__6717__6720__6769__6772__6775__6778)),happ(happ(Vvar__3__radd__6634,happ(happ(Vvar__4__rmul__6639,Vvar__var__var__var__var__var__14__x__6715__6718__6767__6770__6773__6776),Vvar__var__var__var__var__var__16__z__6717__6720__6769__6772__6775__6778)),happ(happ(Vvar__4__rmul__6639,Vvar__var__var__var__var__var__15__y__6716__6719__6768__6771__6774__6777),Vvar__var__var__var__var__var__16__z__6717__6720__6769__6772__6775__6778)))) ) ) )
                        & ! [Vvar__var__var__var__var__var__var__15__x__6722__6724__6779__6781__6783__6785__6787] :
                            ( t(Vvar__var__var__var__var__var__var__15__x__6722__6724__6779__6781__6783__6785__6787,Vvar__0__R__6631)
                           => ! [Vvar__var__var__var__var__var__var__16__y__6723__6725__6780__6782__6784__6786__6788] :
                                ( t(Vvar__var__var__var__var__var__var__16__y__6723__6725__6780__6782__6784__6786__6788,Vvar__0__R__6631)
                               => p(happ(happ(Vvar__7__req__6652,happ(happ(Vvar__5__rsub__6644,Vvar__var__var__var__var__var__var__15__x__6722__6724__6779__6781__6783__6785__6787),Vvar__var__var__var__var__var__var__16__y__6723__6725__6780__6782__6784__6786__6788)),happ(happ(Vvar__3__radd__6634,Vvar__var__var__var__var__var__var__15__x__6722__6724__6779__6781__6783__6785__6787),happ(Vvar__6__ropp__6649,Vvar__var__var__var__var__var__var__16__y__6723__6725__6780__6782__6784__6786__6788)))) ) )
                        & ! [Vvar__var__var__var__var__var__var__16__x__6727__6728__6789__6790__6791__6792__6793] :
                            ( t(Vvar__var__var__var__var__var__var__16__x__6727__6728__6789__6790__6791__6792__6793,Vvar__0__R__6631)
                           => p(happ(happ(Vvar__7__req__6652,happ(happ(Vvar__3__radd__6634,Vvar__var__var__var__var__var__var__16__x__6727__6728__6789__6790__6791__6792__6793),happ(Vvar__6__ropp__6649,Vvar__var__var__var__var__var__var__16__x__6727__6728__6789__6790__6791__6792__6793))),Vvar__1__rO__6632)) )
                        & p(c_24True) ) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Ring_theory.semi_morph',axiom,
    ! [Vvar__0__R__33285,Vvar__1__rO__33286,Vvar__2__rI__33287,Vvar__3__radd__33288,Vvar__4__rmul__33293,Vvar__5__req__33298,Vvar__6__C__33303,Vvar__7__cO__33304,Vvar__8__cI__33305,Vvar__9__cadd__33306,Vvar__10__cmul__33311,Vvar__11__ceqb__33316,Vvar__12__phi__33321] :
      ( cType___24t(Vvar__0__R__33285)
     => ( t(Vvar__1__rO__33286,Vvar__0__R__33285)
       => ( t(Vvar__2__rI__33287,Vvar__0__R__33285)
         => ( c_24__type__33538___24t(Vvar__0__R__33285,Vvar__1__rO__33286,Vvar__2__rI__33287,Vvar__3__radd__33288,Vvar__4__rmul__33293,Vvar__5__req__33298,Vvar__6__C__33303,Vvar__7__cO__33304,Vvar__8__cI__33305,Vvar__9__cadd__33306,Vvar__10__cmul__33311,Vvar__11__ceqb__33316,Vvar__12__phi__33321,Vvar__3__radd__33288)
           => ( c_24__type__33663___24t(Vvar__0__R__33285,Vvar__1__rO__33286,Vvar__2__rI__33287,Vvar__3__radd__33288,Vvar__4__rmul__33293,Vvar__5__req__33298,Vvar__6__C__33303,Vvar__7__cO__33304,Vvar__8__cI__33305,Vvar__9__cadd__33306,Vvar__10__cmul__33311,Vvar__11__ceqb__33316,Vvar__12__phi__33321,Vvar__4__rmul__33293)
             => ( c_24__type__33788___24t(Vvar__0__R__33285,Vvar__1__rO__33286,Vvar__2__rI__33287,Vvar__3__radd__33288,Vvar__4__rmul__33293,Vvar__5__req__33298,Vvar__6__C__33303,Vvar__7__cO__33304,Vvar__8__cI__33305,Vvar__9__cadd__33306,Vvar__10__cmul__33311,Vvar__11__ceqb__33316,Vvar__12__phi__33321,Vvar__5__req__33298)
               => ( cType___24t(Vvar__6__C__33303)
                 => ( t(Vvar__7__cO__33304,Vvar__6__C__33303)
                   => ( t(Vvar__8__cI__33305,Vvar__6__C__33303)
                     => ( c_24__type__33913___24t(Vvar__0__R__33285,Vvar__1__rO__33286,Vvar__2__rI__33287,Vvar__3__radd__33288,Vvar__4__rmul__33293,Vvar__5__req__33298,Vvar__6__C__33303,Vvar__7__cO__33304,Vvar__8__cI__33305,Vvar__9__cadd__33306,Vvar__10__cmul__33311,Vvar__11__ceqb__33316,Vvar__12__phi__33321,Vvar__9__cadd__33306)
                       => ( c_24__type__34038___24t(Vvar__0__R__33285,Vvar__1__rO__33286,Vvar__2__rI__33287,Vvar__3__radd__33288,Vvar__4__rmul__33293,Vvar__5__req__33298,Vvar__6__C__33303,Vvar__7__cO__33304,Vvar__8__cI__33305,Vvar__9__cadd__33306,Vvar__10__cmul__33311,Vvar__11__ceqb__33316,Vvar__12__phi__33321,Vvar__10__cmul__33311)
                         => ( c_24__type__34163___24t(Vvar__0__R__33285,Vvar__1__rO__33286,Vvar__2__rI__33287,Vvar__3__radd__33288,Vvar__4__rmul__33293,Vvar__5__req__33298,Vvar__6__C__33303,Vvar__7__cO__33304,Vvar__8__cI__33305,Vvar__9__cadd__33306,Vvar__10__cmul__33311,Vvar__11__ceqb__33316,Vvar__12__phi__33321,Vvar__11__ceqb__33316)
                           => ( c_24__type__34274___24t(Vvar__0__R__33285,Vvar__1__rO__33286,Vvar__2__rI__33287,Vvar__3__radd__33288,Vvar__4__rmul__33293,Vvar__5__req__33298,Vvar__6__C__33303,Vvar__7__cO__33304,Vvar__8__cI__33305,Vvar__9__cadd__33306,Vvar__10__cmul__33311,Vvar__11__ceqb__33316,Vvar__12__phi__33321,Vvar__12__phi__33321)
                             => ( cCoq_2esetoid__ring_2eRing__theory_2esemi__morph___24a13(Vvar__0__R__33285,Vvar__1__rO__33286,Vvar__2__rI__33287,Vvar__3__radd__33288,Vvar__4__rmul__33293,Vvar__5__req__33298,Vvar__6__C__33303,Vvar__7__cO__33304,Vvar__8__cI__33305,Vvar__9__cadd__33306,Vvar__10__cmul__33311,Vvar__11__ceqb__33316,Vvar__12__phi__33321)
                               => ( p(happ(happ(Vvar__5__req__33298,happ(Vvar__12__phi__33321,Vvar__7__cO__33304)),Vvar__1__rO__33286))
                                  & p(happ(happ(Vvar__5__req__33298,happ(Vvar__12__phi__33321,Vvar__8__cI__33305)),Vvar__2__rI__33287))
                                  & ! [Vvar__var__var__var__var__var__var__15__x__33367__33369__33383__33385__33387__33389__33391] :
                                      ( t(Vvar__var__var__var__var__var__var__15__x__33367__33369__33383__33385__33387__33389__33391,Vvar__6__C__33303)
                                     => ! [Vvar__var__var__var__var__var__var__16__y__33368__33370__33384__33386__33388__33390__33392] :
                                          ( t(Vvar__var__var__var__var__var__var__16__y__33368__33370__33384__33386__33388__33390__33392,Vvar__6__C__33303)
                                         => p(happ(happ(Vvar__5__req__33298,happ(Vvar__12__phi__33321,happ(happ(Vvar__9__cadd__33306,Vvar__var__var__var__var__var__var__15__x__33367__33369__33383__33385__33387__33389__33391),Vvar__var__var__var__var__var__var__16__y__33368__33370__33384__33386__33388__33390__33392))),happ(happ(Vvar__3__radd__33288,happ(Vvar__12__phi__33321,Vvar__var__var__var__var__var__var__15__x__33367__33369__33383__33385__33387__33389__33391)),happ(Vvar__12__phi__33321,Vvar__var__var__var__var__var__var__16__y__33368__33370__33384__33386__33388__33390__33392)))) ) )
                                  & ! [Vvar__var__var__var__var__var__var__16__x__33372__33374__33393__33395__33397__33399__33401] :
                                      ( t(Vvar__var__var__var__var__var__var__16__x__33372__33374__33393__33395__33397__33399__33401,Vvar__6__C__33303)
                                     => ! [Vvar__var__var__var__var__var__var__17__y__33373__33375__33394__33396__33398__33400__33402] :
                                          ( t(Vvar__var__var__var__var__var__var__17__y__33373__33375__33394__33396__33398__33400__33402,Vvar__6__C__33303)
                                         => p(happ(happ(Vvar__5__req__33298,happ(Vvar__12__phi__33321,happ(happ(Vvar__10__cmul__33311,Vvar__var__var__var__var__var__var__16__x__33372__33374__33393__33395__33397__33399__33401),Vvar__var__var__var__var__var__var__17__y__33373__33375__33394__33396__33398__33400__33402))),happ(happ(Vvar__4__rmul__33293,happ(Vvar__12__phi__33321,Vvar__var__var__var__var__var__var__16__x__33372__33374__33393__33395__33397__33399__33401)),happ(Vvar__12__phi__33321,Vvar__var__var__var__var__var__var__17__y__33373__33375__33394__33396__33398__33400__33402)))) ) )
                                  & ! [Vvar__var__var__var__var__var__17__x__33377__33380__33403__33406__33409__33412] :
                                      ( t(Vvar__var__var__var__var__var__17__x__33377__33380__33403__33406__33409__33412,Vvar__6__C__33303)
                                     => ! [Vvar__var__var__var__var__var__18__y__33378__33381__33404__33407__33410__33413] :
                                          ( t(Vvar__var__var__var__var__var__18__y__33378__33381__33404__33407__33410__33413,Vvar__6__C__33303)
                                         => ( happ(happ(Vvar__11__ceqb__33316,Vvar__var__var__var__var__var__17__x__33377__33380__33403__33406__33409__33412),Vvar__var__var__var__var__var__18__y__33378__33381__33404__33407__33410__33413) = cCoq_2eInit_2eDatatypes_2etrue
                                           => p(happ(happ(Vvar__5__req__33298,happ(Vvar__12__phi__33321,Vvar__var__var__var__var__var__17__x__33377__33380__33403__33406__33409__33412)),happ(Vvar__12__phi__33321,Vvar__var__var__var__var__var__18__y__33378__33381__33404__33407__33410__33413))) ) ) )
                                  & p(c_24True) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Ring_theory.semi_ring_theory',axiom,
    ! [Vvar__0__R__32799,Vvar__1__rO__32800,Vvar__2__rI__32801,Vvar__3__radd__32802,Vvar__4__rmul__32807,Vvar__5__req__32812] :
      ( cType___24t(Vvar__0__R__32799)
     => ( t(Vvar__1__rO__32800,Vvar__0__R__32799)
       => ( t(Vvar__2__rI__32801,Vvar__0__R__32799)
         => ( c_24__type__32967___24t(Vvar__0__R__32799,Vvar__1__rO__32800,Vvar__2__rI__32801,Vvar__3__radd__32802,Vvar__4__rmul__32807,Vvar__5__req__32812,Vvar__3__radd__32802)
           => ( c_24__type__33006___24t(Vvar__0__R__32799,Vvar__1__rO__32800,Vvar__2__rI__32801,Vvar__3__radd__32802,Vvar__4__rmul__32807,Vvar__5__req__32812,Vvar__4__rmul__32807)
             => ( c_24__type__33045___24t(Vvar__0__R__32799,Vvar__1__rO__32800,Vvar__2__rI__32801,Vvar__3__radd__32802,Vvar__4__rmul__32807,Vvar__5__req__32812,Vvar__5__req__32812)
               => ( cCoq_2esetoid__ring_2eRing__theory_2esemi__ring__theory___24a6(Vvar__0__R__32799,Vvar__1__rO__32800,Vvar__2__rI__32801,Vvar__3__radd__32802,Vvar__4__rmul__32807,Vvar__5__req__32812)
                 => ( ! [Vvar__var__var__var__var__var__6__n__32837__32838__32876__32877__32878__32879] :
                        ( t(Vvar__var__var__var__var__var__6__n__32837__32838__32876__32877__32878__32879,Vvar__0__R__32799)
                       => p(happ(happ(Vvar__5__req__32812,happ(happ(Vvar__3__radd__32802,Vvar__1__rO__32800),Vvar__var__var__var__var__var__6__n__32837__32838__32876__32877__32878__32879)),Vvar__var__var__var__var__var__6__n__32837__32838__32876__32877__32878__32879)) )
                    & ! [Vvar__var__var__var__var__7__n__32840__32842__32880__32882__32884] :
                        ( t(Vvar__var__var__var__var__7__n__32840__32842__32880__32882__32884,Vvar__0__R__32799)
                       => ! [Vvar__var__var__var__var__8__m__32841__32843__32881__32883__32885] :
                            ( t(Vvar__var__var__var__var__8__m__32841__32843__32881__32883__32885,Vvar__0__R__32799)
                           => p(happ(happ(Vvar__5__req__32812,happ(happ(Vvar__3__radd__32802,Vvar__var__var__var__var__7__n__32840__32842__32880__32882__32884),Vvar__var__var__var__var__8__m__32841__32843__32881__32883__32885)),happ(happ(Vvar__3__radd__32802,Vvar__var__var__var__var__8__m__32841__32843__32881__32883__32885),Vvar__var__var__var__var__7__n__32840__32842__32880__32882__32884))) ) )
                    & ! [Vvar__var__var__var__var__8__n__32845__32848__32886__32889__32892] :
                        ( t(Vvar__var__var__var__var__8__n__32845__32848__32886__32889__32892,Vvar__0__R__32799)
                       => ! [Vvar__var__var__var__var__9__m__32846__32849__32887__32890__32893] :
                            ( t(Vvar__var__var__var__var__9__m__32846__32849__32887__32890__32893,Vvar__0__R__32799)
                           => ! [Vvar__var__var__var__var__10__p__32847__32850__32888__32891__32894] :
                                ( t(Vvar__var__var__var__var__10__p__32847__32850__32888__32891__32894,Vvar__0__R__32799)
                               => p(happ(happ(Vvar__5__req__32812,happ(happ(Vvar__3__radd__32802,Vvar__var__var__var__var__8__n__32845__32848__32886__32889__32892),happ(happ(Vvar__3__radd__32802,Vvar__var__var__var__var__9__m__32846__32849__32887__32890__32893),Vvar__var__var__var__var__10__p__32847__32850__32888__32891__32894))),happ(happ(Vvar__3__radd__32802,happ(happ(Vvar__3__radd__32802,Vvar__var__var__var__var__8__n__32845__32848__32886__32889__32892),Vvar__var__var__var__var__9__m__32846__32849__32887__32890__32893)),Vvar__var__var__var__var__10__p__32847__32850__32888__32891__32894))) ) ) )
                    & ! [Vvar__var__var__var__var__var__9__n__32852__32853__32895__32896__32897__32898] :
                        ( t(Vvar__var__var__var__var__var__9__n__32852__32853__32895__32896__32897__32898,Vvar__0__R__32799)
                       => p(happ(happ(Vvar__5__req__32812,happ(happ(Vvar__4__rmul__32807,Vvar__2__rI__32801),Vvar__var__var__var__var__var__9__n__32852__32853__32895__32896__32897__32898)),Vvar__var__var__var__var__var__9__n__32852__32853__32895__32896__32897__32898)) )
                    & ! [Vvar__var__var__var__var__var__10__n__32855__32856__32899__32900__32901__32902] :
                        ( t(Vvar__var__var__var__var__var__10__n__32855__32856__32899__32900__32901__32902,Vvar__0__R__32799)
                       => p(happ(happ(Vvar__5__req__32812,happ(happ(Vvar__4__rmul__32807,Vvar__1__rO__32800),Vvar__var__var__var__var__var__10__n__32855__32856__32899__32900__32901__32902)),Vvar__1__rO__32800)) )
                    & ! [Vvar__var__var__var__var__11__n__32858__32860__32903__32905__32907] :
                        ( t(Vvar__var__var__var__var__11__n__32858__32860__32903__32905__32907,Vvar__0__R__32799)
                       => ! [Vvar__var__var__var__var__12__m__32859__32861__32904__32906__32908] :
                            ( t(Vvar__var__var__var__var__12__m__32859__32861__32904__32906__32908,Vvar__0__R__32799)
                           => p(happ(happ(Vvar__5__req__32812,happ(happ(Vvar__4__rmul__32807,Vvar__var__var__var__var__11__n__32858__32860__32903__32905__32907),Vvar__var__var__var__var__12__m__32859__32861__32904__32906__32908)),happ(happ(Vvar__4__rmul__32807,Vvar__var__var__var__var__12__m__32859__32861__32904__32906__32908),Vvar__var__var__var__var__11__n__32858__32860__32903__32905__32907))) ) )
                    & ! [Vvar__var__var__var__var__12__n__32863__32866__32909__32912__32915] :
                        ( t(Vvar__var__var__var__var__12__n__32863__32866__32909__32912__32915,Vvar__0__R__32799)
                       => ! [Vvar__var__var__var__var__13__m__32864__32867__32910__32913__32916] :
                            ( t(Vvar__var__var__var__var__13__m__32864__32867__32910__32913__32916,Vvar__0__R__32799)
                           => ! [Vvar__var__var__var__var__14__p__32865__32868__32911__32914__32917] :
                                ( t(Vvar__var__var__var__var__14__p__32865__32868__32911__32914__32917,Vvar__0__R__32799)
                               => p(happ(happ(Vvar__5__req__32812,happ(happ(Vvar__4__rmul__32807,Vvar__var__var__var__var__12__n__32863__32866__32909__32912__32915),happ(happ(Vvar__4__rmul__32807,Vvar__var__var__var__var__13__m__32864__32867__32910__32913__32916),Vvar__var__var__var__var__14__p__32865__32868__32911__32914__32917))),happ(happ(Vvar__4__rmul__32807,happ(happ(Vvar__4__rmul__32807,Vvar__var__var__var__var__12__n__32863__32866__32909__32912__32915),Vvar__var__var__var__var__13__m__32864__32867__32910__32913__32916)),Vvar__var__var__var__var__14__p__32865__32868__32911__32914__32917))) ) ) )
                    & ! [Vvar__var__var__var__var__var__13__n__32870__32873__32918__32921__32924__32927] :
                        ( t(Vvar__var__var__var__var__var__13__n__32870__32873__32918__32921__32924__32927,Vvar__0__R__32799)
                       => ! [Vvar__var__var__var__var__var__14__m__32871__32874__32919__32922__32925__32928] :
                            ( t(Vvar__var__var__var__var__var__14__m__32871__32874__32919__32922__32925__32928,Vvar__0__R__32799)
                           => ! [Vvar__var__var__var__var__var__15__p__32872__32875__32920__32923__32926__32929] :
                                ( t(Vvar__var__var__var__var__var__15__p__32872__32875__32920__32923__32926__32929,Vvar__0__R__32799)
                               => p(happ(happ(Vvar__5__req__32812,happ(happ(Vvar__4__rmul__32807,happ(happ(Vvar__3__radd__32802,Vvar__var__var__var__var__var__13__n__32870__32873__32918__32921__32924__32927),Vvar__var__var__var__var__var__14__m__32871__32874__32919__32922__32925__32928)),Vvar__var__var__var__var__var__15__p__32872__32875__32920__32923__32926__32929)),happ(happ(Vvar__3__radd__32802,happ(happ(Vvar__4__rmul__32807,Vvar__var__var__var__var__var__13__n__32870__32873__32918__32921__32924__32927),Vvar__var__var__var__var__var__15__p__32872__32875__32920__32923__32926__32929)),happ(happ(Vvar__4__rmul__32807,Vvar__var__var__var__var__var__14__m__32871__32874__32919__32922__32925__32928),Vvar__var__var__var__var__var__15__p__32872__32875__32920__32923__32926__32929)))) ) ) )
                    & p(c_24True) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Ring_theory.sign_theory',axiom,
    ! [Vvar__0__C__14934,Vvar__1__copp__14935,Vvar__2__ceqb__14938,Vvar__3__get__sign__14943] :
      ( cType___24t(Vvar__0__C__14934)
     => ( c_24__type__14990___24t(Vvar__0__C__14934,Vvar__1__copp__14935,Vvar__2__ceqb__14938,Vvar__3__get__sign__14943,Vvar__1__copp__14935)
       => ( c_24__type__15009___24t(Vvar__0__C__14934,Vvar__1__copp__14935,Vvar__2__ceqb__14938,Vvar__3__get__sign__14943,Vvar__2__ceqb__14938)
         => ( c_24__type__15023___24t(Vvar__0__C__14934,Vvar__1__copp__14935,Vvar__2__ceqb__14938,Vvar__3__get__sign__14943,Vvar__3__get__sign__14943)
           => ( cCoq_2esetoid__ring_2eRing__theory_2esign__theory___24a4(Vvar__0__C__14934,Vvar__1__copp__14935,Vvar__2__ceqb__14938,Vvar__3__get__sign__14943)
             => ( ! [Vvar__var__var__var__var__var__4__c__14960__14963__14966__14969__14972__14975] :
                    ( t(Vvar__var__var__var__var__var__4__c__14960__14963__14966__14969__14972__14975,Vvar__0__C__14934)
                   => ! [Vvar__var__var__var__var__var__5__c_27__14961__14964__14967__14970__14973__14976] :
                        ( t(Vvar__var__var__var__var__var__5__c_27__14961__14964__14967__14970__14973__14976,Vvar__0__C__14934)
                       => ( happ(Vvar__3__get__sign__14943,Vvar__var__var__var__var__var__4__c__14960__14963__14966__14969__14972__14975) = cCoq_2eInit_2eDatatypes_2eSome___24a2(Vvar__0__C__14934,Vvar__var__var__var__var__var__5__c_27__14961__14964__14967__14970__14973__14976)
                         => happ(happ(Vvar__2__ceqb__14938,Vvar__var__var__var__var__var__4__c__14960__14963__14966__14969__14972__14975),happ(Vvar__1__copp__14935,Vvar__var__var__var__var__var__5__c_27__14961__14964__14967__14970__14973__14976)) = cCoq_2eInit_2eDatatypes_2etrue ) ) )
                & p(c_24True) ) ) ) ) ) ) ).

fof('$_inversion_Coq.setoid_ring.Ring_theory.sring_eq_ext',axiom,
    ! [Vvar__0__R__33063,Vvar__1__radd__33064,Vvar__2__rmul__33069,Vvar__3__req__33074] :
      ( cType___24t(Vvar__0__R__33063)
     => ( c_24__type__33149___24t(Vvar__0__R__33063,Vvar__1__radd__33064,Vvar__2__rmul__33069,Vvar__3__req__33074,Vvar__1__radd__33064)
       => ( c_24__type__33172___24t(Vvar__0__R__33063,Vvar__1__radd__33064,Vvar__2__rmul__33069,Vvar__3__req__33074,Vvar__2__rmul__33069)
         => ( c_24__type__33195___24t(Vvar__0__R__33063,Vvar__1__radd__33064,Vvar__2__rmul__33069,Vvar__3__req__33074,Vvar__3__req__33074)
           => ( cCoq_2esetoid__ring_2eRing__theory_2esring__eq__ext___24a4(Vvar__0__R__33063,Vvar__1__radd__33064,Vvar__2__rmul__33069,Vvar__3__req__33074)
             => ( cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__33218___24a4(Vvar__0__R__33063,Vvar__1__radd__33064,Vvar__2__rmul__33069,Vvar__3__req__33074),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__33063,c_24__type__33236___24a4(Vvar__0__R__33063,Vvar__1__radd__33064,Vvar__2__rmul__33069,Vvar__3__req__33074),Vvar__3__req__33074,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__33063,Vvar__0__R__33063,Vvar__3__req__33074,Vvar__3__req__33074)),Vvar__1__radd__33064)
                & cCoq_2eClasses_2eMorphisms_2eProper___24a3(c_24__type__33262___24a4(Vvar__0__R__33063,Vvar__1__radd__33064,Vvar__2__rmul__33069,Vvar__3__req__33074),cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__33063,c_24__type__33280___24a4(Vvar__0__R__33063,Vvar__1__radd__33064,Vvar__2__rmul__33069,Vvar__3__req__33074),Vvar__3__req__33074,cCoq_2eClasses_2eMorphisms_2erespectful___24a4(Vvar__0__R__33063,Vvar__0__R__33063,Vvar__3__req__33074,Vvar__3__req__33074)),Vvar__2__rmul__33069)
                & p(c_24True) ) ) ) ) ) ) ).

fof('$_inversion_Hammer.Tactics.Reconstr.ReconstrT',axiom,
    ! [VX26241] :
      ( cHammer_2eTactics_2eReconstr_2eReconstrT___24t(VX26241)
     => ( VX26241 = cHammer_2eTactics_2eReconstr_2eEmpty
        | VX26241 = cHammer_2eTactics_2eReconstr_2eAllHyps ) ) ).

fof('$_inversion_Norm.step',axiom,
    ! [Vvar__0___24Anonymous__266,Vvar__1___24Anonymous__267] :
      ( cNorm_2etm___24t(Vvar__0___24Anonymous__266)
     => ( cNorm_2etm___24t(Vvar__1___24Anonymous__267)
       => ( cNorm_2estep___24a2(Vvar__0___24Anonymous__266,Vvar__1___24Anonymous__267)
         => ( ? [Vvar__0__x__269] :
                ( cCoq_2eStrings_2eString_2estring___24t(Vvar__0__x__269)
                & ? [Vvar__1__T11__270] :
                    ( cNorm_2ety___24t(Vvar__1__T11__270)
                    & ? [Vvar__2__t12__271] :
                        ( cNorm_2etm___24t(Vvar__2__t12__271)
                        & ? [Vvar__3__v2__272] :
                            ( cNorm_2etm___24t(Vvar__3__v2__272)
                            & cNorm_2evalue___24a1(Vvar__3__v2__272)
                            & Vvar__1___24Anonymous__267 = c_24__case__Norm_2etm_242929___24a5(Vvar__0___24Anonymous__266,Vvar__1___24Anonymous__267,Vvar__0__x__269,Vvar__2__t12__271,Vvar__3__v2__272)
                            & Vvar__0___24Anonymous__266 = cNorm_2eapp___24a2(cNorm_2eabs___24a3(Vvar__0__x__269,Vvar__1__T11__270,Vvar__2__t12__271),Vvar__3__v2__272) ) ) ) )
            | ? [Vvar__0__t1__290] :
                ( cNorm_2etm___24t(Vvar__0__t1__290)
                & ? [Vvar__1__t1_27__291] :
                    ( cNorm_2etm___24t(Vvar__1__t1_27__291)
                    & ? [Vvar__2__t2__292] :
                        ( cNorm_2etm___24t(Vvar__2__t2__292)
                        & cNorm_2estep___24a2(Vvar__0__t1__290,Vvar__1__t1_27__291)
                        & Vvar__1___24Anonymous__267 = cNorm_2eapp___24a2(Vvar__1__t1_27__291,Vvar__2__t2__292)
                        & Vvar__0___24Anonymous__266 = cNorm_2eapp___24a2(Vvar__0__t1__290,Vvar__2__t2__292) ) ) )
            | ? [Vvar__0__v1__294] :
                ( cNorm_2etm___24t(Vvar__0__v1__294)
                & ? [Vvar__1__t2__295] :
                    ( cNorm_2etm___24t(Vvar__1__t2__295)
                    & ? [Vvar__2__t2_27__296] :
                        ( cNorm_2etm___24t(Vvar__2__t2_27__296)
                        & cNorm_2evalue___24a1(Vvar__0__v1__294)
                        & cNorm_2estep___24a2(Vvar__1__t2__295,Vvar__2__t2_27__296)
                        & Vvar__1___24Anonymous__267 = cNorm_2eapp___24a2(Vvar__0__v1__294,Vvar__2__t2_27__296)
                        & Vvar__0___24Anonymous__266 = cNorm_2eapp___24a2(Vvar__0__v1__294,Vvar__1__t2__295) ) ) )
            | ? [Vvar__0__t1__299] :
                ( cNorm_2etm___24t(Vvar__0__t1__299)
                & ? [Vvar__1__t1_27__300] :
                    ( cNorm_2etm___24t(Vvar__1__t1_27__300)
                    & ? [Vvar__2__t2__301] :
                        ( cNorm_2etm___24t(Vvar__2__t2__301)
                        & cNorm_2estep___24a2(Vvar__0__t1__299,Vvar__1__t1_27__300)
                        & Vvar__1___24Anonymous__267 = cNorm_2epair___24a2(Vvar__1__t1_27__300,Vvar__2__t2__301)
                        & Vvar__0___24Anonymous__266 = cNorm_2epair___24a2(Vvar__0__t1__299,Vvar__2__t2__301) ) ) )
            | ? [Vvar__0__v1__303] :
                ( cNorm_2etm___24t(Vvar__0__v1__303)
                & ? [Vvar__1__t2__304] :
                    ( cNorm_2etm___24t(Vvar__1__t2__304)
                    & ? [Vvar__2__t2_27__305] :
                        ( cNorm_2etm___24t(Vvar__2__t2_27__305)
                        & cNorm_2evalue___24a1(Vvar__0__v1__303)
                        & cNorm_2estep___24a2(Vvar__1__t2__304,Vvar__2__t2_27__305)
                        & Vvar__1___24Anonymous__267 = cNorm_2epair___24a2(Vvar__0__v1__303,Vvar__2__t2_27__305)
                        & Vvar__0___24Anonymous__266 = cNorm_2epair___24a2(Vvar__0__v1__303,Vvar__1__t2__304) ) ) )
            | ? [Vvar__0__t1__308] :
                ( cNorm_2etm___24t(Vvar__0__t1__308)
                & ? [Vvar__1__t1_27__309] :
                    ( cNorm_2etm___24t(Vvar__1__t1_27__309)
                    & cNorm_2estep___24a2(Vvar__0__t1__308,Vvar__1__t1_27__309)
                    & Vvar__1___24Anonymous__267 = cNorm_2efst___24a1(Vvar__1__t1_27__309)
                    & Vvar__0___24Anonymous__266 = cNorm_2efst___24a1(Vvar__0__t1__308) ) )
            | ? [Vvar__0__v1__311] :
                ( cNorm_2etm___24t(Vvar__0__v1__311)
                & ? [Vvar__1__v2__312] :
                    ( cNorm_2etm___24t(Vvar__1__v2__312)
                    & cNorm_2evalue___24a1(Vvar__0__v1__311)
                    & cNorm_2evalue___24a1(Vvar__1__v2__312)
                    & Vvar__1___24Anonymous__267 = Vvar__0__v1__311
                    & Vvar__0___24Anonymous__266 = cNorm_2efst___24a1(cNorm_2epair___24a2(Vvar__0__v1__311,Vvar__1__v2__312)) ) )
            | ? [Vvar__0__t1__315] :
                ( cNorm_2etm___24t(Vvar__0__t1__315)
                & ? [Vvar__1__t1_27__316] :
                    ( cNorm_2etm___24t(Vvar__1__t1_27__316)
                    & cNorm_2estep___24a2(Vvar__0__t1__315,Vvar__1__t1_27__316)
                    & Vvar__1___24Anonymous__267 = cNorm_2esnd___24a1(Vvar__1__t1_27__316)
                    & Vvar__0___24Anonymous__266 = cNorm_2esnd___24a1(Vvar__0__t1__315) ) )
            | ? [Vvar__0__v1__318] :
                ( cNorm_2etm___24t(Vvar__0__v1__318)
                & ? [Vvar__1__v2__319] :
                    ( cNorm_2etm___24t(Vvar__1__v2__319)
                    & cNorm_2evalue___24a1(Vvar__0__v1__318)
                    & cNorm_2evalue___24a1(Vvar__1__v2__319)
                    & Vvar__1___24Anonymous__267 = Vvar__1__v2__319
                    & Vvar__0___24Anonymous__266 = cNorm_2esnd___24a1(cNorm_2epair___24a2(Vvar__0__v1__318,Vvar__1__v2__319)) ) )
            | ? [Vvar__0__t1__322] :
                ( cNorm_2etm___24t(Vvar__0__t1__322)
                & ? [Vvar__1__t2__323] :
                    ( cNorm_2etm___24t(Vvar__1__t2__323)
                    & Vvar__1___24Anonymous__267 = Vvar__0__t1__322
                    & Vvar__0___24Anonymous__266 = cNorm_2etest___24a3(cNorm_2etru,Vvar__0__t1__322,Vvar__1__t2__323) ) )
            | ? [Vvar__0__t1__324] :
                ( cNorm_2etm___24t(Vvar__0__t1__324)
                & ? [Vvar__1__t2__325] :
                    ( cNorm_2etm___24t(Vvar__1__t2__325)
                    & Vvar__1___24Anonymous__267 = Vvar__1__t2__325
                    & Vvar__0___24Anonymous__266 = cNorm_2etest___24a3(cNorm_2efls,Vvar__0__t1__324,Vvar__1__t2__325) ) )
            | ? [Vvar__0__t0__326] :
                ( cNorm_2etm___24t(Vvar__0__t0__326)
                & ? [Vvar__1__t0_27__327] :
                    ( cNorm_2etm___24t(Vvar__1__t0_27__327)
                    & ? [Vvar__2__t1__328] :
                        ( cNorm_2etm___24t(Vvar__2__t1__328)
                        & ? [Vvar__3__t2__329] :
                            ( cNorm_2etm___24t(Vvar__3__t2__329)
                            & cNorm_2estep___24a2(Vvar__0__t0__326,Vvar__1__t0_27__327)
                            & Vvar__1___24Anonymous__267 = cNorm_2etest___24a3(Vvar__1__t0_27__327,Vvar__2__t1__328,Vvar__3__t2__329)
                            & Vvar__0___24Anonymous__266 = cNorm_2etest___24a3(Vvar__0__t0__326,Vvar__2__t1__328,Vvar__3__t2__329) ) ) ) ) ) ) ) ) ).

fof('$_inversion_Norm.tm',axiom,
    ! [VX4580] :
      ( cNorm_2etm___24t(VX4580)
     => ( ? [Vvar__0___24Anonymous__4581] :
            ( cCoq_2eStrings_2eString_2estring___24t(Vvar__0___24Anonymous__4581)
            & VX4580 = cNorm_2evar___24a1(Vvar__0___24Anonymous__4581) )
        | ? [Vvar__0___24Anonymous__4582] :
            ( cNorm_2etm___24t(Vvar__0___24Anonymous__4582)
            & ? [Vvar__1___24Anonymous__4583] :
                ( cNorm_2etm___24t(Vvar__1___24Anonymous__4583)
                & VX4580 = cNorm_2eapp___24a2(Vvar__0___24Anonymous__4582,Vvar__1___24Anonymous__4583) ) )
        | ? [Vvar__0___24Anonymous__4584] :
            ( cCoq_2eStrings_2eString_2estring___24t(Vvar__0___24Anonymous__4584)
            & ? [Vvar__1___24Anonymous__4585] :
                ( cNorm_2ety___24t(Vvar__1___24Anonymous__4585)
                & ? [Vvar__2___24Anonymous__4586] :
                    ( cNorm_2etm___24t(Vvar__2___24Anonymous__4586)
                    & VX4580 = cNorm_2eabs___24a3(Vvar__0___24Anonymous__4584,Vvar__1___24Anonymous__4585,Vvar__2___24Anonymous__4586) ) ) )
        | ? [Vvar__0___24Anonymous__4587] :
            ( cNorm_2etm___24t(Vvar__0___24Anonymous__4587)
            & ? [Vvar__1___24Anonymous__4588] :
                ( cNorm_2etm___24t(Vvar__1___24Anonymous__4588)
                & VX4580 = cNorm_2epair___24a2(Vvar__0___24Anonymous__4587,Vvar__1___24Anonymous__4588) ) )
        | ? [Vvar__0___24Anonymous__4589] :
            ( cNorm_2etm___24t(Vvar__0___24Anonymous__4589)
            & VX4580 = cNorm_2efst___24a1(Vvar__0___24Anonymous__4589) )
        | ? [Vvar__0___24Anonymous__4590] :
            ( cNorm_2etm___24t(Vvar__0___24Anonymous__4590)
            & VX4580 = cNorm_2esnd___24a1(Vvar__0___24Anonymous__4590) )
        | VX4580 = cNorm_2etru
        | VX4580 = cNorm_2efls
        | ? [Vvar__0___24Anonymous__4591] :
            ( cNorm_2etm___24t(Vvar__0___24Anonymous__4591)
            & ? [Vvar__1___24Anonymous__4592] :
                ( cNorm_2etm___24t(Vvar__1___24Anonymous__4592)
                & ? [Vvar__2___24Anonymous__4593] :
                    ( cNorm_2etm___24t(Vvar__2___24Anonymous__4593)
                    & VX4580 = cNorm_2etest___24a3(Vvar__0___24Anonymous__4591,Vvar__1___24Anonymous__4592,Vvar__2___24Anonymous__4593) ) ) ) ) ) ).

fof('$_inversion_Norm.ty',axiom,
    ! [VX4735] :
      ( cNorm_2ety___24t(VX4735)
     => ( VX4735 = cNorm_2eBool
        | ? [Vvar__0___24Anonymous__4736] :
            ( cNorm_2ety___24t(Vvar__0___24Anonymous__4736)
            & ? [Vvar__1___24Anonymous__4737] :
                ( cNorm_2ety___24t(Vvar__1___24Anonymous__4737)
                & VX4735 = cNorm_2eArrow___24a2(Vvar__0___24Anonymous__4736,Vvar__1___24Anonymous__4737) ) )
        | ? [Vvar__0___24Anonymous__4738] :
            ( cNorm_2ety___24t(Vvar__0___24Anonymous__4738)
            & ? [Vvar__1___24Anonymous__4739] :
                ( cNorm_2ety___24t(Vvar__1___24Anonymous__4739)
                & VX4735 = cNorm_2eProd___24a2(Vvar__0___24Anonymous__4738,Vvar__1___24Anonymous__4739) ) ) ) ) ).

fof('$_inversion_Norm.value',axiom,
    ! [Vvar__0___24Anonymous__4535] :
      ( cNorm_2etm___24t(Vvar__0___24Anonymous__4535)
     => ( cNorm_2evalue___24a1(Vvar__0___24Anonymous__4535)
       => ( ? [Vvar__0__x__4537] :
              ( cCoq_2eStrings_2eString_2estring___24t(Vvar__0__x__4537)
              & ? [Vvar__1__T11__4538] :
                  ( cNorm_2ety___24t(Vvar__1__T11__4538)
                  & ? [Vvar__2__t12__4539] :
                      ( cNorm_2etm___24t(Vvar__2__t12__4539)
                      & Vvar__0___24Anonymous__4535 = cNorm_2eabs___24a3(Vvar__0__x__4537,Vvar__1__T11__4538,Vvar__2__t12__4539) ) ) )
          | ? [Vvar__0__v1__4540] :
              ( cNorm_2etm___24t(Vvar__0__v1__4540)
              & ? [Vvar__1__v2__4541] :
                  ( cNorm_2etm___24t(Vvar__1__v2__4541)
                  & cNorm_2evalue___24a1(Vvar__0__v1__4540)
                  & cNorm_2evalue___24a1(Vvar__1__v2__4541)
                  & Vvar__0___24Anonymous__4535 = cNorm_2epair___24a2(Vvar__0__v1__4540,Vvar__1__v2__4541) ) )
          | Vvar__0___24Anonymous__4535 = cNorm_2etru
          | Vvar__0___24Anonymous__4535 = cNorm_2efls ) ) ) ).

fof('$_inversion_PLF.Imp.AExp.aevalR',axiom,
    ! [Vvar__0___24Anonymous__44103,Vvar__1___24Anonymous__44104] :
      ( cPLF_2eImp_2eAExp_2eaexp___24t(Vvar__0___24Anonymous__44103)
     => ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__44104)
       => ( cPLF_2eImp_2eAExp_2eaevalR___24a2(Vvar__0___24Anonymous__44103,Vvar__1___24Anonymous__44104)
         => ( ? [Vvar__0__n__44106] :
                ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__44106)
                & Vvar__1___24Anonymous__44104 = Vvar__0__n__44106
                & Vvar__0___24Anonymous__44103 = cPLF_2eImp_2eAExp_2eANum___24a1(Vvar__0__n__44106) )
            | ? [Vvar__0__e1__44107] :
                ( cPLF_2eImp_2eAExp_2eaexp___24t(Vvar__0__e1__44107)
                & ? [Vvar__1__e2__44108] :
                    ( cPLF_2eImp_2eAExp_2eaexp___24t(Vvar__1__e2__44108)
                    & ? [Vvar__2__n1__44109] :
                        ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n1__44109)
                        & ? [Vvar__3__n2__44110] :
                            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__3__n2__44110)
                            & cPLF_2eImp_2eAExp_2eaevalR___24a2(Vvar__0__e1__44107,Vvar__2__n1__44109)
                            & cPLF_2eImp_2eAExp_2eaevalR___24a2(Vvar__1__e2__44108,Vvar__3__n2__44110)
                            & Vvar__1___24Anonymous__44104 = c_24__case__Coq_2eInit_2eDatatypes_2enat_2444186___24a4(Vvar__0___24Anonymous__44103,Vvar__1___24Anonymous__44104,Vvar__2__n1__44109,Vvar__3__n2__44110)
                            & Vvar__0___24Anonymous__44103 = cPLF_2eImp_2eAExp_2eAPlus___24a2(Vvar__0__e1__44107,Vvar__1__e2__44108) ) ) ) )
            | ? [Vvar__0__e1__44115] :
                ( cPLF_2eImp_2eAExp_2eaexp___24t(Vvar__0__e1__44115)
                & ? [Vvar__1__e2__44116] :
                    ( cPLF_2eImp_2eAExp_2eaexp___24t(Vvar__1__e2__44116)
                    & ? [Vvar__2__n1__44117] :
                        ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n1__44117)
                        & ? [Vvar__3__n2__44118] :
                            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__3__n2__44118)
                            & cPLF_2eImp_2eAExp_2eaevalR___24a2(Vvar__0__e1__44115,Vvar__2__n1__44117)
                            & cPLF_2eImp_2eAExp_2eaevalR___24a2(Vvar__1__e2__44116,Vvar__3__n2__44118)
                            & Vvar__1___24Anonymous__44104 = c_24__case__Coq_2eInit_2eDatatypes_2enat_2444295___24a4(Vvar__0___24Anonymous__44103,Vvar__1___24Anonymous__44104,Vvar__2__n1__44117,Vvar__3__n2__44118)
                            & Vvar__0___24Anonymous__44103 = cPLF_2eImp_2eAExp_2eAMinus___24a2(Vvar__0__e1__44115,Vvar__1__e2__44116) ) ) ) )
            | ? [Vvar__0__e1__44125] :
                ( cPLF_2eImp_2eAExp_2eaexp___24t(Vvar__0__e1__44125)
                & ? [Vvar__1__e2__44126] :
                    ( cPLF_2eImp_2eAExp_2eaexp___24t(Vvar__1__e2__44126)
                    & ? [Vvar__2__n1__44127] :
                        ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n1__44127)
                        & ? [Vvar__3__n2__44128] :
                            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__3__n2__44128)
                            & cPLF_2eImp_2eAExp_2eaevalR___24a2(Vvar__0__e1__44125,Vvar__2__n1__44127)
                            & cPLF_2eImp_2eAExp_2eaevalR___24a2(Vvar__1__e2__44126,Vvar__3__n2__44128)
                            & Vvar__1___24Anonymous__44104 = c_24__case__Coq_2eInit_2eDatatypes_2enat_2444389___24a4(Vvar__0___24Anonymous__44103,Vvar__1___24Anonymous__44104,Vvar__2__n1__44127,Vvar__3__n2__44128)
                            & Vvar__0___24Anonymous__44103 = cPLF_2eImp_2eAExp_2eAMult___24a2(Vvar__0__e1__44125,Vvar__1__e2__44126) ) ) ) ) ) ) ) ) ).

fof('$_inversion_PLF.Imp.AExp.aevalR_first_try.TooHardToRead.aevalR',axiom,
    ! [Vvar__0___24Anonymous__44769,Vvar__1___24Anonymous__44770] :
      ( cPLF_2eImp_2eAExp_2eaexp___24t(Vvar__0___24Anonymous__44769)
     => ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__44770)
       => ( cPLF_2eImp_2eAExp_2eaevalR__first__try_2eTooHardToRead_2eaevalR___24a2(Vvar__0___24Anonymous__44769,Vvar__1___24Anonymous__44770)
         => ( ? [Vvar__0__n__44772] :
                ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__44772)
                & Vvar__1___24Anonymous__44770 = Vvar__0__n__44772
                & Vvar__0___24Anonymous__44769 = cPLF_2eImp_2eAExp_2eANum___24a1(Vvar__0__n__44772) )
            | ? [Vvar__0__e1__44773] :
                ( cPLF_2eImp_2eAExp_2eaexp___24t(Vvar__0__e1__44773)
                & ? [Vvar__1__e2__44774] :
                    ( cPLF_2eImp_2eAExp_2eaexp___24t(Vvar__1__e2__44774)
                    & ? [Vvar__2__n1__44775] :
                        ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n1__44775)
                        & ? [Vvar__3__n2__44776] :
                            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__3__n2__44776)
                            & cPLF_2eImp_2eAExp_2eaevalR__first__try_2eTooHardToRead_2eaevalR___24a2(Vvar__0__e1__44773,Vvar__2__n1__44775)
                            & cPLF_2eImp_2eAExp_2eaevalR__first__try_2eTooHardToRead_2eaevalR___24a2(Vvar__1__e2__44774,Vvar__3__n2__44776)
                            & Vvar__1___24Anonymous__44770 = c_24__case__Coq_2eInit_2eDatatypes_2enat_2444186___24a4(Vvar__0___24Anonymous__44769,Vvar__1___24Anonymous__44770,Vvar__2__n1__44775,Vvar__3__n2__44776)
                            & Vvar__0___24Anonymous__44769 = cPLF_2eImp_2eAExp_2eAPlus___24a2(Vvar__0__e1__44773,Vvar__1__e2__44774) ) ) ) )
            | ? [Vvar__0__e1__44781] :
                ( cPLF_2eImp_2eAExp_2eaexp___24t(Vvar__0__e1__44781)
                & ? [Vvar__1__e2__44782] :
                    ( cPLF_2eImp_2eAExp_2eaexp___24t(Vvar__1__e2__44782)
                    & ? [Vvar__2__n1__44783] :
                        ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n1__44783)
                        & ? [Vvar__3__n2__44784] :
                            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__3__n2__44784)
                            & cPLF_2eImp_2eAExp_2eaevalR__first__try_2eTooHardToRead_2eaevalR___24a2(Vvar__0__e1__44781,Vvar__2__n1__44783)
                            & cPLF_2eImp_2eAExp_2eaevalR__first__try_2eTooHardToRead_2eaevalR___24a2(Vvar__1__e2__44782,Vvar__3__n2__44784)
                            & Vvar__1___24Anonymous__44770 = c_24__case__Coq_2eInit_2eDatatypes_2enat_2444295___24a4(Vvar__0___24Anonymous__44769,Vvar__1___24Anonymous__44770,Vvar__2__n1__44783,Vvar__3__n2__44784)
                            & Vvar__0___24Anonymous__44769 = cPLF_2eImp_2eAExp_2eAMinus___24a2(Vvar__0__e1__44781,Vvar__1__e2__44782) ) ) ) )
            | ? [Vvar__0__e1__44791] :
                ( cPLF_2eImp_2eAExp_2eaexp___24t(Vvar__0__e1__44791)
                & ? [Vvar__1__e2__44792] :
                    ( cPLF_2eImp_2eAExp_2eaexp___24t(Vvar__1__e2__44792)
                    & ? [Vvar__2__n1__44793] :
                        ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n1__44793)
                        & ? [Vvar__3__n2__44794] :
                            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__3__n2__44794)
                            & cPLF_2eImp_2eAExp_2eaevalR__first__try_2eTooHardToRead_2eaevalR___24a2(Vvar__0__e1__44791,Vvar__2__n1__44793)
                            & cPLF_2eImp_2eAExp_2eaevalR__first__try_2eTooHardToRead_2eaevalR___24a2(Vvar__1__e2__44792,Vvar__3__n2__44794)
                            & Vvar__1___24Anonymous__44770 = c_24__case__Coq_2eInit_2eDatatypes_2enat_2444389___24a4(Vvar__0___24Anonymous__44769,Vvar__1___24Anonymous__44770,Vvar__2__n1__44793,Vvar__3__n2__44794)
                            & Vvar__0___24Anonymous__44769 = cPLF_2eImp_2eAExp_2eAMult___24a2(Vvar__0__e1__44791,Vvar__1__e2__44792) ) ) ) ) ) ) ) ) ).

fof('$_inversion_PLF.Imp.AExp.aevalR_first_try.aevalR',axiom,
    ! [Vvar__0___24Anonymous__45673,Vvar__1___24Anonymous__45674] :
      ( cPLF_2eImp_2eAExp_2eaexp___24t(Vvar__0___24Anonymous__45673)
     => ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__45674)
       => ( cPLF_2eImp_2eAExp_2eaevalR__first__try_2eaevalR___24a2(Vvar__0___24Anonymous__45673,Vvar__1___24Anonymous__45674)
         => ( ? [Vvar__0__n__45676] :
                ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__45676)
                & Vvar__1___24Anonymous__45674 = Vvar__0__n__45676
                & Vvar__0___24Anonymous__45673 = cPLF_2eImp_2eAExp_2eANum___24a1(Vvar__0__n__45676) )
            | ? [Vvar__0__e1__45677] :
                ( cPLF_2eImp_2eAExp_2eaexp___24t(Vvar__0__e1__45677)
                & ? [Vvar__1__e2__45678] :
                    ( cPLF_2eImp_2eAExp_2eaexp___24t(Vvar__1__e2__45678)
                    & ? [Vvar__2__n1__45679] :
                        ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n1__45679)
                        & ? [Vvar__3__n2__45680] :
                            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__3__n2__45680)
                            & cPLF_2eImp_2eAExp_2eaevalR__first__try_2eaevalR___24a2(Vvar__0__e1__45677,Vvar__2__n1__45679)
                            & cPLF_2eImp_2eAExp_2eaevalR__first__try_2eaevalR___24a2(Vvar__1__e2__45678,Vvar__3__n2__45680)
                            & Vvar__1___24Anonymous__45674 = c_24__case__Coq_2eInit_2eDatatypes_2enat_2444186___24a4(Vvar__0___24Anonymous__45673,Vvar__1___24Anonymous__45674,Vvar__2__n1__45679,Vvar__3__n2__45680)
                            & Vvar__0___24Anonymous__45673 = cPLF_2eImp_2eAExp_2eAPlus___24a2(Vvar__0__e1__45677,Vvar__1__e2__45678) ) ) ) )
            | ? [Vvar__0__e1__45685] :
                ( cPLF_2eImp_2eAExp_2eaexp___24t(Vvar__0__e1__45685)
                & ? [Vvar__1__e2__45686] :
                    ( cPLF_2eImp_2eAExp_2eaexp___24t(Vvar__1__e2__45686)
                    & ? [Vvar__2__n1__45687] :
                        ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n1__45687)
                        & ? [Vvar__3__n2__45688] :
                            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__3__n2__45688)
                            & cPLF_2eImp_2eAExp_2eaevalR__first__try_2eaevalR___24a2(Vvar__0__e1__45685,Vvar__2__n1__45687)
                            & cPLF_2eImp_2eAExp_2eaevalR__first__try_2eaevalR___24a2(Vvar__1__e2__45686,Vvar__3__n2__45688)
                            & Vvar__1___24Anonymous__45674 = c_24__case__Coq_2eInit_2eDatatypes_2enat_2444295___24a4(Vvar__0___24Anonymous__45673,Vvar__1___24Anonymous__45674,Vvar__2__n1__45687,Vvar__3__n2__45688)
                            & Vvar__0___24Anonymous__45673 = cPLF_2eImp_2eAExp_2eAMinus___24a2(Vvar__0__e1__45685,Vvar__1__e2__45686) ) ) ) )
            | ? [Vvar__0__e1__45695] :
                ( cPLF_2eImp_2eAExp_2eaexp___24t(Vvar__0__e1__45695)
                & ? [Vvar__1__e2__45696] :
                    ( cPLF_2eImp_2eAExp_2eaexp___24t(Vvar__1__e2__45696)
                    & ? [Vvar__2__n1__45697] :
                        ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n1__45697)
                        & ? [Vvar__3__n2__45698] :
                            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__3__n2__45698)
                            & cPLF_2eImp_2eAExp_2eaevalR__first__try_2eaevalR___24a2(Vvar__0__e1__45695,Vvar__2__n1__45697)
                            & cPLF_2eImp_2eAExp_2eaevalR__first__try_2eaevalR___24a2(Vvar__1__e2__45696,Vvar__3__n2__45698)
                            & Vvar__1___24Anonymous__45674 = c_24__case__Coq_2eInit_2eDatatypes_2enat_2444389___24a4(Vvar__0___24Anonymous__45673,Vvar__1___24Anonymous__45674,Vvar__2__n1__45697,Vvar__3__n2__45698)
                            & Vvar__0___24Anonymous__45673 = cPLF_2eImp_2eAExp_2eAMult___24a2(Vvar__0__e1__45695,Vvar__1__e2__45696) ) ) ) ) ) ) ) ) ).

fof('$_inversion_PLF.Imp.AExp.aexp',axiom,
    ! [VX29194] :
      ( cPLF_2eImp_2eAExp_2eaexp___24t(VX29194)
     => ( ? [Vvar__0__n__29195] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__29195)
            & VX29194 = cPLF_2eImp_2eAExp_2eANum___24a1(Vvar__0__n__29195) )
        | ? [Vvar__0__a1__29196] :
            ( cPLF_2eImp_2eAExp_2eaexp___24t(Vvar__0__a1__29196)
            & ? [Vvar__1__a2__29197] :
                ( cPLF_2eImp_2eAExp_2eaexp___24t(Vvar__1__a2__29197)
                & VX29194 = cPLF_2eImp_2eAExp_2eAPlus___24a2(Vvar__0__a1__29196,Vvar__1__a2__29197) ) )
        | ? [Vvar__0__a1__29198] :
            ( cPLF_2eImp_2eAExp_2eaexp___24t(Vvar__0__a1__29198)
            & ? [Vvar__1__a2__29199] :
                ( cPLF_2eImp_2eAExp_2eaexp___24t(Vvar__1__a2__29199)
                & VX29194 = cPLF_2eImp_2eAExp_2eAMinus___24a2(Vvar__0__a1__29198,Vvar__1__a2__29199) ) )
        | ? [Vvar__0__a1__29200] :
            ( cPLF_2eImp_2eAExp_2eaexp___24t(Vvar__0__a1__29200)
            & ? [Vvar__1__a2__29201] :
                ( cPLF_2eImp_2eAExp_2eaexp___24t(Vvar__1__a2__29201)
                & VX29194 = cPLF_2eImp_2eAExp_2eAMult___24a2(Vvar__0__a1__29200,Vvar__1__a2__29201) ) ) ) ) ).

fof('$_inversion_PLF.Imp.AExp.bexp',axiom,
    ! [VX34888] :
      ( cPLF_2eImp_2eAExp_2ebexp___24t(VX34888)
     => ( VX34888 = cPLF_2eImp_2eAExp_2eBTrue
        | VX34888 = cPLF_2eImp_2eAExp_2eBFalse
        | ? [Vvar__0__a1__34889] :
            ( cPLF_2eImp_2eAExp_2eaexp___24t(Vvar__0__a1__34889)
            & ? [Vvar__1__a2__34890] :
                ( cPLF_2eImp_2eAExp_2eaexp___24t(Vvar__1__a2__34890)
                & VX34888 = cPLF_2eImp_2eAExp_2eBEq___24a2(Vvar__0__a1__34889,Vvar__1__a2__34890) ) )
        | ? [Vvar__0__a1__34891] :
            ( cPLF_2eImp_2eAExp_2eaexp___24t(Vvar__0__a1__34891)
            & ? [Vvar__1__a2__34892] :
                ( cPLF_2eImp_2eAExp_2eaexp___24t(Vvar__1__a2__34892)
                & VX34888 = cPLF_2eImp_2eAExp_2eBLe___24a2(Vvar__0__a1__34891,Vvar__1__a2__34892) ) )
        | ? [Vvar__0__b__34893] :
            ( cPLF_2eImp_2eAExp_2ebexp___24t(Vvar__0__b__34893)
            & VX34888 = cPLF_2eImp_2eAExp_2eBNot___24a1(Vvar__0__b__34893) )
        | ? [Vvar__0__b1__34894] :
            ( cPLF_2eImp_2eAExp_2ebexp___24t(Vvar__0__b1__34894)
            & ? [Vvar__1__b2__34895] :
                ( cPLF_2eImp_2eAExp_2ebexp___24t(Vvar__1__b2__34895)
                & VX34888 = cPLF_2eImp_2eAExp_2eBAnd___24a2(Vvar__0__b1__34894,Vvar__1__b2__34895) ) ) ) ) ).

fof('$_inversion_PLF.Imp.BreakImp.com',axiom,
    ! [VX34945] :
      ( cPLF_2eImp_2eBreakImp_2ecom___24t(VX34945)
     => ( VX34945 = cPLF_2eImp_2eBreakImp_2eCSkip
        | VX34945 = cPLF_2eImp_2eBreakImp_2eCBreak
        | ? [Vvar__0__x__34946] :
            ( cCoq_2eStrings_2eString_2estring___24t(Vvar__0__x__34946)
            & ? [Vvar__1__a__34947] :
                ( cPLF_2eImp_2eaexp___24t(Vvar__1__a__34947)
                & VX34945 = cPLF_2eImp_2eBreakImp_2eCAss___24a2(Vvar__0__x__34946,Vvar__1__a__34947) ) )
        | ? [Vvar__0__c1__34948] :
            ( cPLF_2eImp_2eBreakImp_2ecom___24t(Vvar__0__c1__34948)
            & ? [Vvar__1__c2__34949] :
                ( cPLF_2eImp_2eBreakImp_2ecom___24t(Vvar__1__c2__34949)
                & VX34945 = cPLF_2eImp_2eBreakImp_2eCSeq___24a2(Vvar__0__c1__34948,Vvar__1__c2__34949) ) )
        | ? [Vvar__0__b__34950] :
            ( cPLF_2eImp_2ebexp___24t(Vvar__0__b__34950)
            & ? [Vvar__1__c1__34951] :
                ( cPLF_2eImp_2eBreakImp_2ecom___24t(Vvar__1__c1__34951)
                & ? [Vvar__2__c2__34952] :
                    ( cPLF_2eImp_2eBreakImp_2ecom___24t(Vvar__2__c2__34952)
                    & VX34945 = cPLF_2eImp_2eBreakImp_2eCIf___24a3(Vvar__0__b__34950,Vvar__1__c1__34951,Vvar__2__c2__34952) ) ) )
        | ? [Vvar__0__b__34953] :
            ( cPLF_2eImp_2ebexp___24t(Vvar__0__b__34953)
            & ? [Vvar__1__c__34954] :
                ( cPLF_2eImp_2eBreakImp_2ecom___24t(Vvar__1__c__34954)
                & VX34945 = cPLF_2eImp_2eBreakImp_2eCWhile___24a2(Vvar__0__b__34953,Vvar__1__c__34954) ) ) ) ) ).

fof('$_inversion_PLF.Imp.BreakImp.result',axiom,
    ! [VX35018] :
      ( cPLF_2eImp_2eBreakImp_2eresult___24t(VX35018)
     => ( VX35018 = cPLF_2eImp_2eBreakImp_2eSContinue
        | VX35018 = cPLF_2eImp_2eBreakImp_2eSBreak ) ) ).

fof('$_inversion_PLF.Imp.aevalR_division.aevalR',axiom,
    ! [Vvar__0___24Anonymous__45046,Vvar__1___24Anonymous__45047] :
      ( cPLF_2eImp_2eaevalR__division_2eaexp___24t(Vvar__0___24Anonymous__45046)
     => ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__45047)
       => ( cPLF_2eImp_2eaevalR__division_2eaevalR___24a2(Vvar__0___24Anonymous__45046,Vvar__1___24Anonymous__45047)
         => ( ? [Vvar__0__n__45049] :
                ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__45049)
                & Vvar__1___24Anonymous__45047 = Vvar__0__n__45049
                & Vvar__0___24Anonymous__45046 = cPLF_2eImp_2eaevalR__division_2eANum___24a1(Vvar__0__n__45049) )
            | ? [Vvar__0__a1__45050] :
                ( cPLF_2eImp_2eaevalR__division_2eaexp___24t(Vvar__0__a1__45050)
                & ? [Vvar__1__a2__45051] :
                    ( cPLF_2eImp_2eaevalR__division_2eaexp___24t(Vvar__1__a2__45051)
                    & ? [Vvar__2__n1__45052] :
                        ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n1__45052)
                        & ? [Vvar__3__n2__45053] :
                            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__3__n2__45053)
                            & cPLF_2eImp_2eaevalR__division_2eaevalR___24a2(Vvar__0__a1__45050,Vvar__2__n1__45052)
                            & cPLF_2eImp_2eaevalR__division_2eaevalR___24a2(Vvar__1__a2__45051,Vvar__3__n2__45053)
                            & Vvar__1___24Anonymous__45047 = c_24__case__Coq_2eInit_2eDatatypes_2enat_2445138___24a4(Vvar__0___24Anonymous__45046,Vvar__1___24Anonymous__45047,Vvar__2__n1__45052,Vvar__3__n2__45053)
                            & Vvar__0___24Anonymous__45046 = cPLF_2eImp_2eaevalR__division_2eAPlus___24a2(Vvar__0__a1__45050,Vvar__1__a2__45051) ) ) ) )
            | ? [Vvar__0__a1__45058] :
                ( cPLF_2eImp_2eaevalR__division_2eaexp___24t(Vvar__0__a1__45058)
                & ? [Vvar__1__a2__45059] :
                    ( cPLF_2eImp_2eaevalR__division_2eaexp___24t(Vvar__1__a2__45059)
                    & ? [Vvar__2__n1__45060] :
                        ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n1__45060)
                        & ? [Vvar__3__n2__45061] :
                            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__3__n2__45061)
                            & cPLF_2eImp_2eaevalR__division_2eaevalR___24a2(Vvar__0__a1__45058,Vvar__2__n1__45060)
                            & cPLF_2eImp_2eaevalR__division_2eaevalR___24a2(Vvar__1__a2__45059,Vvar__3__n2__45061)
                            & Vvar__1___24Anonymous__45047 = c_24__case__Coq_2eInit_2eDatatypes_2enat_2445247___24a4(Vvar__0___24Anonymous__45046,Vvar__1___24Anonymous__45047,Vvar__2__n1__45060,Vvar__3__n2__45061)
                            & Vvar__0___24Anonymous__45046 = cPLF_2eImp_2eaevalR__division_2eAMinus___24a2(Vvar__0__a1__45058,Vvar__1__a2__45059) ) ) ) )
            | ? [Vvar__0__a1__45068] :
                ( cPLF_2eImp_2eaevalR__division_2eaexp___24t(Vvar__0__a1__45068)
                & ? [Vvar__1__a2__45069] :
                    ( cPLF_2eImp_2eaevalR__division_2eaexp___24t(Vvar__1__a2__45069)
                    & ? [Vvar__2__n1__45070] :
                        ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n1__45070)
                        & ? [Vvar__3__n2__45071] :
                            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__3__n2__45071)
                            & cPLF_2eImp_2eaevalR__division_2eaevalR___24a2(Vvar__0__a1__45068,Vvar__2__n1__45070)
                            & cPLF_2eImp_2eaevalR__division_2eaevalR___24a2(Vvar__1__a2__45069,Vvar__3__n2__45071)
                            & Vvar__1___24Anonymous__45047 = c_24__case__Coq_2eInit_2eDatatypes_2enat_2445341___24a4(Vvar__0___24Anonymous__45046,Vvar__1___24Anonymous__45047,Vvar__2__n1__45070,Vvar__3__n2__45071)
                            & Vvar__0___24Anonymous__45046 = cPLF_2eImp_2eaevalR__division_2eAMult___24a2(Vvar__0__a1__45068,Vvar__1__a2__45069) ) ) ) )
            | ? [Vvar__0__a1__45076] :
                ( cPLF_2eImp_2eaevalR__division_2eaexp___24t(Vvar__0__a1__45076)
                & ? [Vvar__1__a2__45077] :
                    ( cPLF_2eImp_2eaevalR__division_2eaexp___24t(Vvar__1__a2__45077)
                    & ? [Vvar__2__n1__45078] :
                        ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n1__45078)
                        & ? [Vvar__3__n2__45079] :
                            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__3__n2__45079)
                            & ? [Vvar__4__n3__45080] :
                                ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__4__n3__45080)
                                & cPLF_2eImp_2eaevalR__division_2eaevalR___24a2(Vvar__0__a1__45076,Vvar__2__n1__45078)
                                & cPLF_2eImp_2eaevalR__division_2eaevalR___24a2(Vvar__1__a2__45077,Vvar__3__n2__45079)
                                & cCoq_2eInit_2ePeano_2egt___24a2(Vvar__3__n2__45079,cCoq_2eInit_2eDatatypes_2eO)
                                & cCoq_2eInit_2eNat_2emul___24a2(Vvar__3__n2__45079,Vvar__4__n3__45080) = Vvar__2__n1__45078
                                & Vvar__1___24Anonymous__45047 = Vvar__4__n3__45080
                                & Vvar__0___24Anonymous__45046 = cPLF_2eImp_2eaevalR__division_2eADiv___24a2(Vvar__0__a1__45076,Vvar__1__a2__45077) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_PLF.Imp.aevalR_division.aexp',axiom,
    ! [VX30731] :
      ( cPLF_2eImp_2eaevalR__division_2eaexp___24t(VX30731)
     => ( ? [Vvar__0__n__30732] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__30732)
            & VX30731 = cPLF_2eImp_2eaevalR__division_2eANum___24a1(Vvar__0__n__30732) )
        | ? [Vvar__0__a1__30733] :
            ( cPLF_2eImp_2eaevalR__division_2eaexp___24t(Vvar__0__a1__30733)
            & ? [Vvar__1__a2__30734] :
                ( cPLF_2eImp_2eaevalR__division_2eaexp___24t(Vvar__1__a2__30734)
                & VX30731 = cPLF_2eImp_2eaevalR__division_2eAPlus___24a2(Vvar__0__a1__30733,Vvar__1__a2__30734) ) )
        | ? [Vvar__0__a1__30735] :
            ( cPLF_2eImp_2eaevalR__division_2eaexp___24t(Vvar__0__a1__30735)
            & ? [Vvar__1__a2__30736] :
                ( cPLF_2eImp_2eaevalR__division_2eaexp___24t(Vvar__1__a2__30736)
                & VX30731 = cPLF_2eImp_2eaevalR__division_2eAMinus___24a2(Vvar__0__a1__30735,Vvar__1__a2__30736) ) )
        | ? [Vvar__0__a1__30737] :
            ( cPLF_2eImp_2eaevalR__division_2eaexp___24t(Vvar__0__a1__30737)
            & ? [Vvar__1__a2__30738] :
                ( cPLF_2eImp_2eaevalR__division_2eaexp___24t(Vvar__1__a2__30738)
                & VX30731 = cPLF_2eImp_2eaevalR__division_2eAMult___24a2(Vvar__0__a1__30737,Vvar__1__a2__30738) ) )
        | ? [Vvar__0__a1__30739] :
            ( cPLF_2eImp_2eaevalR__division_2eaexp___24t(Vvar__0__a1__30739)
            & ? [Vvar__1__a2__30740] :
                ( cPLF_2eImp_2eaevalR__division_2eaexp___24t(Vvar__1__a2__30740)
                & VX30731 = cPLF_2eImp_2eaevalR__division_2eADiv___24a2(Vvar__0__a1__30739,Vvar__1__a2__30740) ) ) ) ) ).

fof('$_inversion_PLF.Imp.aevalR_extended.aevalR',axiom,
    ! [Vvar__0___24Anonymous__45367,Vvar__1___24Anonymous__45368] :
      ( cPLF_2eImp_2eaevalR__extended_2eaexp___24t(Vvar__0___24Anonymous__45367)
     => ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__45368)
       => ( cPLF_2eImp_2eaevalR__extended_2eaevalR___24a2(Vvar__0___24Anonymous__45367,Vvar__1___24Anonymous__45368)
         => ( ? [Vvar__0__n__45370] :
                ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__45370)
                & Vvar__1___24Anonymous__45368 = Vvar__0__n__45370
                & Vvar__0___24Anonymous__45367 = cPLF_2eImp_2eaevalR__extended_2eAAny )
            | ? [Vvar__0__n__45371] :
                ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__45371)
                & Vvar__1___24Anonymous__45368 = Vvar__0__n__45371
                & Vvar__0___24Anonymous__45367 = cPLF_2eImp_2eaevalR__extended_2eANum___24a1(Vvar__0__n__45371) )
            | ? [Vvar__0__a1__45372] :
                ( cPLF_2eImp_2eaevalR__extended_2eaexp___24t(Vvar__0__a1__45372)
                & ? [Vvar__1__a2__45373] :
                    ( cPLF_2eImp_2eaevalR__extended_2eaexp___24t(Vvar__1__a2__45373)
                    & ? [Vvar__2__n1__45374] :
                        ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n1__45374)
                        & ? [Vvar__3__n2__45375] :
                            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__3__n2__45375)
                            & cPLF_2eImp_2eaevalR__extended_2eaevalR___24a2(Vvar__0__a1__45372,Vvar__2__n1__45374)
                            & cPLF_2eImp_2eaevalR__extended_2eaevalR___24a2(Vvar__1__a2__45373,Vvar__3__n2__45375)
                            & Vvar__1___24Anonymous__45368 = c_24__case__Coq_2eInit_2eDatatypes_2enat_2445451___24a4(Vvar__0___24Anonymous__45367,Vvar__1___24Anonymous__45368,Vvar__2__n1__45374,Vvar__3__n2__45375)
                            & Vvar__0___24Anonymous__45367 = cPLF_2eImp_2eaevalR__extended_2eAPlus___24a2(Vvar__0__a1__45372,Vvar__1__a2__45373) ) ) ) )
            | ? [Vvar__0__a1__45380] :
                ( cPLF_2eImp_2eaevalR__extended_2eaexp___24t(Vvar__0__a1__45380)
                & ? [Vvar__1__a2__45381] :
                    ( cPLF_2eImp_2eaevalR__extended_2eaexp___24t(Vvar__1__a2__45381)
                    & ? [Vvar__2__n1__45382] :
                        ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n1__45382)
                        & ? [Vvar__3__n2__45383] :
                            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__3__n2__45383)
                            & cPLF_2eImp_2eaevalR__extended_2eaevalR___24a2(Vvar__0__a1__45380,Vvar__2__n1__45382)
                            & cPLF_2eImp_2eaevalR__extended_2eaevalR___24a2(Vvar__1__a2__45381,Vvar__3__n2__45383)
                            & Vvar__1___24Anonymous__45368 = c_24__case__Coq_2eInit_2eDatatypes_2enat_2445560___24a4(Vvar__0___24Anonymous__45367,Vvar__1___24Anonymous__45368,Vvar__2__n1__45382,Vvar__3__n2__45383)
                            & Vvar__0___24Anonymous__45367 = cPLF_2eImp_2eaevalR__extended_2eAMinus___24a2(Vvar__0__a1__45380,Vvar__1__a2__45381) ) ) ) )
            | ? [Vvar__0__a1__45390] :
                ( cPLF_2eImp_2eaevalR__extended_2eaexp___24t(Vvar__0__a1__45390)
                & ? [Vvar__1__a2__45391] :
                    ( cPLF_2eImp_2eaevalR__extended_2eaexp___24t(Vvar__1__a2__45391)
                    & ? [Vvar__2__n1__45392] :
                        ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n1__45392)
                        & ? [Vvar__3__n2__45393] :
                            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__3__n2__45393)
                            & cPLF_2eImp_2eaevalR__extended_2eaevalR___24a2(Vvar__0__a1__45390,Vvar__2__n1__45392)
                            & cPLF_2eImp_2eaevalR__extended_2eaevalR___24a2(Vvar__1__a2__45391,Vvar__3__n2__45393)
                            & Vvar__1___24Anonymous__45368 = c_24__case__Coq_2eInit_2eDatatypes_2enat_2445654___24a4(Vvar__0___24Anonymous__45367,Vvar__1___24Anonymous__45368,Vvar__2__n1__45392,Vvar__3__n2__45393)
                            & Vvar__0___24Anonymous__45367 = cPLF_2eImp_2eaevalR__extended_2eAMult___24a2(Vvar__0__a1__45390,Vvar__1__a2__45391) ) ) ) ) ) ) ) ) ).

fof('$_inversion_PLF.Imp.aevalR_extended.aexp',axiom,
    ! [VX35205] :
      ( cPLF_2eImp_2eaevalR__extended_2eaexp___24t(VX35205)
     => ( VX35205 = cPLF_2eImp_2eaevalR__extended_2eAAny
        | ? [Vvar__0__n__35206] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__35206)
            & VX35205 = cPLF_2eImp_2eaevalR__extended_2eANum___24a1(Vvar__0__n__35206) )
        | ? [Vvar__0__a1__35207] :
            ( cPLF_2eImp_2eaevalR__extended_2eaexp___24t(Vvar__0__a1__35207)
            & ? [Vvar__1__a2__35208] :
                ( cPLF_2eImp_2eaevalR__extended_2eaexp___24t(Vvar__1__a2__35208)
                & VX35205 = cPLF_2eImp_2eaevalR__extended_2eAPlus___24a2(Vvar__0__a1__35207,Vvar__1__a2__35208) ) )
        | ? [Vvar__0__a1__35209] :
            ( cPLF_2eImp_2eaevalR__extended_2eaexp___24t(Vvar__0__a1__35209)
            & ? [Vvar__1__a2__35210] :
                ( cPLF_2eImp_2eaevalR__extended_2eaexp___24t(Vvar__1__a2__35210)
                & VX35205 = cPLF_2eImp_2eaevalR__extended_2eAMinus___24a2(Vvar__0__a1__35209,Vvar__1__a2__35210) ) )
        | ? [Vvar__0__a1__35211] :
            ( cPLF_2eImp_2eaevalR__extended_2eaexp___24t(Vvar__0__a1__35211)
            & ? [Vvar__1__a2__35212] :
                ( cPLF_2eImp_2eaevalR__extended_2eaexp___24t(Vvar__1__a2__35212)
                & VX35205 = cPLF_2eImp_2eaevalR__extended_2eAMult___24a2(Vvar__0__a1__35211,Vvar__1__a2__35212) ) ) ) ) ).

fof('$_inversion_PLF.Imp.aexp',axiom,
    ! [VX25433] :
      ( cPLF_2eImp_2eaexp___24t(VX25433)
     => ( ? [Vvar__0__n__25434] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__25434)
            & VX25433 = cPLF_2eImp_2eANum___24a1(Vvar__0__n__25434) )
        | ? [Vvar__0__x__25435] :
            ( cCoq_2eStrings_2eString_2estring___24t(Vvar__0__x__25435)
            & VX25433 = cPLF_2eImp_2eAId___24a1(Vvar__0__x__25435) )
        | ? [Vvar__0__a1__25436] :
            ( cPLF_2eImp_2eaexp___24t(Vvar__0__a1__25436)
            & ? [Vvar__1__a2__25437] :
                ( cPLF_2eImp_2eaexp___24t(Vvar__1__a2__25437)
                & VX25433 = cPLF_2eImp_2eAPlus___24a2(Vvar__0__a1__25436,Vvar__1__a2__25437) ) )
        | ? [Vvar__0__a1__25438] :
            ( cPLF_2eImp_2eaexp___24t(Vvar__0__a1__25438)
            & ? [Vvar__1__a2__25439] :
                ( cPLF_2eImp_2eaexp___24t(Vvar__1__a2__25439)
                & VX25433 = cPLF_2eImp_2eAMinus___24a2(Vvar__0__a1__25438,Vvar__1__a2__25439) ) )
        | ? [Vvar__0__a1__25440] :
            ( cPLF_2eImp_2eaexp___24t(Vvar__0__a1__25440)
            & ? [Vvar__1__a2__25441] :
                ( cPLF_2eImp_2eaexp___24t(Vvar__1__a2__25441)
                & VX25433 = cPLF_2eImp_2eAMult___24a2(Vvar__0__a1__25440,Vvar__1__a2__25441) ) ) ) ) ).

fof('$_inversion_PLF.Imp.bexp',axiom,
    ! [VX25495] :
      ( cPLF_2eImp_2ebexp___24t(VX25495)
     => ( VX25495 = cPLF_2eImp_2eBTrue
        | VX25495 = cPLF_2eImp_2eBFalse
        | ? [Vvar__0__a1__25496] :
            ( cPLF_2eImp_2eaexp___24t(Vvar__0__a1__25496)
            & ? [Vvar__1__a2__25497] :
                ( cPLF_2eImp_2eaexp___24t(Vvar__1__a2__25497)
                & VX25495 = cPLF_2eImp_2eBEq___24a2(Vvar__0__a1__25496,Vvar__1__a2__25497) ) )
        | ? [Vvar__0__a1__25498] :
            ( cPLF_2eImp_2eaexp___24t(Vvar__0__a1__25498)
            & ? [Vvar__1__a2__25499] :
                ( cPLF_2eImp_2eaexp___24t(Vvar__1__a2__25499)
                & VX25495 = cPLF_2eImp_2eBLe___24a2(Vvar__0__a1__25498,Vvar__1__a2__25499) ) )
        | ? [Vvar__0__b__25500] :
            ( cPLF_2eImp_2ebexp___24t(Vvar__0__b__25500)
            & VX25495 = cPLF_2eImp_2eBNot___24a1(Vvar__0__b__25500) )
        | ? [Vvar__0__b1__25501] :
            ( cPLF_2eImp_2ebexp___24t(Vvar__0__b1__25501)
            & ? [Vvar__1__b2__25502] :
                ( cPLF_2eImp_2ebexp___24t(Vvar__1__b2__25502)
                & VX25495 = cPLF_2eImp_2eBAnd___24a2(Vvar__0__b1__25501,Vvar__1__b2__25502) ) ) ) ) ).

fof('$_inversion_PLF.Imp.ceval',axiom,
    ! [Vvar__0___24Anonymous__35491,Vvar__1___24Anonymous__35492,Vvar__2___24Anonymous__35493] :
      ( cPLF_2eImp_2ecom___24t(Vvar__0___24Anonymous__35491)
     => ( cPLF_2eImp_2estate___24t(Vvar__1___24Anonymous__35492)
       => ( cPLF_2eImp_2estate___24t(Vvar__2___24Anonymous__35493)
         => ( cPLF_2eImp_2eceval___24a3(Vvar__0___24Anonymous__35491,Vvar__1___24Anonymous__35492,Vvar__2___24Anonymous__35493)
           => ( ? [Vvar__0__st__35495] :
                  ( cPLF_2eImp_2estate___24t(Vvar__0__st__35495)
                  & Vvar__2___24Anonymous__35493 = Vvar__0__st__35495
                  & Vvar__1___24Anonymous__35492 = Vvar__0__st__35495
                  & Vvar__0___24Anonymous__35491 = cPLF_2eImp_2eCSkip )
              | ? [Vvar__0__st__35496] :
                  ( cPLF_2eImp_2estate___24t(Vvar__0__st__35496)
                  & ? [Vvar__1__a1__35497] :
                      ( cPLF_2eImp_2eaexp___24t(Vvar__1__a1__35497)
                      & ? [Vvar__2__n__35498] :
                          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n__35498)
                          & ? [Vvar__3__x__35499] :
                              ( cCoq_2eStrings_2eString_2estring___24t(Vvar__3__x__35499)
                              & cPLF_2eImp_2eaeval___24a2(Vvar__0__st__35496,Vvar__1__a1__35497) = Vvar__2__n__35498
                              & Vvar__2___24Anonymous__35493 = c_24__lam__35549___24a6(Vvar__0___24Anonymous__35491,Vvar__1___24Anonymous__35492,Vvar__2___24Anonymous__35493,Vvar__0__st__35496,Vvar__2__n__35498,Vvar__3__x__35499)
                              & Vvar__1___24Anonymous__35492 = Vvar__0__st__35496
                              & Vvar__0___24Anonymous__35491 = cPLF_2eImp_2eCAss___24a2(Vvar__3__x__35499,Vvar__1__a1__35497) ) ) ) )
              | ? [Vvar__0__c1__35503] :
                  ( cPLF_2eImp_2ecom___24t(Vvar__0__c1__35503)
                  & ? [Vvar__1__c2__35504] :
                      ( cPLF_2eImp_2ecom___24t(Vvar__1__c2__35504)
                      & ? [Vvar__2__st__35505] :
                          ( cPLF_2eImp_2estate___24t(Vvar__2__st__35505)
                          & ? [Vvar__3__st_27__35506] :
                              ( cPLF_2eImp_2estate___24t(Vvar__3__st_27__35506)
                              & ? [Vvar__4__st_27_27__35507] :
                                  ( cPLF_2eImp_2estate___24t(Vvar__4__st_27_27__35507)
                                  & cPLF_2eImp_2eceval___24a3(Vvar__0__c1__35503,Vvar__2__st__35505,Vvar__3__st_27__35506)
                                  & cPLF_2eImp_2eceval___24a3(Vvar__1__c2__35504,Vvar__3__st_27__35506,Vvar__4__st_27_27__35507)
                                  & Vvar__2___24Anonymous__35493 = Vvar__4__st_27_27__35507
                                  & Vvar__1___24Anonymous__35492 = Vvar__2__st__35505
                                  & Vvar__0___24Anonymous__35491 = cPLF_2eImp_2eCSeq___24a2(Vvar__0__c1__35503,Vvar__1__c2__35504) ) ) ) ) )
              | ? [Vvar__0__st__35510] :
                  ( cPLF_2eImp_2estate___24t(Vvar__0__st__35510)
                  & ? [Vvar__1__st_27__35511] :
                      ( cPLF_2eImp_2estate___24t(Vvar__1__st_27__35511)
                      & ? [Vvar__2__b__35512] :
                          ( cPLF_2eImp_2ebexp___24t(Vvar__2__b__35512)
                          & ? [Vvar__3__c1__35513] :
                              ( cPLF_2eImp_2ecom___24t(Vvar__3__c1__35513)
                              & ? [Vvar__4__c2__35514] :
                                  ( cPLF_2eImp_2ecom___24t(Vvar__4__c2__35514)
                                  & cPLF_2eImp_2ebeval___24a2(Vvar__0__st__35510,Vvar__2__b__35512) = cCoq_2eInit_2eDatatypes_2etrue
                                  & cPLF_2eImp_2eceval___24a3(Vvar__3__c1__35513,Vvar__0__st__35510,Vvar__1__st_27__35511)
                                  & Vvar__2___24Anonymous__35493 = Vvar__1__st_27__35511
                                  & Vvar__1___24Anonymous__35492 = Vvar__0__st__35510
                                  & Vvar__0___24Anonymous__35491 = cPLF_2eImp_2eCIf___24a3(Vvar__2__b__35512,Vvar__3__c1__35513,Vvar__4__c2__35514) ) ) ) ) )
              | ? [Vvar__0__st__35517] :
                  ( cPLF_2eImp_2estate___24t(Vvar__0__st__35517)
                  & ? [Vvar__1__st_27__35518] :
                      ( cPLF_2eImp_2estate___24t(Vvar__1__st_27__35518)
                      & ? [Vvar__2__b__35519] :
                          ( cPLF_2eImp_2ebexp___24t(Vvar__2__b__35519)
                          & ? [Vvar__3__c1__35520] :
                              ( cPLF_2eImp_2ecom___24t(Vvar__3__c1__35520)
                              & ? [Vvar__4__c2__35521] :
                                  ( cPLF_2eImp_2ecom___24t(Vvar__4__c2__35521)
                                  & cPLF_2eImp_2ebeval___24a2(Vvar__0__st__35517,Vvar__2__b__35519) = cCoq_2eInit_2eDatatypes_2efalse
                                  & cPLF_2eImp_2eceval___24a3(Vvar__4__c2__35521,Vvar__0__st__35517,Vvar__1__st_27__35518)
                                  & Vvar__2___24Anonymous__35493 = Vvar__1__st_27__35518
                                  & Vvar__1___24Anonymous__35492 = Vvar__0__st__35517
                                  & Vvar__0___24Anonymous__35491 = cPLF_2eImp_2eCIf___24a3(Vvar__2__b__35519,Vvar__3__c1__35520,Vvar__4__c2__35521) ) ) ) ) )
              | ? [Vvar__0__b__35524] :
                  ( cPLF_2eImp_2ebexp___24t(Vvar__0__b__35524)
                  & ? [Vvar__1__st__35525] :
                      ( cPLF_2eImp_2estate___24t(Vvar__1__st__35525)
                      & ? [Vvar__2__c__35526] :
                          ( cPLF_2eImp_2ecom___24t(Vvar__2__c__35526)
                          & cPLF_2eImp_2ebeval___24a2(Vvar__1__st__35525,Vvar__0__b__35524) = cCoq_2eInit_2eDatatypes_2efalse
                          & Vvar__2___24Anonymous__35493 = Vvar__1__st__35525
                          & Vvar__1___24Anonymous__35492 = Vvar__1__st__35525
                          & Vvar__0___24Anonymous__35491 = cPLF_2eImp_2eCWhile___24a2(Vvar__0__b__35524,Vvar__2__c__35526) ) ) )
              | ? [Vvar__0__st__35528] :
                  ( cPLF_2eImp_2estate___24t(Vvar__0__st__35528)
                  & ? [Vvar__1__st_27__35529] :
                      ( cPLF_2eImp_2estate___24t(Vvar__1__st_27__35529)
                      & ? [Vvar__2__st_27_27__35530] :
                          ( cPLF_2eImp_2estate___24t(Vvar__2__st_27_27__35530)
                          & ? [Vvar__3__b__35531] :
                              ( cPLF_2eImp_2ebexp___24t(Vvar__3__b__35531)
                              & ? [Vvar__4__c__35532] :
                                  ( cPLF_2eImp_2ecom___24t(Vvar__4__c__35532)
                                  & cPLF_2eImp_2ebeval___24a2(Vvar__0__st__35528,Vvar__3__b__35531) = cCoq_2eInit_2eDatatypes_2etrue
                                  & cPLF_2eImp_2eceval___24a3(Vvar__4__c__35532,Vvar__0__st__35528,Vvar__1__st_27__35529)
                                  & cPLF_2eImp_2eceval___24a3(cPLF_2eImp_2eCWhile___24a2(Vvar__3__b__35531,Vvar__4__c__35532),Vvar__1__st_27__35529,Vvar__2__st_27_27__35530)
                                  & Vvar__2___24Anonymous__35493 = Vvar__2__st_27_27__35530
                                  & Vvar__1___24Anonymous__35492 = Vvar__0__st__35528
                                  & Vvar__0___24Anonymous__35491 = cPLF_2eImp_2eCWhile___24a2(Vvar__3__b__35531,Vvar__4__c__35532) ) ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_PLF.Imp.com',axiom,
    ! [VX25552] :
      ( cPLF_2eImp_2ecom___24t(VX25552)
     => ( VX25552 = cPLF_2eImp_2eCSkip
        | ? [Vvar__0__x__25553] :
            ( cCoq_2eStrings_2eString_2estring___24t(Vvar__0__x__25553)
            & ? [Vvar__1__a__25554] :
                ( cPLF_2eImp_2eaexp___24t(Vvar__1__a__25554)
                & VX25552 = cPLF_2eImp_2eCAss___24a2(Vvar__0__x__25553,Vvar__1__a__25554) ) )
        | ? [Vvar__0__c1__25555] :
            ( cPLF_2eImp_2ecom___24t(Vvar__0__c1__25555)
            & ? [Vvar__1__c2__25556] :
                ( cPLF_2eImp_2ecom___24t(Vvar__1__c2__25556)
                & VX25552 = cPLF_2eImp_2eCSeq___24a2(Vvar__0__c1__25555,Vvar__1__c2__25556) ) )
        | ? [Vvar__0__b__25557] :
            ( cPLF_2eImp_2ebexp___24t(Vvar__0__b__25557)
            & ? [Vvar__1__c1__25558] :
                ( cPLF_2eImp_2ecom___24t(Vvar__1__c1__25558)
                & ? [Vvar__2__c2__25559] :
                    ( cPLF_2eImp_2ecom___24t(Vvar__2__c2__25559)
                    & VX25552 = cPLF_2eImp_2eCIf___24a3(Vvar__0__b__25557,Vvar__1__c1__25558,Vvar__2__c2__25559) ) ) )
        | ? [Vvar__0__b__25560] :
            ( cPLF_2eImp_2ebexp___24t(Vvar__0__b__25560)
            & ? [Vvar__1__c__25561] :
                ( cPLF_2eImp_2ecom___24t(Vvar__1__c__25561)
                & VX25552 = cPLF_2eImp_2eCWhile___24a2(Vvar__0__b__25560,Vvar__1__c__25561) ) ) ) ) ).

fof('$_inversion_PLF.Imp.sinstr',axiom,
    ! [VX32340] :
      ( cPLF_2eImp_2esinstr___24t(VX32340)
     => ( ? [Vvar__0__n__32341] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__32341)
            & VX32340 = cPLF_2eImp_2eSPush___24a1(Vvar__0__n__32341) )
        | ? [Vvar__0__x__32342] :
            ( cCoq_2eStrings_2eString_2estring___24t(Vvar__0__x__32342)
            & VX32340 = cPLF_2eImp_2eSLoad___24a1(Vvar__0__x__32342) )
        | VX32340 = cPLF_2eImp_2eSPlus
        | VX32340 = cPLF_2eImp_2eSMinus
        | VX32340 = cPLF_2eImp_2eSMult ) ) ).

fof('$_inversion_PLF.Smallstep.CImp.com',axiom,
    ! [VX29290] :
      ( cPLF_2eSmallstep_2eCImp_2ecom___24t(VX29290)
     => ( VX29290 = cPLF_2eSmallstep_2eCImp_2eCSkip
        | ? [Vvar__0___24Anonymous__29291] :
            ( cCoq_2eStrings_2eString_2estring___24t(Vvar__0___24Anonymous__29291)
            & ? [Vvar__1___24Anonymous__29292] :
                ( cPLF_2eImp_2eaexp___24t(Vvar__1___24Anonymous__29292)
                & VX29290 = cPLF_2eSmallstep_2eCImp_2eCAss___24a2(Vvar__0___24Anonymous__29291,Vvar__1___24Anonymous__29292) ) )
        | ? [Vvar__0___24Anonymous__29293] :
            ( cPLF_2eSmallstep_2eCImp_2ecom___24t(Vvar__0___24Anonymous__29293)
            & ? [Vvar__1___24Anonymous__29294] :
                ( cPLF_2eSmallstep_2eCImp_2ecom___24t(Vvar__1___24Anonymous__29294)
                & VX29290 = cPLF_2eSmallstep_2eCImp_2eCSeq___24a2(Vvar__0___24Anonymous__29293,Vvar__1___24Anonymous__29294) ) )
        | ? [Vvar__0___24Anonymous__29295] :
            ( cPLF_2eImp_2ebexp___24t(Vvar__0___24Anonymous__29295)
            & ? [Vvar__1___24Anonymous__29296] :
                ( cPLF_2eSmallstep_2eCImp_2ecom___24t(Vvar__1___24Anonymous__29296)
                & ? [Vvar__2___24Anonymous__29297] :
                    ( cPLF_2eSmallstep_2eCImp_2ecom___24t(Vvar__2___24Anonymous__29297)
                    & VX29290 = cPLF_2eSmallstep_2eCImp_2eCIf___24a3(Vvar__0___24Anonymous__29295,Vvar__1___24Anonymous__29296,Vvar__2___24Anonymous__29297) ) ) )
        | ? [Vvar__0___24Anonymous__29298] :
            ( cPLF_2eImp_2ebexp___24t(Vvar__0___24Anonymous__29298)
            & ? [Vvar__1___24Anonymous__29299] :
                ( cPLF_2eSmallstep_2eCImp_2ecom___24t(Vvar__1___24Anonymous__29299)
                & VX29290 = cPLF_2eSmallstep_2eCImp_2eCWhile___24a2(Vvar__0___24Anonymous__29298,Vvar__1___24Anonymous__29299) ) )
        | ? [Vvar__0___24Anonymous__29300] :
            ( cPLF_2eSmallstep_2eCImp_2ecom___24t(Vvar__0___24Anonymous__29300)
            & ? [Vvar__1___24Anonymous__29301] :
                ( cPLF_2eSmallstep_2eCImp_2ecom___24t(Vvar__1___24Anonymous__29301)
                & VX29290 = cPLF_2eSmallstep_2eCImp_2eCPar___24a2(Vvar__0___24Anonymous__29300,Vvar__1___24Anonymous__29301) ) ) ) ) ).

fof('$_inversion_PLF.Smallstep.Combined.step',axiom,
    ! [Vvar__0___24Anonymous__44431,Vvar__1___24Anonymous__44432] :
      ( cPLF_2eSmallstep_2eCombined_2etm___24t(Vvar__0___24Anonymous__44431)
     => ( cPLF_2eSmallstep_2eCombined_2etm___24t(Vvar__1___24Anonymous__44432)
       => ( cPLF_2eSmallstep_2eCombined_2estep___24a2(Vvar__0___24Anonymous__44431,Vvar__1___24Anonymous__44432)
         => ( ? [Vvar__0__n1__44434] :
                ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n1__44434)
                & ? [Vvar__1__n2__44435] :
                    ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__n2__44435)
                    & Vvar__1___24Anonymous__44432 = cPLF_2eSmallstep_2eCombined_2eC___24a1(c_24__case__Coq_2eInit_2eDatatypes_2enat_2444509___24a4(Vvar__0___24Anonymous__44431,Vvar__1___24Anonymous__44432,Vvar__0__n1__44434,Vvar__1__n2__44435))
                    & Vvar__0___24Anonymous__44431 = cPLF_2eSmallstep_2eCombined_2eP___24a2(cPLF_2eSmallstep_2eCombined_2eC___24a1(Vvar__0__n1__44434),cPLF_2eSmallstep_2eCombined_2eC___24a1(Vvar__1__n2__44435)) ) )
            | ? [Vvar__0__t1__44438] :
                ( cPLF_2eSmallstep_2eCombined_2etm___24t(Vvar__0__t1__44438)
                & ? [Vvar__1__t1_27__44439] :
                    ( cPLF_2eSmallstep_2eCombined_2etm___24t(Vvar__1__t1_27__44439)
                    & ? [Vvar__2__t2__44440] :
                        ( cPLF_2eSmallstep_2eCombined_2etm___24t(Vvar__2__t2__44440)
                        & cPLF_2eSmallstep_2eCombined_2estep___24a2(Vvar__0__t1__44438,Vvar__1__t1_27__44439)
                        & Vvar__1___24Anonymous__44432 = cPLF_2eSmallstep_2eCombined_2eP___24a2(Vvar__1__t1_27__44439,Vvar__2__t2__44440)
                        & Vvar__0___24Anonymous__44431 = cPLF_2eSmallstep_2eCombined_2eP___24a2(Vvar__0__t1__44438,Vvar__2__t2__44440) ) ) )
            | ? [Vvar__0__v1__44442] :
                ( cPLF_2eSmallstep_2eCombined_2etm___24t(Vvar__0__v1__44442)
                & ? [Vvar__1__t2__44443] :
                    ( cPLF_2eSmallstep_2eCombined_2etm___24t(Vvar__1__t2__44443)
                    & ? [Vvar__2__t2_27__44444] :
                        ( cPLF_2eSmallstep_2eCombined_2etm___24t(Vvar__2__t2_27__44444)
                        & cPLF_2eSmallstep_2eCombined_2evalue___24a1(Vvar__0__v1__44442)
                        & cPLF_2eSmallstep_2eCombined_2estep___24a2(Vvar__1__t2__44443,Vvar__2__t2_27__44444)
                        & Vvar__1___24Anonymous__44432 = cPLF_2eSmallstep_2eCombined_2eP___24a2(Vvar__0__v1__44442,Vvar__2__t2_27__44444)
                        & Vvar__0___24Anonymous__44431 = cPLF_2eSmallstep_2eCombined_2eP___24a2(Vvar__0__v1__44442,Vvar__1__t2__44443) ) ) )
            | ? [Vvar__0__t1__44447] :
                ( cPLF_2eSmallstep_2eCombined_2etm___24t(Vvar__0__t1__44447)
                & ? [Vvar__1__t2__44448] :
                    ( cPLF_2eSmallstep_2eCombined_2etm___24t(Vvar__1__t2__44448)
                    & Vvar__1___24Anonymous__44432 = Vvar__0__t1__44447
                    & Vvar__0___24Anonymous__44431 = cPLF_2eSmallstep_2eCombined_2etest___24a3(cPLF_2eSmallstep_2eCombined_2etru,Vvar__0__t1__44447,Vvar__1__t2__44448) ) )
            | ? [Vvar__0__t1__44449] :
                ( cPLF_2eSmallstep_2eCombined_2etm___24t(Vvar__0__t1__44449)
                & ? [Vvar__1__t2__44450] :
                    ( cPLF_2eSmallstep_2eCombined_2etm___24t(Vvar__1__t2__44450)
                    & Vvar__1___24Anonymous__44432 = Vvar__1__t2__44450
                    & Vvar__0___24Anonymous__44431 = cPLF_2eSmallstep_2eCombined_2etest___24a3(cPLF_2eSmallstep_2eCombined_2efls,Vvar__0__t1__44449,Vvar__1__t2__44450) ) )
            | ? [Vvar__0__t1__44451] :
                ( cPLF_2eSmallstep_2eCombined_2etm___24t(Vvar__0__t1__44451)
                & ? [Vvar__1__t1_27__44452] :
                    ( cPLF_2eSmallstep_2eCombined_2etm___24t(Vvar__1__t1_27__44452)
                    & ? [Vvar__2__t2__44453] :
                        ( cPLF_2eSmallstep_2eCombined_2etm___24t(Vvar__2__t2__44453)
                        & ? [Vvar__3__t3__44454] :
                            ( cPLF_2eSmallstep_2eCombined_2etm___24t(Vvar__3__t3__44454)
                            & cPLF_2eSmallstep_2eCombined_2estep___24a2(Vvar__0__t1__44451,Vvar__1__t1_27__44452)
                            & Vvar__1___24Anonymous__44432 = cPLF_2eSmallstep_2eCombined_2etest___24a3(Vvar__1__t1_27__44452,Vvar__2__t2__44453,Vvar__3__t3__44454)
                            & Vvar__0___24Anonymous__44431 = cPLF_2eSmallstep_2eCombined_2etest___24a3(Vvar__0__t1__44451,Vvar__2__t2__44453,Vvar__3__t3__44454) ) ) ) ) ) ) ) ) ).

fof('$_inversion_PLF.Smallstep.Combined.tm',axiom,
    ! [VX35019] :
      ( cPLF_2eSmallstep_2eCombined_2etm___24t(VX35019)
     => ( ? [Vvar__0___24Anonymous__35020] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__35020)
            & VX35019 = cPLF_2eSmallstep_2eCombined_2eC___24a1(Vvar__0___24Anonymous__35020) )
        | ? [Vvar__0___24Anonymous__35021] :
            ( cPLF_2eSmallstep_2eCombined_2etm___24t(Vvar__0___24Anonymous__35021)
            & ? [Vvar__1___24Anonymous__35022] :
                ( cPLF_2eSmallstep_2eCombined_2etm___24t(Vvar__1___24Anonymous__35022)
                & VX35019 = cPLF_2eSmallstep_2eCombined_2eP___24a2(Vvar__0___24Anonymous__35021,Vvar__1___24Anonymous__35022) ) )
        | VX35019 = cPLF_2eSmallstep_2eCombined_2etru
        | VX35019 = cPLF_2eSmallstep_2eCombined_2efls
        | ? [Vvar__0___24Anonymous__35023] :
            ( cPLF_2eSmallstep_2eCombined_2etm___24t(Vvar__0___24Anonymous__35023)
            & ? [Vvar__1___24Anonymous__35024] :
                ( cPLF_2eSmallstep_2eCombined_2etm___24t(Vvar__1___24Anonymous__35024)
                & ? [Vvar__2___24Anonymous__35025] :
                    ( cPLF_2eSmallstep_2eCombined_2etm___24t(Vvar__2___24Anonymous__35025)
                    & VX35019 = cPLF_2eSmallstep_2eCombined_2etest___24a3(Vvar__0___24Anonymous__35023,Vvar__1___24Anonymous__35024,Vvar__2___24Anonymous__35025) ) ) ) ) ) ).

fof('$_inversion_PLF.Smallstep.Combined.value',axiom,
    ! [Vvar__0___24Anonymous__44428] :
      ( cPLF_2eSmallstep_2eCombined_2etm___24t(Vvar__0___24Anonymous__44428)
     => ( cPLF_2eSmallstep_2eCombined_2evalue___24a1(Vvar__0___24Anonymous__44428)
       => ( ? [Vvar__0__n__44430] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__44430)
              & Vvar__0___24Anonymous__44428 = cPLF_2eSmallstep_2eCombined_2eC___24a1(Vvar__0__n__44430) )
          | Vvar__0___24Anonymous__44428 = cPLF_2eSmallstep_2eCombined_2etru
          | Vvar__0___24Anonymous__44428 = cPLF_2eSmallstep_2eCombined_2efls ) ) ) ).

fof('$_inversion_PLF.Smallstep.SimpleArith1.step',axiom,
    ! [Vvar__0___24Anonymous__44684,Vvar__1___24Anonymous__44685] :
      ( cPLF_2eSmallstep_2etm___24t(Vvar__0___24Anonymous__44684)
     => ( cPLF_2eSmallstep_2etm___24t(Vvar__1___24Anonymous__44685)
       => ( cPLF_2eSmallstep_2eSimpleArith1_2estep___24a2(Vvar__0___24Anonymous__44684,Vvar__1___24Anonymous__44685)
         => ( ? [Vvar__0__n1__44687] :
                ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n1__44687)
                & ? [Vvar__1__n2__44688] :
                    ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__n2__44688)
                    & Vvar__1___24Anonymous__44685 = cPLF_2eSmallstep_2eC___24a1(c_24__case__Coq_2eInit_2eDatatypes_2enat_24101___24a4(Vvar__0___24Anonymous__44684,Vvar__1___24Anonymous__44685,Vvar__0__n1__44687,Vvar__1__n2__44688))
                    & Vvar__0___24Anonymous__44684 = cPLF_2eSmallstep_2eP___24a2(cPLF_2eSmallstep_2eC___24a1(Vvar__0__n1__44687),cPLF_2eSmallstep_2eC___24a1(Vvar__1__n2__44688)) ) )
            | ? [Vvar__0__t1__44691] :
                ( cPLF_2eSmallstep_2etm___24t(Vvar__0__t1__44691)
                & ? [Vvar__1__t1_27__44692] :
                    ( cPLF_2eSmallstep_2etm___24t(Vvar__1__t1_27__44692)
                    & ? [Vvar__2__t2__44693] :
                        ( cPLF_2eSmallstep_2etm___24t(Vvar__2__t2__44693)
                        & cPLF_2eSmallstep_2eSimpleArith1_2estep___24a2(Vvar__0__t1__44691,Vvar__1__t1_27__44692)
                        & Vvar__1___24Anonymous__44685 = cPLF_2eSmallstep_2eP___24a2(Vvar__1__t1_27__44692,Vvar__2__t2__44693)
                        & Vvar__0___24Anonymous__44684 = cPLF_2eSmallstep_2eP___24a2(Vvar__0__t1__44691,Vvar__2__t2__44693) ) ) )
            | ? [Vvar__0__n1__44695] :
                ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n1__44695)
                & ? [Vvar__1__t2__44696] :
                    ( cPLF_2eSmallstep_2etm___24t(Vvar__1__t2__44696)
                    & ? [Vvar__2__t2_27__44697] :
                        ( cPLF_2eSmallstep_2etm___24t(Vvar__2__t2_27__44697)
                        & cPLF_2eSmallstep_2eSimpleArith1_2estep___24a2(Vvar__1__t2__44696,Vvar__2__t2_27__44697)
                        & Vvar__1___24Anonymous__44685 = cPLF_2eSmallstep_2eP___24a2(cPLF_2eSmallstep_2eC___24a1(Vvar__0__n1__44695),Vvar__2__t2_27__44697)
                        & Vvar__0___24Anonymous__44684 = cPLF_2eSmallstep_2eP___24a2(cPLF_2eSmallstep_2eC___24a1(Vvar__0__n1__44695),Vvar__1__t2__44696) ) ) ) ) ) ) ) ).

fof('$_inversion_PLF.Smallstep.Temp1.step',axiom,
    ! [Vvar__0___24Anonymous__141,Vvar__1___24Anonymous__142] :
      ( cPLF_2eSmallstep_2etm___24t(Vvar__0___24Anonymous__141)
     => ( cPLF_2eSmallstep_2etm___24t(Vvar__1___24Anonymous__142)
       => ( cPLF_2eSmallstep_2eTemp1_2estep___24a2(Vvar__0___24Anonymous__141,Vvar__1___24Anonymous__142)
         => ( ? [Vvar__0__n1__144] :
                ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n1__144)
                & ? [Vvar__1__n2__145] :
                    ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__n2__145)
                    & Vvar__1___24Anonymous__142 = cPLF_2eSmallstep_2eC___24a1(c_24__case__Coq_2eInit_2eDatatypes_2enat_24101___24a4(Vvar__0___24Anonymous__141,Vvar__1___24Anonymous__142,Vvar__0__n1__144,Vvar__1__n2__145))
                    & Vvar__0___24Anonymous__141 = cPLF_2eSmallstep_2eP___24a2(cPLF_2eSmallstep_2eC___24a1(Vvar__0__n1__144),cPLF_2eSmallstep_2eC___24a1(Vvar__1__n2__145)) ) )
            | ? [Vvar__0__t1__148] :
                ( cPLF_2eSmallstep_2etm___24t(Vvar__0__t1__148)
                & ? [Vvar__1__t1_27__149] :
                    ( cPLF_2eSmallstep_2etm___24t(Vvar__1__t1_27__149)
                    & ? [Vvar__2__t2__150] :
                        ( cPLF_2eSmallstep_2etm___24t(Vvar__2__t2__150)
                        & cPLF_2eSmallstep_2eTemp1_2estep___24a2(Vvar__0__t1__148,Vvar__1__t1_27__149)
                        & Vvar__1___24Anonymous__142 = cPLF_2eSmallstep_2eP___24a2(Vvar__1__t1_27__149,Vvar__2__t2__150)
                        & Vvar__0___24Anonymous__141 = cPLF_2eSmallstep_2eP___24a2(Vvar__0__t1__148,Vvar__2__t2__150) ) ) )
            | ? [Vvar__0__v1__152] :
                ( cPLF_2eSmallstep_2etm___24t(Vvar__0__v1__152)
                & ? [Vvar__1__t2__153] :
                    ( cPLF_2eSmallstep_2etm___24t(Vvar__1__t2__153)
                    & ? [Vvar__2__t2_27__154] :
                        ( cPLF_2eSmallstep_2etm___24t(Vvar__2__t2_27__154)
                        & cPLF_2eSmallstep_2eTemp1_2evalue___24a1(Vvar__0__v1__152)
                        & cPLF_2eSmallstep_2eTemp1_2estep___24a2(Vvar__1__t2__153,Vvar__2__t2_27__154)
                        & Vvar__1___24Anonymous__142 = cPLF_2eSmallstep_2eP___24a2(Vvar__0__v1__152,Vvar__2__t2_27__154)
                        & Vvar__0___24Anonymous__141 = cPLF_2eSmallstep_2eP___24a2(Vvar__0__v1__152,Vvar__1__t2__153) ) ) ) ) ) ) ) ).

fof('$_inversion_PLF.Smallstep.Temp1.value',axiom,
    ! [Vvar__0___24Anonymous__136] :
      ( cPLF_2eSmallstep_2etm___24t(Vvar__0___24Anonymous__136)
     => ( cPLF_2eSmallstep_2eTemp1_2evalue___24a1(Vvar__0___24Anonymous__136)
       => ( ? [Vvar__0__n__138] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__138)
              & Vvar__0___24Anonymous__136 = cPLF_2eSmallstep_2eC___24a1(Vvar__0__n__138) )
          | ? [Vvar__0__t1__139] :
              ( cPLF_2eSmallstep_2etm___24t(Vvar__0__t1__139)
              & ? [Vvar__1__n2__140] :
                  ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__n2__140)
                  & Vvar__0___24Anonymous__136 = cPLF_2eSmallstep_2eP___24a2(Vvar__0__t1__139,cPLF_2eSmallstep_2eC___24a1(Vvar__1__n2__140)) ) ) ) ) ) ).

fof('$_inversion_PLF.Smallstep.Temp2.step',axiom,
    ! [Vvar__0___24Anonymous__4807,Vvar__1___24Anonymous__4808] :
      ( cPLF_2eSmallstep_2etm___24t(Vvar__0___24Anonymous__4807)
     => ( cPLF_2eSmallstep_2etm___24t(Vvar__1___24Anonymous__4808)
       => ( cPLF_2eSmallstep_2eTemp2_2estep___24a2(Vvar__0___24Anonymous__4807,Vvar__1___24Anonymous__4808)
         => ( ? [Vvar__0__n__4810] :
                ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__4810)
                & Vvar__1___24Anonymous__4808 = cPLF_2eSmallstep_2eP___24a2(cPLF_2eSmallstep_2eC___24a1(Vvar__0__n__4810),cPLF_2eSmallstep_2eC___24a1(cCoq_2eInit_2eDatatypes_2eO))
                & Vvar__0___24Anonymous__4807 = cPLF_2eSmallstep_2eC___24a1(Vvar__0__n__4810) )
            | ? [Vvar__0__n1__4811] :
                ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n1__4811)
                & ? [Vvar__1__n2__4812] :
                    ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__n2__4812)
                    & Vvar__1___24Anonymous__4808 = cPLF_2eSmallstep_2eC___24a1(c_24__case__Coq_2eInit_2eDatatypes_2enat_24101___24a4(Vvar__0___24Anonymous__4807,Vvar__1___24Anonymous__4808,Vvar__0__n1__4811,Vvar__1__n2__4812))
                    & Vvar__0___24Anonymous__4807 = cPLF_2eSmallstep_2eP___24a2(cPLF_2eSmallstep_2eC___24a1(Vvar__0__n1__4811),cPLF_2eSmallstep_2eC___24a1(Vvar__1__n2__4812)) ) )
            | ? [Vvar__0__t1__4815] :
                ( cPLF_2eSmallstep_2etm___24t(Vvar__0__t1__4815)
                & ? [Vvar__1__t1_27__4816] :
                    ( cPLF_2eSmallstep_2etm___24t(Vvar__1__t1_27__4816)
                    & ? [Vvar__2__t2__4817] :
                        ( cPLF_2eSmallstep_2etm___24t(Vvar__2__t2__4817)
                        & cPLF_2eSmallstep_2eTemp2_2estep___24a2(Vvar__0__t1__4815,Vvar__1__t1_27__4816)
                        & Vvar__1___24Anonymous__4808 = cPLF_2eSmallstep_2eP___24a2(Vvar__1__t1_27__4816,Vvar__2__t2__4817)
                        & Vvar__0___24Anonymous__4807 = cPLF_2eSmallstep_2eP___24a2(Vvar__0__t1__4815,Vvar__2__t2__4817) ) ) )
            | ? [Vvar__0__v1__4819] :
                ( cPLF_2eSmallstep_2etm___24t(Vvar__0__v1__4819)
                & ? [Vvar__1__t2__4820] :
                    ( cPLF_2eSmallstep_2etm___24t(Vvar__1__t2__4820)
                    & ? [Vvar__2__t2_27__4821] :
                        ( cPLF_2eSmallstep_2etm___24t(Vvar__2__t2_27__4821)
                        & cPLF_2eSmallstep_2eTemp2_2evalue___24a1(Vvar__0__v1__4819)
                        & cPLF_2eSmallstep_2eTemp2_2estep___24a2(Vvar__1__t2__4820,Vvar__2__t2_27__4821)
                        & Vvar__1___24Anonymous__4808 = cPLF_2eSmallstep_2eP___24a2(Vvar__0__v1__4819,Vvar__2__t2_27__4821)
                        & Vvar__0___24Anonymous__4807 = cPLF_2eSmallstep_2eP___24a2(Vvar__0__v1__4819,Vvar__1__t2__4820) ) ) ) ) ) ) ) ).

fof('$_inversion_PLF.Smallstep.Temp2.value',axiom,
    ! [Vvar__0___24Anonymous__4804] :
      ( cPLF_2eSmallstep_2etm___24t(Vvar__0___24Anonymous__4804)
     => ( cPLF_2eSmallstep_2eTemp2_2evalue___24a1(Vvar__0___24Anonymous__4804)
       => ? [Vvar__0__n__4806] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__4806)
            & Vvar__0___24Anonymous__4804 = cPLF_2eSmallstep_2eC___24a1(Vvar__0__n__4806) ) ) ) ).

fof('$_inversion_PLF.Smallstep.Temp3.step',axiom,
    ! [Vvar__0___24Anonymous__4880,Vvar__1___24Anonymous__4881] :
      ( cPLF_2eSmallstep_2etm___24t(Vvar__0___24Anonymous__4880)
     => ( cPLF_2eSmallstep_2etm___24t(Vvar__1___24Anonymous__4881)
       => ( cPLF_2eSmallstep_2eTemp3_2estep___24a2(Vvar__0___24Anonymous__4880,Vvar__1___24Anonymous__4881)
         => ( ? [Vvar__0__n1__4883] :
                ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n1__4883)
                & ? [Vvar__1__n2__4884] :
                    ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__n2__4884)
                    & Vvar__1___24Anonymous__4881 = cPLF_2eSmallstep_2eC___24a1(c_24__case__Coq_2eInit_2eDatatypes_2enat_24101___24a4(Vvar__0___24Anonymous__4880,Vvar__1___24Anonymous__4881,Vvar__0__n1__4883,Vvar__1__n2__4884))
                    & Vvar__0___24Anonymous__4880 = cPLF_2eSmallstep_2eP___24a2(cPLF_2eSmallstep_2eC___24a1(Vvar__0__n1__4883),cPLF_2eSmallstep_2eC___24a1(Vvar__1__n2__4884)) ) )
            | ? [Vvar__0__t1__4887] :
                ( cPLF_2eSmallstep_2etm___24t(Vvar__0__t1__4887)
                & ? [Vvar__1__t1_27__4888] :
                    ( cPLF_2eSmallstep_2etm___24t(Vvar__1__t1_27__4888)
                    & ? [Vvar__2__t2__4889] :
                        ( cPLF_2eSmallstep_2etm___24t(Vvar__2__t2__4889)
                        & cPLF_2eSmallstep_2eTemp3_2estep___24a2(Vvar__0__t1__4887,Vvar__1__t1_27__4888)
                        & Vvar__1___24Anonymous__4881 = cPLF_2eSmallstep_2eP___24a2(Vvar__1__t1_27__4888,Vvar__2__t2__4889)
                        & Vvar__0___24Anonymous__4880 = cPLF_2eSmallstep_2eP___24a2(Vvar__0__t1__4887,Vvar__2__t2__4889) ) ) ) ) ) ) ) ).

fof('$_inversion_PLF.Smallstep.Temp3.value',axiom,
    ! [Vvar__0___24Anonymous__4877] :
      ( cPLF_2eSmallstep_2etm___24t(Vvar__0___24Anonymous__4877)
     => ( cPLF_2eSmallstep_2eTemp3_2evalue___24a1(Vvar__0___24Anonymous__4877)
       => ? [Vvar__0__n__4879] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__4879)
            & Vvar__0___24Anonymous__4877 = cPLF_2eSmallstep_2eC___24a1(Vvar__0__n__4879) ) ) ) ).

fof('$_inversion_PLF.Smallstep.Temp4.Temp5.step',axiom,
    ! [Vvar__0___24Anonymous__44757,Vvar__1___24Anonymous__44758] :
      ( cPLF_2eSmallstep_2eTemp4_2etm___24t(Vvar__0___24Anonymous__44757)
     => ( cPLF_2eSmallstep_2eTemp4_2etm___24t(Vvar__1___24Anonymous__44758)
       => ( cPLF_2eSmallstep_2eTemp4_2eTemp5_2estep___24a2(Vvar__0___24Anonymous__44757,Vvar__1___24Anonymous__44758)
         => ( ? [Vvar__0__t1__44760] :
                ( cPLF_2eSmallstep_2eTemp4_2etm___24t(Vvar__0__t1__44760)
                & ? [Vvar__1__t2__44761] :
                    ( cPLF_2eSmallstep_2eTemp4_2etm___24t(Vvar__1__t2__44761)
                    & Vvar__1___24Anonymous__44758 = Vvar__0__t1__44760
                    & Vvar__0___24Anonymous__44757 = cPLF_2eSmallstep_2eTemp4_2etest___24a3(cPLF_2eSmallstep_2eTemp4_2etru,Vvar__0__t1__44760,Vvar__1__t2__44761) ) )
            | ? [Vvar__0__t1__44762] :
                ( cPLF_2eSmallstep_2eTemp4_2etm___24t(Vvar__0__t1__44762)
                & ? [Vvar__1__t2__44763] :
                    ( cPLF_2eSmallstep_2eTemp4_2etm___24t(Vvar__1__t2__44763)
                    & Vvar__1___24Anonymous__44758 = Vvar__1__t2__44763
                    & Vvar__0___24Anonymous__44757 = cPLF_2eSmallstep_2eTemp4_2etest___24a3(cPLF_2eSmallstep_2eTemp4_2efls,Vvar__0__t1__44762,Vvar__1__t2__44763) ) )
            | ? [Vvar__0__t1__44764] :
                ( cPLF_2eSmallstep_2eTemp4_2etm___24t(Vvar__0__t1__44764)
                & ? [Vvar__1__t1_27__44765] :
                    ( cPLF_2eSmallstep_2eTemp4_2etm___24t(Vvar__1__t1_27__44765)
                    & ? [Vvar__2__t2__44766] :
                        ( cPLF_2eSmallstep_2eTemp4_2etm___24t(Vvar__2__t2__44766)
                        & ? [Vvar__3__t3__44767] :
                            ( cPLF_2eSmallstep_2eTemp4_2etm___24t(Vvar__3__t3__44767)
                            & cPLF_2eSmallstep_2eTemp4_2eTemp5_2estep___24a2(Vvar__0__t1__44764,Vvar__1__t1_27__44765)
                            & Vvar__1___24Anonymous__44758 = cPLF_2eSmallstep_2eTemp4_2etest___24a3(Vvar__1__t1_27__44765,Vvar__2__t2__44766,Vvar__3__t3__44767)
                            & Vvar__0___24Anonymous__44757 = cPLF_2eSmallstep_2eTemp4_2etest___24a3(Vvar__0__t1__44764,Vvar__2__t2__44766,Vvar__3__t3__44767) ) ) ) ) ) ) ) ) ).

fof('$_inversion_PLF.Smallstep.Temp4.step',axiom,
    ! [Vvar__0___24Anonymous__30553,Vvar__1___24Anonymous__30554] :
      ( cPLF_2eSmallstep_2eTemp4_2etm___24t(Vvar__0___24Anonymous__30553)
     => ( cPLF_2eSmallstep_2eTemp4_2etm___24t(Vvar__1___24Anonymous__30554)
       => ( cPLF_2eSmallstep_2eTemp4_2estep___24a2(Vvar__0___24Anonymous__30553,Vvar__1___24Anonymous__30554)
         => ( ? [Vvar__0__t1__30556] :
                ( cPLF_2eSmallstep_2eTemp4_2etm___24t(Vvar__0__t1__30556)
                & ? [Vvar__1__t2__30557] :
                    ( cPLF_2eSmallstep_2eTemp4_2etm___24t(Vvar__1__t2__30557)
                    & Vvar__1___24Anonymous__30554 = Vvar__0__t1__30556
                    & Vvar__0___24Anonymous__30553 = cPLF_2eSmallstep_2eTemp4_2etest___24a3(cPLF_2eSmallstep_2eTemp4_2etru,Vvar__0__t1__30556,Vvar__1__t2__30557) ) )
            | ? [Vvar__0__t1__30558] :
                ( cPLF_2eSmallstep_2eTemp4_2etm___24t(Vvar__0__t1__30558)
                & ? [Vvar__1__t2__30559] :
                    ( cPLF_2eSmallstep_2eTemp4_2etm___24t(Vvar__1__t2__30559)
                    & Vvar__1___24Anonymous__30554 = Vvar__1__t2__30559
                    & Vvar__0___24Anonymous__30553 = cPLF_2eSmallstep_2eTemp4_2etest___24a3(cPLF_2eSmallstep_2eTemp4_2efls,Vvar__0__t1__30558,Vvar__1__t2__30559) ) )
            | ? [Vvar__0__t1__30560] :
                ( cPLF_2eSmallstep_2eTemp4_2etm___24t(Vvar__0__t1__30560)
                & ? [Vvar__1__t1_27__30561] :
                    ( cPLF_2eSmallstep_2eTemp4_2etm___24t(Vvar__1__t1_27__30561)
                    & ? [Vvar__2__t2__30562] :
                        ( cPLF_2eSmallstep_2eTemp4_2etm___24t(Vvar__2__t2__30562)
                        & ? [Vvar__3__t3__30563] :
                            ( cPLF_2eSmallstep_2eTemp4_2etm___24t(Vvar__3__t3__30563)
                            & cPLF_2eSmallstep_2eTemp4_2estep___24a2(Vvar__0__t1__30560,Vvar__1__t1_27__30561)
                            & Vvar__1___24Anonymous__30554 = cPLF_2eSmallstep_2eTemp4_2etest___24a3(Vvar__1__t1_27__30561,Vvar__2__t2__30562,Vvar__3__t3__30563)
                            & Vvar__0___24Anonymous__30553 = cPLF_2eSmallstep_2eTemp4_2etest___24a3(Vvar__0__t1__30560,Vvar__2__t2__30562,Vvar__3__t3__30563) ) ) ) ) ) ) ) ) ).

fof('$_inversion_PLF.Smallstep.Temp4.tm',axiom,
    ! [VX30532] :
      ( cPLF_2eSmallstep_2eTemp4_2etm___24t(VX30532)
     => ( VX30532 = cPLF_2eSmallstep_2eTemp4_2etru
        | VX30532 = cPLF_2eSmallstep_2eTemp4_2efls
        | ? [Vvar__0___24Anonymous__30533] :
            ( cPLF_2eSmallstep_2eTemp4_2etm___24t(Vvar__0___24Anonymous__30533)
            & ? [Vvar__1___24Anonymous__30534] :
                ( cPLF_2eSmallstep_2eTemp4_2etm___24t(Vvar__1___24Anonymous__30534)
                & ? [Vvar__2___24Anonymous__30535] :
                    ( cPLF_2eSmallstep_2eTemp4_2etm___24t(Vvar__2___24Anonymous__30535)
                    & VX30532 = cPLF_2eSmallstep_2eTemp4_2etest___24a3(Vvar__0___24Anonymous__30533,Vvar__1___24Anonymous__30534,Vvar__2___24Anonymous__30535) ) ) ) ) ) ).

fof('$_inversion_PLF.Smallstep.Temp4.value',axiom,
    ! [Vvar__0___24Anonymous__44755] :
      ( cPLF_2eSmallstep_2eTemp4_2etm___24t(Vvar__0___24Anonymous__44755)
     => ( cPLF_2eSmallstep_2eTemp4_2evalue___24a1(Vvar__0___24Anonymous__44755)
       => ( Vvar__0___24Anonymous__44755 = cPLF_2eSmallstep_2eTemp4_2etru
          | Vvar__0___24Anonymous__44755 = cPLF_2eSmallstep_2eTemp4_2efls ) ) ) ).

fof('$_inversion_PLF.Smallstep.astep',axiom,
    ! [Vvar__0___24Anonymous__42639,Vvar__1___24Anonymous__42640,Vvar__2___24Anonymous__42641] :
      ( cPLF_2eImp_2estate___24t(Vvar__0___24Anonymous__42639)
     => ( cPLF_2eImp_2eaexp___24t(Vvar__1___24Anonymous__42640)
       => ( cPLF_2eImp_2eaexp___24t(Vvar__2___24Anonymous__42641)
         => ( cPLF_2eSmallstep_2eastep___24a3(Vvar__0___24Anonymous__42639,Vvar__1___24Anonymous__42640,Vvar__2___24Anonymous__42641)
           => ( ? [Vvar__0__st__42643] :
                  ( cPLF_2eImp_2estate___24t(Vvar__0__st__42643)
                  & ? [Vvar__1__i__42644] :
                      ( cCoq_2eStrings_2eString_2estring___24t(Vvar__1__i__42644)
                      & Vvar__2___24Anonymous__42641 = cPLF_2eImp_2eANum___24a1(happ(Vvar__0__st__42643,Vvar__1__i__42644))
                      & Vvar__1___24Anonymous__42640 = cPLF_2eImp_2eAId___24a1(Vvar__1__i__42644)
                      & Vvar__0___24Anonymous__42639 = Vvar__0__st__42643 ) )
              | ? [Vvar__0__st__42645] :
                  ( cPLF_2eImp_2estate___24t(Vvar__0__st__42645)
                  & ? [Vvar__1__a1__42646] :
                      ( cPLF_2eImp_2eaexp___24t(Vvar__1__a1__42646)
                      & ? [Vvar__2__a1_27__42647] :
                          ( cPLF_2eImp_2eaexp___24t(Vvar__2__a1_27__42647)
                          & ? [Vvar__3__a2__42648] :
                              ( cPLF_2eImp_2eaexp___24t(Vvar__3__a2__42648)
                              & cPLF_2eSmallstep_2eastep___24a3(Vvar__0__st__42645,Vvar__1__a1__42646,Vvar__2__a1_27__42647)
                              & Vvar__2___24Anonymous__42641 = cPLF_2eImp_2eAPlus___24a2(Vvar__2__a1_27__42647,Vvar__3__a2__42648)
                              & Vvar__1___24Anonymous__42640 = cPLF_2eImp_2eAPlus___24a2(Vvar__1__a1__42646,Vvar__3__a2__42648)
                              & Vvar__0___24Anonymous__42639 = Vvar__0__st__42645 ) ) ) )
              | ? [Vvar__0__st__42650] :
                  ( cPLF_2eImp_2estate___24t(Vvar__0__st__42650)
                  & ? [Vvar__1__v1__42651] :
                      ( cPLF_2eImp_2eaexp___24t(Vvar__1__v1__42651)
                      & ? [Vvar__2__a2__42652] :
                          ( cPLF_2eImp_2eaexp___24t(Vvar__2__a2__42652)
                          & ? [Vvar__3__a2_27__42653] :
                              ( cPLF_2eImp_2eaexp___24t(Vvar__3__a2_27__42653)
                              & cPLF_2eSmallstep_2eaval___24a1(Vvar__1__v1__42651)
                              & cPLF_2eSmallstep_2eastep___24a3(Vvar__0__st__42650,Vvar__2__a2__42652,Vvar__3__a2_27__42653)
                              & Vvar__2___24Anonymous__42641 = cPLF_2eImp_2eAPlus___24a2(Vvar__1__v1__42651,Vvar__3__a2_27__42653)
                              & Vvar__1___24Anonymous__42640 = cPLF_2eImp_2eAPlus___24a2(Vvar__1__v1__42651,Vvar__2__a2__42652)
                              & Vvar__0___24Anonymous__42639 = Vvar__0__st__42650 ) ) ) )
              | ? [Vvar__0__st__42656] :
                  ( cPLF_2eImp_2estate___24t(Vvar__0__st__42656)
                  & ? [Vvar__1__n1__42657] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__n1__42657)
                      & ? [Vvar__2__n2__42658] :
                          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n2__42658)
                          & Vvar__2___24Anonymous__42641 = cPLF_2eImp_2eANum___24a1(c_24__case__Coq_2eInit_2eDatatypes_2enat_2442757___24a5(Vvar__0___24Anonymous__42639,Vvar__1___24Anonymous__42640,Vvar__2___24Anonymous__42641,Vvar__1__n1__42657,Vvar__2__n2__42658))
                          & Vvar__1___24Anonymous__42640 = cPLF_2eImp_2eAPlus___24a2(cPLF_2eImp_2eANum___24a1(Vvar__1__n1__42657),cPLF_2eImp_2eANum___24a1(Vvar__2__n2__42658))
                          & Vvar__0___24Anonymous__42639 = Vvar__0__st__42656 ) ) )
              | ? [Vvar__0__st__42661] :
                  ( cPLF_2eImp_2estate___24t(Vvar__0__st__42661)
                  & ? [Vvar__1__a1__42662] :
                      ( cPLF_2eImp_2eaexp___24t(Vvar__1__a1__42662)
                      & ? [Vvar__2__a1_27__42663] :
                          ( cPLF_2eImp_2eaexp___24t(Vvar__2__a1_27__42663)
                          & ? [Vvar__3__a2__42664] :
                              ( cPLF_2eImp_2eaexp___24t(Vvar__3__a2__42664)
                              & cPLF_2eSmallstep_2eastep___24a3(Vvar__0__st__42661,Vvar__1__a1__42662,Vvar__2__a1_27__42663)
                              & Vvar__2___24Anonymous__42641 = cPLF_2eImp_2eAMinus___24a2(Vvar__2__a1_27__42663,Vvar__3__a2__42664)
                              & Vvar__1___24Anonymous__42640 = cPLF_2eImp_2eAMinus___24a2(Vvar__1__a1__42662,Vvar__3__a2__42664)
                              & Vvar__0___24Anonymous__42639 = Vvar__0__st__42661 ) ) ) )
              | ? [Vvar__0__st__42666] :
                  ( cPLF_2eImp_2estate___24t(Vvar__0__st__42666)
                  & ? [Vvar__1__v1__42667] :
                      ( cPLF_2eImp_2eaexp___24t(Vvar__1__v1__42667)
                      & ? [Vvar__2__a2__42668] :
                          ( cPLF_2eImp_2eaexp___24t(Vvar__2__a2__42668)
                          & ? [Vvar__3__a2_27__42669] :
                              ( cPLF_2eImp_2eaexp___24t(Vvar__3__a2_27__42669)
                              & cPLF_2eSmallstep_2eaval___24a1(Vvar__1__v1__42667)
                              & cPLF_2eSmallstep_2eastep___24a3(Vvar__0__st__42666,Vvar__2__a2__42668,Vvar__3__a2_27__42669)
                              & Vvar__2___24Anonymous__42641 = cPLF_2eImp_2eAMinus___24a2(Vvar__1__v1__42667,Vvar__3__a2_27__42669)
                              & Vvar__1___24Anonymous__42640 = cPLF_2eImp_2eAMinus___24a2(Vvar__1__v1__42667,Vvar__2__a2__42668)
                              & Vvar__0___24Anonymous__42639 = Vvar__0__st__42666 ) ) ) )
              | ? [Vvar__0__st__42672] :
                  ( cPLF_2eImp_2estate___24t(Vvar__0__st__42672)
                  & ? [Vvar__1__n1__42673] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__n1__42673)
                      & ? [Vvar__2__n2__42674] :
                          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n2__42674)
                          & Vvar__2___24Anonymous__42641 = cPLF_2eImp_2eANum___24a1(c_24__case__Coq_2eInit_2eDatatypes_2enat_2442879___24a5(Vvar__0___24Anonymous__42639,Vvar__1___24Anonymous__42640,Vvar__2___24Anonymous__42641,Vvar__1__n1__42673,Vvar__2__n2__42674))
                          & Vvar__1___24Anonymous__42640 = cPLF_2eImp_2eAMinus___24a2(cPLF_2eImp_2eANum___24a1(Vvar__1__n1__42673),cPLF_2eImp_2eANum___24a1(Vvar__2__n2__42674))
                          & Vvar__0___24Anonymous__42639 = Vvar__0__st__42672 ) ) )
              | ? [Vvar__0__st__42679] :
                  ( cPLF_2eImp_2estate___24t(Vvar__0__st__42679)
                  & ? [Vvar__1__a1__42680] :
                      ( cPLF_2eImp_2eaexp___24t(Vvar__1__a1__42680)
                      & ? [Vvar__2__a1_27__42681] :
                          ( cPLF_2eImp_2eaexp___24t(Vvar__2__a1_27__42681)
                          & ? [Vvar__3__a2__42682] :
                              ( cPLF_2eImp_2eaexp___24t(Vvar__3__a2__42682)
                              & cPLF_2eSmallstep_2eastep___24a3(Vvar__0__st__42679,Vvar__1__a1__42680,Vvar__2__a1_27__42681)
                              & Vvar__2___24Anonymous__42641 = cPLF_2eImp_2eAMult___24a2(Vvar__2__a1_27__42681,Vvar__3__a2__42682)
                              & Vvar__1___24Anonymous__42640 = cPLF_2eImp_2eAMult___24a2(Vvar__1__a1__42680,Vvar__3__a2__42682)
                              & Vvar__0___24Anonymous__42639 = Vvar__0__st__42679 ) ) ) )
              | ? [Vvar__0__st__42684] :
                  ( cPLF_2eImp_2estate___24t(Vvar__0__st__42684)
                  & ? [Vvar__1__v1__42685] :
                      ( cPLF_2eImp_2eaexp___24t(Vvar__1__v1__42685)
                      & ? [Vvar__2__a2__42686] :
                          ( cPLF_2eImp_2eaexp___24t(Vvar__2__a2__42686)
                          & ? [Vvar__3__a2_27__42687] :
                              ( cPLF_2eImp_2eaexp___24t(Vvar__3__a2_27__42687)
                              & cPLF_2eSmallstep_2eaval___24a1(Vvar__1__v1__42685)
                              & cPLF_2eSmallstep_2eastep___24a3(Vvar__0__st__42684,Vvar__2__a2__42686,Vvar__3__a2_27__42687)
                              & Vvar__2___24Anonymous__42641 = cPLF_2eImp_2eAMult___24a2(Vvar__1__v1__42685,Vvar__3__a2_27__42687)
                              & Vvar__1___24Anonymous__42640 = cPLF_2eImp_2eAMult___24a2(Vvar__1__v1__42685,Vvar__2__a2__42686)
                              & Vvar__0___24Anonymous__42639 = Vvar__0__st__42684 ) ) ) )
              | ? [Vvar__0__st__42690] :
                  ( cPLF_2eImp_2estate___24t(Vvar__0__st__42690)
                  & ? [Vvar__1__n1__42691] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__n1__42691)
                      & ? [Vvar__2__n2__42692] :
                          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n2__42692)
                          & Vvar__2___24Anonymous__42641 = cPLF_2eImp_2eANum___24a1(c_24__case__Coq_2eInit_2eDatatypes_2enat_2442987___24a5(Vvar__0___24Anonymous__42639,Vvar__1___24Anonymous__42640,Vvar__2___24Anonymous__42641,Vvar__1__n1__42691,Vvar__2__n2__42692))
                          & Vvar__1___24Anonymous__42640 = cPLF_2eImp_2eAMult___24a2(cPLF_2eImp_2eANum___24a1(Vvar__1__n1__42691),cPLF_2eImp_2eANum___24a1(Vvar__2__n2__42692))
                          & Vvar__0___24Anonymous__42639 = Vvar__0__st__42690 ) ) ) ) ) ) ) ) ).

fof('$_inversion_PLF.Smallstep.aval',axiom,
    ! [Vvar__0___24Anonymous__42636] :
      ( cPLF_2eImp_2eaexp___24t(Vvar__0___24Anonymous__42636)
     => ( cPLF_2eSmallstep_2eaval___24a1(Vvar__0___24Anonymous__42636)
       => ? [Vvar__0__n__42638] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__42638)
            & Vvar__0___24Anonymous__42636 = cPLF_2eImp_2eANum___24a1(Vvar__0__n__42638) ) ) ) ).

fof('$_inversion_PLF.Smallstep.bstep',axiom,
    ! [Vvar__0___24Anonymous__43008,Vvar__1___24Anonymous__43009,Vvar__2___24Anonymous__43010] :
      ( cPLF_2eImp_2estate___24t(Vvar__0___24Anonymous__43008)
     => ( cPLF_2eImp_2ebexp___24t(Vvar__1___24Anonymous__43009)
       => ( cPLF_2eImp_2ebexp___24t(Vvar__2___24Anonymous__43010)
         => ( cPLF_2eSmallstep_2ebstep___24a3(Vvar__0___24Anonymous__43008,Vvar__1___24Anonymous__43009,Vvar__2___24Anonymous__43010)
           => ( ? [Vvar__0__st__43012] :
                  ( cPLF_2eImp_2estate___24t(Vvar__0__st__43012)
                  & ? [Vvar__1__a1__43013] :
                      ( cPLF_2eImp_2eaexp___24t(Vvar__1__a1__43013)
                      & ? [Vvar__2__a1_27__43014] :
                          ( cPLF_2eImp_2eaexp___24t(Vvar__2__a1_27__43014)
                          & ? [Vvar__3__a2__43015] :
                              ( cPLF_2eImp_2eaexp___24t(Vvar__3__a2__43015)
                              & cPLF_2eSmallstep_2eastep___24a3(Vvar__0__st__43012,Vvar__1__a1__43013,Vvar__2__a1_27__43014)
                              & Vvar__2___24Anonymous__43010 = cPLF_2eImp_2eBEq___24a2(Vvar__2__a1_27__43014,Vvar__3__a2__43015)
                              & Vvar__1___24Anonymous__43009 = cPLF_2eImp_2eBEq___24a2(Vvar__1__a1__43013,Vvar__3__a2__43015)
                              & Vvar__0___24Anonymous__43008 = Vvar__0__st__43012 ) ) ) )
              | ? [Vvar__0__st__43017] :
                  ( cPLF_2eImp_2estate___24t(Vvar__0__st__43017)
                  & ? [Vvar__1__v1__43018] :
                      ( cPLF_2eImp_2eaexp___24t(Vvar__1__v1__43018)
                      & ? [Vvar__2__a2__43019] :
                          ( cPLF_2eImp_2eaexp___24t(Vvar__2__a2__43019)
                          & ? [Vvar__3__a2_27__43020] :
                              ( cPLF_2eImp_2eaexp___24t(Vvar__3__a2_27__43020)
                              & cPLF_2eSmallstep_2eaval___24a1(Vvar__1__v1__43018)
                              & cPLF_2eSmallstep_2eastep___24a3(Vvar__0__st__43017,Vvar__2__a2__43019,Vvar__3__a2_27__43020)
                              & Vvar__2___24Anonymous__43010 = cPLF_2eImp_2eBEq___24a2(Vvar__1__v1__43018,Vvar__3__a2_27__43020)
                              & Vvar__1___24Anonymous__43009 = cPLF_2eImp_2eBEq___24a2(Vvar__1__v1__43018,Vvar__2__a2__43019)
                              & Vvar__0___24Anonymous__43008 = Vvar__0__st__43017 ) ) ) )
              | ? [Vvar__0__st__43023] :
                  ( cPLF_2eImp_2estate___24t(Vvar__0__st__43023)
                  & ? [Vvar__1__n1__43024] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__n1__43024)
                      & ? [Vvar__2__n2__43025] :
                          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n2__43025)
                          & Vvar__2___24Anonymous__43010 = c_24__case__Coq_2eInit_2eDatatypes_2ebool_2443239___24a5(Vvar__0___24Anonymous__43008,Vvar__1___24Anonymous__43009,Vvar__2___24Anonymous__43010,Vvar__1__n1__43024,Vvar__2__n2__43025)
                          & Vvar__1___24Anonymous__43009 = cPLF_2eImp_2eBEq___24a2(cPLF_2eImp_2eANum___24a1(Vvar__1__n1__43024),cPLF_2eImp_2eANum___24a1(Vvar__2__n2__43025))
                          & Vvar__0___24Anonymous__43008 = Vvar__0__st__43023 ) ) )
              | ? [Vvar__0__st__43050] :
                  ( cPLF_2eImp_2estate___24t(Vvar__0__st__43050)
                  & ? [Vvar__1__a1__43051] :
                      ( cPLF_2eImp_2eaexp___24t(Vvar__1__a1__43051)
                      & ? [Vvar__2__a1_27__43052] :
                          ( cPLF_2eImp_2eaexp___24t(Vvar__2__a1_27__43052)
                          & ? [Vvar__3__a2__43053] :
                              ( cPLF_2eImp_2eaexp___24t(Vvar__3__a2__43053)
                              & cPLF_2eSmallstep_2eastep___24a3(Vvar__0__st__43050,Vvar__1__a1__43051,Vvar__2__a1_27__43052)
                              & Vvar__2___24Anonymous__43010 = cPLF_2eImp_2eBLe___24a2(Vvar__2__a1_27__43052,Vvar__3__a2__43053)
                              & Vvar__1___24Anonymous__43009 = cPLF_2eImp_2eBLe___24a2(Vvar__1__a1__43051,Vvar__3__a2__43053)
                              & Vvar__0___24Anonymous__43008 = Vvar__0__st__43050 ) ) ) )
              | ? [Vvar__0__st__43055] :
                  ( cPLF_2eImp_2estate___24t(Vvar__0__st__43055)
                  & ? [Vvar__1__v1__43056] :
                      ( cPLF_2eImp_2eaexp___24t(Vvar__1__v1__43056)
                      & ? [Vvar__2__a2__43057] :
                          ( cPLF_2eImp_2eaexp___24t(Vvar__2__a2__43057)
                          & ? [Vvar__3__a2_27__43058] :
                              ( cPLF_2eImp_2eaexp___24t(Vvar__3__a2_27__43058)
                              & cPLF_2eSmallstep_2eaval___24a1(Vvar__1__v1__43056)
                              & cPLF_2eSmallstep_2eastep___24a3(Vvar__0__st__43055,Vvar__2__a2__43057,Vvar__3__a2_27__43058)
                              & Vvar__2___24Anonymous__43010 = cPLF_2eImp_2eBLe___24a2(Vvar__1__v1__43056,Vvar__3__a2_27__43058)
                              & Vvar__1___24Anonymous__43009 = cPLF_2eImp_2eBLe___24a2(Vvar__1__v1__43056,Vvar__2__a2__43057)
                              & Vvar__0___24Anonymous__43008 = Vvar__0__st__43055 ) ) ) )
              | ? [Vvar__0__st__43061] :
                  ( cPLF_2eImp_2estate___24t(Vvar__0__st__43061)
                  & ? [Vvar__1__n1__43062] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__n1__43062)
                      & ? [Vvar__2__n2__43063] :
                          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n2__43063)
                          & Vvar__2___24Anonymous__43010 = c_24__case__Coq_2eInit_2eDatatypes_2ebool_2443570___24a5(Vvar__0___24Anonymous__43008,Vvar__1___24Anonymous__43009,Vvar__2___24Anonymous__43010,Vvar__1__n1__43062,Vvar__2__n2__43063)
                          & Vvar__1___24Anonymous__43009 = cPLF_2eImp_2eBLe___24a2(cPLF_2eImp_2eANum___24a1(Vvar__1__n1__43062),cPLF_2eImp_2eANum___24a1(Vvar__2__n2__43063))
                          & Vvar__0___24Anonymous__43008 = Vvar__0__st__43061 ) ) )
              | ? [Vvar__0__st__43082] :
                  ( cPLF_2eImp_2estate___24t(Vvar__0__st__43082)
                  & ? [Vvar__1__b1__43083] :
                      ( cPLF_2eImp_2ebexp___24t(Vvar__1__b1__43083)
                      & ? [Vvar__2__b1_27__43084] :
                          ( cPLF_2eImp_2ebexp___24t(Vvar__2__b1_27__43084)
                          & cPLF_2eSmallstep_2ebstep___24a3(Vvar__0__st__43082,Vvar__1__b1__43083,Vvar__2__b1_27__43084)
                          & Vvar__2___24Anonymous__43010 = cPLF_2eImp_2eBNot___24a1(Vvar__2__b1_27__43084)
                          & Vvar__1___24Anonymous__43009 = cPLF_2eImp_2eBNot___24a1(Vvar__1__b1__43083)
                          & Vvar__0___24Anonymous__43008 = Vvar__0__st__43082 ) ) )
              | ? [Vvar__0__st__43086] :
                  ( cPLF_2eImp_2estate___24t(Vvar__0__st__43086)
                  & Vvar__2___24Anonymous__43010 = cPLF_2eImp_2eBFalse
                  & Vvar__1___24Anonymous__43009 = cPLF_2eImp_2eBNot___24a1(cPLF_2eImp_2eBTrue)
                  & Vvar__0___24Anonymous__43008 = Vvar__0__st__43086 )
              | ? [Vvar__0__st__43087] :
                  ( cPLF_2eImp_2estate___24t(Vvar__0__st__43087)
                  & Vvar__2___24Anonymous__43010 = cPLF_2eImp_2eBTrue
                  & Vvar__1___24Anonymous__43009 = cPLF_2eImp_2eBNot___24a1(cPLF_2eImp_2eBFalse)
                  & Vvar__0___24Anonymous__43008 = Vvar__0__st__43087 )
              | ? [Vvar__0__st__43088] :
                  ( cPLF_2eImp_2estate___24t(Vvar__0__st__43088)
                  & ? [Vvar__1__b2__43089] :
                      ( cPLF_2eImp_2ebexp___24t(Vvar__1__b2__43089)
                      & ? [Vvar__2__b2_27__43090] :
                          ( cPLF_2eImp_2ebexp___24t(Vvar__2__b2_27__43090)
                          & cPLF_2eSmallstep_2ebstep___24a3(Vvar__0__st__43088,Vvar__1__b2__43089,Vvar__2__b2_27__43090)
                          & Vvar__2___24Anonymous__43010 = cPLF_2eImp_2eBAnd___24a2(cPLF_2eImp_2eBTrue,Vvar__2__b2_27__43090)
                          & Vvar__1___24Anonymous__43009 = cPLF_2eImp_2eBAnd___24a2(cPLF_2eImp_2eBTrue,Vvar__1__b2__43089)
                          & Vvar__0___24Anonymous__43008 = Vvar__0__st__43088 ) ) )
              | ? [Vvar__0__st__43092] :
                  ( cPLF_2eImp_2estate___24t(Vvar__0__st__43092)
                  & ? [Vvar__1__b1__43093] :
                      ( cPLF_2eImp_2ebexp___24t(Vvar__1__b1__43093)
                      & ? [Vvar__2__b1_27__43094] :
                          ( cPLF_2eImp_2ebexp___24t(Vvar__2__b1_27__43094)
                          & ? [Vvar__3__b2__43095] :
                              ( cPLF_2eImp_2ebexp___24t(Vvar__3__b2__43095)
                              & cPLF_2eSmallstep_2ebstep___24a3(Vvar__0__st__43092,Vvar__1__b1__43093,Vvar__2__b1_27__43094)
                              & Vvar__2___24Anonymous__43010 = cPLF_2eImp_2eBAnd___24a2(Vvar__2__b1_27__43094,Vvar__3__b2__43095)
                              & Vvar__1___24Anonymous__43009 = cPLF_2eImp_2eBAnd___24a2(Vvar__1__b1__43093,Vvar__3__b2__43095)
                              & Vvar__0___24Anonymous__43008 = Vvar__0__st__43092 ) ) ) )
              | ? [Vvar__0__st__43097] :
                  ( cPLF_2eImp_2estate___24t(Vvar__0__st__43097)
                  & Vvar__2___24Anonymous__43010 = cPLF_2eImp_2eBTrue
                  & Vvar__1___24Anonymous__43009 = cPLF_2eImp_2eBAnd___24a2(cPLF_2eImp_2eBTrue,cPLF_2eImp_2eBTrue)
                  & Vvar__0___24Anonymous__43008 = Vvar__0__st__43097 )
              | ? [Vvar__0__st__43098] :
                  ( cPLF_2eImp_2estate___24t(Vvar__0__st__43098)
                  & Vvar__2___24Anonymous__43010 = cPLF_2eImp_2eBFalse
                  & Vvar__1___24Anonymous__43009 = cPLF_2eImp_2eBAnd___24a2(cPLF_2eImp_2eBTrue,cPLF_2eImp_2eBFalse)
                  & Vvar__0___24Anonymous__43008 = Vvar__0__st__43098 )
              | ? [Vvar__0__st__43099] :
                  ( cPLF_2eImp_2estate___24t(Vvar__0__st__43099)
                  & ? [Vvar__1__b2__43100] :
                      ( cPLF_2eImp_2ebexp___24t(Vvar__1__b2__43100)
                      & Vvar__2___24Anonymous__43010 = cPLF_2eImp_2eBFalse
                      & Vvar__1___24Anonymous__43009 = cPLF_2eImp_2eBAnd___24a2(cPLF_2eImp_2eBFalse,Vvar__1__b2__43100)
                      & Vvar__0___24Anonymous__43008 = Vvar__0__st__43099 ) ) ) ) ) ) ) ).

fof('$_inversion_PLF.Smallstep.eval',axiom,
    ! [Vvar__0___24Anonymous__42552,Vvar__1___24Anonymous__42553] :
      ( cPLF_2eSmallstep_2etm___24t(Vvar__0___24Anonymous__42552)
     => ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1___24Anonymous__42553)
       => ( cPLF_2eSmallstep_2eeval___24a2(Vvar__0___24Anonymous__42552,Vvar__1___24Anonymous__42553)
         => ( ? [Vvar__0__n__42555] :
                ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__42555)
                & Vvar__1___24Anonymous__42553 = Vvar__0__n__42555
                & Vvar__0___24Anonymous__42552 = cPLF_2eSmallstep_2eC___24a1(Vvar__0__n__42555) )
            | ? [Vvar__0__t1__42556] :
                ( cPLF_2eSmallstep_2etm___24t(Vvar__0__t1__42556)
                & ? [Vvar__1__t2__42557] :
                    ( cPLF_2eSmallstep_2etm___24t(Vvar__1__t2__42557)
                    & ? [Vvar__2__n1__42558] :
                        ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__2__n1__42558)
                        & ? [Vvar__3__n2__42559] :
                            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__3__n2__42559)
                            & cPLF_2eSmallstep_2eeval___24a2(Vvar__0__t1__42556,Vvar__2__n1__42558)
                            & cPLF_2eSmallstep_2eeval___24a2(Vvar__1__t2__42557,Vvar__3__n2__42559)
                            & Vvar__1___24Anonymous__42553 = c_24__case__Coq_2eInit_2eDatatypes_2enat_2442617___24a4(Vvar__0___24Anonymous__42552,Vvar__1___24Anonymous__42553,Vvar__2__n1__42558,Vvar__3__n2__42559)
                            & Vvar__0___24Anonymous__42552 = cPLF_2eSmallstep_2eP___24a2(Vvar__0__t1__42556,Vvar__1__t2__42557) ) ) ) ) ) ) ) ) ).

fof('$_inversion_PLF.Smallstep.multi',axiom,
    ! [Vvar__0__X__4779,Vvar__1__R__4780,Vvar__1___24Anonymous__4781,Vvar__2___24Anonymous__4782] :
      ( cType___24t(Vvar__0__X__4779)
     => ( cPLF_2eSmallstep_2erelation___24t(Vvar__0__X__4779,Vvar__1__R__4780)
       => ( t(Vvar__1___24Anonymous__4781,Vvar__0__X__4779)
         => ( t(Vvar__2___24Anonymous__4782,Vvar__0__X__4779)
           => ( cPLF_2eSmallstep_2emulti___24a4(Vvar__0__X__4779,Vvar__1__R__4780,Vvar__1___24Anonymous__4781,Vvar__2___24Anonymous__4782)
             => ( ? [Vvar__2__x__4786] :
                    ( t(Vvar__2__x__4786,Vvar__0__X__4779)
                    & Vvar__2___24Anonymous__4782 = Vvar__2__x__4786
                    & Vvar__1___24Anonymous__4781 = Vvar__2__x__4786 )
                | ? [Vvar__2__x__4789] :
                    ( t(Vvar__2__x__4789,Vvar__0__X__4779)
                    & ? [Vvar__3__y__4790] :
                        ( t(Vvar__3__y__4790,Vvar__0__X__4779)
                        & ? [Vvar__4__z__4791] :
                            ( t(Vvar__4__z__4791,Vvar__0__X__4779)
                            & p(happ(happ(Vvar__1__R__4780,Vvar__2__x__4789),Vvar__3__y__4790))
                            & cPLF_2eSmallstep_2emulti___24a4(Vvar__0__X__4779,Vvar__1__R__4780,Vvar__3__y__4790,Vvar__4__z__4791)
                            & Vvar__2___24Anonymous__4782 = Vvar__4__z__4791
                            & Vvar__1___24Anonymous__4781 = Vvar__2__x__4789 ) ) ) ) ) ) ) ) ) ).

fof('$_inversion_PLF.Smallstep.step',axiom,
    ! [Vvar__0___24Anonymous__32,Vvar__1___24Anonymous__33] :
      ( cPLF_2eSmallstep_2etm___24t(Vvar__0___24Anonymous__32)
     => ( cPLF_2eSmallstep_2etm___24t(Vvar__1___24Anonymous__33)
       => ( cPLF_2eSmallstep_2estep___24a2(Vvar__0___24Anonymous__32,Vvar__1___24Anonymous__33)
         => ( ? [Vvar__0__n1__35] :
                ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n1__35)
                & ? [Vvar__1__n2__36] :
                    ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__1__n2__36)
                    & Vvar__1___24Anonymous__33 = cPLF_2eSmallstep_2eC___24a1(c_24__case__Coq_2eInit_2eDatatypes_2enat_24101___24a4(Vvar__0___24Anonymous__32,Vvar__1___24Anonymous__33,Vvar__0__n1__35,Vvar__1__n2__36))
                    & Vvar__0___24Anonymous__32 = cPLF_2eSmallstep_2eP___24a2(cPLF_2eSmallstep_2eC___24a1(Vvar__0__n1__35),cPLF_2eSmallstep_2eC___24a1(Vvar__1__n2__36)) ) )
            | ? [Vvar__0__t1__39] :
                ( cPLF_2eSmallstep_2etm___24t(Vvar__0__t1__39)
                & ? [Vvar__1__t1_27__40] :
                    ( cPLF_2eSmallstep_2etm___24t(Vvar__1__t1_27__40)
                    & ? [Vvar__2__t2__41] :
                        ( cPLF_2eSmallstep_2etm___24t(Vvar__2__t2__41)
                        & cPLF_2eSmallstep_2estep___24a2(Vvar__0__t1__39,Vvar__1__t1_27__40)
                        & Vvar__1___24Anonymous__33 = cPLF_2eSmallstep_2eP___24a2(Vvar__1__t1_27__40,Vvar__2__t2__41)
                        & Vvar__0___24Anonymous__32 = cPLF_2eSmallstep_2eP___24a2(Vvar__0__t1__39,Vvar__2__t2__41) ) ) )
            | ? [Vvar__0__v1__43] :
                ( cPLF_2eSmallstep_2etm___24t(Vvar__0__v1__43)
                & ? [Vvar__1__t2__44] :
                    ( cPLF_2eSmallstep_2etm___24t(Vvar__1__t2__44)
                    & ? [Vvar__2__t2_27__45] :
                        ( cPLF_2eSmallstep_2etm___24t(Vvar__2__t2_27__45)
                        & cPLF_2eSmallstep_2evalue___24a1(Vvar__0__v1__43)
                        & cPLF_2eSmallstep_2estep___24a2(Vvar__1__t2__44,Vvar__2__t2_27__45)
                        & Vvar__1___24Anonymous__33 = cPLF_2eSmallstep_2eP___24a2(Vvar__0__v1__43,Vvar__2__t2_27__45)
                        & Vvar__0___24Anonymous__32 = cPLF_2eSmallstep_2eP___24a2(Vvar__0__v1__43,Vvar__1__t2__44) ) ) ) ) ) ) ) ).

fof('$_inversion_PLF.Smallstep.tm',axiom,
    ! [VX11] :
      ( cPLF_2eSmallstep_2etm___24t(VX11)
     => ( ? [Vvar__0___24Anonymous__12] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__12)
            & VX11 = cPLF_2eSmallstep_2eC___24a1(Vvar__0___24Anonymous__12) )
        | ? [Vvar__0___24Anonymous__13] :
            ( cPLF_2eSmallstep_2etm___24t(Vvar__0___24Anonymous__13)
            & ? [Vvar__1___24Anonymous__14] :
                ( cPLF_2eSmallstep_2etm___24t(Vvar__1___24Anonymous__14)
                & VX11 = cPLF_2eSmallstep_2eP___24a2(Vvar__0___24Anonymous__13,Vvar__1___24Anonymous__14) ) ) ) ) ).

fof('$_inversion_PLF.Smallstep.value',axiom,
    ! [Vvar__0___24Anonymous__29] :
      ( cPLF_2eSmallstep_2etm___24t(Vvar__0___24Anonymous__29)
     => ( cPLF_2eSmallstep_2evalue___24a1(Vvar__0___24Anonymous__29)
       => ? [Vvar__0__n__31] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0__n__31)
            & Vvar__0___24Anonymous__29 = cPLF_2eSmallstep_2eC___24a1(Vvar__0__n__31) ) ) ) ).

fof('$_lam_32329',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] : c_24__lam__32329___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = happ(Vv__CANONICAL__2,Vv__CANONICAL__3) ).

fof('$_lam_32339',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] : c_24__lam__32339___24a4(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3) = happ(Vv__CANONICAL__2,Vv__CANONICAL__3) ).

fof('$_lam_35549',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6] :
      ( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__5)
     => ( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__6)
       => ( ( cPLF_2eMaps_2eeqb__string___24a2(Vv__CANONICAL__5,Vv__CANONICAL__6) = cCoq_2eInit_2eDatatypes_2etrue
            & c_24__lam__35549___24a7(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6) = Vv__CANONICAL__4 )
          | ( cPLF_2eMaps_2eeqb__string___24a2(Vv__CANONICAL__5,Vv__CANONICAL__6) = cCoq_2eInit_2eDatatypes_2efalse
            & c_24__lam__35549___24a7(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6) = happ(Vv__CANONICAL__3,Vv__CANONICAL__6) ) ) ) ) ).

fof('$_lam_42274',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
      ( c_24__lam__42274___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_42282',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
      ( c_24__lam__42282___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_42290',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
      ( c_24__lam__42290___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_42298',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3] :
      ( c_24__lam__42298___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_44548',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__44548___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = Vv__CANONICAL__0 ).

fof('$_lam_44570',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1] : c_24__lam__44570___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = Vv__CANONICAL__0 ).

fof('$_lam_44633',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
     => ( ( Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2eO
          & c_24__lam__44633___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eInit_2eDatatypes_2etrue )
        | ? [Vvar__0___24Anonymous__44634] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__44634)
            & Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__44634)
            & c_24__lam__44633___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat___24a2(Vv__CANONICAL__0,Vvar__0___24Anonymous__44634) ) ) ) ).

fof('$_lam_44640',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
     => ( ( Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2eO
          & c_24__lam__44640___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2eInit_2eDatatypes_2efalse )
        | ? [Vvar__0___24Anonymous__44641] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__44641)
            & Vv__CANONICAL__1 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__44641)
            & c_24__lam__44640___24a2(Vv__CANONICAL__0,Vv__CANONICAL__1) = cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat___24a2(Vv__CANONICAL__0,Vvar__0___24Anonymous__44641) ) ) ) ).

fof('$_lam_44644',axiom,
    ! [Vv__CANONICAL__0] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
     => ( ( Vv__CANONICAL__0 = cCoq_2eInit_2eDatatypes_2eO
          & c_24__lam__44644___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2etrue )
        | ? [Vvar__0___24Anonymous__44645] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(Vvar__0___24Anonymous__44645)
            & Vv__CANONICAL__0 = cCoq_2eInit_2eDatatypes_2eS___24a1(Vvar__0___24Anonymous__44645)
            & c_24__lam__44644___24a1(Vv__CANONICAL__0) = cCoq_2eInit_2eDatatypes_2efalse ) ) ) ).

fof('$_prop_15792',axiom,
    ! [V0__n,V1__m] :
      ( p(c_24__prop__15792___24a2(V0__n,V1__m))
    <=> V0__n = V1__m ) ).

fof('$_prop_29548',axiom,
    ! [Vvar__0___24Anonymous__29524,Vvar__0__S__29526,Vvar__1__x__29527,Vvar__2__y__29528] :
      ( p(c_24__prop__29548___24a4(Vvar__0___24Anonymous__29524,Vvar__0__S__29526,Vvar__1__x__29527,Vvar__2__y__29528))
    <=> Vvar__1__x__29527 = Vvar__2__y__29528 ) ).

fof('$_prop_29549',axiom,
    ! [Vvar__0___24Anonymous__29524,Vvar__0__x__29529,Vvar__1__y__29530] :
      ( p(c_24__prop__29549___24a3(Vvar__0___24Anonymous__29524,Vvar__0__x__29529,Vvar__1__y__29530))
    <=> Vvar__0__x__29529 = Vvar__1__y__29530 ) ).

fof('$_prop_29550',axiom,
    ! [Vvar__0___24Anonymous__29524,Vvar__0__x__29531,Vvar__1__s__29532] :
      ( p(c_24__prop__29550___24a3(Vvar__0___24Anonymous__29524,Vvar__0__x__29531,Vvar__1__s__29532))
    <=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(Vvar__0__x__29531,Vvar__1__s__29532) = cCoq_2eInit_2eDatatypes_2etrue ) ).

fof('$_prop_29551',axiom,
    ! [Vvar__0___24Anonymous__29524,Vvar__0__P__29533,Vvar__1__Q__29534] :
      ( p(c_24__prop__29551___24a3(Vvar__0___24Anonymous__29524,Vvar__0__P__29533,Vvar__1__Q__29534))
    <=> ( p(Vvar__0__P__29533)
        & p(Vvar__1__Q__29534) ) ) ).

fof('$_prop_29552',axiom,
    ! [Vvar__0___24Anonymous__29524,Vvar__0__P__29537,Vvar__1__Q__29538] :
      ( p(c_24__prop__29552___24a3(Vvar__0___24Anonymous__29524,Vvar__0__P__29537,Vvar__1__Q__29538))
    <=> ( p(Vvar__0__P__29537)
        | p(Vvar__1__Q__29538) ) ) ).

fof('$_prop_29553',axiom,
    ! [Vvar__0___24Anonymous__29524,Vvar__0__P__29541,Vvar__1__Q__29542] :
      ( p(c_24__prop__29553___24a3(Vvar__0___24Anonymous__29524,Vvar__0__P__29541,Vvar__1__Q__29542))
    <=> ( p(Vvar__0__P__29541)
       => p(Vvar__1__Q__29542) ) ) ).

fof('$_prop_29554',axiom,
    ! [Vvar__0___24Anonymous__29524,Vvar__0__P__29546] :
      ( p(c_24__prop__29554___24a2(Vvar__0___24Anonymous__29524,Vvar__0__P__29546))
    <=> ~ p(Vvar__0__P__29546) ) ).

fof('$_prop_35092',axiom,
    ! [Vvar__0___24Anonymous__35079,Vvar__0__s__35083] :
      ( p(c_24__prop__35092___24a2(Vvar__0___24Anonymous__35079,Vvar__0__s__35083))
    <=> ! [Vvar__1__a__35084] :
          ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vvar__1__a__35084)
         => ~ cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(Vvar__1__a__35084,Vvar__0__s__35083) ) ) ).

fof('$_prop_35093',axiom,
    ! [Vvar__0___24Anonymous__35079,Vvar__0__s1__35085,Vvar__1__s2__35086] :
      ( p(c_24__prop__35093___24a3(Vvar__0___24Anonymous__35079,Vvar__0__s1__35085,Vvar__1__s2__35086))
    <=> ! [Vvar__2__a__35087] :
          ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vvar__2__a__35087)
         => ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(Vvar__2__a__35087,Vvar__0__s1__35085)
           => cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(Vvar__2__a__35087,Vvar__1__s2__35086) ) ) ) ).

fof('$_prop_35094',axiom,
    ! [Vvar__0___24Anonymous__35079,Vvar__0__s1__35089,Vvar__1__s2__35090] :
      ( p(c_24__prop__35094___24a3(Vvar__0___24Anonymous__35079,Vvar__0__s1__35089,Vvar__1__s2__35090))
    <=> ! [Vvar__2__a__35091] :
          ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vvar__2__a__35091)
         => ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(Vvar__2__a__35091,Vvar__0__s1__35089)
          <=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(Vvar__2__a__35091,Vvar__1__s2__35090) ) ) ) ).

fof('$_prop_4765',axiom,
    ! [V0__x,V1__y] :
      ( p(c_24__prop__4765___24a2(V0__x,V1__y))
    <=> V0__x = V1__y ) ).

fof('$_prop_4766',axiom,
    ! [V0__x,V1__y] :
      ( p(c_24__prop__4766___24a2(V0__x,V1__y))
    <=> V0__x != V1__y ) ).

fof('$_prop_4767',axiom,
    ! [V0__x,V1__y] :
      ( p(c_24__prop__4767___24a2(V0__x,V1__y))
    <=> V0__x = V1__y ) ).

fof('$_prop_4768',axiom,
    ! [V0__x,V1__y] :
      ( p(c_24__prop__4768___24a2(V0__x,V1__y))
    <=> V0__x != V1__y ) ).

fof('$_type_10078',axiom,
    ! [Vvar__10079] :
      ( c_24__type__10078___24t(Vvar__10079)
    <=> ! [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__10079,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_11447',axiom,
    ! [Vvar__11448] :
      ( c_24__type__11447___24t(Vvar__11448)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__6582___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__11448,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).

fof('$_type_11701',axiom,
    ! [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__11702] :
      ( c_24__type__11701___24t(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__11702)
    <=> ! [Vv__CANONICAL__8] :
          ( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__9] :
              ( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__11702,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_11764',axiom,
    ! [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__11765] :
      ( c_24__type__11764___24t(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__11765)
    <=> ! [Vv__CANONICAL__8] :
          ( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__9] :
              ( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__11765,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_11827',axiom,
    ! [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__11828] :
      ( c_24__type__11827___24t(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__11828)
    <=> ! [Vv__CANONICAL__8] :
          ( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__9] :
              ( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__11828,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_11881',axiom,
    ! [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__11882] :
      ( c_24__type__11881___24t(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__11882)
    <=> ! [Vv__CANONICAL__8] :
          ( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
         => t(happ(Vvar__11882,Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ).

fof('$_type_11944',axiom,
    ! [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__11945] :
      ( c_24__type__11944___24t(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__11945)
    <=> ! [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__11945,Vv__CANONICAL__8),Vv__CANONICAL__9)) ) ) ) ).

fof('$_type_12151',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__12152] :
      ( c_24__type__12151___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__12152)
    <=> ! [Vv__CANONICAL__5] :
          ( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__6] :
              ( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__12152,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_12181',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__12182] :
      ( c_24__type__12181___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__12182)
    <=> ! [Vv__CANONICAL__5] :
          ( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__6] :
              ( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__12182,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_12205',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__12206] :
      ( c_24__type__12205___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__12206)
    <=> ! [Vv__CANONICAL__5] :
          ( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
         => t(happ(Vvar__12206,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).

fof('$_type_12235',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__12236] :
      ( c_24__type__12235___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__12236)
    <=> ! [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__12236,Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ).

fof('$_type_12265',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__12266] :
      ( c_24__type__12265___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__12266)
    <=> ! [Vv__CANONICAL__5] :
          ( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__6] :
              ( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__12266,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_12289',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__12290] :
      ( c_24__type__12289___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__12290)
    <=> ! [Vv__CANONICAL__5] :
          ( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
         => t(happ(Vvar__12290,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).

fof('$_type_12322',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__12323] :
      ( c_24__type__12322___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__12323)
    <=> ! [Vv__CANONICAL__5] :
          ( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__6] :
              ( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__12323,Vv__CANONICAL__5),Vv__CANONICAL__6),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_12346',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__12347] :
      ( c_24__type__12346___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__12347)
    <=> ! [Vv__CANONICAL__5] :
          ( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
         => t(happ(Vvar__12347,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).

fof('$_type_12373',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__12374] :
      ( c_24__type__12373___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__12374)
    <=> ! [Vv__CANONICAL__5] :
          ( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
         => t(happ(Vvar__12374,Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ).

fof('$_type_125',axiom,
    ! [Vvar__126] :
      ( c_24__type__125___24t(Vvar__126)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cPLF_2eSmallstep_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
                 => cProp___24t(happ(happ(happ(Vvar__126,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_12772',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__12773] :
      ( c_24__type__12772___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__12773)
    <=> ! [Vv__CANONICAL__17] :
          ( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__18] :
              ( t(Vv__CANONICAL__18,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__12773,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_12985',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__12986] :
      ( c_24__type__12985___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__12986)
    <=> ! [Vv__CANONICAL__17] :
          ( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__18] :
              ( t(Vv__CANONICAL__18,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__12986,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_13198',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__13199] :
      ( c_24__type__13198___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__13199)
    <=> ! [Vv__CANONICAL__17] :
          ( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__18] :
              ( t(Vv__CANONICAL__18,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__13199,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_13393',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__13394] :
      ( c_24__type__13393___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__13394)
    <=> ! [Vv__CANONICAL__17] :
          ( t(Vv__CANONICAL__17,Vv__CANONICAL__0)
         => t(happ(Vvar__13394,Vv__CANONICAL__17),Vv__CANONICAL__0) ) ) ).

fof('$_type_13606',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__13607] :
      ( c_24__type__13606___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__13607)
    <=> ! [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__13607,Vv__CANONICAL__17),Vv__CANONICAL__18)) ) ) ) ).

fof('$_type_13819',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__13820] :
      ( c_24__type__13819___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__13820)
    <=> ! [Vv__CANONICAL__17] :
          ( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
         => ! [Vv__CANONICAL__18] :
              ( t(Vv__CANONICAL__18,Vv__CANONICAL__8)
             => t(happ(happ(Vvar__13820,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__8) ) ) ) ).

fof('$_type_14032',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__14033] :
      ( c_24__type__14032___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__14033)
    <=> ! [Vv__CANONICAL__17] :
          ( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
         => ! [Vv__CANONICAL__18] :
              ( t(Vv__CANONICAL__18,Vv__CANONICAL__8)
             => t(happ(happ(Vvar__14033,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__8) ) ) ) ).

fof('$_type_14245',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__14246] :
      ( c_24__type__14245___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__14246)
    <=> ! [Vv__CANONICAL__17] :
          ( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
         => ! [Vv__CANONICAL__18] :
              ( t(Vv__CANONICAL__18,Vv__CANONICAL__8)
             => t(happ(happ(Vvar__14246,Vv__CANONICAL__17),Vv__CANONICAL__18),Vv__CANONICAL__8) ) ) ) ).

fof('$_type_14440',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__14441] :
      ( c_24__type__14440___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__14441)
    <=> ! [Vv__CANONICAL__17] :
          ( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
         => t(happ(Vvar__14441,Vv__CANONICAL__17),Vv__CANONICAL__8) ) ) ).

fof('$_type_14653',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__14654] :
      ( c_24__type__14653___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__14654)
    <=> ! [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__14654,Vv__CANONICAL__17),Vv__CANONICAL__18)) ) ) ) ).

fof('$_type_14848',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__14849] :
      ( c_24__type__14848___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__14849)
    <=> ! [Vv__CANONICAL__17] :
          ( t(Vv__CANONICAL__17,Vv__CANONICAL__8)
         => t(happ(Vvar__14849,Vv__CANONICAL__17),Vv__CANONICAL__0) ) ) ).

fof('$_type_14990',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__14991] :
      ( c_24__type__14990___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__14991)
    <=> ! [Vv__CANONICAL__4] :
          ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
         => t(happ(Vvar__14991,Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ).

fof('$_type_15009',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__15010] :
      ( c_24__type__15009___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__15010)
    <=> ! [Vv__CANONICAL__4] :
          ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__5] :
              ( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
             => cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__15010,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).

fof('$_type_15023',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__15024] :
      ( c_24__type__15023___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__15024)
    <=> ! [Vv__CANONICAL__4] :
          ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
         => cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__0,happ(Vvar__15024,Vv__CANONICAL__4)) ) ) ).

fof('$_type_15168',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__15169] :
      ( c_24__type__15168___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__15169)
    <=> ! [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__15169,Vv__CANONICAL__7),Vv__CANONICAL__8)) ) ) ) ).

fof('$_type_15218',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__15219] :
      ( c_24__type__15218___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__15219)
    <=> ! [Vv__CANONICAL__7] :
          ( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
         => ! [Vv__CANONICAL__8] :
              ( t(Vv__CANONICAL__8,Vv__CANONICAL__2)
             => t(happ(happ(Vvar__15219,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__2) ) ) ) ).

fof('$_type_15268',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__15269] :
      ( c_24__type__15268___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__15269)
    <=> ! [Vv__CANONICAL__7] :
          ( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
         => ! [Vv__CANONICAL__8] :
              ( t(Vv__CANONICAL__8,Vv__CANONICAL__2)
             => t(happ(happ(Vvar__15269,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__2) ) ) ) ).

fof('$_type_15310',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__15311] :
      ( c_24__type__15310___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__15311)
    <=> ! [Vv__CANONICAL__7] :
          ( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
         => t(happ(Vvar__15311,Vv__CANONICAL__7),Vv__CANONICAL__0) ) ) ).

fof('$_type_15360',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__15361] :
      ( c_24__type__15360___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__15361)
    <=> ! [Vv__CANONICAL__7] :
          ( t(Vv__CANONICAL__7,Vv__CANONICAL__2)
         => ! [Vv__CANONICAL__8] :
              ( t(Vv__CANONICAL__8,Vv__CANONICAL__2)
             => cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__2,Vv__CANONICAL__2,happ(happ(Vvar__15361,Vv__CANONICAL__7),Vv__CANONICAL__8)) ) ) ) ).

fof('$_type_15436',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__15437] :
      ( c_24__type__15436___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__15437)
    <=> ! [Vv__CANONICAL__2] :
          ( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
         => ! [Vv__CANONICAL__3] :
              ( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
             => cCoq_2eInit_2eDatatypes_2eprod___24t(Vv__CANONICAL__1,Vv__CANONICAL__1,happ(happ(Vvar__15437,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).

fof('$_type_15545',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__15546] :
      ( c_24__type__15545___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__15546)
    <=> ! [Vv__CANONICAL__7] :
          ( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__8] :
              ( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__15546,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_15589',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__15590] :
      ( c_24__type__15589___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__15590)
    <=> ! [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__15590,Vv__CANONICAL__7),Vv__CANONICAL__8)) ) ) ) ).

fof('$_type_15625',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__15626] :
      ( c_24__type__15625___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__15626)
    <=> ! [Vv__CANONICAL__7] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__7)
         => t(happ(Vvar__15626,Vv__CANONICAL__7),Vv__CANONICAL__4) ) ) ).

fof('$_type_15669',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__15670] :
      ( c_24__type__15669___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vvar__15670)
    <=> ! [Vv__CANONICAL__7] :
          ( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__8] :
              ( t(Vv__CANONICAL__8,Vv__CANONICAL__4)
             => t(happ(happ(Vvar__15670,Vv__CANONICAL__7),Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_15688',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__15689] :
      ( c_24__type__15688___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__15689)
    <=> ! [Vv__CANONICAL__2] :
          ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__3] :
              ( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
             => t(happ(happ(Vvar__15689,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_15822',axiom,
    ! [Vvar__15823] :
      ( c_24__type__15822___24t(Vvar__15823)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
         => cCoq_2eNumbers_2eBinNums_2eN___24t(happ(Vvar__15823,Vv__CANONICAL__0)) ) ) ).

fof('$_type_15824',axiom,
    ! [Vvar__15825] :
      ( c_24__type__15824___24t(Vvar__15825)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
         => cType___24t(happ(Vvar__15825,Vv__CANONICAL__0)) ) ) ).

fof('$_type_211',axiom,
    ! [Vvar__212] :
      ( c_24__type__211___24t(Vvar__212)
    <=> ! [Vv__CANONICAL__0] :
          ( cNorm_2etm___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cNorm_2etm___24t(Vv__CANONICAL__1)
             => cProp___24t(happ(happ(Vvar__212,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_23684',axiom,
    ! [Vvar__23685] :
      ( c_24__type__23684___24t(Vvar__23685)
    <=> ! [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__23685,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_23687',axiom,
    ! [Vvar__23688] :
      ( c_24__type__23687___24t(Vvar__23688)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
         => cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__23688,Vv__CANONICAL__0)) ) ) ).

fof('$_type_23699',axiom,
    ! [Vvar__23700] :
      ( c_24__type__23699___24t(Vvar__23700)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__23700,Vv__CANONICAL__0)) ) ) ).

fof('$_type_23704',axiom,
    ! [Vvar__23705] :
      ( c_24__type__23704___24t(Vvar__23705)
    <=> ! [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__23705,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_23706',axiom,
    ! [Vvar__23707] :
      ( c_24__type__23706___24t(Vvar__23707)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => cCoq_2eInit_2eDatatypes_2eoption___24t(Vv__CANONICAL__0,happ(Vvar__23707,Vv__CANONICAL__0)) ) ) ).

fof('$_type_23739',axiom,
    ! [Vvar__23740] :
      ( c_24__type__23739___24t(Vvar__23740)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cType___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
                 => cCoq_2eInit_2eDatatypes_2esum___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(happ(Vvar__23740,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_23747',axiom,
    ! [Vvar__23748] :
      ( c_24__type__23747___24t(Vvar__23748)
    <=> ! [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__23748,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_type_23749',axiom,
    ! [Vvar__23750] :
      ( c_24__type__23749___24t(Vvar__23750)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,happ(Vvar__23750,Vv__CANONICAL__0)) ) ) ).

fof('$_type_23754',axiom,
    ! [Vvar__23755] :
      ( c_24__type__23754___24t(Vvar__23755)
    <=> ! [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__23755,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_23770',axiom,
    ! [Vvar__23771] :
      ( c_24__type__23770___24t(Vvar__23771)
    <=> ! [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__23771,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_23773',axiom,
    ! [Vvar__23774] :
      ( c_24__type__23773___24t(Vvar__23774)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vv__CANONICAL__0)
         => cCoq_2eInit_2eDatatypes_2ecomparison___24t(happ(Vvar__23774,Vv__CANONICAL__0)) ) ) ).

fof('$_type_23815',axiom,
    ! [Vvar__23816] :
      ( c_24__type__23815___24t(Vvar__23816)
    <=> ! [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__23816,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_type_23960',axiom,
    ! [Vvar__23961] :
      ( c_24__type__23960___24t(Vvar__23961)
    <=> ! [Vv__CANONICAL__0] :
          ( cProp___24t(Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__23961,Vv__CANONICAL__0)) ) ) ).

fof('$_type_24',axiom,
    ! [Vvar__25] :
      ( c_24__type__24___24t(Vvar__25)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
         => cPLF_2eSmallstep_2etm___24t(happ(Vvar__25,Vv__CANONICAL__0)) ) ) ).

fof('$_type_24094',axiom,
    ! [Vvar__24095] :
      ( c_24__type__24094___24t(Vvar__24095)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDecimal_2euint___24t(Vv__CANONICAL__0)
         => cCoq_2eInit_2eDecimal_2euint___24t(happ(Vvar__24095,Vv__CANONICAL__0)) ) ) ).

fof('$_type_25011',axiom,
    ! [Vv__CANONICAL__0,Vvar__25012] :
      ( c_24__type__25011___24t(Vv__CANONICAL__0,Vvar__25012)
    <=> ! [Vv__CANONICAL__1] :
          ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
         => cType___24t(happ(Vvar__25012,Vv__CANONICAL__1)) ) ) ).

fof('$_type_25490',axiom,
    ! [Vvar__25491] :
      ( c_24__type__25490___24t(Vvar__25491)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
         => cPLF_2eImp_2eaexp___24t(happ(Vvar__25491,Vv__CANONICAL__0)) ) ) ).

fof('$_type_25493',axiom,
    ! [Vvar__25494] :
      ( c_24__type__25493___24t(Vvar__25494)
    <=> ! [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__25494,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_25826',axiom,
    ! [Vvar__25827] :
      ( c_24__type__25826___24t(Vvar__25827)
    <=> ! [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__25827,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_25835',axiom,
    ! [Vvar__25836] :
      ( c_24__type__25835___24t(Vvar__25836)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
             => cCoq_2eInit_2eDatatypes_2ecomparison___24t(happ(happ(Vvar__25836,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_25840',axiom,
    ! [Vvar__25841] :
      ( c_24__type__25840___24t(Vvar__25841)
    <=> ! [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__25841,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_25910',axiom,
    ! [Vv__CANONICAL__0,Vvar__25911] :
      ( c_24__type__25910___24t(Vv__CANONICAL__0,Vvar__25911)
    <=> ! [Vv__CANONICAL__1] :
          ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__25911,Vv__CANONICAL__1)) ) ) ).

fof('$_type_25997',axiom,
    ! [Vvar__25998] :
      ( c_24__type__25997___24t(Vvar__25998)
    <=> ! [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__25998,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_26014',axiom,
    ! [Vvar__26015] :
      ( c_24__type__26014___24t(Vvar__26015)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
         => cCoq_2eReals_2eRdefinitions_2eR___24t(happ(Vvar__26015,Vv__CANONICAL__0)) ) ) ).

fof('$_type_26173',axiom,
    ! [Vvar__26174] :
      ( c_24__type__26173___24t(Vvar__26174)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
         => cCoq_2emicromega_2eRMicromega_2eRcst___24t(happ(Vvar__26174,Vv__CANONICAL__0)) ) ) ).

fof('$_type_26196',axiom,
    ! [Vvar__26197] :
      ( c_24__type__26196___24t(Vvar__26197)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eReals_2eRdefinitions_2eR___24t(Vv__CANONICAL__0)
         => cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__26197,Vv__CANONICAL__0)) ) ) ).

fof('$_type_26216',axiom,
    ! [Vvar__26217] :
      ( c_24__type__26216___24t(Vvar__26217)
    <=> ! [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__26217,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_26231',axiom,
    ! [Vvar__26232] :
      ( c_24__type__26231___24t(Vvar__26232)
    <=> ! [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__26232,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_26239',axiom,
    ! [Vvar__26240] :
      ( c_24__type__26239___24t(Vvar__26240)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
         => cCoq_2eReals_2eRdefinitions_2eR___24t(happ(Vvar__26240,Vv__CANONICAL__0)) ) ) ).

fof('$_type_26507',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__26508] :
      ( c_24__type__26507___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__26508)
    <=> ! [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__26508,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).

fof('$_type_27',axiom,
    ! [Vvar__28] :
      ( c_24__type__27___24t(Vvar__28)
    <=> ! [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__28,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_27353',axiom,
    ! [Vvar__27354] :
      ( c_24__type__27353___24t(Vvar__27354)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__9314___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__27354,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_type_27359',axiom,
    ! [Vvar__27360] :
      ( c_24__type__27359___24t(Vvar__27360)
    <=> ! [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__27360,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_27362',axiom,
    ! [Vvar__27363] :
      ( c_24__type__27362___24t(Vvar__27363)
    <=> ! [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__27363,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_27368',axiom,
    ! [Vvar__27369] :
      ( c_24__type__27368___24t(Vvar__27369)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__27369,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_27643',axiom,
    ! [Vvar__27644] :
      ( c_24__type__27643___24t(Vvar__27644)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cType___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__4775___24t(Vv__CANONICAL__1,Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( c_24__type__27653___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
                     => cProp___24t(happ(happ(happ(happ(Vvar__27644,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_type_27653',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__27654] :
      ( c_24__type__27653___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__27654)
    <=> ! [Vv__CANONICAL__2] :
          ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__3] :
              ( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
             => t(happ(happ(Vvar__27654,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__1) ) ) ) ).

fof('$_type_27745',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__27746] :
      ( c_24__type__27745___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__27746)
    <=> ! [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__27746,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).

fof('$_type_27768',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__27769] :
      ( c_24__type__27768___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__27769)
    <=> ! [Vv__CANONICAL__2] :
          ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__27769,Vv__CANONICAL__2)) ) ) ).

fof('$_type_27772',axiom,
    ! [Vvar__27773] :
      ( c_24__type__27772___24t(Vvar__27773)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__25910___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => cType___24t(happ(happ(Vvar__27773,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_27790',axiom,
    ! [Vvar__27791] :
      ( c_24__type__27790___24t(Vvar__27791)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__25910___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
                 => ( p(happ(Vv__CANONICAL__1,Vv__CANONICAL__2))
                   => cCoq_2eInit_2eSpecif_2esig___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(happ(Vvar__27791,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ) ).

fof('$_type_27807',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__27808] :
      ( c_24__type__27807___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__27808)
    <=> ! [Vv__CANONICAL__2] :
          ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
         => cType___24t(happ(Vvar__27808,Vv__CANONICAL__2)) ) ) ).

fof('$_type_27811',axiom,
    ! [Vvar__27812] :
      ( c_24__type__27811___24t(Vvar__27812)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__25011___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => cType___24t(happ(happ(Vvar__27812,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_27836',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__27837] :
      ( c_24__type__27836___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__27837)
    <=> ! [Vv__CANONICAL__2] :
          ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__27837,Vv__CANONICAL__2)) ) ) ).

fof('$_type_27842',axiom,
    ! [Vvar__27843] :
      ( c_24__type__27842___24t(Vvar__27843)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__25910___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( cCoq_2eInit_2eSpecif_2esig___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
                 => t(happ(happ(happ(Vvar__27843,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).

fof('$_type_27860',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__27861] :
      ( c_24__type__27860___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__27861)
    <=> ! [Vv__CANONICAL__2] :
          ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
         => cType___24t(happ(Vvar__27861,Vv__CANONICAL__2)) ) ) ).

fof('$_type_27866',axiom,
    ! [Vvar__27867] :
      ( c_24__type__27866___24t(Vvar__27867)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__25011___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( cCoq_2eInit_2eSpecif_2esigT___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
                 => t(happ(happ(happ(Vvar__27867,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).

fof('$_type_27970',axiom,
    ! [Vvar__27971] :
      ( c_24__type__27970___24t(Vvar__27971)
    <=> ! [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__27971,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_28026',axiom,
    ! [Vvar__28027] :
      ( c_24__type__28026___24t(Vvar__28027)
    <=> ! [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__28027,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_type_28937',axiom,
    ! [Vvar__28938] :
      ( c_24__type__28937___24t(Vvar__28938)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
             => cType___24t(happ(happ(Vvar__28938,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_29075',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__29076] :
      ( c_24__type__29075___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__29076)
    <=> ! [Vv__CANONICAL__4] :
          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__4)
         => cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__29076,Vv__CANONICAL__4)) ) ) ).

fof('$_type_29084',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__29085] :
      ( c_24__type__29084___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__29085)
    <=> ! [Vv__CANONICAL__4] :
          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__4)
         => cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__29085,Vv__CANONICAL__4)) ) ) ).

fof('$_type_29147',axiom,
    ! [Vvar__29148] :
      ( c_24__type__29147___24t(Vvar__29148)
    <=> ! [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__29148,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_29192',axiom,
    ! [Vvar__29193] :
      ( c_24__type__29192___24t(Vvar__29193)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
         => cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__29193,Vv__CANONICAL__0)) ) ) ).

fof('$_type_29237',axiom,
    ! [Vvar__29238] :
      ( c_24__type__29237___24t(Vvar__29238)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
         => cPLF_2eImp_2eAExp_2eaexp___24t(happ(Vvar__29238,Vv__CANONICAL__0)) ) ) ).

fof('$_type_29240',axiom,
    ! [Vvar__29241] :
      ( c_24__type__29240___24t(Vvar__29241)
    <=> ! [Vv__CANONICAL__0] :
          ( cPLF_2eImp_2eAExp_2eaexp___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cPLF_2eImp_2eAExp_2eaexp___24t(Vv__CANONICAL__1)
             => cPLF_2eImp_2eAExp_2eaexp___24t(happ(happ(Vvar__29241,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_29560',axiom,
    ! [Vvar__29561] :
      ( c_24__type__29560___24t(Vvar__29561)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__2)
                 => cProp___24t(happ(happ(happ(Vvar__29561,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_29675',axiom,
    ! [Vvar__29676] :
      ( c_24__type__29675___24t(Vvar__29676)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
         => cCoq_2eNumbers_2eBinNums_2eN___24t(happ(Vvar__29676,Vv__CANONICAL__0)) ) ) ).

fof('$_type_29683',axiom,
    ! [Vvar__29684] :
      ( c_24__type__29683___24t(Vvar__29684)
    <=> ! [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__29684,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_29752',axiom,
    ! [Vvar__29753] :
      ( c_24__type__29752___24t(Vvar__29753)
    <=> ! [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__29753,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_29800',axiom,
    ! [Vvar__29801] :
      ( c_24__type__29800___24t(Vvar__29801)
    <=> ! [Vv__CANONICAL__0] :
          ( c_24__type__29802___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__29802___24t(Vv__CANONICAL__1)
             => cProp___24t(happ(happ(Vvar__29801,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_29802',axiom,
    ! [Vvar__29803] :
      ( c_24__type__29802___24t(Vvar__29803)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
         => cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__29803,Vv__CANONICAL__0)) ) ) ).

fof('$_type_29964',axiom,
    ! [Vvar__29965] :
      ( c_24__type__29964___24t(Vvar__29965)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
         => cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__29965,Vv__CANONICAL__0)) ) ) ).

fof('$_type_29987',axiom,
    ! [Vvar__29988] :
      ( c_24__type__29987___24t(Vvar__29988)
    <=> ! [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__29988,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_29990',axiom,
    ! [Vvar__29991] :
      ( c_24__type__29990___24t(Vvar__29991)
    <=> ! [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__29991,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_29998',axiom,
    ! [Vvar__29999] :
      ( c_24__type__29998___24t(Vvar__29999)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(Vv__CANONICAL__1)
             => cCoq_2eInit_2eDatatypes_2ecomparison___24t(happ(happ(Vvar__29999,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_30033',axiom,
    ! [Vvar__30034] :
      ( c_24__type__30033___24t(Vvar__30034)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__1)
             => cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__30034,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_30297',axiom,
    ! [Vvar__30298] :
      ( c_24__type__30297___24t(Vvar__30298)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__1)
             => cProp___24t(happ(happ(Vvar__30298,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_30490',axiom,
    ! [Vvar__30491] :
      ( c_24__type__30490___24t(Vvar__30491)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
         => cType___24t(happ(Vvar__30491,Vv__CANONICAL__0)) ) ) ).

fof('$_type_30551',axiom,
    ! [Vvar__30552] :
      ( c_24__type__30551___24t(Vvar__30552)
    <=> ! [Vv__CANONICAL__0] :
          ( cPLF_2eSmallstep_2eTemp4_2etm___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cPLF_2eSmallstep_2eTemp4_2etm___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( cPLF_2eSmallstep_2eTemp4_2etm___24t(Vv__CANONICAL__2)
                 => cPLF_2eSmallstep_2eTemp4_2etm___24t(happ(happ(happ(Vvar__30552,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_30586',axiom,
    ! [Vvar__30587] :
      ( c_24__type__30586___24t(Vvar__30587)
    <=> ! [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__30587,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_30593',axiom,
    ! [Vvar__30594] :
      ( c_24__type__30593___24t(Vvar__30594)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
         => cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__30594,Vv__CANONICAL__0)) ) ) ).

fof('$_type_30597',axiom,
    ! [Vvar__30598] :
      ( c_24__type__30597___24t(Vvar__30598)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
         => cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(Vvar__30598,Vv__CANONICAL__0)) ) ) ).

fof('$_type_30716',axiom,
    ! [Vvar__30717] :
      ( c_24__type__30716___24t(Vvar__30717)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
         => cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__30717,Vv__CANONICAL__0)) ) ) ).

fof('$_type_30796',axiom,
    ! [Vvar__30797] :
      ( c_24__type__30796___24t(Vvar__30797)
    <=> ! [Vv__CANONICAL__0] :
          ( cPLF_2eImp_2eaevalR__division_2eaexp___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cPLF_2eImp_2eaevalR__division_2eaexp___24t(Vv__CANONICAL__1)
             => cPLF_2eImp_2eaevalR__division_2eaexp___24t(happ(happ(Vvar__30797,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_30799',axiom,
    ! [Vv__CANONICAL__0,Vvar__30800] :
      ( c_24__type__30799___24t(Vv__CANONICAL__0,Vvar__30800)
    <=> ! [Vv__CANONICAL__1] :
          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
         => t(happ(Vvar__30800,Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ).

fof('$_type_30891',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__30892] :
      ( c_24__type__30891___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__30892)
    <=> ! [Vv__CANONICAL__6] :
          ( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
         => cType___24t(happ(Vvar__30892,Vv__CANONICAL__6)) ) ) ).

fof('$_type_30910',axiom,
    ! [Vvar__30911] :
      ( c_24__type__30910___24t(Vvar__30911)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cProp___24t(Vv__CANONICAL__1)
             => cType___24t(happ(happ(Vvar__30911,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_30965',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__30966] :
      ( c_24__type__30965___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__30966)
    <=> ! [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__30966,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).

fof('$_type_31005',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__31006] :
      ( c_24__type__31005___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__31006)
    <=> ! [Vv__CANONICAL__3] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
         => cProp___24t(happ(Vvar__31006,Vv__CANONICAL__3)) ) ) ).

fof('$_type_31026',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__31027] :
      ( c_24__type__31026___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__31027)
    <=> ! [Vv__CANONICAL__3] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
         => cProp___24t(happ(Vvar__31027,Vv__CANONICAL__3)) ) ) ).

fof('$_type_31061',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__31062] :
      ( c_24__type__31061___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__31062)
    <=> ! [Vv__CANONICAL__5] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__5)
         => cProp___24t(happ(Vvar__31062,Vv__CANONICAL__5)) ) ) ).

fof('$_type_31069',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__31070] :
      ( c_24__type__31069___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__31070)
    <=> ! [Vv__CANONICAL__5] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__5)
         => cProp___24t(happ(Vvar__31070,Vv__CANONICAL__5)) ) ) ).

fof('$_type_31071',axiom,
    ! [Vvar__31072] :
      ( c_24__type__31071___24t(Vvar__31072)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__31072,Vv__CANONICAL__0)) ) ) ).

fof('$_type_31081',axiom,
    ! [Vvar__31082] :
      ( c_24__type__31081___24t(Vvar__31082)
    <=> ! [Vv__CANONICAL__0] :
          ( cProp___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__1)
             => cType___24t(happ(happ(Vvar__31082,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_31174',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__31175] :
      ( c_24__type__31174___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__31175)
    <=> ! [Vv__CANONICAL__6] :
          ( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
         => cType___24t(happ(Vvar__31175,Vv__CANONICAL__6)) ) ) ).

fof('$_type_31378',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__31379] :
      ( c_24__type__31378___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__31379)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__11] :
              ( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__31379,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_31471',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__31472] :
      ( c_24__type__31471___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__31472)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__11] :
              ( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__31472,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_31564',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__31565] :
      ( c_24__type__31564___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__31565)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__11] :
              ( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__31565,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_31646',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__31647] :
      ( c_24__type__31646___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__31647)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => t(happ(Vvar__31647,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).

fof('$_type_31739',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__31740] :
      ( c_24__type__31739___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__31740)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__11] :
              ( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__31740,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_31821',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__31822] :
      ( c_24__type__31821___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__31822)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => t(happ(Vvar__31822,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).

fof('$_type_31914',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__31915] :
      ( c_24__type__31914___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__31915)
    <=> ! [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__31915,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).

fof('$_type_32068',axiom,
    ! [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__32069] :
      ( c_24__type__32068___24t(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__32069)
    <=> ! [Vv__CANONICAL__8] :
          ( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__9] :
              ( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__32069,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_32131',axiom,
    ! [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__32132] :
      ( c_24__type__32131___24t(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__32132)
    <=> ! [Vv__CANONICAL__8] :
          ( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__9] :
              ( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__32132,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_32194',axiom,
    ! [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__32195] :
      ( c_24__type__32194___24t(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__32195)
    <=> ! [Vv__CANONICAL__8] :
          ( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__9] :
              ( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__32195,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_32248',axiom,
    ! [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__32249] :
      ( c_24__type__32248___24t(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__32249)
    <=> ! [Vv__CANONICAL__8] :
          ( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
         => t(happ(Vvar__32249,Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ).

fof('$_type_32311',axiom,
    ! [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__32312] :
      ( c_24__type__32311___24t(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__32312)
    <=> ! [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__32312,Vv__CANONICAL__8),Vv__CANONICAL__9)) ) ) ) ).

fof('$_type_32321',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__32322] :
      ( c_24__type__32321___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__32322)
    <=> ! [Vv__CANONICAL__2] :
          ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
         => t(happ(Vvar__32322,Vv__CANONICAL__2),happ(Vv__CANONICAL__1,Vv__CANONICAL__2)) ) ) ).

fof('$_type_32332',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__32333] :
      ( c_24__type__32332___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__32333)
    <=> ! [Vv__CANONICAL__2] :
          ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
         => t(happ(Vvar__32333,Vv__CANONICAL__2),Vv__CANONICAL__1) ) ) ).

fof('$_type_32380',axiom,
    ! [Vvar__32381] :
      ( c_24__type__32380___24t(Vvar__32381)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__6582___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( c_24__type__6582___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__32381,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).

fof('$_type_32430',axiom,
    ! [Vvar__32431] :
      ( c_24__type__32430___24t(Vvar__32431)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__32431,Vv__CANONICAL__0)) ) ) ).

fof('$_type_32433',axiom,
    ! [Vv__CANONICAL__0,Vvar__32434] :
      ( c_24__type__32433___24t(Vv__CANONICAL__0,Vvar__32434)
    <=> ! [Vv__CANONICAL__1] :
          ( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__1)
         => t(happ(Vvar__32434,Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ).

fof('$_type_32516',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__32517] :
      ( c_24__type__32516___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__32517)
    <=> ! [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__32517,Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ).

fof('$_type_32535',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__32536] :
      ( c_24__type__32535___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__32536)
    <=> ! [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__32536,Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ).

fof('$_type_32555',axiom,
    ! [Vvar__32556] :
      ( c_24__type__32555___24t(Vvar__32556)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__4775___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__4775___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__32556,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).

fof('$_type_32665',axiom,
    ! [Vvar__32666] :
      ( c_24__type__32665___24t(Vvar__32666)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
             => cProp___24t(happ(happ(Vvar__32666,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_32722',axiom,
    ! [Vvar__32723] :
      ( c_24__type__32722___24t(Vvar__32723)
    <=> ! [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__32723,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_32773',axiom,
    ! [Vvar__32774] :
      ( c_24__type__32773___24t(Vvar__32774)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__6582___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__32774,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).

fof('$_type_32794',axiom,
    ! [Vvar__32795] :
      ( c_24__type__32794___24t(Vvar__32795)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__6582___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__32795,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).

fof('$_type_32967',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__32968] :
      ( c_24__type__32967___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__32968)
    <=> ! [Vv__CANONICAL__6] :
          ( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__7] :
              ( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__32968,Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_33006',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__33007] :
      ( c_24__type__33006___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__33007)
    <=> ! [Vv__CANONICAL__6] :
          ( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__7] :
              ( t(Vv__CANONICAL__7,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__33007,Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_33045',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__33046] :
      ( c_24__type__33045___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__33046)
    <=> ! [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__33046,Vv__CANONICAL__6),Vv__CANONICAL__7)) ) ) ) ).

fof('$_type_33149',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__33150] :
      ( c_24__type__33149___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__33150)
    <=> ! [Vv__CANONICAL__4] :
          ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__5] :
              ( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__33150,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_33172',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__33173] :
      ( c_24__type__33172___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__33173)
    <=> ! [Vv__CANONICAL__4] :
          ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__5] :
              ( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__33173,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_33195',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__33196] :
      ( c_24__type__33195___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__33196)
    <=> ! [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__33196,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).

fof('$_type_33218',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__33219] :
      ( c_24__type__33218___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__33219)
    <=> ! [Vv__CANONICAL__4] :
          ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__5] :
              ( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__33219,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_33236',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__33237] :
      ( c_24__type__33236___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__33237)
    <=> ! [Vv__CANONICAL__4] :
          ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
         => t(happ(Vvar__33237,Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ).

fof('$_type_33262',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__33263] :
      ( c_24__type__33262___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__33263)
    <=> ! [Vv__CANONICAL__4] :
          ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__5] :
              ( t(Vv__CANONICAL__5,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__33263,Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_33280',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__33281] :
      ( c_24__type__33280___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__33281)
    <=> ! [Vv__CANONICAL__4] :
          ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
         => t(happ(Vvar__33281,Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ).

fof('$_type_33538',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__33539] :
      ( c_24__type__33538___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__33539)
    <=> ! [Vv__CANONICAL__13] :
          ( t(Vv__CANONICAL__13,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__14] :
              ( t(Vv__CANONICAL__14,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__33539,Vv__CANONICAL__13),Vv__CANONICAL__14),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_33663',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__33664] :
      ( c_24__type__33663___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__33664)
    <=> ! [Vv__CANONICAL__13] :
          ( t(Vv__CANONICAL__13,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__14] :
              ( t(Vv__CANONICAL__14,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__33664,Vv__CANONICAL__13),Vv__CANONICAL__14),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_33788',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__33789] :
      ( c_24__type__33788___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__33789)
    <=> ! [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__33789,Vv__CANONICAL__13),Vv__CANONICAL__14)) ) ) ) ).

fof('$_type_33913',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__33914] :
      ( c_24__type__33913___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__33914)
    <=> ! [Vv__CANONICAL__13] :
          ( t(Vv__CANONICAL__13,Vv__CANONICAL__6)
         => ! [Vv__CANONICAL__14] :
              ( t(Vv__CANONICAL__14,Vv__CANONICAL__6)
             => t(happ(happ(Vvar__33914,Vv__CANONICAL__13),Vv__CANONICAL__14),Vv__CANONICAL__6) ) ) ) ).

fof('$_type_34038',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__34039] :
      ( c_24__type__34038___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__34039)
    <=> ! [Vv__CANONICAL__13] :
          ( t(Vv__CANONICAL__13,Vv__CANONICAL__6)
         => ! [Vv__CANONICAL__14] :
              ( t(Vv__CANONICAL__14,Vv__CANONICAL__6)
             => t(happ(happ(Vvar__34039,Vv__CANONICAL__13),Vv__CANONICAL__14),Vv__CANONICAL__6) ) ) ) ).

fof('$_type_34163',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__34164] :
      ( c_24__type__34163___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__34164)
    <=> ! [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__34164,Vv__CANONICAL__13),Vv__CANONICAL__14)) ) ) ) ).

fof('$_type_34274',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__34275] :
      ( c_24__type__34274___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,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__34275)
    <=> ! [Vv__CANONICAL__13] :
          ( t(Vv__CANONICAL__13,Vv__CANONICAL__6)
         => t(happ(Vvar__34275,Vv__CANONICAL__13),Vv__CANONICAL__0) ) ) ).

fof('$_type_34284',axiom,
    ! [Vvar__34285] :
      ( c_24__type__34284___24t(Vvar__34285)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__34285,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_34536',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__34537] :
      ( c_24__type__34536___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__34537)
    <=> ! [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__34537,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).

fof('$_type_34569',axiom,
    ! [Vvar__34570] :
      ( c_24__type__34569___24t(Vvar__34570)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cType___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__4775___24t(Vv__CANONICAL__1,Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( c_24__type__34579___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__3)
                     => ! [Vv__CANONICAL__4] :
                          ( c_24__type__27653___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__4)
                         => cProp___24t(happ(happ(happ(happ(happ(Vvar__34570,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).

fof('$_type_34579',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__34580] :
      ( c_24__type__34579___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__34580)
    <=> ! [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__34580,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).

fof('$_type_34659',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__34660] :
      ( c_24__type__34659___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__34660)
    <=> ! [Vv__CANONICAL__3] :
          ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__34660,Vv__CANONICAL__3)) ) ) ).

fof('$_type_34667',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__34668] :
      ( c_24__type__34667___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__34668)
    <=> ! [Vv__CANONICAL__3] :
          ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__34668,Vv__CANONICAL__3)) ) ) ).

fof('$_type_34675',axiom,
    ! [Vvar__34676] :
      ( c_24__type__34675___24t(Vvar__34676)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__25910___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__25910___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
                 => cType___24t(happ(happ(happ(Vvar__34676,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_34715',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__34716] :
      ( c_24__type__34715___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__34716)
    <=> ! [Vv__CANONICAL__3] :
          ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
         => cType___24t(happ(Vvar__34716,Vv__CANONICAL__3)) ) ) ).

fof('$_type_34723',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__34724] :
      ( c_24__type__34723___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__34724)
    <=> ! [Vv__CANONICAL__3] :
          ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
         => cType___24t(happ(Vvar__34724,Vv__CANONICAL__3)) ) ) ).

fof('$_type_34731',axiom,
    ! [Vvar__34732] :
      ( c_24__type__34731___24t(Vvar__34732)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__25011___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__25011___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
                 => cType___24t(happ(happ(happ(Vvar__34732,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_34748',axiom,
    ! [Vvar__34749] :
      ( c_24__type__34748___24t(Vvar__34749)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ( p(c_24False)
           => t(happ(Vvar__34749,Vv__CANONICAL__0),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_34872',axiom,
    ! [Vvar__34873] :
      ( c_24__type__34872___24t(Vvar__34873)
    <=> ! [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__34873,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_35109',axiom,
    ! [Vvar__35110] :
      ( c_24__type__35109___24t(Vvar__35110)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__6591___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__35110,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).

fof('$_type_35124',axiom,
    ! [Vvar__35125] :
      ( c_24__type__35124___24t(Vvar__35125)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__6582___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__35125,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).

fof('$_type_35255',axiom,
    ! [Vvar__35256] :
      ( c_24__type__35255___24t(Vvar__35256)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__0)
         => cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__35256,Vv__CANONICAL__0)) ) ) ).

fof('$_type_35285',axiom,
    ! [Vvar__35286] :
      ( c_24__type__35285___24t(Vvar__35286)
    <=> ! [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__35286,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_35291',axiom,
    ! [Vvar__35292] :
      ( c_24__type__35291___24t(Vvar__35292)
    <=> ! [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__35292,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_35293',axiom,
    ! [Vvar__35294] :
      ( c_24__type__35293___24t(Vvar__35294)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eByte_2ebyte___24t(Vv__CANONICAL__0)
         => cCoq_2eInit_2eByte_2ebyte___24t(happ(Vvar__35294,Vv__CANONICAL__0)) ) ) ).

fof('$_type_35299',axiom,
    ! [Vv__CANONICAL__0,Vvar__35300] :
      ( c_24__type__35299___24t(Vv__CANONICAL__0,Vvar__35300)
    <=> ! [Vv__CANONICAL__1] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
         => cType___24t(happ(Vvar__35300,Vv__CANONICAL__1)) ) ) ).

fof('$_type_35312',axiom,
    ! [Vvar__35313] :
      ( c_24__type__35312___24t(Vvar__35313)
    <=> ! [Vv__CANONICAL__0] :
          ( c_24__type__15824___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__35317___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
                     => t(happ(happ(happ(happ(Vvar__35313,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),happ(Vv__CANONICAL__0,Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_type_35317',axiom,
    ! [Vv__CANONICAL__0,Vvar__35318] :
      ( c_24__type__35317___24t(Vv__CANONICAL__0,Vvar__35318)
    <=> ! [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__35318,Vv__CANONICAL__1),Vv__CANONICAL__2),happ(Vv__CANONICAL__0,cCoq_2eInit_2eDatatypes_2eS___24a1(Vv__CANONICAL__1))) ) ) ) ).

fof('$_type_35322',axiom,
    ! [Vvar__35323] :
      ( c_24__type__35322___24t(Vvar__35323)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cType___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
                 => cCoq_2eInit_2eDatatypes_2esum___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(happ(Vvar__35323,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_35334',axiom,
    ! [Vvar__35335] :
      ( c_24__type__35334___24t(Vvar__35335)
    <=> ! [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__35335,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).

fof('$_type_35346',axiom,
    ! [Vvar__35347] :
      ( c_24__type__35346___24t(Vvar__35347)
    <=> ! [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__35347,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__1) ) ) ) ) ).

fof('$_type_35348',axiom,
    ! [Vvar__35349] :
      ( c_24__type__35348___24t(Vvar__35349)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDecimal_2euint___24t(Vv__CANONICAL__0)
         => cCoq_2eInit_2eDecimal_2eint___24t(happ(Vvar__35349,Vv__CANONICAL__0)) ) ) ).

fof('$_type_35361',axiom,
    ! [Vvar__35362] :
      ( c_24__type__35361___24t(Vvar__35362)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDecimal_2eint___24t(Vv__CANONICAL__0)
         => cCoq_2eInit_2eDecimal_2eint___24t(happ(Vvar__35362,Vv__CANONICAL__0)) ) ) ).

fof('$_type_35364',axiom,
    ! [Vvar__35365] :
      ( c_24__type__35364___24t(Vvar__35365)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
             => cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__35365,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_35367',axiom,
    ! [Vvar__35368] :
      ( c_24__type__35367___24t(Vvar__35368)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
             => cCoq_2emicromega_2eEnvRing_2ePExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__35368,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_35370',axiom,
    ! [Vvar__35371] :
      ( c_24__type__35370___24t(Vvar__35371)
    <=> ! [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__35371,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_35375',axiom,
    ! [Vvar__35376] :
      ( c_24__type__35375___24t(Vvar__35376)
    <=> ! [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__35376,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_35383',axiom,
    ! [Vvar__35384] :
      ( c_24__type__35383___24t(Vvar__35384)
    <=> ! [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__35384,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_type_35386',axiom,
    ! [Vvar__35387] :
      ( c_24__type__35386___24t(Vvar__35387)
    <=> ! [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__35387,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_35396',axiom,
    ! [Vvar__35397] :
      ( c_24__type__35396___24t(Vvar__35397)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
             => ! [Vv__CANONICAL__2] :
                  ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
                 => ( Vv__CANONICAL__1 = Vv__CANONICAL__2
                   => cProp___24t(happ(happ(happ(Vvar__35397,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ) ).

fof('$_type_35399',axiom,
    ! [Vvar__35400] :
      ( c_24__type__35399___24t(Vvar__35400)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
             => cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__35400,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_35402',axiom,
    ! [Vvar__35403] :
      ( c_24__type__35402___24t(Vvar__35403)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__1)
             => cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__35403,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_35407',axiom,
    ! [Vvar__35408] :
      ( c_24__type__35407___24t(Vvar__35408)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
                 => cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,happ(happ(happ(Vvar__35408,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_35410',axiom,
    ! [Vvar__35411] :
      ( c_24__type__35410___24t(Vvar__35411)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => cCoq_2esetoid__ring_2eField__theory_2eFExpr___24t(Vv__CANONICAL__0,happ(happ(Vvar__35411,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_35420',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__35421] :
      ( c_24__type__35420___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__35421)
    <=> ! [Vv__CANONICAL__2] :
          ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
         => t(happ(Vvar__35421,Vv__CANONICAL__2),happ(Vv__CANONICAL__1,Vv__CANONICAL__2)) ) ) ).

fof('$_type_35425',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__35426] :
      ( c_24__type__35425___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__35426)
    <=> ! [Vv__CANONICAL__2] :
          ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
         => t(happ(Vvar__35426,Vv__CANONICAL__2),happ(Vv__CANONICAL__1,Vv__CANONICAL__2)) ) ) ).

fof('$_type_35431',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__35432] :
      ( c_24__type__35431___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__35432)
    <=> ! [Vv__CANONICAL__2] :
          ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
         => t(happ(Vvar__35432,Vv__CANONICAL__2),happ(Vv__CANONICAL__1,Vv__CANONICAL__2)) ) ) ).

fof('$_type_35436',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__35437] :
      ( c_24__type__35436___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__35437)
    <=> ! [Vv__CANONICAL__2] :
          ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
         => t(happ(Vvar__35437,Vv__CANONICAL__2),happ(Vv__CANONICAL__1,Vv__CANONICAL__2)) ) ) ).

fof('$_type_35447',axiom,
    ! [Vv__CANONICAL__0,Vvar__35448] :
      ( c_24__type__35447___24t(Vv__CANONICAL__0,Vvar__35448)
    <=> ! [Vv__CANONICAL__1] :
          ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__2] :
              ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
             => cCoq_2eInit_2eDatatypes_2ecomparison___24t(happ(happ(Vvar__35448,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).

fof('$_type_35458',axiom,
    ! [Vvar__35459] :
      ( c_24__type__35458___24t(Vvar__35459)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__35447___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
                 => ! [Vv__CANONICAL__3] :
                      ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
                     => t(happ(happ(happ(happ(Vvar__35459,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).

fof('$_type_35475',axiom,
    ! [Vvar__35476] :
      ( c_24__type__35475___24t(Vvar__35476)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__0)
         => cPLF_2eImp_2eaexp___24t(happ(Vvar__35476,Vv__CANONICAL__0)) ) ) ).

fof('$_type_35480',axiom,
    ! [Vvar__35481] :
      ( c_24__type__35480___24t(Vvar__35481)
    <=> ! [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__35481,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_35483',axiom,
    ! [Vvar__35484] :
      ( c_24__type__35483___24t(Vvar__35484)
    <=> ! [Vv__CANONICAL__0] :
          ( cPLF_2eImp_2ebexp___24t(Vv__CANONICAL__0)
         => cPLF_2eImp_2ebexp___24t(happ(Vvar__35484,Vv__CANONICAL__0)) ) ) ).

fof('$_type_35486',axiom,
    ! [Vvar__35487] :
      ( c_24__type__35486___24t(Vvar__35487)
    <=> ! [Vv__CANONICAL__0] :
          ( cPLF_2eImp_2ebexp___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cPLF_2eImp_2ebexp___24t(Vv__CANONICAL__1)
             => cPLF_2eImp_2ebexp___24t(happ(happ(Vvar__35487,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_35489',axiom,
    ! [Vvar__35490] :
      ( c_24__type__35489___24t(Vvar__35490)
    <=> ! [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__35490,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_35550',axiom,
    ! [Vvar__35551] :
      ( c_24__type__35550___24t(Vvar__35551)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
         => cPLF_2eImp_2esinstr___24t(happ(Vvar__35551,Vv__CANONICAL__0)) ) ) ).

fof('$_type_35552',axiom,
    ! [Vvar__35553] :
      ( c_24__type__35552___24t(Vvar__35553)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__0)
         => cPLF_2eImp_2esinstr___24t(happ(Vvar__35553,Vv__CANONICAL__0)) ) ) ).

fof('$_type_35556',axiom,
    ! [Vvar__35557] :
      ( c_24__type__35556___24t(Vvar__35557)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
             => cCoq_2esetoid__ring_2eInitialRing_2ehypo___24t(happ(happ(Vvar__35557,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_35567',axiom,
    ! [Vvar__35568] :
      ( c_24__type__35567___24t(Vvar__35568)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
             => ! [Vv__CANONICAL__2] :
                  ( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
                 => t(happ(happ(happ(Vvar__35568,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).

fof('$_type_35579',axiom,
    ! [Vvar__35580] :
      ( c_24__type__35579___24t(Vvar__35580)
    <=> ! [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__35580,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_35604',axiom,
    ! [Vvar__35605] :
      ( c_24__type__35604___24t(Vvar__35605)
    <=> ! [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__35605,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).

fof('$_type_35628',axiom,
    ! [Vvar__35629] :
      ( c_24__type__35628___24t(Vvar__35629)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
                 => t(happ(happ(happ(Vvar__35629,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ) ).

fof('$_type_35652',axiom,
    ! [Vvar__35653] :
      ( c_24__type__35652___24t(Vvar__35653)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cType___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__15688___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__1,Vv__CANONICAL__3)
                     => ! [Vv__CANONICAL__4] :
                          ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
                         => t(happ(happ(happ(happ(happ(Vvar__35653,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).

fof('$_type_35681',axiom,
    ! [Vvar__35682] :
      ( c_24__type__35681___24t(Vvar__35682)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cType___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__35688___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__35682,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__0) ) ) ) ) ) ) ).

fof('$_type_35688',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__35689] :
      ( c_24__type__35688___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__35689)
    <=> ! [Vv__CANONICAL__2] :
          ( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
         => ! [Vv__CANONICAL__3] :
              ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__35689,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_35737',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__35738] :
      ( c_24__type__35737___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__35738)
    <=> ! [Vv__CANONICAL__3] :
          ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__35738,Vv__CANONICAL__3)) ) ) ).

fof('$_type_35761',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__35762] :
      ( c_24__type__35761___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__35762)
    <=> ! [Vv__CANONICAL__3] :
          ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__35762,Vv__CANONICAL__3)) ) ) ).

fof('$_type_35808',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__35809] :
      ( c_24__type__35808___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vvar__35809)
    <=> ! [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__35809,Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ).

fof('$_type_35843',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__35844] :
      ( c_24__type__35843___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__35844)
    <=> ! [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__35844,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).

fof('$_type_35863',axiom,
    ! [Vvar__35864] :
      ( c_24__type__35863___24t(Vvar__35864)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
         => cCoq_2eInit_2eDatatypes_2ebool___24t(happ(Vvar__35864,Vv__CANONICAL__0)) ) ) ).

fof('$_type_35879',axiom,
    ! [Vvar__35880] :
      ( c_24__type__35879___24t(Vvar__35880)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
                     => cCoq_2eInit_2eDatatypes_2enat___24t(happ(happ(happ(happ(Vvar__35880,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_type_35891',axiom,
    ! [Vvar__35892] :
      ( c_24__type__35891___24t(Vvar__35892)
    <=> ! [Vv__CANONICAL__0] :
          ( c_24__type__35863___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__35863___24t(Vv__CANONICAL__1)
             => cProp___24t(happ(happ(Vvar__35892,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_36436',axiom,
    ! [Vvar__36437] :
      ( c_24__type__36436___24t(Vvar__36437)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vv__CANONICAL__0)
         => cCoq_2emicromega_2eRMicromega_2eRcst___24t(happ(Vvar__36437,Vv__CANONICAL__0)) ) ) ).

fof('$_type_36439',axiom,
    ! [Vvar__36440] :
      ( c_24__type__36439___24t(Vvar__36440)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vv__CANONICAL__1)
             => cCoq_2emicromega_2eRMicromega_2eRcst___24t(happ(happ(Vvar__36440,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_36443',axiom,
    ! [Vvar__36444] :
      ( c_24__type__36443___24t(Vvar__36444)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2emicromega_2eRMicromega_2eRcst___24t(Vv__CANONICAL__0)
         => cCoq_2emicromega_2eRMicromega_2eRcst___24t(happ(Vvar__36444,Vv__CANONICAL__0)) ) ) ).

fof('$_type_36461',axiom,
    ! [Vvar__36462] :
      ( c_24__type__36461___24t(Vvar__36462)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__25910___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( cProp___24t(Vv__CANONICAL__3)
                     => cProp___24t(happ(happ(happ(happ(Vvar__36462,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_type_36487',axiom,
    ! [Vvar__36488] :
      ( c_24__type__36487___24t(Vvar__36488)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__25910___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( cCoq_2eInit_2eDatatypes_2elist___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
                 => cProp___24t(happ(happ(happ(Vvar__36488,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_36716',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__36717] :
      ( c_24__type__36716___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__36717)
    <=> ! [Vv__CANONICAL__6] :
          ( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
         => cType___24t(happ(Vvar__36717,Vv__CANONICAL__6)) ) ) ).

fof('$_type_36745',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__36746] :
      ( c_24__type__36745___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__36746)
    <=> ! [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__36746,Vv__CANONICAL__6),Vv__CANONICAL__7)) ) ) ) ).

fof('$_type_36782',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__36783] :
      ( c_24__type__36782___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__36783)
    <=> ! [Vv__CANONICAL__6] :
          ( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__7] :
              ( t(Vv__CANONICAL__7,happ(Vv__CANONICAL__1,Vv__CANONICAL__6))
             => ! [Vv__CANONICAL__8] :
                  ( t(Vv__CANONICAL__8,happ(Vv__CANONICAL__1,Vv__CANONICAL__6))
                 => cProp___24t(happ(happ(happ(Vvar__36783,Vv__CANONICAL__6),Vv__CANONICAL__7),Vv__CANONICAL__8)) ) ) ) ) ).

fof('$_type_36854',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__36855] :
      ( c_24__type__36854___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__36855)
    <=> ! [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__36855,Vv__CANONICAL__6),Vv__CANONICAL__7)) ) ) ) ).

fof('$_type_36879',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__36880] :
      ( c_24__type__36879___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__36880)
    <=> ! [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__36880,Vv__CANONICAL__6),Vv__CANONICAL__7)) ) ) ) ).

fof('$_type_36921',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__36922] :
      ( c_24__type__36921___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__36922)
    <=> ! [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__36922,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).

fof('$_type_36972',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__36973] :
      ( c_24__type__36972___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__36973)
    <=> ! [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__36973,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).

fof('$_type_37507',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__37508] :
      ( c_24__type__37507___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__37508)
    <=> ! [Vv__CANONICAL__22] :
          ( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__23] :
              ( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__37508,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_37853',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__37854] :
      ( c_24__type__37853___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__37854)
    <=> ! [Vv__CANONICAL__22] :
          ( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__23] :
              ( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__37854,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_38199',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__38200] :
      ( c_24__type__38199___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__38200)
    <=> ! [Vv__CANONICAL__22] :
          ( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__23] :
              ( t(Vv__CANONICAL__23,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__38200,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_38522',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__38523] :
      ( c_24__type__38522___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__38523)
    <=> ! [Vv__CANONICAL__22] :
          ( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
         => t(happ(Vvar__38523,Vv__CANONICAL__22),Vv__CANONICAL__0) ) ) ).

fof('$_type_38868',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__38869] :
      ( c_24__type__38868___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__38869)
    <=> ! [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__38869,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).

fof('$_type_39214',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__39215] :
      ( c_24__type__39214___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__39215)
    <=> ! [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__39215,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).

fof('$_type_39560',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__39561] :
      ( c_24__type__39560___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__39561)
    <=> ! [Vv__CANONICAL__22] :
          ( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
         => ! [Vv__CANONICAL__23] :
              ( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
             => t(happ(happ(Vvar__39561,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__9) ) ) ) ).

fof('$_type_39906',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__39907] :
      ( c_24__type__39906___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__39907)
    <=> ! [Vv__CANONICAL__22] :
          ( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
         => ! [Vv__CANONICAL__23] :
              ( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
             => t(happ(happ(Vvar__39907,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__9) ) ) ) ).

fof('$_type_40252',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__40253] :
      ( c_24__type__40252___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__40253)
    <=> ! [Vv__CANONICAL__22] :
          ( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
         => ! [Vv__CANONICAL__23] :
              ( t(Vv__CANONICAL__23,Vv__CANONICAL__9)
             => t(happ(happ(Vvar__40253,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__9) ) ) ) ).

fof('$_type_40575',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__40576] :
      ( c_24__type__40575___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__40576)
    <=> ! [Vv__CANONICAL__22] :
          ( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
         => t(happ(Vvar__40576,Vv__CANONICAL__22),Vv__CANONICAL__9) ) ) ).

fof('$_type_40921',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__40922] :
      ( c_24__type__40921___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__40922)
    <=> ! [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__40922,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).

fof('$_type_41267',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__41268] :
      ( c_24__type__41267___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__41268)
    <=> ! [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__41268,Vv__CANONICAL__22),Vv__CANONICAL__23)) ) ) ) ).

fof('$_type_41590',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__41591] :
      ( c_24__type__41590___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__41591)
    <=> ! [Vv__CANONICAL__22] :
          ( t(Vv__CANONICAL__22,Vv__CANONICAL__9)
         => t(happ(Vvar__41591,Vv__CANONICAL__22),Vv__CANONICAL__0) ) ) ).

fof('$_type_41913',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__41914] :
      ( c_24__type__41913___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__41914)
    <=> ! [Vv__CANONICAL__22] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__22)
         => t(happ(Vvar__41914,Vv__CANONICAL__22),Vv__CANONICAL__19) ) ) ).

fof('$_type_42259',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__42260] :
      ( c_24__type__42259___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vv__CANONICAL__6,Vv__CANONICAL__7,Vv__CANONICAL__8,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__42260)
    <=> ! [Vv__CANONICAL__22] :
          ( t(Vv__CANONICAL__22,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__23] :
              ( t(Vv__CANONICAL__23,Vv__CANONICAL__19)
             => t(happ(happ(Vvar__42260,Vv__CANONICAL__22),Vv__CANONICAL__23),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_42341',axiom,
    ! [Vvar__42342] :
      ( c_24__type__42341___24t(Vvar__42342)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__4775___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( c_24__type__4775___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
                     => ! [Vv__CANONICAL__4] :
                          ( c_24__type__4775___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__42342,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5),Vv__CANONICAL__6)) ) ) ) ) ) ) ) ) ).

fof('$_type_42360',axiom,
    ! [Vvar__42361] :
      ( c_24__type__42360___24t(Vvar__42361)
    <=> ! [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__42361,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_42365',axiom,
    ! [Vvar__42366] :
      ( c_24__type__42365___24t(Vvar__42366)
    <=> ! [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__42366,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_42373',axiom,
    ! [Vvar__42374] :
      ( c_24__type__42373___24t(Vvar__42374)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,Vv__CANONICAL__3)
                     => cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(Vv__CANONICAL__0,happ(happ(happ(happ(Vvar__42374,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_type_42376',axiom,
    ! [Vvar__42377] :
      ( c_24__type__42376___24t(Vvar__42377)
    <=> ! [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__42377,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_42379',axiom,
    ! [Vvar__42380] :
      ( c_24__type__42379___24t(Vvar__42380)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24t(Vv__CANONICAL__0,happ(Vvar__42380,Vv__CANONICAL__0)) ) ) ).

fof('$_type_42472',axiom,
    ! [Vvar__42473] :
      ( c_24__type__42472___24t(Vvar__42473)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__6582___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
                 => ! [Vv__CANONICAL__3] :
                      ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
                     => t(happ(happ(happ(happ(Vvar__42473,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).

fof('$_type_42510',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__42511] :
      ( c_24__type__42510___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__42511)
    <=> ! [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__42511,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).

fof('$_type_42550',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__42551] :
      ( c_24__type__42550___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__42551)
    <=> ! [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__42551,Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ).

fof('$_type_43787',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__43788] :
      ( c_24__type__43787___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__43788)
    <=> ! [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__43788,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).

fof('$_type_43822',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__43823] :
      ( c_24__type__43822___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__43823)
    <=> ! [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__43823,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).

fof('$_type_43857',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__43858] :
      ( c_24__type__43857___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vvar__43858)
    <=> ! [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__43858,Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ).

fof('$_type_43866',axiom,
    ! [Vvar__43867] :
      ( c_24__type__43866___24t(Vvar__43867)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__25011___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
                 => ! [Vv__CANONICAL__3] :
                      ( t(Vv__CANONICAL__3,happ(Vv__CANONICAL__1,Vv__CANONICAL__2))
                     => cCoq_2eInit_2eSpecif_2esigT___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(happ(happ(Vvar__43867,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_type_43875',axiom,
    ! [Vvar__43876] :
      ( c_24__type__43875___24t(Vvar__43876)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cType___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( cType___24t(Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( cType___24t(Vv__CANONICAL__3)
                     => cCoq_2emicromega_2eTauto_2eGFormula___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,happ(happ(happ(happ(Vvar__43876,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_type_43893',axiom,
    ! [Vvar__43894] :
      ( c_24__type__43893___24t(Vvar__43894)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cType___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( cType___24t(Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( cType___24t(Vv__CANONICAL__3)
                     => ! [Vv__CANONICAL__4] :
                          ( t(Vv__CANONICAL__4,Vv__CANONICAL__1)
                         => cCoq_2emicromega_2eTauto_2eGFormula___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,happ(happ(happ(happ(happ(Vvar__43894,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4)) ) ) ) ) ) ) ).

fof('$_type_43910',axiom,
    ! [Vvar__43911] :
      ( c_24__type__43910___24t(Vvar__43911)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cType___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( cType___24t(Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( cType___24t(Vv__CANONICAL__3)
                     => ! [Vv__CANONICAL__4] :
                          ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
                         => ! [Vv__CANONICAL__5] :
                              ( t(Vv__CANONICAL__5,Vv__CANONICAL__2)
                             => cCoq_2emicromega_2eTauto_2eGFormula___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,happ(happ(happ(happ(happ(happ(Vvar__43911,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__4),Vv__CANONICAL__5)) ) ) ) ) ) ) ) ).

fof('$_type_43944',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__43945] :
      ( c_24__type__43944___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vvar__43945)
    <=> ! [Vv__CANONICAL__4] :
          ( t(Vv__CANONICAL__4,Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__43945,Vv__CANONICAL__4)) ) ) ).

fof('$_type_43995',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__43996] :
      ( c_24__type__43995___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vv__CANONICAL__2,Vv__CANONICAL__3,Vv__CANONICAL__4,Vv__CANONICAL__5,Vvar__43996)
    <=> ! [Vv__CANONICAL__6] :
          ( t(Vv__CANONICAL__6,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__7] :
              ( t(Vv__CANONICAL__7,Vv__CANONICAL__1)
             => cProp___24t(happ(happ(Vvar__43996,Vv__CANONICAL__6),Vv__CANONICAL__7)) ) ) ) ).

fof('$_type_44001',axiom,
    ! [Vvar__44002] :
      ( c_24__type__44001___24t(Vvar__44002)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__4775___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => cProp___24t(happ(happ(Vvar__44002,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_44013',axiom,
    ! [Vvar__44014] :
      ( c_24__type__44013___24t(Vvar__44014)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__44016___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
                 => ! [Vv__CANONICAL__3] :
                      ( t(Vv__CANONICAL__3,Vv__CANONICAL__0)
                     => cProp___24t(happ(happ(happ(happ(Vvar__44014,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ) ) ).

fof('$_type_44016',axiom,
    ! [Vv__CANONICAL__0,Vvar__44017] :
      ( c_24__type__44016___24t(Vv__CANONICAL__0,Vvar__44017)
    <=> ! [Vv__CANONICAL__1] :
          ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
         => cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__44017,Vv__CANONICAL__1)) ) ) ).

fof('$_type_44098',axiom,
    ! [Vvar__44099] :
      ( c_24__type__44098___24t(Vvar__44099)
    <=> ! [Vv__CANONICAL__0] :
          ( cPLF_2eImp_2eAExp_2ebexp___24t(Vv__CANONICAL__0)
         => cPLF_2eImp_2eAExp_2ebexp___24t(happ(Vvar__44099,Vv__CANONICAL__0)) ) ) ).

fof('$_type_44101',axiom,
    ! [Vvar__44102] :
      ( c_24__type__44101___24t(Vvar__44102)
    <=> ! [Vv__CANONICAL__0] :
          ( cPLF_2eImp_2eAExp_2ebexp___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cPLF_2eImp_2eAExp_2ebexp___24t(Vv__CANONICAL__1)
             => cPLF_2eImp_2eAExp_2ebexp___24t(happ(happ(Vvar__44102,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_44412',axiom,
    ! [Vvar__44413] :
      ( c_24__type__44412___24t(Vvar__44413)
    <=> ! [Vv__CANONICAL__0] :
          ( cPLF_2eImp_2eBreakImp_2ecom___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cPLF_2eImp_2eBreakImp_2ecom___24t(Vv__CANONICAL__1)
             => cPLF_2eImp_2eBreakImp_2ecom___24t(happ(happ(Vvar__44413,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_44415',axiom,
    ! [Vvar__44416] :
      ( c_24__type__44415___24t(Vvar__44416)
    <=> ! [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__44416,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_44418',axiom,
    ! [Vvar__44419] :
      ( c_24__type__44418___24t(Vvar__44419)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
         => cPLF_2eSmallstep_2eCombined_2etm___24t(happ(Vvar__44419,Vv__CANONICAL__0)) ) ) ).

fof('$_type_44421',axiom,
    ! [Vvar__44422] :
      ( c_24__type__44421___24t(Vvar__44422)
    <=> ! [Vv__CANONICAL__0] :
          ( cPLF_2eSmallstep_2eCombined_2etm___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cPLF_2eSmallstep_2eCombined_2etm___24t(Vv__CANONICAL__1)
             => cPLF_2eSmallstep_2eCombined_2etm___24t(happ(happ(Vvar__44422,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_44426',axiom,
    ! [Vvar__44427] :
      ( c_24__type__44426___24t(Vvar__44427)
    <=> ! [Vv__CANONICAL__0] :
          ( cPLF_2eSmallstep_2eCombined_2etm___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cPLF_2eSmallstep_2eCombined_2etm___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( cPLF_2eSmallstep_2eCombined_2etm___24t(Vv__CANONICAL__2)
                 => cPLF_2eSmallstep_2eCombined_2etm___24t(happ(happ(happ(Vvar__44427,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_44560',axiom,
    ! [Vvar__44561] :
      ( c_24__type__44560___24t(Vvar__44561)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__44565___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__3)
                     => t(happ(happ(happ(happ(Vvar__44561,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).

fof('$_type_44565',axiom,
    ! [Vv__CANONICAL__0,Vvar__44566] :
      ( c_24__type__44565___24t(Vv__CANONICAL__0,Vvar__44566)
    <=> ! [Vv__CANONICAL__1] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(Vv__CANONICAL__1)
         => ! [Vv__CANONICAL__2] :
              ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__44566,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_44582',axiom,
    ! [Vvar__44583] :
      ( c_24__type__44582___24t(Vvar__44583)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
             => ! [Vv__CANONICAL__2] :
                  ( c_24__type__44587___24t(Vv__CANONICAL__0,Vv__CANONICAL__2)
                 => ! [Vv__CANONICAL__3] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__3)
                     => t(happ(happ(happ(happ(Vvar__44583,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__0) ) ) ) ) ) ).

fof('$_type_44587',axiom,
    ! [Vv__CANONICAL__0,Vvar__44588] :
      ( c_24__type__44587___24t(Vv__CANONICAL__0,Vvar__44588)
    <=> ! [Vv__CANONICAL__1] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
         => ! [Vv__CANONICAL__2] :
              ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__44588,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_44593',axiom,
    ! [Vvar__44594] :
      ( c_24__type__44593___24t(Vvar__44594)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2ebool___24t(Vv__CANONICAL__0)
         => cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__44594,Vv__CANONICAL__0)) ) ) ).

fof('$_type_44599',axiom,
    ! [Vvar__44600] :
      ( c_24__type__44599___24t(Vvar__44600)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
         => cCoq_2ePArith_2eBinPosDef_2ePos_2emask___24t(happ(Vvar__44600,Vv__CANONICAL__0)) ) ) ).

fof('$_type_44647',axiom,
    ! [Vvar__44648] :
      ( c_24__type__44647___24t(Vvar__44648)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__1)
             => cCoq_2eInit_2eDatatypes_2ebool___24t(happ(happ(Vvar__44648,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_44654',axiom,
    ! [Vvar__44655] :
      ( c_24__type__44654___24t(Vvar__44655)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
         => cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(Vvar__44655,Vv__CANONICAL__0)) ) ) ).

fof('$_type_44677',axiom,
    ! [Vvar__44678] :
      ( c_24__type__44677___24t(Vvar__44678)
    <=> ! [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__44678,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_44753',axiom,
    ! [Vvar__44754] :
      ( c_24__type__44753___24t(Vvar__44754)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__1)
             => cProp___24t(happ(happ(Vvar__44754,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_45000',axiom,
    ! [Vvar__45001] :
      ( c_24__type__45000___24t(Vvar__45001)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
         => cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__45001,Vv__CANONICAL__0)) ) ) ).

fof('$_type_45004',axiom,
    ! [Vvar__45005] :
      ( c_24__type__45004___24t(Vvar__45005)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
         => cCoq_2eNumbers_2eBinNums_2eN___24t(happ(Vvar__45005,Vv__CANONICAL__0)) ) ) ).

fof('$_type_45037',axiom,
    ! [Vvar__45038] :
      ( c_24__type__45037___24t(Vvar__45038)
    <=> ! [Vv__CANONICAL__0] :
          ( c_24__type__30716___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( c_24__type__30716___24t(Vv__CANONICAL__1)
             => cProp___24t(happ(happ(Vvar__45038,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_45041',axiom,
    ! [Vvar__45042] :
      ( c_24__type__45041___24t(Vvar__45042)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
         => cPLF_2eImp_2eaevalR__division_2eaexp___24t(happ(Vvar__45042,Vv__CANONICAL__0)) ) ) ).

fof('$_type_4524',axiom,
    ! [Vvar__4525] :
      ( c_24__type__4524___24t(Vvar__4525)
    <=> ! [Vv__CANONICAL__0] :
          ( cNorm_2etm___24t(Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__4525,Vv__CANONICAL__0)) ) ) ).

fof('$_type_45360',axiom,
    ! [Vvar__45361] :
      ( c_24__type__45360___24t(Vvar__45361)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
         => cPLF_2eImp_2eaevalR__extended_2eaexp___24t(happ(Vvar__45361,Vv__CANONICAL__0)) ) ) ).

fof('$_type_45363',axiom,
    ! [Vvar__45364] :
      ( c_24__type__45363___24t(Vvar__45364)
    <=> ! [Vv__CANONICAL__0] :
          ( cPLF_2eImp_2eaevalR__extended_2eaexp___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cPLF_2eImp_2eaevalR__extended_2eaexp___24t(Vv__CANONICAL__1)
             => cPLF_2eImp_2eaevalR__extended_2eaexp___24t(happ(happ(Vvar__45364,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_4578',axiom,
    ! [Vvar__4579] :
      ( c_24__type__4578___24t(Vvar__4579)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cNorm_2etm___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( cNorm_2etm___24t(Vv__CANONICAL__2)
                 => cNorm_2etm___24t(happ(happ(happ(Vvar__4579,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_45900',axiom,
    ! [Vvar__45901] :
      ( c_24__type__45900___24t(Vvar__45901)
    <=> ! [Vv__CANONICAL__0] :
          ( cNorm_2ety___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cNorm_2ety___24t(Vv__CANONICAL__1)
             => cNorm_2ety___24t(happ(happ(Vvar__45901,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_4725',axiom,
    ! [Vvar__4726] :
      ( c_24__type__4725___24t(Vvar__4726)
    <=> ! [Vv__CANONICAL__0] :
          ( cNorm_2etm___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cNorm_2etm___24t(Vv__CANONICAL__1)
             => cNorm_2etm___24t(happ(happ(Vvar__4726,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_4730',axiom,
    ! [Vvar__4731] :
      ( c_24__type__4730___24t(Vvar__4731)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cNorm_2ety___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( cNorm_2etm___24t(Vv__CANONICAL__2)
                 => cNorm_2etm___24t(happ(happ(happ(Vvar__4731,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_4733',axiom,
    ! [Vvar__4734] :
      ( c_24__type__4733___24t(Vvar__4734)
    <=> ! [Vv__CANONICAL__0] :
          ( cNorm_2etm___24t(Vv__CANONICAL__0)
         => cNorm_2etm___24t(happ(Vvar__4734,Vv__CANONICAL__0)) ) ) ).

fof('$_type_4770',axiom,
    ! [Vvar__4771] :
      ( c_24__type__4770___24t(Vvar__4771)
    <=> ! [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__4771,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_4775',axiom,
    ! [Vv__CANONICAL__0,Vvar__4776] :
      ( c_24__type__4775___24t(Vv__CANONICAL__0,Vvar__4776)
    <=> ! [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__4776,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).

fof('$_type_4777',axiom,
    ! [Vvar__4778] :
      ( c_24__type__4777___24t(Vvar__4778)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => cType___24t(happ(Vvar__4778,Vv__CANONICAL__0)) ) ) ).

fof('$_type_4794',axiom,
    ! [Vvar__4795] :
      ( c_24__type__4794___24t(Vvar__4795)
    <=> ! [Vv__CANONICAL__0] :
          ( cPLF_2eSmallstep_2etm___24t(Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__4795,Vv__CANONICAL__0)) ) ) ).

fof('$_type_4797',axiom,
    ! [Vvar__4798] :
      ( c_24__type__4797___24t(Vvar__4798)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cPLF_2eSmallstep_2erelation___24t(Vv__CANONICAL__0,Vv__CANONICAL__1)
             => cProp___24t(happ(happ(Vvar__4798,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_4800',axiom,
    ! [Vvar__4801] :
      ( c_24__type__4800___24t(Vvar__4801)
    <=> ! [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__4801,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_4802',axiom,
    ! [Vvar__4803] :
      ( c_24__type__4802___24t(Vvar__4803)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__4803,Vv__CANONICAL__0)) ) ) ).

fof('$_type_5474',axiom,
    ! [Vvar__5475] :
      ( c_24__type__5474___24t(Vvar__5475)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eStrings_2eString_2estring___24t(Vv__CANONICAL__0)
         => cNorm_2etm___24t(happ(Vvar__5475,Vv__CANONICAL__0)) ) ) ).

fof('$_type_5479',axiom,
    ! [Vvar__5480] :
      ( c_24__type__5479___24t(Vvar__5480)
    <=> ! [Vv__CANONICAL__0] :
          ( cNorm_2etm___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cNorm_2etm___24t(Vv__CANONICAL__1)
             => ! [Vv__CANONICAL__2] :
                  ( cNorm_2etm___24t(Vv__CANONICAL__2)
                 => cNorm_2etm___24t(happ(happ(happ(Vvar__5480,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_5493',axiom,
    ! [Vvar__5494] :
      ( c_24__type__5493___24t(Vvar__5494)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(Vv__CANONICAL__0)
         => cCoq_2eInit_2eDatatypes_2enat___24t(happ(Vvar__5494,Vv__CANONICAL__0)) ) ) ).

fof('$_type_5933',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__5934] :
      ( c_24__type__5933___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__5934)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__11] :
              ( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__5934,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_6034',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__6035] :
      ( c_24__type__6034___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__6035)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__11] :
              ( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__6035,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_6135',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__6136] :
      ( c_24__type__6135___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__6136)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__11] :
              ( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__6136,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_6225',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__6226] :
      ( c_24__type__6225___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__6226)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => t(happ(Vvar__6226,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).

fof('$_type_6326',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__6327] :
      ( c_24__type__6326___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__6327)
    <=> ! [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__6327,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).

fof('$_type_6427',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__6428] :
      ( c_24__type__6427___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__6428)
    <=> ! [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__6428,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).

fof('$_type_6528',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__6529] :
      ( c_24__type__6528___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__6529)
    <=> ! [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__6529,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).

fof('$_type_6582',axiom,
    ! [Vv__CANONICAL__0,Vvar__6583] :
      ( c_24__type__6582___24t(Vv__CANONICAL__0,Vvar__6583)
    <=> ! [Vv__CANONICAL__1] :
          ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__2] :
              ( t(Vv__CANONICAL__2,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__6583,Vv__CANONICAL__1),Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_6591',axiom,
    ! [Vv__CANONICAL__0,Vvar__6592] :
      ( c_24__type__6591___24t(Vv__CANONICAL__0,Vvar__6592)
    <=> ! [Vv__CANONICAL__1] :
          ( t(Vv__CANONICAL__1,Vv__CANONICAL__0)
         => t(happ(Vvar__6592,Vv__CANONICAL__1),Vv__CANONICAL__0) ) ) ).

fof('$_type_6629',axiom,
    ! [Vvar__6630] :
      ( c_24__type__6629___24t(Vvar__6630)
    <=> ! [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__6630,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_6855',axiom,
    ! [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__6856] :
      ( c_24__type__6855___24t(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__6856)
    <=> ! [Vv__CANONICAL__8] :
          ( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__9] :
              ( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__6856,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_6918',axiom,
    ! [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__6919] :
      ( c_24__type__6918___24t(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__6919)
    <=> ! [Vv__CANONICAL__8] :
          ( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__9] :
              ( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__6919,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_6981',axiom,
    ! [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__6982] :
      ( c_24__type__6981___24t(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__6982)
    <=> ! [Vv__CANONICAL__8] :
          ( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__9] :
              ( t(Vv__CANONICAL__9,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__6982,Vv__CANONICAL__8),Vv__CANONICAL__9),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_7035',axiom,
    ! [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__7036] :
      ( c_24__type__7035___24t(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__7036)
    <=> ! [Vv__CANONICAL__8] :
          ( t(Vv__CANONICAL__8,Vv__CANONICAL__0)
         => t(happ(Vvar__7036,Vv__CANONICAL__8),Vv__CANONICAL__0) ) ) ).

fof('$_type_7098',axiom,
    ! [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__7099] :
      ( c_24__type__7098___24t(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__7099)
    <=> ! [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__7099,Vv__CANONICAL__8),Vv__CANONICAL__9)) ) ) ) ).

fof('$_type_7119',axiom,
    ! [Vvar__7120] :
      ( c_24__type__7119___24t(Vvar__7120)
    <=> ! [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__7120,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_7148',axiom,
    ! [Vvar__7149] :
      ( c_24__type__7148___24t(Vvar__7149)
    <=> ! [Vv__CANONICAL__0] :
          ( cProp___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cProp___24t(Vv__CANONICAL__1)
             => cType___24t(happ(happ(Vvar__7149,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_7171',axiom,
    ! [Vvar__7172] :
      ( c_24__type__7171___24t(Vvar__7172)
    <=> ! [Vv__CANONICAL__0] :
          ( cProp___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cProp___24t(Vv__CANONICAL__1)
             => ( p(Vv__CANONICAL__0)
               => cCoq_2eInit_2eSpecif_2esumbool___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(Vvar__7172,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ).

fof('$_type_7176',axiom,
    ! [Vvar__7177] :
      ( c_24__type__7176___24t(Vvar__7177)
    <=> ! [Vv__CANONICAL__0] :
          ( cProp___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cProp___24t(Vv__CANONICAL__1)
             => ( p(Vv__CANONICAL__1)
               => cCoq_2eInit_2eSpecif_2esumbool___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,happ(happ(Vvar__7177,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ) ).

fof('$_type_7344',axiom,
    ! [Vvar__7345] :
      ( c_24__type__7344___24t(Vvar__7345)
    <=> ! [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__7345,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_7381',axiom,
    ! [Vvar__7382] :
      ( c_24__type__7381___24t(Vvar__7382)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(Vv__CANONICAL__1)
             => cProp___24t(happ(happ(Vvar__7382,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_7396',axiom,
    ! [Vvar__7397] :
      ( c_24__type__7396___24t(Vvar__7397)
    <=> ! [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__7397,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_7398',axiom,
    ! [Vvar__7399] :
      ( c_24__type__7398___24t(Vvar__7399)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
         => cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__7399,Vv__CANONICAL__0)) ) ) ).

fof('$_type_7401',axiom,
    ! [Vvar__7402] :
      ( c_24__type__7401___24t(Vvar__7402)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(Vv__CANONICAL__0)
         => cProp___24t(happ(Vvar__7402,Vv__CANONICAL__0)) ) ) ).

fof('$_type_7406',axiom,
    ! [Vvar__7407] :
      ( c_24__type__7406___24t(Vvar__7407)
    <=> ! [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__7407,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_7408',axiom,
    ! [Vvar__7409] :
      ( c_24__type__7408___24t(Vvar__7409)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
         => cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(Vvar__7409,Vv__CANONICAL__0)) ) ) ).

fof('$_type_7426',axiom,
    ! [Vvar__7427] :
      ( c_24__type__7426___24t(Vvar__7427)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(Vv__CANONICAL__0)
         => cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__7427,Vv__CANONICAL__0)) ) ) ).

fof('$_type_7450',axiom,
    ! [Vvar__7451] :
      ( c_24__type__7450___24t(Vvar__7451)
    <=> ! [Vv__CANONICAL__0] :
          ( cType___24t(Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__1] :
              ( cType___24t(Vv__CANONICAL__1)
             => cType___24t(happ(happ(Vvar__7451,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_7488',axiom,
    ! [Vvar__7489] :
      ( c_24__type__7488___24t(Vvar__7489)
    <=> ! [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__7489,Vv__CANONICAL__0),Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ) ).

fof('$_type_7685',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__7686] :
      ( c_24__type__7685___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__7686)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__11] :
              ( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__7686,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_7778',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__7779] :
      ( c_24__type__7778___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__7779)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__11] :
              ( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__7779,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_7871',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__7872] :
      ( c_24__type__7871___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__7872)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__11] :
              ( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__7872,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_7953',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__7954] :
      ( c_24__type__7953___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__7954)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => t(happ(Vvar__7954,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).

fof('$_type_8046',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__8047] :
      ( c_24__type__8046___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__8047)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => ! [Vv__CANONICAL__11] :
              ( t(Vv__CANONICAL__11,Vv__CANONICAL__0)
             => t(happ(happ(Vvar__8047,Vv__CANONICAL__10),Vv__CANONICAL__11),Vv__CANONICAL__0) ) ) ) ).

fof('$_type_8128',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__8129] :
      ( c_24__type__8128___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__8129)
    <=> ! [Vv__CANONICAL__10] :
          ( t(Vv__CANONICAL__10,Vv__CANONICAL__0)
         => t(happ(Vvar__8129,Vv__CANONICAL__10),Vv__CANONICAL__0) ) ) ).

fof('$_type_8221',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,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__8222] :
      ( c_24__type__8221___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,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__8222)
    <=> ! [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__8222,Vv__CANONICAL__10),Vv__CANONICAL__11)) ) ) ) ).

fof('$_type_8921',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__8922] :
      ( c_24__type__8921___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__8922)
    <=> ! [Vv__CANONICAL__2] :
          ( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
         => t(happ(Vvar__8922,Vv__CANONICAL__2),Vv__CANONICAL__0) ) ) ).

fof('$_type_9',axiom,
    ! [Vvar__10] :
      ( c_24__type__9___24t(Vvar__10)
    <=> ! [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__10,Vv__CANONICAL__0),Vv__CANONICAL__1)) ) ) ) ).

fof('$_type_9314',axiom,
    ! [Vv__CANONICAL__0,Vvar__9315] :
      ( c_24__type__9314___24t(Vv__CANONICAL__0,Vvar__9315)
    <=> ! [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__9315,Vv__CANONICAL__1),Vv__CANONICAL__2)) ) ) ) ).

fof('$_type_9338',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__9339] :
      ( c_24__type__9338___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__9339)
    <=> ! [Vv__CANONICAL__2] :
          ( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
         => ! [Vv__CANONICAL__3] :
              ( t(Vv__CANONICAL__3,Vv__CANONICAL__1)
             => t(happ(happ(Vvar__9339,Vv__CANONICAL__2),Vv__CANONICAL__3),Vv__CANONICAL__1) ) ) ) ).

fof('$_type_9352',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__9353] :
      ( c_24__type__9352___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__9353)
    <=> ! [Vv__CANONICAL__2] :
          ( t(Vv__CANONICAL__2,Vv__CANONICAL__1)
         => t(happ(Vvar__9353,Vv__CANONICAL__2),Vv__CANONICAL__1) ) ) ).

fof('$_type_9359',axiom,
    ! [Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__9360] :
      ( c_24__type__9359___24t(Vv__CANONICAL__0,Vv__CANONICAL__1,Vvar__9360)
    <=> ! [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__9360,Vv__CANONICAL__2),Vv__CANONICAL__3)) ) ) ) ).

fof('$_type_9774',axiom,
    ! [Vvar__9775] :
      ( c_24__type__9774___24t(Vvar__9775)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vv__CANONICAL__0)
         => cCoq_2eNumbers_2eBinNums_2eZ___24t(happ(Vvar__9775,Vv__CANONICAL__0)) ) ) ).

fof('$_type_9779',axiom,
    ! [Vvar__9780] :
      ( c_24__type__9779___24t(Vvar__9780)
    <=> ! [Vv__CANONICAL__0] :
          ( cCoq_2eQArith_2eQArith__base_2eQ___24t(Vv__CANONICAL__0)
         => cCoq_2eNumbers_2eBinNums_2epositive___24t(happ(Vvar__9780,Vv__CANONICAL__0)) ) ) ).

fof('$_typeof_Coq.Arith.EqNat.eq_nat',axiom,
    c_24__type__6629___24t(cCoq_2eArith_2eEqNat_2eeq__nat) ).

fof('$_typeof_Coq.Arith.PeanoNat.Nat.b2n',axiom,
    c_24__type__44593___24t(cCoq_2eArith_2ePeanoNat_2eNat_2eb2n) ).

fof('$_typeof_Coq.Arith.PeanoNat.Nat.divide',axiom,
    c_24__type__6629___24t(cCoq_2eArith_2ePeanoNat_2eNat_2edivide) ).

fof('$_typeof_Coq.Arith.PeanoNat.Nat.eq',axiom,
    c_24__type__6629___24t(cCoq_2eArith_2ePeanoNat_2eNat_2eeq) ).

fof('$_typeof_Coq.Arith.PeanoNat.Nat.eqf',axiom,
    c_24__type__35891___24t(cCoq_2eArith_2ePeanoNat_2eNat_2eeqf) ).

fof('$_typeof_Coq.Arith.PeanoNat.Nat.le',axiom,
    c_24__type__6629___24t(cCoq_2eArith_2ePeanoNat_2eNat_2ele) ).

fof('$_typeof_Coq.Arith.PeanoNat.Nat.lt',axiom,
    c_24__type__6629___24t(cCoq_2eArith_2ePeanoNat_2eNat_2elt) ).

fof('$_typeof_Coq.Arith.PeanoNat.Nat.recursion',axiom,
    c_24__type__44582___24t(cCoq_2eArith_2ePeanoNat_2eNat_2erecursion) ).

fof('$_typeof_Coq.Arith.Plus.tail_plus',axiom,
    c_24__type__9___24t(cCoq_2eArith_2ePlus_2etail__plus) ).

fof('$_typeof_Coq.Arith.Wf_nat.ltof',axiom,
    c_24__type__44013___24t(cCoq_2eArith_2eWf__nat_2eltof) ).

fof('$_typeof_Coq.Bool.Bool.Is_true',axiom,
    c_24__type__31071___24t(cCoq_2eBool_2eBool_2eIs__true) ).

fof('$_typeof_Coq.Bool.Bool.eqb',axiom,
    c_24__type__23684___24t(cCoq_2eBool_2eBool_2eeqb) ).

fof('$_typeof_Coq.Bool.Bool.ifb',axiom,
    c_24__type__35291___24t(cCoq_2eBool_2eBool_2eifb) ).

fof('$_typeof_Coq.Bool.Bool.reflect',axiom,
    c_24__type__31081___24t(cCoq_2eBool_2eBool_2ereflect) ).

fof('$_typeof_Coq.Bool.Bvector.Bvector',axiom,
    c_24__type__15824___24t(cCoq_2eBool_2eBvector_2eBvector) ).

fof('$_typeof_Coq.Bool.Zerob.zerob',axiom,
    c_24__type__35863___24t(cCoq_2eBool_2eZerob_2ezerob) ).

fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.Equal',axiom,
    c_24__type__30297___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eEqual) ).

fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.In',axiom,
    c_24__type__7381___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn) ).

fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.Leaf',axiom,
    cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eLeaf) ).

fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.Node',axiom,
    c_24__type__44677___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.empty',axiom,
    cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eempty) ).

fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.eq',axiom,
    c_24__type__30297___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eeq) ).

fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.mem',axiom,
    c_24__type__30033___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem) ).

fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.t',axiom,
    cType___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2et) ).

fof('$_typeof_Coq.FSets.FSetPositive.PositiveSet.tree',axiom,
    cType___24t(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2etree) ).

fof('$_typeof_Coq.Init.Byte.byte',axiom,
    cType___24t(cCoq_2eInit_2eByte_2ebyte) ).

fof('$_typeof_Coq.Init.Byte.byte_of_byte',axiom,
    c_24__type__35293___24t(cCoq_2eInit_2eByte_2ebyte__of__byte) ).

fof('$_typeof_Coq.Init.Byte.x00',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex00) ).

fof('$_typeof_Coq.Init.Byte.x01',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex01) ).

fof('$_typeof_Coq.Init.Byte.x02',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex02) ).

fof('$_typeof_Coq.Init.Byte.x03',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex03) ).

fof('$_typeof_Coq.Init.Byte.x04',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex04) ).

fof('$_typeof_Coq.Init.Byte.x05',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex05) ).

fof('$_typeof_Coq.Init.Byte.x06',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex06) ).

fof('$_typeof_Coq.Init.Byte.x07',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex07) ).

fof('$_typeof_Coq.Init.Byte.x08',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex08) ).

fof('$_typeof_Coq.Init.Byte.x09',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex09) ).

fof('$_typeof_Coq.Init.Byte.x0a',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex0a) ).

fof('$_typeof_Coq.Init.Byte.x0b',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex0b) ).

fof('$_typeof_Coq.Init.Byte.x0c',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex0c) ).

fof('$_typeof_Coq.Init.Byte.x0d',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex0d) ).

fof('$_typeof_Coq.Init.Byte.x0e',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex0e) ).

fof('$_typeof_Coq.Init.Byte.x0f',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex0f) ).

fof('$_typeof_Coq.Init.Byte.x10',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex10) ).

fof('$_typeof_Coq.Init.Byte.x11',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex11) ).

fof('$_typeof_Coq.Init.Byte.x12',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex12) ).

fof('$_typeof_Coq.Init.Byte.x13',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex13) ).

fof('$_typeof_Coq.Init.Byte.x14',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex14) ).

fof('$_typeof_Coq.Init.Byte.x15',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex15) ).

fof('$_typeof_Coq.Init.Byte.x16',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex16) ).

fof('$_typeof_Coq.Init.Byte.x17',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex17) ).

fof('$_typeof_Coq.Init.Byte.x18',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex18) ).

fof('$_typeof_Coq.Init.Byte.x19',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex19) ).

fof('$_typeof_Coq.Init.Byte.x1a',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex1a) ).

fof('$_typeof_Coq.Init.Byte.x1b',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex1b) ).

fof('$_typeof_Coq.Init.Byte.x1c',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex1c) ).

fof('$_typeof_Coq.Init.Byte.x1d',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex1d) ).

fof('$_typeof_Coq.Init.Byte.x1e',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex1e) ).

fof('$_typeof_Coq.Init.Byte.x1f',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex1f) ).

fof('$_typeof_Coq.Init.Byte.x20',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex20) ).

fof('$_typeof_Coq.Init.Byte.x21',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex21) ).

fof('$_typeof_Coq.Init.Byte.x22',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex22) ).

fof('$_typeof_Coq.Init.Byte.x23',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex23) ).

fof('$_typeof_Coq.Init.Byte.x24',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex24) ).

fof('$_typeof_Coq.Init.Byte.x25',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex25) ).

fof('$_typeof_Coq.Init.Byte.x26',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex26) ).

fof('$_typeof_Coq.Init.Byte.x27',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex27) ).

fof('$_typeof_Coq.Init.Byte.x28',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex28) ).

fof('$_typeof_Coq.Init.Byte.x29',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex29) ).

fof('$_typeof_Coq.Init.Byte.x2a',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex2a) ).

fof('$_typeof_Coq.Init.Byte.x2b',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex2b) ).

fof('$_typeof_Coq.Init.Byte.x2c',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex2c) ).

fof('$_typeof_Coq.Init.Byte.x2d',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex2d) ).

fof('$_typeof_Coq.Init.Byte.x2e',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex2e) ).

fof('$_typeof_Coq.Init.Byte.x2f',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex2f) ).

fof('$_typeof_Coq.Init.Byte.x30',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex30) ).

fof('$_typeof_Coq.Init.Byte.x31',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex31) ).

fof('$_typeof_Coq.Init.Byte.x32',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex32) ).

fof('$_typeof_Coq.Init.Byte.x33',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex33) ).

fof('$_typeof_Coq.Init.Byte.x34',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex34) ).

fof('$_typeof_Coq.Init.Byte.x35',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex35) ).

fof('$_typeof_Coq.Init.Byte.x36',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex36) ).

fof('$_typeof_Coq.Init.Byte.x37',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex37) ).

fof('$_typeof_Coq.Init.Byte.x38',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex38) ).

fof('$_typeof_Coq.Init.Byte.x39',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex39) ).

fof('$_typeof_Coq.Init.Byte.x3a',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex3a) ).

fof('$_typeof_Coq.Init.Byte.x3b',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex3b) ).

fof('$_typeof_Coq.Init.Byte.x3c',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex3c) ).

fof('$_typeof_Coq.Init.Byte.x3d',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex3d) ).

fof('$_typeof_Coq.Init.Byte.x3e',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex3e) ).

fof('$_typeof_Coq.Init.Byte.x3f',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex3f) ).

fof('$_typeof_Coq.Init.Byte.x40',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex40) ).

fof('$_typeof_Coq.Init.Byte.x41',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex41) ).

fof('$_typeof_Coq.Init.Byte.x42',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex42) ).

fof('$_typeof_Coq.Init.Byte.x43',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex43) ).

fof('$_typeof_Coq.Init.Byte.x44',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex44) ).

fof('$_typeof_Coq.Init.Byte.x45',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex45) ).

fof('$_typeof_Coq.Init.Byte.x46',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex46) ).

fof('$_typeof_Coq.Init.Byte.x47',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex47) ).

fof('$_typeof_Coq.Init.Byte.x48',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex48) ).

fof('$_typeof_Coq.Init.Byte.x49',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex49) ).

fof('$_typeof_Coq.Init.Byte.x4a',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex4a) ).

fof('$_typeof_Coq.Init.Byte.x4b',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex4b) ).

fof('$_typeof_Coq.Init.Byte.x4c',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex4c) ).

fof('$_typeof_Coq.Init.Byte.x4d',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex4d) ).

fof('$_typeof_Coq.Init.Byte.x4e',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex4e) ).

fof('$_typeof_Coq.Init.Byte.x4f',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex4f) ).

fof('$_typeof_Coq.Init.Byte.x50',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex50) ).

fof('$_typeof_Coq.Init.Byte.x51',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex51) ).

fof('$_typeof_Coq.Init.Byte.x52',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex52) ).

fof('$_typeof_Coq.Init.Byte.x53',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex53) ).

fof('$_typeof_Coq.Init.Byte.x54',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex54) ).

fof('$_typeof_Coq.Init.Byte.x55',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex55) ).

fof('$_typeof_Coq.Init.Byte.x56',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex56) ).

fof('$_typeof_Coq.Init.Byte.x57',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex57) ).

fof('$_typeof_Coq.Init.Byte.x58',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex58) ).

fof('$_typeof_Coq.Init.Byte.x59',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex59) ).

fof('$_typeof_Coq.Init.Byte.x5a',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex5a) ).

fof('$_typeof_Coq.Init.Byte.x5b',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex5b) ).

fof('$_typeof_Coq.Init.Byte.x5c',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex5c) ).

fof('$_typeof_Coq.Init.Byte.x5d',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex5d) ).

fof('$_typeof_Coq.Init.Byte.x5e',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex5e) ).

fof('$_typeof_Coq.Init.Byte.x5f',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex5f) ).

fof('$_typeof_Coq.Init.Byte.x60',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex60) ).

fof('$_typeof_Coq.Init.Byte.x61',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex61) ).

fof('$_typeof_Coq.Init.Byte.x62',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex62) ).

fof('$_typeof_Coq.Init.Byte.x63',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex63) ).

fof('$_typeof_Coq.Init.Byte.x64',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex64) ).

fof('$_typeof_Coq.Init.Byte.x65',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex65) ).

fof('$_typeof_Coq.Init.Byte.x66',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex66) ).

fof('$_typeof_Coq.Init.Byte.x67',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex67) ).

fof('$_typeof_Coq.Init.Byte.x68',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex68) ).

fof('$_typeof_Coq.Init.Byte.x69',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex69) ).

fof('$_typeof_Coq.Init.Byte.x6a',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex6a) ).

fof('$_typeof_Coq.Init.Byte.x6b',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex6b) ).

fof('$_typeof_Coq.Init.Byte.x6c',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex6c) ).

fof('$_typeof_Coq.Init.Byte.x6d',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex6d) ).

fof('$_typeof_Coq.Init.Byte.x6e',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex6e) ).

fof('$_typeof_Coq.Init.Byte.x6f',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex6f) ).

fof('$_typeof_Coq.Init.Byte.x70',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex70) ).

fof('$_typeof_Coq.Init.Byte.x71',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex71) ).

fof('$_typeof_Coq.Init.Byte.x72',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex72) ).

fof('$_typeof_Coq.Init.Byte.x73',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex73) ).

fof('$_typeof_Coq.Init.Byte.x74',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex74) ).

fof('$_typeof_Coq.Init.Byte.x75',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex75) ).

fof('$_typeof_Coq.Init.Byte.x76',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex76) ).

fof('$_typeof_Coq.Init.Byte.x77',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex77) ).

fof('$_typeof_Coq.Init.Byte.x78',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex78) ).

fof('$_typeof_Coq.Init.Byte.x79',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex79) ).

fof('$_typeof_Coq.Init.Byte.x7a',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex7a) ).

fof('$_typeof_Coq.Init.Byte.x7b',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex7b) ).

fof('$_typeof_Coq.Init.Byte.x7c',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex7c) ).

fof('$_typeof_Coq.Init.Byte.x7d',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex7d) ).

fof('$_typeof_Coq.Init.Byte.x7e',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex7e) ).

fof('$_typeof_Coq.Init.Byte.x7f',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex7f) ).

fof('$_typeof_Coq.Init.Byte.x80',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex80) ).

fof('$_typeof_Coq.Init.Byte.x81',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex81) ).

fof('$_typeof_Coq.Init.Byte.x82',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex82) ).

fof('$_typeof_Coq.Init.Byte.x83',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex83) ).

fof('$_typeof_Coq.Init.Byte.x84',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex84) ).

fof('$_typeof_Coq.Init.Byte.x85',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex85) ).

fof('$_typeof_Coq.Init.Byte.x86',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex86) ).

fof('$_typeof_Coq.Init.Byte.x87',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex87) ).

fof('$_typeof_Coq.Init.Byte.x88',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex88) ).

fof('$_typeof_Coq.Init.Byte.x89',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex89) ).

fof('$_typeof_Coq.Init.Byte.x8a',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex8a) ).

fof('$_typeof_Coq.Init.Byte.x8b',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex8b) ).

fof('$_typeof_Coq.Init.Byte.x8c',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex8c) ).

fof('$_typeof_Coq.Init.Byte.x8d',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex8d) ).

fof('$_typeof_Coq.Init.Byte.x8e',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex8e) ).

fof('$_typeof_Coq.Init.Byte.x8f',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex8f) ).

fof('$_typeof_Coq.Init.Byte.x90',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex90) ).

fof('$_typeof_Coq.Init.Byte.x91',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex91) ).

fof('$_typeof_Coq.Init.Byte.x92',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex92) ).

fof('$_typeof_Coq.Init.Byte.x93',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex93) ).

fof('$_typeof_Coq.Init.Byte.x94',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex94) ).

fof('$_typeof_Coq.Init.Byte.x95',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex95) ).

fof('$_typeof_Coq.Init.Byte.x96',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex96) ).

fof('$_typeof_Coq.Init.Byte.x97',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex97) ).

fof('$_typeof_Coq.Init.Byte.x98',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex98) ).

fof('$_typeof_Coq.Init.Byte.x99',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex99) ).

fof('$_typeof_Coq.Init.Byte.x9a',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex9a) ).

fof('$_typeof_Coq.Init.Byte.x9b',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex9b) ).

fof('$_typeof_Coq.Init.Byte.x9c',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex9c) ).

fof('$_typeof_Coq.Init.Byte.x9d',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex9d) ).

fof('$_typeof_Coq.Init.Byte.x9e',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex9e) ).

fof('$_typeof_Coq.Init.Byte.x9f',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2ex9f) ).

fof('$_typeof_Coq.Init.Byte.xa0',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exa0) ).

fof('$_typeof_Coq.Init.Byte.xa1',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exa1) ).

fof('$_typeof_Coq.Init.Byte.xa2',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exa2) ).

fof('$_typeof_Coq.Init.Byte.xa3',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exa3) ).

fof('$_typeof_Coq.Init.Byte.xa4',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exa4) ).

fof('$_typeof_Coq.Init.Byte.xa5',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exa5) ).

fof('$_typeof_Coq.Init.Byte.xa6',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exa6) ).

fof('$_typeof_Coq.Init.Byte.xa7',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exa7) ).

fof('$_typeof_Coq.Init.Byte.xa8',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exa8) ).

fof('$_typeof_Coq.Init.Byte.xa9',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exa9) ).

fof('$_typeof_Coq.Init.Byte.xaa',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exaa) ).

fof('$_typeof_Coq.Init.Byte.xab',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exab) ).

fof('$_typeof_Coq.Init.Byte.xac',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exac) ).

fof('$_typeof_Coq.Init.Byte.xad',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exad) ).

fof('$_typeof_Coq.Init.Byte.xae',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exae) ).

fof('$_typeof_Coq.Init.Byte.xaf',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exaf) ).

fof('$_typeof_Coq.Init.Byte.xb0',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exb0) ).

fof('$_typeof_Coq.Init.Byte.xb1',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exb1) ).

fof('$_typeof_Coq.Init.Byte.xb2',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exb2) ).

fof('$_typeof_Coq.Init.Byte.xb3',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exb3) ).

fof('$_typeof_Coq.Init.Byte.xb4',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exb4) ).

fof('$_typeof_Coq.Init.Byte.xb5',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exb5) ).

fof('$_typeof_Coq.Init.Byte.xb6',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exb6) ).

fof('$_typeof_Coq.Init.Byte.xb7',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exb7) ).

fof('$_typeof_Coq.Init.Byte.xb8',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exb8) ).

fof('$_typeof_Coq.Init.Byte.xb9',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exb9) ).

fof('$_typeof_Coq.Init.Byte.xba',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exba) ).

fof('$_typeof_Coq.Init.Byte.xbb',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exbb) ).

fof('$_typeof_Coq.Init.Byte.xbc',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exbc) ).

fof('$_typeof_Coq.Init.Byte.xbd',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exbd) ).

fof('$_typeof_Coq.Init.Byte.xbe',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exbe) ).

fof('$_typeof_Coq.Init.Byte.xbf',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exbf) ).

fof('$_typeof_Coq.Init.Byte.xc0',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exc0) ).

fof('$_typeof_Coq.Init.Byte.xc1',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exc1) ).

fof('$_typeof_Coq.Init.Byte.xc2',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exc2) ).

fof('$_typeof_Coq.Init.Byte.xc3',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exc3) ).

fof('$_typeof_Coq.Init.Byte.xc4',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exc4) ).

fof('$_typeof_Coq.Init.Byte.xc5',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exc5) ).

fof('$_typeof_Coq.Init.Byte.xc6',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exc6) ).

fof('$_typeof_Coq.Init.Byte.xc7',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exc7) ).

fof('$_typeof_Coq.Init.Byte.xc8',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exc8) ).

fof('$_typeof_Coq.Init.Byte.xc9',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exc9) ).

fof('$_typeof_Coq.Init.Byte.xca',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exca) ).

fof('$_typeof_Coq.Init.Byte.xcb',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2excb) ).

fof('$_typeof_Coq.Init.Byte.xcc',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2excc) ).

fof('$_typeof_Coq.Init.Byte.xcd',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2excd) ).

fof('$_typeof_Coq.Init.Byte.xce',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exce) ).

fof('$_typeof_Coq.Init.Byte.xcf',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2excf) ).

fof('$_typeof_Coq.Init.Byte.xd0',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exd0) ).

fof('$_typeof_Coq.Init.Byte.xd1',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exd1) ).

fof('$_typeof_Coq.Init.Byte.xd2',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exd2) ).

fof('$_typeof_Coq.Init.Byte.xd3',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exd3) ).

fof('$_typeof_Coq.Init.Byte.xd4',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exd4) ).

fof('$_typeof_Coq.Init.Byte.xd5',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exd5) ).

fof('$_typeof_Coq.Init.Byte.xd6',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exd6) ).

fof('$_typeof_Coq.Init.Byte.xd7',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exd7) ).

fof('$_typeof_Coq.Init.Byte.xd8',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exd8) ).

fof('$_typeof_Coq.Init.Byte.xd9',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exd9) ).

fof('$_typeof_Coq.Init.Byte.xda',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exda) ).

fof('$_typeof_Coq.Init.Byte.xdb',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exdb) ).

fof('$_typeof_Coq.Init.Byte.xdc',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exdc) ).

fof('$_typeof_Coq.Init.Byte.xdd',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exdd) ).

fof('$_typeof_Coq.Init.Byte.xde',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exde) ).

fof('$_typeof_Coq.Init.Byte.xdf',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exdf) ).

fof('$_typeof_Coq.Init.Byte.xe0',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exe0) ).

fof('$_typeof_Coq.Init.Byte.xe1',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exe1) ).

fof('$_typeof_Coq.Init.Byte.xe2',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exe2) ).

fof('$_typeof_Coq.Init.Byte.xe3',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exe3) ).

fof('$_typeof_Coq.Init.Byte.xe4',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exe4) ).

fof('$_typeof_Coq.Init.Byte.xe5',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exe5) ).

fof('$_typeof_Coq.Init.Byte.xe6',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exe6) ).

fof('$_typeof_Coq.Init.Byte.xe7',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exe7) ).

fof('$_typeof_Coq.Init.Byte.xe8',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exe8) ).

fof('$_typeof_Coq.Init.Byte.xe9',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exe9) ).

fof('$_typeof_Coq.Init.Byte.xea',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exea) ).

fof('$_typeof_Coq.Init.Byte.xeb',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exeb) ).

fof('$_typeof_Coq.Init.Byte.xec',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exec) ).

fof('$_typeof_Coq.Init.Byte.xed',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exed) ).

fof('$_typeof_Coq.Init.Byte.xee',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exee) ).

fof('$_typeof_Coq.Init.Byte.xef',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exef) ).

fof('$_typeof_Coq.Init.Byte.xf0',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exf0) ).

fof('$_typeof_Coq.Init.Byte.xf1',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exf1) ).

fof('$_typeof_Coq.Init.Byte.xf2',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exf2) ).

fof('$_typeof_Coq.Init.Byte.xf3',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exf3) ).

fof('$_typeof_Coq.Init.Byte.xf4',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exf4) ).

fof('$_typeof_Coq.Init.Byte.xf5',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exf5) ).

fof('$_typeof_Coq.Init.Byte.xf6',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exf6) ).

fof('$_typeof_Coq.Init.Byte.xf7',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exf7) ).

fof('$_typeof_Coq.Init.Byte.xf8',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exf8) ).

fof('$_typeof_Coq.Init.Byte.xf9',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exf9) ).

fof('$_typeof_Coq.Init.Byte.xfa',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exfa) ).

fof('$_typeof_Coq.Init.Byte.xfb',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exfb) ).

fof('$_typeof_Coq.Init.Byte.xfc',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exfc) ).

fof('$_typeof_Coq.Init.Byte.xfd',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exfd) ).

fof('$_typeof_Coq.Init.Byte.xfe',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exfe) ).

fof('$_typeof_Coq.Init.Byte.xff',axiom,
    cCoq_2eInit_2eByte_2ebyte___24t(cCoq_2eInit_2eByte_2exff) ).

fof('$_typeof_Coq.Init.Datatypes.CompOpp',axiom,
    c_24__type__23773___24t(cCoq_2eInit_2eDatatypes_2eCompOpp) ).

fof('$_typeof_Coq.Init.Datatypes.CompareSpecT',axiom,
    c_24__type__23815___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__23706___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__5493___24t(cCoq_2eInit_2eDatatypes_2eS) ).

fof('$_typeof_Coq.Init.Datatypes.Some',axiom,
    c_24__type__23704___24t(cCoq_2eInit_2eDatatypes_2eSome) ).

fof('$_typeof_Coq.Init.Datatypes.andb',axiom,
    c_24__type__23684___24t(cCoq_2eInit_2eDatatypes_2eandb) ).

fof('$_typeof_Coq.Init.Datatypes.app',axiom,
    c_24__type__7488___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__23754___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__35334___24t(cCoq_2eInit_2eDatatypes_2efst) ).

fof('$_typeof_Coq.Init.Datatypes.id',axiom,
    cCoq_2eInit_2eDatatypes_2eID___24t(cCoq_2eInit_2eDatatypes_2eid) ).

fof('$_typeof_Coq.Init.Datatypes.implb',axiom,
    c_24__type__23684___24t(cCoq_2eInit_2eDatatypes_2eimplb) ).

fof('$_typeof_Coq.Init.Datatypes.inl',axiom,
    c_24__type__23739___24t(cCoq_2eInit_2eDatatypes_2einl) ).

fof('$_typeof_Coq.Init.Datatypes.inr',axiom,
    c_24__type__35322___24t(cCoq_2eInit_2eDatatypes_2einr) ).

fof('$_typeof_Coq.Init.Datatypes.length',axiom,
    c_24__type__23770___24t(cCoq_2eInit_2eDatatypes_2elength) ).

fof('$_typeof_Coq.Init.Datatypes.list',axiom,
    c_24__type__4777___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__35312___24t(cCoq_2eInit_2eDatatypes_2enat__rect) ).

fof('$_typeof_Coq.Init.Datatypes.negb',axiom,
    c_24__type__23687___24t(cCoq_2eInit_2eDatatypes_2enegb) ).

fof('$_typeof_Coq.Init.Datatypes.nil',axiom,
    c_24__type__23749___24t(cCoq_2eInit_2eDatatypes_2enil) ).

fof('$_typeof_Coq.Init.Datatypes.option',axiom,
    c_24__type__4777___24t(cCoq_2eInit_2eDatatypes_2eoption) ).

fof('$_typeof_Coq.Init.Datatypes.orb',axiom,
    c_24__type__23684___24t(cCoq_2eInit_2eDatatypes_2eorb) ).

fof('$_typeof_Coq.Init.Datatypes.pair',axiom,
    c_24__type__23747___24t(cCoq_2eInit_2eDatatypes_2epair) ).

fof('$_typeof_Coq.Init.Datatypes.prod',axiom,
    c_24__type__7450___24t(cCoq_2eInit_2eDatatypes_2eprod) ).

fof('$_typeof_Coq.Init.Datatypes.snd',axiom,
    c_24__type__35346___24t(cCoq_2eInit_2eDatatypes_2esnd) ).

fof('$_typeof_Coq.Init.Datatypes.sum',axiom,
    c_24__type__7450___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__23684___24t(cCoq_2eInit_2eDatatypes_2exorb) ).

fof('$_typeof_Coq.Init.Decimal.D0',axiom,
    c_24__type__24094___24t(cCoq_2eInit_2eDecimal_2eD0) ).

fof('$_typeof_Coq.Init.Decimal.D1',axiom,
    c_24__type__24094___24t(cCoq_2eInit_2eDecimal_2eD1) ).

fof('$_typeof_Coq.Init.Decimal.D2',axiom,
    c_24__type__24094___24t(cCoq_2eInit_2eDecimal_2eD2) ).

fof('$_typeof_Coq.Init.Decimal.D3',axiom,
    c_24__type__24094___24t(cCoq_2eInit_2eDecimal_2eD3) ).

fof('$_typeof_Coq.Init.Decimal.D4',axiom,
    c_24__type__24094___24t(cCoq_2eInit_2eDecimal_2eD4) ).

fof('$_typeof_Coq.Init.Decimal.D5',axiom,
    c_24__type__24094___24t(cCoq_2eInit_2eDecimal_2eD5) ).

fof('$_typeof_Coq.Init.Decimal.D6',axiom,
    c_24__type__24094___24t(cCoq_2eInit_2eDecimal_2eD6) ).

fof('$_typeof_Coq.Init.Decimal.D7',axiom,
    c_24__type__24094___24t(cCoq_2eInit_2eDecimal_2eD7) ).

fof('$_typeof_Coq.Init.Decimal.D8',axiom,
    c_24__type__24094___24t(cCoq_2eInit_2eDecimal_2eD8) ).

fof('$_typeof_Coq.Init.Decimal.D9',axiom,
    c_24__type__24094___24t(cCoq_2eInit_2eDecimal_2eD9) ).

fof('$_typeof_Coq.Init.Decimal.Nil',axiom,
    cCoq_2eInit_2eDecimal_2euint___24t(cCoq_2eInit_2eDecimal_2eNil) ).

fof('$_typeof_Coq.Init.Decimal.Pos',axiom,
    c_24__type__35348___24t(cCoq_2eInit_2eDecimal_2ePos) ).

fof('$_typeof_Coq.Init.Decimal.decimal',axiom,
    cType___24t(cCoq_2eInit_2eDecimal_2edecimal) ).

fof('$_typeof_Coq.Init.Decimal.int',axiom,
    cType___24t(cCoq_2eInit_2eDecimal_2eint) ).

fof('$_typeof_Coq.Init.Decimal.int_of_int',axiom,
    c_24__type__35361___24t(cCoq_2eInit_2eDecimal_2eint__of__int) ).

fof('$_typeof_Coq.Init.Decimal.nzhead',axiom,
    c_24__type__24094___24t(cCoq_2eInit_2eDecimal_2enzhead) ).

fof('$_typeof_Coq.Init.Decimal.uint',axiom,
    cType___24t(cCoq_2eInit_2eDecimal_2euint) ).

fof('$_typeof_Coq.Init.Decimal.uint_of_uint',axiom,
    c_24__type__24094___24t(cCoq_2eInit_2eDecimal_2euint__of__uint) ).

fof('$_typeof_Coq.Init.Logic_Type.notT',axiom,
    c_24__type__32430___24t(cCoq_2eInit_2eLogic__Type_2enotT) ).

fof('$_typeof_Coq.Init.Nat.add',axiom,
    c_24__type__9___24t(cCoq_2eInit_2eNat_2eadd) ).

fof('$_typeof_Coq.Init.Nat.compare',axiom,
    c_24__type__25835___24t(cCoq_2eInit_2eNat_2ecompare) ).

fof('$_typeof_Coq.Init.Nat.div2',axiom,
    c_24__type__5493___24t(cCoq_2eInit_2eNat_2ediv2) ).

fof('$_typeof_Coq.Init.Nat.double',axiom,
    c_24__type__5493___24t(cCoq_2eInit_2eNat_2edouble) ).

fof('$_typeof_Coq.Init.Nat.eqb',axiom,
    c_24__type__25826___24t(cCoq_2eInit_2eNat_2eeqb) ).

fof('$_typeof_Coq.Init.Nat.even',axiom,
    c_24__type__35863___24t(cCoq_2eInit_2eNat_2eeven) ).

fof('$_typeof_Coq.Init.Nat.leb',axiom,
    c_24__type__25826___24t(cCoq_2eInit_2eNat_2eleb) ).

fof('$_typeof_Coq.Init.Nat.log2_iter',axiom,
    c_24__type__35879___24t(cCoq_2eInit_2eNat_2elog2__iter) ).

fof('$_typeof_Coq.Init.Nat.max',axiom,
    c_24__type__9___24t(cCoq_2eInit_2eNat_2emax) ).

fof('$_typeof_Coq.Init.Nat.min',axiom,
    c_24__type__9___24t(cCoq_2eInit_2eNat_2emin) ).

fof('$_typeof_Coq.Init.Nat.mul',axiom,
    c_24__type__9___24t(cCoq_2eInit_2eNat_2emul) ).

fof('$_typeof_Coq.Init.Nat.pow',axiom,
    c_24__type__9___24t(cCoq_2eInit_2eNat_2epow) ).

fof('$_typeof_Coq.Init.Nat.pred',axiom,
    c_24__type__5493___24t(cCoq_2eInit_2eNat_2epred) ).

fof('$_typeof_Coq.Init.Nat.square',axiom,
    c_24__type__5493___24t(cCoq_2eInit_2eNat_2esquare) ).

fof('$_typeof_Coq.Init.Nat.sub',axiom,
    c_24__type__9___24t(cCoq_2eInit_2eNat_2esub) ).

fof('$_typeof_Coq.Init.Nat.succ',axiom,
    c_24__type__5493___24t(cCoq_2eInit_2eNat_2esucc) ).

fof('$_typeof_Coq.Init.Nat.t',axiom,
    cType___24t(cCoq_2eInit_2eNat_2et) ).

fof('$_typeof_Coq.Init.Nat.tail_add',axiom,
    c_24__type__9___24t(cCoq_2eInit_2eNat_2etail__add) ).

fof('$_typeof_Coq.Init.Nat.testbit',axiom,
    c_24__type__25826___24t(cCoq_2eInit_2eNat_2etestbit) ).

fof('$_typeof_Coq.Init.Nat.zero',axiom,
    cCoq_2eInit_2eDatatypes_2enat___24t(cCoq_2eInit_2eNat_2ezero) ).

fof('$_typeof_Coq.Init.Peano.IsSucc',axiom,
    c_24__type__23699___24t(cCoq_2eInit_2ePeano_2eIsSucc) ).

fof('$_typeof_Coq.Init.Peano.ge',axiom,
    c_24__type__6629___24t(cCoq_2eInit_2ePeano_2ege) ).

fof('$_typeof_Coq.Init.Peano.gt',axiom,
    c_24__type__6629___24t(cCoq_2eInit_2ePeano_2egt) ).

fof('$_typeof_Coq.Init.Peano.lt',axiom,
    c_24__type__6629___24t(cCoq_2eInit_2ePeano_2elt) ).

fof('$_typeof_Coq.Init.Specif.Exc',axiom,
    c_24__type__4777___24t(cCoq_2eInit_2eSpecif_2eExc) ).

fof('$_typeof_Coq.Init.Specif.except',axiom,
    c_24__type__34748___24t(cCoq_2eInit_2eSpecif_2eexcept) ).

fof('$_typeof_Coq.Init.Specif.exist',axiom,
    c_24__type__27790___24t(cCoq_2eInit_2eSpecif_2eexist) ).

fof('$_typeof_Coq.Init.Specif.existT',axiom,
    c_24__type__43866___24t(cCoq_2eInit_2eSpecif_2eexistT) ).

fof('$_typeof_Coq.Init.Specif.left',axiom,
    c_24__type__7171___24t(cCoq_2eInit_2eSpecif_2eleft) ).

fof('$_typeof_Coq.Init.Specif.proj1_sig',axiom,
    c_24__type__27842___24t(cCoq_2eInit_2eSpecif_2eproj1__sig) ).

fof('$_typeof_Coq.Init.Specif.projT1',axiom,
    c_24__type__27866___24t(cCoq_2eInit_2eSpecif_2eprojT1) ).

fof('$_typeof_Coq.Init.Specif.right',axiom,
    c_24__type__7176___24t(cCoq_2eInit_2eSpecif_2eright) ).

fof('$_typeof_Coq.Init.Specif.sig',axiom,
    c_24__type__27772___24t(cCoq_2eInit_2eSpecif_2esig) ).

fof('$_typeof_Coq.Init.Specif.sig2',axiom,
    c_24__type__34675___24t(cCoq_2eInit_2eSpecif_2esig2) ).

fof('$_typeof_Coq.Init.Specif.sigT',axiom,
    c_24__type__27811___24t(cCoq_2eInit_2eSpecif_2esigT) ).

fof('$_typeof_Coq.Init.Specif.sigT2',axiom,
    c_24__type__34731___24t(cCoq_2eInit_2eSpecif_2esigT2) ).

fof('$_typeof_Coq.Init.Specif.sumbool',axiom,
    c_24__type__7148___24t(cCoq_2eInit_2eSpecif_2esumbool) ).

fof('$_typeof_Coq.Init.Specif.sumor',axiom,
    c_24__type__30910___24t(cCoq_2eInit_2eSpecif_2esumor) ).

fof('$_typeof_Coq.Init.Wf.well_founded',axiom,
    c_24__type__44001___24t(cCoq_2eInit_2eWf_2ewell__founded) ).

fof('$_typeof_Coq.Lists.List.In',axiom,
    c_24__type__35579___24t(cCoq_2eLists_2eList_2eIn) ).

fof('$_typeof_Coq.Lists.List.fold_left',axiom,
    c_24__type__35652___24t(cCoq_2eLists_2eList_2efold__left) ).

fof('$_typeof_Coq.Lists.List.fold_right',axiom,
    c_24__type__35681___24t(cCoq_2eLists_2eList_2efold__right) ).

fof('$_typeof_Coq.Lists.List.hd',axiom,
    c_24__type__35567___24t(cCoq_2eLists_2eList_2ehd) ).

fof('$_typeof_Coq.Lists.List.last',axiom,
    c_24__type__35628___24t(cCoq_2eLists_2eList_2elast) ).

fof('$_typeof_Coq.Lists.List.nth',axiom,
    c_24__type__35604___24t(cCoq_2eLists_2eList_2enth) ).

fof('$_typeof_Coq.Lists.SetoidList.transpose',axiom,
    c_24__type__27643___24t(cCoq_2eLists_2eSetoidList_2etranspose) ).

fof('$_typeof_Coq.Lists.SetoidList.transpose2',axiom,
    c_24__type__27643___24t(cCoq_2eLists_2eSetoidList_2etranspose2) ).

fof('$_typeof_Coq.Lists.SetoidList.transpose_restr',axiom,
    c_24__type__34569___24t(cCoq_2eLists_2eSetoidList_2etranspose__restr) ).

fof('$_typeof_Coq.Lists.SetoidList.transpose_restr2',axiom,
    c_24__type__34569___24t(cCoq_2eLists_2eSetoidList_2etranspose__restr2) ).

fof('$_typeof_Coq.Logic.Decidable.decidable',axiom,
    c_24__type__23960___24t(cCoq_2eLogic_2eDecidable_2edecidable) ).

fof('$_typeof_Coq.Logic.EqdepFacts.UIP_on_',axiom,
    c_24__type__35396___24t(cCoq_2eLogic_2eEqdepFacts_2eUIP__on__) ).

fof('$_typeof_Coq.NArith.BinNat.N.divide',axiom,
    c_24__type__29752___24t(cCoq_2eNArith_2eBinNat_2eN_2edivide) ).

fof('$_typeof_Coq.NArith.BinNat.N.eq',axiom,
    c_24__type__29752___24t(cCoq_2eNArith_2eBinNat_2eN_2eeq) ).

fof('$_typeof_Coq.NArith.BinNat.N.eqf',axiom,
    c_24__type__29800___24t(cCoq_2eNArith_2eBinNat_2eN_2eeqf) ).

fof('$_typeof_Coq.NArith.BinNat.N.le',axiom,
    c_24__type__29752___24t(cCoq_2eNArith_2eBinNat_2eN_2ele) ).

fof('$_typeof_Coq.NArith.BinNat.N.lt',axiom,
    c_24__type__29752___24t(cCoq_2eNArith_2eBinNat_2eN_2elt) ).

fof('$_typeof_Coq.NArith.BinNat.N.recursion',axiom,
    c_24__type__44560___24t(cCoq_2eNArith_2eBinNat_2eN_2erecursion) ).

fof('$_typeof_Coq.NArith.BinNatDef.N.add',axiom,
    c_24__type__29683___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eadd) ).

fof('$_typeof_Coq.NArith.BinNatDef.N.div2',axiom,
    c_24__type__29675___24t(cCoq_2eNArith_2eBinNatDef_2eN_2ediv2) ).

fof('$_typeof_Coq.NArith.BinNatDef.N.even',axiom,
    c_24__type__29802___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eeven) ).

fof('$_typeof_Coq.NArith.BinNatDef.N.lxor',axiom,
    c_24__type__29683___24t(cCoq_2eNArith_2eBinNatDef_2eN_2elxor) ).

fof('$_typeof_Coq.NArith.BinNatDef.N.max',axiom,
    c_24__type__29683___24t(cCoq_2eNArith_2eBinNatDef_2eN_2emax) ).

fof('$_typeof_Coq.NArith.BinNatDef.N.min',axiom,
    c_24__type__29683___24t(cCoq_2eNArith_2eBinNatDef_2eN_2emin) ).

fof('$_typeof_Coq.NArith.BinNatDef.N.mul',axiom,
    c_24__type__29683___24t(cCoq_2eNArith_2eBinNatDef_2eN_2emul) ).

fof('$_typeof_Coq.NArith.BinNatDef.N.pred',axiom,
    c_24__type__29675___24t(cCoq_2eNArith_2eBinNatDef_2eN_2epred) ).

fof('$_typeof_Coq.NArith.BinNatDef.N.succ',axiom,
    c_24__type__29675___24t(cCoq_2eNArith_2eBinNatDef_2eN_2esucc) ).

fof('$_typeof_Coq.NArith.BinNatDef.N.t',axiom,
    cType___24t(cCoq_2eNArith_2eBinNatDef_2eN_2et) ).

fof('$_typeof_Coq.NArith.BinNatDef.N.testbit',axiom,
    c_24__type__25840___24t(cCoq_2eNArith_2eBinNatDef_2eN_2etestbit) ).

fof('$_typeof_Coq.NArith.BinNatDef.N.to_nat',axiom,
    c_24__type__35255___24t(cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat) ).

fof('$_typeof_Coq.NArith.BinNatDef.N.zero',axiom,
    cCoq_2eNumbers_2eBinNums_2eN___24t(cCoq_2eNArith_2eBinNatDef_2eN_2ezero) ).

fof('$_typeof_Coq.NArith.Ndigits.eqf',axiom,
    c_24__type__35891___24t(cCoq_2eNArith_2eNdigits_2eeqf) ).

fof('$_typeof_Coq.Numbers.BinNums.N',axiom,
    cType___24t(cCoq_2eNumbers_2eBinNums_2eN) ).

fof('$_typeof_Coq.Numbers.BinNums.N0',axiom,
    cCoq_2eNumbers_2eBinNums_2eN___24t(cCoq_2eNumbers_2eBinNums_2eN0) ).

fof('$_typeof_Coq.Numbers.BinNums.Npos',axiom,
    c_24__type__15822___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__7426___24t(cCoq_2eNumbers_2eBinNums_2eZneg) ).

fof('$_typeof_Coq.Numbers.BinNums.Zpos',axiom,
    c_24__type__7426___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__7408___24t(cCoq_2eNumbers_2eBinNums_2exI) ).

fof('$_typeof_Coq.Numbers.BinNums.xO',axiom,
    c_24__type__7408___24t(cCoq_2eNumbers_2eBinNums_2exO) ).

fof('$_typeof_Coq.PArith.BinPos.Pos.PeanoView',axiom,
    c_24__type__30490___24t(cCoq_2ePArith_2eBinPos_2ePos_2ePeanoView) ).

fof('$_typeof_Coq.PArith.BinPos.Pos.eq',axiom,
    c_24__type__4800___24t(cCoq_2ePArith_2eBinPos_2ePos_2eeq) ).

fof('$_typeof_Coq.PArith.BinPos.Pos.lt',axiom,
    c_24__type__4800___24t(cCoq_2ePArith_2eBinPos_2ePos_2elt) ).

fof('$_typeof_Coq.PArith.BinPos.Pos.switch_Eq',axiom,
    c_24__type__29998___24t(cCoq_2ePArith_2eBinPos_2ePos_2eswitch__Eq) ).

fof('$_typeof_Coq.PArith.BinPosDef.Pos.IsNeg',axiom,
    cCoq_2ePArith_2eBinPosDef_2ePos_2emask___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNeg) ).

fof('$_typeof_Coq.PArith.BinPosDef.Pos.IsNul',axiom,
    cCoq_2ePArith_2eBinPosDef_2ePos_2emask___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eIsNul) ).

fof('$_typeof_Coq.PArith.BinPosDef.Pos.IsPos',axiom,
    c_24__type__44599___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos) ).

fof('$_typeof_Coq.PArith.BinPosDef.Pos.compare',axiom,
    c_24__type__29987___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare) ).

fof('$_typeof_Coq.PArith.BinPosDef.Pos.div2',axiom,
    c_24__type__7408___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2ediv2) ).

fof('$_typeof_Coq.PArith.BinPosDef.Pos.eqb',axiom,
    c_24__type__29990___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb) ).

fof('$_typeof_Coq.PArith.BinPosDef.Pos.iter',axiom,
    c_24__type__35109___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eiter) ).

fof('$_typeof_Coq.PArith.BinPosDef.Pos.iter_op',axiom,
    c_24__type__35124___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eiter__op) ).

fof('$_typeof_Coq.PArith.BinPosDef.Pos.mask',axiom,
    cType___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2emask) ).

fof('$_typeof_Coq.PArith.BinPosDef.Pos.max',axiom,
    c_24__type__7344___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2emax) ).

fof('$_typeof_Coq.PArith.BinPosDef.Pos.min',axiom,
    c_24__type__7344___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2emin) ).

fof('$_typeof_Coq.PArith.BinPosDef.Pos.mul',axiom,
    c_24__type__7344___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2emul) ).

fof('$_typeof_Coq.PArith.BinPosDef.Pos.of_nat',axiom,
    c_24__type__44654___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__nat) ).

fof('$_typeof_Coq.PArith.BinPosDef.Pos.of_succ_nat',axiom,
    c_24__type__44654___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat) ).

fof('$_typeof_Coq.PArith.BinPosDef.Pos.size_nat',axiom,
    c_24__type__29964___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2esize__nat) ).

fof('$_typeof_Coq.PArith.BinPosDef.Pos.sub',axiom,
    c_24__type__7344___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2esub) ).

fof('$_typeof_Coq.PArith.BinPosDef.Pos.succ',axiom,
    c_24__type__7408___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc) ).

fof('$_typeof_Coq.PArith.BinPosDef.Pos.t',axiom,
    cType___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2et) ).

fof('$_typeof_Coq.PArith.BinPosDef.Pos.testbit_nat',axiom,
    c_24__type__44647___24t(cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat) ).

fof('$_typeof_Coq.QArith.QArith_base.Q',axiom,
    cType___24t(cCoq_2eQArith_2eQArith__base_2eQ) ).

fof('$_typeof_Coq.QArith.QArith_base.Qden',axiom,
    c_24__type__9779___24t(cCoq_2eQArith_2eQArith__base_2eQden) ).

fof('$_typeof_Coq.QArith.QArith_base.Qmake',axiom,
    c_24__type__25997___24t(cCoq_2eQArith_2eQArith__base_2eQmake) ).

fof('$_typeof_Coq.QArith.QArith_base.Qnum',axiom,
    c_24__type__9774___24t(cCoq_2eQArith_2eQArith__base_2eQnum) ).

fof('$_typeof_Coq.Reals.RIneq.Rsqr',axiom,
    c_24__type__26014___24t(cCoq_2eReals_2eRIneq_2eRsqr) ).

fof('$_typeof_Coq.Reals.RIneq.negreal',axiom,
    cType___24t(cCoq_2eReals_2eRIneq_2enegreal) ).

fof('$_typeof_Coq.Reals.RIneq.nonnegreal',axiom,
    cType___24t(cCoq_2eReals_2eRIneq_2enonnegreal) ).

fof('$_typeof_Coq.Reals.RIneq.nonposreal',axiom,
    cType___24t(cCoq_2eReals_2eRIneq_2enonposreal) ).

fof('$_typeof_Coq.Reals.RIneq.nonzeroreal',axiom,
    cType___24t(cCoq_2eReals_2eRIneq_2enonzeroreal) ).

fof('$_typeof_Coq.Reals.RIneq.posreal',axiom,
    cType___24t(cCoq_2eReals_2eRIneq_2eposreal) ).

fof('$_typeof_Coq.Reals.Rdefinitions.IZR',axiom,
    c_24__type__26239___24t(cCoq_2eReals_2eRdefinitions_2eIZR) ).

fof('$_typeof_Coq.Reals.Rdefinitions.R',axiom,
    cType___24t(cCoq_2eReals_2eRdefinitions_2eR) ).

fof('$_typeof_Coq.Reals.Rdefinitions.R0',axiom,
    cCoq_2eReals_2eRdefinitions_2eR___24t(cCoq_2eReals_2eRdefinitions_2eR0) ).

fof('$_typeof_Coq.Reals.Rdefinitions.R1',axiom,
    cCoq_2eReals_2eRdefinitions_2eR___24t(cCoq_2eReals_2eRdefinitions_2eR1) ).

fof('$_typeof_Coq.Reals.Rdefinitions.Rge',axiom,
    c_24__type__26231___24t(cCoq_2eReals_2eRdefinitions_2eRge) ).

fof('$_typeof_Coq.Reals.Rdefinitions.Rgt',axiom,
    c_24__type__26231___24t(cCoq_2eReals_2eRdefinitions_2eRgt) ).

fof('$_typeof_Coq.Reals.Rdefinitions.Rinv',axiom,
    c_24__type__26014___24t(cCoq_2eReals_2eRdefinitions_2eRinv) ).

fof('$_typeof_Coq.Reals.Rdefinitions.Rle',axiom,
    c_24__type__26231___24t(cCoq_2eReals_2eRdefinitions_2eRle) ).

fof('$_typeof_Coq.Reals.Rdefinitions.Rlt',axiom,
    c_24__type__26231___24t(cCoq_2eReals_2eRdefinitions_2eRlt) ).

fof('$_typeof_Coq.Reals.Rdefinitions.Rmult',axiom,
    c_24__type__26216___24t(cCoq_2eReals_2eRdefinitions_2eRmult) ).

fof('$_typeof_Coq.Reals.Rdefinitions.Ropp',axiom,
    c_24__type__26014___24t(cCoq_2eReals_2eRdefinitions_2eRopp) ).

fof('$_typeof_Coq.Reals.Rdefinitions.Rplus',axiom,
    c_24__type__26216___24t(cCoq_2eReals_2eRdefinitions_2eRplus) ).

fof('$_typeof_Coq.Reals.Rdefinitions.up',axiom,
    c_24__type__26196___24t(cCoq_2eReals_2eRdefinitions_2eup) ).

fof('$_typeof_Coq.Reals.Rfunctions.Z_spec',axiom,
    c_24__type__32722___24t(cCoq_2eReals_2eRfunctions_2eZ__spec) ).

fof('$_typeof_Coq.Relations.Relation_Definitions.relation',axiom,
    c_24__type__4777___24t(cCoq_2eRelations_2eRelation__Definitions_2erelation) ).

fof('$_typeof_Coq.Setoids.Setoid.Setoid_Theory',axiom,
    c_24__type__7119___24t(cCoq_2eSetoids_2eSetoid_2eSetoid__Theory) ).

fof('$_typeof_Coq.Sets.Relations_1.Relation',axiom,
    c_24__type__4777___24t(cCoq_2eSets_2eRelations__1_2eRelation) ).

fof('$_typeof_Coq.Strings.Ascii.Ascii',axiom,
    c_24__type__35285___24t(cCoq_2eStrings_2eAscii_2eAscii) ).

fof('$_typeof_Coq.Strings.Ascii.ascii',axiom,
    cType___24t(cCoq_2eStrings_2eAscii_2eascii) ).

fof('$_typeof_Coq.Strings.String.EmptyString',axiom,
    cCoq_2eStrings_2eString_2estring___24t(cCoq_2eStrings_2eString_2eEmptyString) ).

fof('$_typeof_Coq.Strings.String.String',axiom,
    c_24__type__27970___24t(cCoq_2eStrings_2eString_2eString) ).

fof('$_typeof_Coq.Strings.String.string',axiom,
    cType___24t(cCoq_2eStrings_2eString_2estring) ).

fof('$_typeof_Coq.Structures.GenericMinMax.gmax',axiom,
    c_24__type__35458___24t(cCoq_2eStructures_2eGenericMinMax_2egmax) ).

fof('$_typeof_Coq.Structures.GenericMinMax.gmin',axiom,
    c_24__type__35458___24t(cCoq_2eStructures_2eGenericMinMax_2egmin) ).

fof('$_typeof_Coq.Structures.OrderedType.Compare',axiom,
    c_24__type__32555___24t(cCoq_2eStructures_2eOrderedType_2eCompare) ).

fof('$_typeof_Coq.Structures.OrderedTypeEx.N_as_OT.eq',axiom,
    c_24__type__29752___24t(cCoq_2eStructures_2eOrderedTypeEx_2eN__as__OT_2eeq) ).

fof('$_typeof_Coq.Structures.OrderedTypeEx.N_as_OT.lt',axiom,
    c_24__type__29752___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__6629___24t(cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2eeq) ).

fof('$_typeof_Coq.Structures.OrderedTypeEx.Nat_as_OT.lt',axiom,
    c_24__type__6629___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__4800___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt) ).

fof('$_typeof_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.eq',axiom,
    c_24__type__4800___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2eeq) ).

fof('$_typeof_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.lt',axiom,
    c_24__type__4800___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2elt) ).

fof('$_typeof_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.t',axiom,
    cType___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2et) ).

fof('$_typeof_Coq.Structures.OrderedTypeEx.Positive_as_OT.eq',axiom,
    c_24__type__4800___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositive__as__OT_2eeq) ).

fof('$_typeof_Coq.Structures.OrderedTypeEx.Positive_as_OT.lt',axiom,
    c_24__type__4800___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositive__as__OT_2elt) ).

fof('$_typeof_Coq.Structures.OrderedTypeEx.Positive_as_OT.t',axiom,
    cType___24t(cCoq_2eStructures_2eOrderedTypeEx_2ePositive__as__OT_2et) ).

fof('$_typeof_Coq.Structures.OrderedTypeEx.String_as_OT.lt',axiom,
    c_24__type__44753___24t(cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2elt) ).

fof('$_typeof_Coq.Structures.OrderedTypeEx.String_as_OT.t',axiom,
    cType___24t(cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2et) ).

fof('$_typeof_Coq.Structures.OrderedTypeEx.Z_as_OT.eq',axiom,
    c_24__type__7406___24t(cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2eeq) ).

fof('$_typeof_Coq.Structures.OrderedTypeEx.Z_as_OT.lt',axiom,
    c_24__type__7406___24t(cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2elt) ).

fof('$_typeof_Coq.Structures.OrderedTypeEx.Z_as_OT.t',axiom,
    cType___24t(cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2et) ).

fof('$_typeof_Coq.Structures.OrdersTac.OEQ',axiom,
    cCoq_2eStructures_2eOrdersTac_2eord___24t(cCoq_2eStructures_2eOrdersTac_2eOEQ) ).

fof('$_typeof_Coq.Structures.OrdersTac.OLE',axiom,
    cCoq_2eStructures_2eOrdersTac_2eord___24t(cCoq_2eStructures_2eOrdersTac_2eOLE) ).

fof('$_typeof_Coq.Structures.OrdersTac.OLT',axiom,
    cCoq_2eStructures_2eOrdersTac_2eord___24t(cCoq_2eStructures_2eOrdersTac_2eOLT) ).

fof('$_typeof_Coq.Structures.OrdersTac.ord',axiom,
    cType___24t(cCoq_2eStructures_2eOrdersTac_2eord) ).

fof('$_typeof_Coq.Vectors.Fin.t',axiom,
    c_24__type__15824___24t(cCoq_2eVectors_2eFin_2et) ).

fof('$_typeof_Coq.Vectors.VectorDef.t',axiom,
    c_24__type__28937___24t(cCoq_2eVectors_2eVectorDef_2et) ).

fof('$_typeof_Coq.ZArith.BinInt.Z.Private_Div.Quot2Div.div',axiom,
    c_24__type__7396___24t(cCoq_2eZArith_2eBinInt_2eZ_2ePrivate__Div_2eQuot2Div_2ediv) ).

fof('$_typeof_Coq.ZArith.BinInt.Z.Private_Div.Quot2Div.modulo',axiom,
    c_24__type__7396___24t(cCoq_2eZArith_2eBinInt_2eZ_2ePrivate__Div_2eQuot2Div_2emodulo) ).

fof('$_typeof_Coq.ZArith.BinInt.Z.divide',axiom,
    c_24__type__7406___24t(cCoq_2eZArith_2eBinInt_2eZ_2edivide) ).

fof('$_typeof_Coq.ZArith.BinInt.Z.eq',axiom,
    c_24__type__7406___24t(cCoq_2eZArith_2eBinInt_2eZ_2eeq) ).

fof('$_typeof_Coq.ZArith.BinInt.Z.eqf',axiom,
    c_24__type__45037___24t(cCoq_2eZArith_2eBinInt_2eZ_2eeqf) ).

fof('$_typeof_Coq.ZArith.BinInt.Z.gt',axiom,
    c_24__type__7406___24t(cCoq_2eZArith_2eBinInt_2eZ_2egt) ).

fof('$_typeof_Coq.ZArith.BinInt.Z.le',axiom,
    c_24__type__7406___24t(cCoq_2eZArith_2eBinInt_2eZ_2ele) ).

fof('$_typeof_Coq.ZArith.BinInt.Z.lt',axiom,
    c_24__type__7406___24t(cCoq_2eZArith_2eBinInt_2eZ_2elt) ).

fof('$_typeof_Coq.ZArith.BinInt.Zne',axiom,
    c_24__type__7406___24t(cCoq_2eZArith_2eBinInt_2eZne) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.abs',axiom,
    c_24__type__7398___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eabs) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.abs_N',axiom,
    c_24__type__45004___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__N) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.abs_nat',axiom,
    c_24__type__45000___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__nat) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.add',axiom,
    c_24__type__7396___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.compare',axiom,
    c_24__type__30586___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.div',axiom,
    c_24__type__7396___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2ediv) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.even',axiom,
    c_24__type__30716___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eeven) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.max',axiom,
    c_24__type__7396___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emax) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.min',axiom,
    c_24__type__7396___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emin) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.modulo',axiom,
    c_24__type__7396___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.mul',axiom,
    c_24__type__7396___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2emul) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.odd',axiom,
    c_24__type__30716___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eodd) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.of_N',axiom,
    c_24__type__30593___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.opp',axiom,
    c_24__type__7398___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eopp) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.pow',axiom,
    c_24__type__7396___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2epow) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.pred',axiom,
    c_24__type__7398___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2epred) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.sub',axiom,
    c_24__type__7396___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2esub) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.succ',axiom,
    c_24__type__7398___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2esucc) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.t',axiom,
    cType___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2et) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.to_N',axiom,
    c_24__type__45004___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eto__N) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.to_nat',axiom,
    c_24__type__45000___24t(cCoq_2eZArith_2eBinIntDef_2eZ_2eto__nat) ).

fof('$_typeof_Coq.ZArith.BinIntDef.Z.to_pos',axiom,
    c_24__type__30597___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__29147___24t(cCoq_2eZArith_2eZbool_2eZeq__bool) ).

fof('$_typeof_Coq.ZArith.Zeven.Zeven',axiom,
    c_24__type__7401___24t(cCoq_2eZArith_2eZeven_2eZeven) ).

fof('$_typeof_Coq.ZArith.Zeven.Zodd',axiom,
    c_24__type__7401___24t(cCoq_2eZArith_2eZeven_2eZodd) ).

fof('$_typeof_Coq.ZArith.Zlogarithm.Is_power',axiom,
    c_24__type__4802___24t(cCoq_2eZArith_2eZlogarithm_2eIs__power) ).

fof('$_typeof_Coq.ZArith.Zlogarithm.log_inf',axiom,
    c_24__type__7426___24t(cCoq_2eZArith_2eZlogarithm_2elog__inf) ).

fof('$_typeof_Coq.ZArith.Znumtheory.Euclid',axiom,
    c_24__type__32722___24t(cCoq_2eZArith_2eZnumtheory_2eEuclid) ).

fof('$_typeof_Coq.ZArith.Zpower.Zdiv_rest_proofs',axiom,
    c_24__type__34872___24t(cCoq_2eZArith_2eZpower_2eZdiv__rest__proofs) ).

fof('$_typeof_Coq.micromega.Env.Env',axiom,
    c_24__type__4777___24t(cCoq_2emicromega_2eEnv_2eEnv) ).

fof('$_typeof_Coq.micromega.EnvRing.Mon',axiom,
    cType___24t(cCoq_2emicromega_2eEnvRing_2eMon) ).

fof('$_typeof_Coq.micromega.EnvRing.PEX',axiom,
    c_24__type__35367___24t(cCoq_2emicromega_2eEnvRing_2ePEX) ).

fof('$_typeof_Coq.micromega.EnvRing.PEc',axiom,
    c_24__type__35364___24t(cCoq_2emicromega_2eEnvRing_2ePEc) ).

fof('$_typeof_Coq.micromega.EnvRing.PExpr',axiom,
    c_24__type__4777___24t(cCoq_2emicromega_2eEnvRing_2ePExpr) ).

fof('$_typeof_Coq.micromega.EnvRing.PX',axiom,
    c_24__type__35383___24t(cCoq_2emicromega_2eEnvRing_2ePX) ).

fof('$_typeof_Coq.micromega.EnvRing.Pc',axiom,
    c_24__type__35370___24t(cCoq_2emicromega_2eEnvRing_2ePc) ).

fof('$_typeof_Coq.micromega.EnvRing.Pinj',axiom,
    c_24__type__35375___24t(cCoq_2emicromega_2eEnvRing_2ePinj) ).

fof('$_typeof_Coq.micromega.EnvRing.Pol',axiom,
    c_24__type__4777___24t(cCoq_2emicromega_2eEnvRing_2ePol) ).

fof('$_typeof_Coq.micromega.EnvRing.mon0',axiom,
    cCoq_2emicromega_2eEnvRing_2eMon___24t(cCoq_2emicromega_2eEnvRing_2emon0) ).

fof('$_typeof_Coq.micromega.EnvRing.vmon',axiom,
    c_24__type__35386___24t(cCoq_2emicromega_2eEnvRing_2evmon) ).

fof('$_typeof_Coq.micromega.EnvRing.zmon',axiom,
    c_24__type__35386___24t(cCoq_2emicromega_2eEnvRing_2ezmon) ).

fof('$_typeof_Coq.micromega.RMicromega.C0',axiom,
    cCoq_2emicromega_2eRMicromega_2eRcst___24t(cCoq_2emicromega_2eRMicromega_2eC0) ).

fof('$_typeof_Coq.micromega.RMicromega.C1',axiom,
    cCoq_2emicromega_2eRMicromega_2eRcst___24t(cCoq_2emicromega_2eRMicromega_2eC1) ).

fof('$_typeof_Coq.micromega.RMicromega.CInv',axiom,
    c_24__type__36443___24t(cCoq_2emicromega_2eRMicromega_2eCInv) ).

fof('$_typeof_Coq.micromega.RMicromega.CMinus',axiom,
    c_24__type__36439___24t(cCoq_2emicromega_2eRMicromega_2eCMinus) ).

fof('$_typeof_Coq.micromega.RMicromega.CMult',axiom,
    c_24__type__36439___24t(cCoq_2emicromega_2eRMicromega_2eCMult) ).

fof('$_typeof_Coq.micromega.RMicromega.COpp',axiom,
    c_24__type__36443___24t(cCoq_2emicromega_2eRMicromega_2eCOpp) ).

fof('$_typeof_Coq.micromega.RMicromega.CPlus',axiom,
    c_24__type__36439___24t(cCoq_2emicromega_2eRMicromega_2eCPlus) ).

fof('$_typeof_Coq.micromega.RMicromega.CQ',axiom,
    c_24__type__36436___24t(cCoq_2emicromega_2eRMicromega_2eCQ) ).

fof('$_typeof_Coq.micromega.RMicromega.CZ',axiom,
    c_24__type__26173___24t(cCoq_2emicromega_2eRMicromega_2eCZ) ).

fof('$_typeof_Coq.micromega.RMicromega.Rcst',axiom,
    cType___24t(cCoq_2emicromega_2eRMicromega_2eRcst) ).

fof('$_typeof_Coq.micromega.Refl.make_conj',axiom,
    c_24__type__36487___24t(cCoq_2emicromega_2eRefl_2emake__conj) ).

fof('$_typeof_Coq.micromega.Refl.make_impl',axiom,
    c_24__type__36461___24t(cCoq_2emicromega_2eRefl_2emake__impl) ).

fof('$_typeof_Coq.micromega.RingMicromega.Equal',axiom,
    cCoq_2emicromega_2eRingMicromega_2eOp1___24t(cCoq_2emicromega_2eRingMicromega_2eEqual) ).

fof('$_typeof_Coq.micromega.RingMicromega.Formula',axiom,
    c_24__type__4777___24t(cCoq_2emicromega_2eRingMicromega_2eFormula) ).

fof('$_typeof_Coq.micromega.RingMicromega.NonEqual',axiom,
    cCoq_2emicromega_2eRingMicromega_2eOp1___24t(cCoq_2emicromega_2eRingMicromega_2eNonEqual) ).

fof('$_typeof_Coq.micromega.RingMicromega.NonStrict',axiom,
    cCoq_2emicromega_2eRingMicromega_2eOp1___24t(cCoq_2emicromega_2eRingMicromega_2eNonStrict) ).

fof('$_typeof_Coq.micromega.RingMicromega.Op1',axiom,
    cType___24t(cCoq_2emicromega_2eRingMicromega_2eOp1) ).

fof('$_typeof_Coq.micromega.RingMicromega.Op2',axiom,
    cType___24t(cCoq_2emicromega_2eRingMicromega_2eOp2) ).

fof('$_typeof_Coq.micromega.RingMicromega.OpEq',axiom,
    cCoq_2emicromega_2eRingMicromega_2eOp2___24t(cCoq_2emicromega_2eRingMicromega_2eOpEq) ).

fof('$_typeof_Coq.micromega.RingMicromega.OpGe',axiom,
    cCoq_2emicromega_2eRingMicromega_2eOp2___24t(cCoq_2emicromega_2eRingMicromega_2eOpGe) ).

fof('$_typeof_Coq.micromega.RingMicromega.OpGt',axiom,
    cCoq_2emicromega_2eRingMicromega_2eOp2___24t(cCoq_2emicromega_2eRingMicromega_2eOpGt) ).

fof('$_typeof_Coq.micromega.RingMicromega.OpLe',axiom,
    cCoq_2emicromega_2eRingMicromega_2eOp2___24t(cCoq_2emicromega_2eRingMicromega_2eOpLe) ).

fof('$_typeof_Coq.micromega.RingMicromega.OpLt',axiom,
    cCoq_2emicromega_2eRingMicromega_2eOp2___24t(cCoq_2emicromega_2eRingMicromega_2eOpLt) ).

fof('$_typeof_Coq.micromega.RingMicromega.OpNEq',axiom,
    cCoq_2emicromega_2eRingMicromega_2eOp2___24t(cCoq_2emicromega_2eRingMicromega_2eOpNEq) ).

fof('$_typeof_Coq.micromega.RingMicromega.PolC',axiom,
    c_24__type__4777___24t(cCoq_2emicromega_2eRingMicromega_2ePolC) ).

fof('$_typeof_Coq.micromega.RingMicromega.PolEnv',axiom,
    c_24__type__4777___24t(cCoq_2emicromega_2eRingMicromega_2ePolEnv) ).

fof('$_typeof_Coq.micromega.RingMicromega.Psatz',axiom,
    c_24__type__4777___24t(cCoq_2emicromega_2eRingMicromega_2ePsatz) ).

fof('$_typeof_Coq.micromega.RingMicromega.Strict',axiom,
    cCoq_2emicromega_2eRingMicromega_2eOp1___24t(cCoq_2emicromega_2eRingMicromega_2eStrict) ).

fof('$_typeof_Coq.micromega.RingMicromega.eval_op1',axiom,
    c_24__type__42341___24t(cCoq_2emicromega_2eRingMicromega_2eeval__op1) ).

fof('$_typeof_Coq.micromega.RingMicromega.ge_bool',axiom,
    c_24__type__25826___24t(cCoq_2emicromega_2eRingMicromega_2ege__bool) ).

fof('$_typeof_Coq.micromega.Tauto.A',axiom,
    c_24__type__43910___24t(cCoq_2emicromega_2eTauto_2eA) ).

fof('$_typeof_Coq.micromega.Tauto.FF',axiom,
    c_24__type__43875___24t(cCoq_2emicromega_2eTauto_2eFF) ).

fof('$_typeof_Coq.micromega.Tauto.GFormula',axiom,
    c_24__type__28026___24t(cCoq_2emicromega_2eTauto_2eGFormula) ).

fof('$_typeof_Coq.micromega.Tauto.TFormula',axiom,
    c_24__type__28026___24t(cCoq_2emicromega_2eTauto_2eTFormula) ).

fof('$_typeof_Coq.micromega.Tauto.TT',axiom,
    c_24__type__43875___24t(cCoq_2emicromega_2eTauto_2eTT) ).

fof('$_typeof_Coq.micromega.Tauto.X',axiom,
    c_24__type__43893___24t(cCoq_2emicromega_2eTauto_2eX) ).

fof('$_typeof_Coq.micromega.Tauto.clause',axiom,
    c_24__type__7450___24t(cCoq_2emicromega_2eTauto_2eclause) ).

fof('$_typeof_Coq.micromega.VarMap.t',axiom,
    c_24__type__4777___24t(cCoq_2emicromega_2eVarMap_2et) ).

fof('$_typeof_Coq.micromega.ZMicromega.DoneProof',axiom,
    cCoq_2emicromega_2eZMicromega_2eZArithProof___24t(cCoq_2emicromega_2eZMicromega_2eDoneProof) ).

fof('$_typeof_Coq.micromega.ZMicromega.Vars.Facts.Add',axiom,
    c_24__type__29560___24t(cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eAdd) ).

fof('$_typeof_Coq.micromega.ZMicromega.ZArithProof',axiom,
    cType___24t(cCoq_2emicromega_2eZMicromega_2eZArithProof) ).

fof('$_typeof_Coq.micromega.ZMicromega.ZWitness',axiom,
    cType___24t(cCoq_2emicromega_2eZMicromega_2eZWitness) ).

fof('$_typeof_Coq.micromega.ZMicromega.coneMember',axiom,
    cType___24t(cCoq_2emicromega_2eZMicromega_2econeMember) ).

fof('$_typeof_Coq.omega.PreOmega.Z_of_N\'',axiom,
    c_24__type__30593___24t(cCoq_2eomega_2ePreOmega_2eZ__of__N_27) ).

fof('$_typeof_Coq.omega.PreOmega.Z_of_nat\'',axiom,
    c_24__type__29192___24t(cCoq_2eomega_2ePreOmega_2eZ__of__nat_27) ).

fof('$_typeof_Coq.omega.PreOmega.Zneg\'',axiom,
    c_24__type__7426___24t(cCoq_2eomega_2ePreOmega_2eZneg_27) ).

fof('$_typeof_Coq.omega.PreOmega.Zpos\'',axiom,
    c_24__type__7426___24t(cCoq_2eomega_2ePreOmega_2eZpos_27) ).

fof('$_typeof_Coq.setoid_ring.ArithRing.protected_to_nat',axiom,
    c_24__type__35255___24t(cCoq_2esetoid__ring_2eArithRing_2eprotected__to__nat) ).

fof('$_typeof_Coq.setoid_ring.Field_theory.FEX',axiom,
    c_24__type__35402___24t(cCoq_2esetoid__ring_2eField__theory_2eFEX) ).

fof('$_typeof_Coq.setoid_ring.Field_theory.FEc',axiom,
    c_24__type__35399___24t(cCoq_2esetoid__ring_2eField__theory_2eFEc) ).

fof('$_typeof_Coq.setoid_ring.Field_theory.FEinv',axiom,
    c_24__type__35410___24t(cCoq_2esetoid__ring_2eField__theory_2eFEinv) ).

fof('$_typeof_Coq.setoid_ring.Field_theory.FEmul',axiom,
    c_24__type__35407___24t(cCoq_2esetoid__ring_2eField__theory_2eFEmul) ).

fof('$_typeof_Coq.setoid_ring.Field_theory.FExpr',axiom,
    c_24__type__4777___24t(cCoq_2esetoid__ring_2eField__theory_2eFExpr) ).

fof('$_typeof_Coq.setoid_ring.Field_theory.linear',axiom,
    c_24__type__4777___24t(cCoq_2esetoid__ring_2eField__theory_2elinear) ).

fof('$_typeof_Coq.setoid_ring.Field_theory.rsplit',axiom,
    c_24__type__4777___24t(cCoq_2esetoid__ring_2eField__theory_2ersplit) ).

fof('$_typeof_Coq.setoid_ring.InitialRing.Nopp',axiom,
    c_24__type__29675___24t(cCoq_2esetoid__ring_2eInitialRing_2eNopp) ).

fof('$_typeof_Coq.setoid_ring.InitialRing.NotConstant',axiom,
    cCoq_2eInit_2eDatatypes_2ebool___24t(cCoq_2esetoid__ring_2eInitialRing_2eNotConstant) ).

fof('$_typeof_Coq.setoid_ring.InitialRing.Nword',axiom,
    cType___24t(cCoq_2esetoid__ring_2eInitialRing_2eNword) ).

fof('$_typeof_Coq.setoid_ring.InitialRing.gen_phiPOS',axiom,
    c_24__type__32380___24t(cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS) ).

fof('$_typeof_Coq.setoid_ring.InitialRing.gen_phiPOS1',axiom,
    c_24__type__32380___24t(cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1) ).

fof('$_typeof_Coq.setoid_ring.InitialRing.hypo',axiom,
    cType___24t(cCoq_2esetoid__ring_2eInitialRing_2ehypo) ).

fof('$_typeof_Coq.setoid_ring.InitialRing.mkhypo',axiom,
    c_24__type__35556___24t(cCoq_2esetoid__ring_2eInitialRing_2emkhypo) ).

fof('$_typeof_Coq.setoid_ring.Ring_polynom.Mon',axiom,
    cType___24t(cCoq_2esetoid__ring_2eRing__polynom_2eMon) ).

fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEI',axiom,
    c_24__type__42379___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEI) ).

fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEO',axiom,
    c_24__type__42379___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEO) ).

fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEX',axiom,
    c_24__type__27362___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEX) ).

fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEadd',axiom,
    c_24__type__10078___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEadd) ).

fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEc',axiom,
    c_24__type__27359___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEc) ).

fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEmul',axiom,
    c_24__type__10078___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEmul) ).

fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEopp',axiom,
    c_24__type__27368___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEopp) ).

fof('$_typeof_Coq.setoid_ring.Ring_polynom.PEsub',axiom,
    c_24__type__10078___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePEsub) ).

fof('$_typeof_Coq.setoid_ring.Ring_polynom.PExpr',axiom,
    c_24__type__4777___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr) ).

fof('$_typeof_Coq.setoid_ring.Ring_polynom.PX',axiom,
    c_24__type__42373___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePX) ).

fof('$_typeof_Coq.setoid_ring.Ring_polynom.Pc',axiom,
    c_24__type__42360___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePc) ).

fof('$_typeof_Coq.setoid_ring.Ring_polynom.Peq',axiom,
    c_24__type__27353___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePeq) ).

fof('$_typeof_Coq.setoid_ring.Ring_polynom.Pinj',axiom,
    c_24__type__42365___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePinj) ).

fof('$_typeof_Coq.setoid_ring.Ring_polynom.Pol',axiom,
    c_24__type__4777___24t(cCoq_2esetoid__ring_2eRing__polynom_2ePol) ).

fof('$_typeof_Coq.setoid_ring.Ring_polynom.mkmult_pow',axiom,
    c_24__type__32773___24t(cCoq_2esetoid__ring_2eRing__polynom_2emkmult__pow) ).

fof('$_typeof_Coq.setoid_ring.Ring_polynom.mon0',axiom,
    cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(cCoq_2esetoid__ring_2eRing__polynom_2emon0) ).

fof('$_typeof_Coq.setoid_ring.Ring_polynom.vmon',axiom,
    c_24__type__42376___24t(cCoq_2esetoid__ring_2eRing__polynom_2evmon) ).

fof('$_typeof_Coq.setoid_ring.Ring_polynom.zmon',axiom,
    c_24__type__42376___24t(cCoq_2esetoid__ring_2eRing__polynom_2ezmon) ).

fof('$_typeof_Coq.setoid_ring.Ring_tac.ring_subst_niter',axiom,
    cCoq_2eInit_2eDatatypes_2enat___24t(cCoq_2esetoid__ring_2eRing__tac_2ering__subst__niter) ).

fof('$_typeof_Coq.setoid_ring.Ring_theory.Abstract',axiom,
    cCoq_2esetoid__ring_2eRing__theory_2ering__kind___24t(cCoq_2esetoid__ring_2eRing__theory_2eAbstract) ).

fof('$_typeof_Coq.setoid_ring.Ring_theory.IDphi',axiom,
    c_24__type__34284___24t(cCoq_2esetoid__ring_2eRing__theory_2eIDphi) ).

fof('$_typeof_Coq.setoid_ring.Ring_theory.SRopp',axiom,
    c_24__type__34284___24t(cCoq_2esetoid__ring_2eRing__theory_2eSRopp) ).

fof('$_typeof_Coq.setoid_ring.Ring_theory.SRsub',axiom,
    c_24__type__42472___24t(cCoq_2esetoid__ring_2eRing__theory_2eSRsub) ).

fof('$_typeof_Coq.setoid_ring.Ring_theory.id_phi_N',axiom,
    c_24__type__29675___24t(cCoq_2esetoid__ring_2eRing__theory_2eid__phi__N) ).

fof('$_typeof_Coq.setoid_ring.Ring_theory.pow_N',axiom,
    c_24__type__11447___24t(cCoq_2esetoid__ring_2eRing__theory_2epow__N) ).

fof('$_typeof_Coq.setoid_ring.Ring_theory.pow_pos',axiom,
    c_24__type__32794___24t(cCoq_2esetoid__ring_2eRing__theory_2epow__pos) ).

fof('$_typeof_Coq.setoid_ring.Ring_theory.ring_kind',axiom,
    cType___24t(cCoq_2esetoid__ring_2eRing__theory_2ering__kind) ).

fof('$_typeof_Hammer.Tactics.Reconstr.AllHyps',axiom,
    cHammer_2eTactics_2eReconstr_2eReconstrT___24t(cHammer_2eTactics_2eReconstr_2eAllHyps) ).

fof('$_typeof_Hammer.Tactics.Reconstr.Empty',axiom,
    cHammer_2eTactics_2eReconstr_2eReconstrT___24t(cHammer_2eTactics_2eReconstr_2eEmpty) ).

fof('$_typeof_Hammer.Tactics.Reconstr.ReconstrT',axiom,
    cType___24t(cHammer_2eTactics_2eReconstr_2eReconstrT) ).

fof('$_typeof_Hammer.Tactics.Reconstr.rdone',axiom,
    c_24__type__32665___24t(cHammer_2eTactics_2eReconstr_2erdone) ).

fof('$_typeof_Hammer.Tactics.Tactics.rdone',axiom,
    c_24__type__32665___24t(cHammer_2eTactics_2eTactics_2erdone) ).

fof('$_typeof_Norm.Arrow',axiom,
    c_24__type__45900___24t(cNorm_2eArrow) ).

fof('$_typeof_Norm.Bool',axiom,
    cNorm_2ety___24t(cNorm_2eBool) ).

fof('$_typeof_Norm.Prod',axiom,
    c_24__type__45900___24t(cNorm_2eProd) ).

fof('$_typeof_Norm.abs',axiom,
    c_24__type__4730___24t(cNorm_2eabs) ).

fof('$_typeof_Norm.app',axiom,
    c_24__type__4725___24t(cNorm_2eapp) ).

fof('$_typeof_Norm.fls',axiom,
    cNorm_2etm___24t(cNorm_2efls) ).

fof('$_typeof_Norm.fst',axiom,
    c_24__type__4733___24t(cNorm_2efst) ).

fof('$_typeof_Norm.pair',axiom,
    c_24__type__4725___24t(cNorm_2epair) ).

fof('$_typeof_Norm.snd',axiom,
    c_24__type__4733___24t(cNorm_2esnd) ).

fof('$_typeof_Norm.subst',axiom,
    c_24__type__4578___24t(cNorm_2esubst) ).

fof('$_typeof_Norm.test',axiom,
    c_24__type__5479___24t(cNorm_2etest) ).

fof('$_typeof_Norm.tm',axiom,
    cType___24t(cNorm_2etm) ).

fof('$_typeof_Norm.tru',axiom,
    cNorm_2etm___24t(cNorm_2etru) ).

fof('$_typeof_Norm.ty',axiom,
    cType___24t(cNorm_2ety) ).

fof('$_typeof_Norm.var',axiom,
    c_24__type__5474___24t(cNorm_2evar) ).

fof('$_typeof_PLF.Imp.AExp.AMinus',axiom,
    c_24__type__29240___24t(cPLF_2eImp_2eAExp_2eAMinus) ).

fof('$_typeof_PLF.Imp.AExp.AMult',axiom,
    c_24__type__29240___24t(cPLF_2eImp_2eAExp_2eAMult) ).

fof('$_typeof_PLF.Imp.AExp.ANum',axiom,
    c_24__type__29237___24t(cPLF_2eImp_2eAExp_2eANum) ).

fof('$_typeof_PLF.Imp.AExp.APlus',axiom,
    c_24__type__29240___24t(cPLF_2eImp_2eAExp_2eAPlus) ).

fof('$_typeof_PLF.Imp.AExp.BAnd',axiom,
    c_24__type__44101___24t(cPLF_2eImp_2eAExp_2eBAnd) ).

fof('$_typeof_PLF.Imp.AExp.BFalse',axiom,
    cPLF_2eImp_2eAExp_2ebexp___24t(cPLF_2eImp_2eAExp_2eBFalse) ).

fof('$_typeof_PLF.Imp.AExp.BNot',axiom,
    c_24__type__44098___24t(cPLF_2eImp_2eAExp_2eBNot) ).

fof('$_typeof_PLF.Imp.AExp.BTrue',axiom,
    cPLF_2eImp_2eAExp_2ebexp___24t(cPLF_2eImp_2eAExp_2eBTrue) ).

fof('$_typeof_PLF.Imp.AExp.aexp',axiom,
    cType___24t(cPLF_2eImp_2eAExp_2eaexp) ).

fof('$_typeof_PLF.Imp.AExp.bexp',axiom,
    cType___24t(cPLF_2eImp_2eAExp_2ebexp) ).

fof('$_typeof_PLF.Imp.AExp.optimize_0plus_b',axiom,
    c_24__type__44098___24t(cPLF_2eImp_2eAExp_2eoptimize__0plus__b) ).

fof('$_typeof_PLF.Imp.AId',axiom,
    c_24__type__35475___24t(cPLF_2eImp_2eAId) ).

fof('$_typeof_PLF.Imp.AMinus',axiom,
    c_24__type__25493___24t(cPLF_2eImp_2eAMinus) ).

fof('$_typeof_PLF.Imp.AMult',axiom,
    c_24__type__25493___24t(cPLF_2eImp_2eAMult) ).

fof('$_typeof_PLF.Imp.ANum',axiom,
    c_24__type__25490___24t(cPLF_2eImp_2eANum) ).

fof('$_typeof_PLF.Imp.APlus',axiom,
    c_24__type__25493___24t(cPLF_2eImp_2eAPlus) ).

fof('$_typeof_PLF.Imp.BAnd',axiom,
    c_24__type__35486___24t(cPLF_2eImp_2eBAnd) ).

fof('$_typeof_PLF.Imp.BEq',axiom,
    c_24__type__35480___24t(cPLF_2eImp_2eBEq) ).

fof('$_typeof_PLF.Imp.BFalse',axiom,
    cPLF_2eImp_2ebexp___24t(cPLF_2eImp_2eBFalse) ).

fof('$_typeof_PLF.Imp.BLe',axiom,
    c_24__type__35480___24t(cPLF_2eImp_2eBLe) ).

fof('$_typeof_PLF.Imp.BNot',axiom,
    c_24__type__35483___24t(cPLF_2eImp_2eBNot) ).

fof('$_typeof_PLF.Imp.BTrue',axiom,
    cPLF_2eImp_2ebexp___24t(cPLF_2eImp_2eBTrue) ).

fof('$_typeof_PLF.Imp.BreakImp.CBreak',axiom,
    cPLF_2eImp_2eBreakImp_2ecom___24t(cPLF_2eImp_2eBreakImp_2eCBreak) ).

fof('$_typeof_PLF.Imp.BreakImp.CSeq',axiom,
    c_24__type__44412___24t(cPLF_2eImp_2eBreakImp_2eCSeq) ).

fof('$_typeof_PLF.Imp.BreakImp.CSkip',axiom,
    cPLF_2eImp_2eBreakImp_2ecom___24t(cPLF_2eImp_2eBreakImp_2eCSkip) ).

fof('$_typeof_PLF.Imp.BreakImp.SBreak',axiom,
    cPLF_2eImp_2eBreakImp_2eresult___24t(cPLF_2eImp_2eBreakImp_2eSBreak) ).

fof('$_typeof_PLF.Imp.BreakImp.SContinue',axiom,
    cPLF_2eImp_2eBreakImp_2eresult___24t(cPLF_2eImp_2eBreakImp_2eSContinue) ).

fof('$_typeof_PLF.Imp.BreakImp.com',axiom,
    cType___24t(cPLF_2eImp_2eBreakImp_2ecom) ).

fof('$_typeof_PLF.Imp.BreakImp.result',axiom,
    cType___24t(cPLF_2eImp_2eBreakImp_2eresult) ).

fof('$_typeof_PLF.Imp.CSeq',axiom,
    c_24__type__35489___24t(cPLF_2eImp_2eCSeq) ).

fof('$_typeof_PLF.Imp.CSkip',axiom,
    cPLF_2eImp_2ecom___24t(cPLF_2eImp_2eCSkip) ).

fof('$_typeof_PLF.Imp.SLoad',axiom,
    c_24__type__35552___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__35550___24t(cPLF_2eImp_2eSPush) ).

fof('$_typeof_PLF.Imp.aevalR_division.ADiv',axiom,
    c_24__type__30796___24t(cPLF_2eImp_2eaevalR__division_2eADiv) ).

fof('$_typeof_PLF.Imp.aevalR_division.AMinus',axiom,
    c_24__type__30796___24t(cPLF_2eImp_2eaevalR__division_2eAMinus) ).

fof('$_typeof_PLF.Imp.aevalR_division.AMult',axiom,
    c_24__type__30796___24t(cPLF_2eImp_2eaevalR__division_2eAMult) ).

fof('$_typeof_PLF.Imp.aevalR_division.ANum',axiom,
    c_24__type__45041___24t(cPLF_2eImp_2eaevalR__division_2eANum) ).

fof('$_typeof_PLF.Imp.aevalR_division.APlus',axiom,
    c_24__type__30796___24t(cPLF_2eImp_2eaevalR__division_2eAPlus) ).

fof('$_typeof_PLF.Imp.aevalR_division.aexp',axiom,
    cType___24t(cPLF_2eImp_2eaevalR__division_2eaexp) ).

fof('$_typeof_PLF.Imp.aevalR_extended.AAny',axiom,
    cPLF_2eImp_2eaevalR__extended_2eaexp___24t(cPLF_2eImp_2eaevalR__extended_2eAAny) ).

fof('$_typeof_PLF.Imp.aevalR_extended.AMinus',axiom,
    c_24__type__45363___24t(cPLF_2eImp_2eaevalR__extended_2eAMinus) ).

fof('$_typeof_PLF.Imp.aevalR_extended.AMult',axiom,
    c_24__type__45363___24t(cPLF_2eImp_2eaevalR__extended_2eAMult) ).

fof('$_typeof_PLF.Imp.aevalR_extended.ANum',axiom,
    c_24__type__45360___24t(cPLF_2eImp_2eaevalR__extended_2eANum) ).

fof('$_typeof_PLF.Imp.aevalR_extended.APlus',axiom,
    c_24__type__45363___24t(cPLF_2eImp_2eaevalR__extended_2eAPlus) ).

fof('$_typeof_PLF.Imp.aevalR_extended.aexp',axiom,
    cType___24t(cPLF_2eImp_2eaevalR__extended_2eaexp) ).

fof('$_typeof_PLF.Imp.aexp',axiom,
    cType___24t(cPLF_2eImp_2eaexp) ).

fof('$_typeof_PLF.Imp.bexp',axiom,
    cType___24t(cPLF_2eImp_2ebexp) ).

fof('$_typeof_PLF.Imp.com',axiom,
    cType___24t(cPLF_2eImp_2ecom) ).

fof('$_typeof_PLF.Imp.pup_to_n',axiom,
    cPLF_2eImp_2ecom___24t(cPLF_2eImp_2epup__to__n) ).

fof('$_typeof_PLF.Imp.sinstr',axiom,
    cType___24t(cPLF_2eImp_2esinstr) ).

fof('$_typeof_PLF.Imp.state',axiom,
    cType___24t(cPLF_2eImp_2estate) ).

fof('$_typeof_PLF.Maps.eqb_string',axiom,
    c_24__type__4770___24t(cPLF_2eMaps_2eeqb__string) ).

fof('$_typeof_PLF.Maps.total_map',axiom,
    c_24__type__4777___24t(cPLF_2eMaps_2etotal__map) ).

fof('$_typeof_PLF.Smallstep.C',axiom,
    c_24__type__24___24t(cPLF_2eSmallstep_2eC) ).

fof('$_typeof_PLF.Smallstep.CImp.CPar',axiom,
    c_24__type__44415___24t(cPLF_2eSmallstep_2eCImp_2eCPar) ).

fof('$_typeof_PLF.Smallstep.CImp.CSeq',axiom,
    c_24__type__44415___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.com',axiom,
    cType___24t(cPLF_2eSmallstep_2eCImp_2ecom) ).

fof('$_typeof_PLF.Smallstep.Combined.C',axiom,
    c_24__type__44418___24t(cPLF_2eSmallstep_2eCombined_2eC) ).

fof('$_typeof_PLF.Smallstep.Combined.P',axiom,
    c_24__type__44421___24t(cPLF_2eSmallstep_2eCombined_2eP) ).

fof('$_typeof_PLF.Smallstep.Combined.fls',axiom,
    cPLF_2eSmallstep_2eCombined_2etm___24t(cPLF_2eSmallstep_2eCombined_2efls) ).

fof('$_typeof_PLF.Smallstep.Combined.test',axiom,
    c_24__type__44426___24t(cPLF_2eSmallstep_2eCombined_2etest) ).

fof('$_typeof_PLF.Smallstep.Combined.tm',axiom,
    cType___24t(cPLF_2eSmallstep_2eCombined_2etm) ).

fof('$_typeof_PLF.Smallstep.Combined.tru',axiom,
    cPLF_2eSmallstep_2eCombined_2etm___24t(cPLF_2eSmallstep_2eCombined_2etru) ).

fof('$_typeof_PLF.Smallstep.P',axiom,
    c_24__type__27___24t(cPLF_2eSmallstep_2eP) ).

fof('$_typeof_PLF.Smallstep.Temp4.fls',axiom,
    cPLF_2eSmallstep_2eTemp4_2etm___24t(cPLF_2eSmallstep_2eTemp4_2efls) ).

fof('$_typeof_PLF.Smallstep.Temp4.test',axiom,
    c_24__type__30551___24t(cPLF_2eSmallstep_2eTemp4_2etest) ).

fof('$_typeof_PLF.Smallstep.Temp4.tm',axiom,
    cType___24t(cPLF_2eSmallstep_2eTemp4_2etm) ).

fof('$_typeof_PLF.Smallstep.Temp4.tru',axiom,
    cPLF_2eSmallstep_2eTemp4_2etm___24t(cPLF_2eSmallstep_2eTemp4_2etru) ).

fof('$_typeof_PLF.Smallstep.compiler_is_correct_statement',axiom,
    cProp___24t(cPLF_2eSmallstep_2ecompiler__is__correct__statement) ).

fof('$_typeof_PLF.Smallstep.normal_form',axiom,
    c_24__type__125___24t(cPLF_2eSmallstep_2enormal__form) ).

fof('$_typeof_PLF.Smallstep.normalizing',axiom,
    c_24__type__4797___24t(cPLF_2eSmallstep_2enormalizing) ).

fof('$_typeof_PLF.Smallstep.relation',axiom,
    c_24__type__4777___24t(cPLF_2eSmallstep_2erelation) ).

fof('$_typeof_PLF.Smallstep.stack',axiom,
    cType___24t(cPLF_2eSmallstep_2estack) ).

fof('$_typeof_PLF.Smallstep.step_normal_form',axiom,
    c_24__type__4794___24t(cPLF_2eSmallstep_2estep__normal__form) ).

fof('$_typeof_PLF.Smallstep.tm',axiom,
    cType___24t(cPLF_2eSmallstep_2etm) ).

fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.eq_refl',axiom,
    ! [V0__x] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
     => V0__x = V0__x ) ).

fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.eq_sym',axiom,
    ! [V0__x] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
         => ( V0__x = V1__y
           => V1__y = V0__x ) ) ) ).

fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.le_antisym',axiom,
    ! [V0__x] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
         => ( cCoq_2eInit_2ePeano_2ele___24a2(V0__x,V1__y)
           => ( cCoq_2eInit_2ePeano_2ele___24a2(V1__y,V0__x)
             => V0__x = V1__y ) ) ) ) ).

fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.le_refl',axiom,
    ! [V0__x] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
     => cCoq_2eInit_2ePeano_2ele___24a2(V0__x,V0__x) ) ).

fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.lt_irrefl',axiom,
    ! [V0__x] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
     => ~ cCoq_2eInit_2ePeano_2elt___24a2(V0__x,V0__x) ) ).

fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.not_ge_lt',axiom,
    ! [V0__x] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
         => ( ~ cCoq_2eInit_2ePeano_2ele___24a2(V1__y,V0__x)
           => cCoq_2eInit_2ePeano_2elt___24a2(V0__x,V1__y) ) ) ) ).

fof('Coq.Arith.PeanoNat.Nat.Private_OrderTac.Tac.not_gt_le',axiom,
    ! [V0__x] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
         => ( ~ cCoq_2eInit_2ePeano_2elt___24a2(V1__y,V0__x)
           => cCoq_2eInit_2ePeano_2ele___24a2(V0__x,V1__y) ) ) ) ).

fof('Coq.Arith.PeanoNat.Nat.Private_Tac.eq_refl',axiom,
    ! [V0__x] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
     => V0__x = V0__x ) ).

fof('Coq.Arith.PeanoNat.Nat.Private_Tac.eq_sym',axiom,
    ! [V0__x] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__y)
         => ( V0__x = V1__y
           => V1__y = V0__x ) ) ) ).

fof('Coq.Arith.PeanoNat.Nat.Private_Tac.le_refl',axiom,
    ! [V0__x] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
     => cCoq_2eInit_2ePeano_2ele___24a2(V0__x,V0__x) ) ).

fof('Coq.Arith.PeanoNat.Nat.Private_Tac.lt_irrefl',axiom,
    ! [V0__x] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
     => ~ cCoq_2eInit_2ePeano_2elt___24a2(V0__x,V0__x) ) ).

fof('Coq.Arith.PeanoNat.Nat.add_comm',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
         => cCoq_2eInit_2eNat_2eadd___24a2(V0__n,V1__m) = cCoq_2eInit_2eNat_2eadd___24a2(V1__m,V0__n) ) ) ).

fof('Coq.Arith.PeanoNat.Nat.divide_refl',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => cCoq_2eArith_2ePeanoNat_2eNat_2edivide___24a2(V0__n,V0__n) ) ).

fof('Coq.Arith.PeanoNat.Nat.eq_equiv',axiom,
    cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(cCoq_2eInit_2eDatatypes_2enat,c_3d___24a1(cCoq_2eInit_2eDatatypes_2enat)) ).

fof('Coq.Arith.PeanoNat.Nat.eq_le_incl',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
         => ( V0__n = V1__m
           => cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m) ) ) ) ).

fof('Coq.Arith.PeanoNat.Nat.le_0_l',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eO,V0__n) ) ).

fof('Coq.Arith.PeanoNat.Nat.le_ge_cases',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
         => ( cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)
            | cCoq_2eInit_2ePeano_2ele___24a2(V1__m,V0__n) ) ) ) ).

fof('Coq.Arith.PeanoNat.Nat.le_gt_cases',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
         => ( cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)
            | cCoq_2eInit_2ePeano_2elt___24a2(V1__m,V0__n) ) ) ) ).

fof('Coq.Arith.PeanoNat.Nat.le_refl',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V0__n) ) ).

fof('Coq.Arith.PeanoNat.Nat.le_trans',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
         => ! [V2__p] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__p)
             => ( cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m)
               => ( cCoq_2eInit_2ePeano_2ele___24a2(V1__m,V2__p)
                 => cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V2__p) ) ) ) ) ) ).

fof('Coq.Arith.PeanoNat.Nat.lt_0_1',axiom,
    cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eInit_2eDatatypes_2eO,cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)) ).

fof('Coq.Arith.PeanoNat.Nat.lt_1_2',axiom,
    cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO),cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO))) ).

fof('Coq.Arith.PeanoNat.Nat.lt_ge_cases',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
         => ( cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)
            | cCoq_2eInit_2ePeano_2ele___24a2(V1__m,V0__n) ) ) ) ).

fof('Coq.Arith.PeanoNat.Nat.lt_irrefl',axiom,
    ! [V0__x] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
     => ~ cCoq_2eInit_2ePeano_2elt___24a2(V0__x,V0__x) ) ).

fof('Coq.Arith.PeanoNat.Nat.lt_le_incl',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
         => ( cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)
           => cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V1__m) ) ) ) ).

fof('Coq.Arith.PeanoNat.Nat.lt_trans',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
         => ! [V2__p] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__p)
             => ( cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)
               => ( cCoq_2eInit_2ePeano_2elt___24a2(V1__m,V2__p)
                 => cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V2__p) ) ) ) ) ) ).

fof('Coq.Arith.PeanoNat.Nat.lt_trichotomy',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
         => ( cCoq_2eInit_2ePeano_2elt___24a2(V0__n,V1__m)
            | V0__n = V1__m
            | cCoq_2eInit_2ePeano_2elt___24a2(V1__m,V0__n) ) ) ) ).

fof('Coq.Arith.PeanoNat.Nat.mul_comm',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__m)
         => cCoq_2eInit_2eNat_2emul___24a2(V0__n,V1__m) = cCoq_2eInit_2eNat_2emul___24a2(V1__m,V0__n) ) ) ).

fof('Coq.Arith.PeanoNat.Nat.one_succ',axiom,
    cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO) ).

fof('Coq.Arith.Wf_nat.lt_wf_double_ind',axiom,
    ! [V0__P] :
      ( c_24__type__6629___24t(V0__P)
     => ( ! [V1__n] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
           => ! [V2__m] :
                ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__m)
               => ( ! [V3__p] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(V3__p)
                     => ! [V4__q] :
                          ( cCoq_2eInit_2eDatatypes_2enat___24t(V4__q)
                         => ( cCoq_2eInit_2ePeano_2elt___24a2(V3__p,V1__n)
                           => p(happ(happ(V0__P,V3__p),V4__q)) ) ) )
                 => ( ! [V4__p] :
                        ( cCoq_2eInit_2eDatatypes_2enat___24t(V4__p)
                       => ( cCoq_2eInit_2ePeano_2elt___24a2(V4__p,V2__m)
                         => p(happ(happ(V0__P,V1__n),V4__p)) ) )
                   => p(happ(happ(V0__P,V1__n),V2__m)) ) ) ) )
       => ! [V2__n] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
           => ! [V3__m] :
                ( cCoq_2eInit_2eDatatypes_2enat___24t(V3__m)
               => p(happ(happ(V0__P,V2__n),V3__m)) ) ) ) ) ).

fof('Coq.Arith.Wf_nat.lt_wf_ind',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => ! [V1__P] :
          ( c_24__type__23699___24t(V1__P)
         => ( ! [V2__n] :
                ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
               => ( ! [V3__m] :
                      ( cCoq_2eInit_2eDatatypes_2enat___24t(V3__m)
                     => ( cCoq_2eInit_2ePeano_2elt___24a2(V3__m,V2__n)
                       => p(happ(V1__P,V3__m)) ) )
                 => p(happ(V1__P,V2__n)) ) )
           => p(happ(V1__P,V0__n)) ) ) ) ).

fof('Coq.Bool.Bool.absurd_eq_bool',axiom,
    ! [V0__b] :
      ( cCoq_2eInit_2eDatatypes_2ebool___24t(V0__b)
     => ! [V1__b_27] :
          ( cCoq_2eInit_2eDatatypes_2ebool___24t(V1__b_27)
         => ( p(c_24False)
           => V0__b = V1__b_27 ) ) ) ).

fof('Coq.Init.Datatypes.idProp',axiom,
    p(cCoq_2eInit_2eDatatypes_2eIDProp) ).

fof('Coq.Init.Datatypes.nat_ind',axiom,
    ! [V0__P] :
      ( c_24__type__23699___24t(V0__P)
     => ( p(happ(V0__P,cCoq_2eInit_2eDatatypes_2eO))
       => ( ! [V2__n] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
             => ( p(happ(V0__P,V2__n))
               => p(happ(V0__P,cCoq_2eInit_2eDatatypes_2eS___24a1(V2__n))) ) )
         => ! [V3__n] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(V3__n)
             => p(happ(V0__P,V3__n)) ) ) ) ) ).

fof('Coq.Init.Peano.le_n',axiom,
    ! [V0__n] :
      ( cCoq_2eInit_2eDatatypes_2enat___24t(V0__n)
     => cCoq_2eInit_2ePeano_2ele___24a2(V0__n,V0__n) ) ).

fof('Coq.Init.Peano.nat_double_ind',axiom,
    ! [V0__R] :
      ( c_24__type__6629___24t(V0__R)
     => ( ! [V1__n] :
            ( cCoq_2eInit_2eDatatypes_2enat___24t(V1__n)
           => p(happ(happ(V0__R,cCoq_2eInit_2eDatatypes_2eO),V1__n)) )
       => ( ! [V2__n] :
              ( cCoq_2eInit_2eDatatypes_2enat___24t(V2__n)
             => p(happ(happ(V0__R,cCoq_2eInit_2eDatatypes_2eS___24a1(V2__n)),cCoq_2eInit_2eDatatypes_2eO)) )
         => ( ! [V3__n] :
                ( cCoq_2eInit_2eDatatypes_2enat___24t(V3__n)
               => ! [V4__m] :
                    ( cCoq_2eInit_2eDatatypes_2enat___24t(V4__m)
                   => ( p(happ(happ(V0__R,V3__n),V4__m))
                     => p(happ(happ(V0__R,cCoq_2eInit_2eDatatypes_2eS___24a1(V3__n)),cCoq_2eInit_2eDatatypes_2eS___24a1(V4__m))) ) ) )
           => ! [V4__n] :
                ( cCoq_2eInit_2eDatatypes_2enat___24t(V4__n)
               => ! [V5__m] :
                    ( cCoq_2eInit_2eDatatypes_2enat___24t(V5__m)
                   => p(happ(happ(V0__R,V4__n),V5__m)) ) ) ) ) ) ) ).

fof('Coq.Logic.Decidable.dec_not_not',axiom,
    ! [V0__P] :
      ( cProp___24t(V0__P)
     => ( cCoq_2eLogic_2eDecidable_2edecidable___24a1(V0__P)
       => ( ( ~ p(V0__P)
           => p(c_24False) )
         => p(V0__P) ) ) ) ).

fof('Coq.Logic.Decidable.not_and_iff',axiom,
    ! [V0__A] :
      ( cProp___24t(V0__A)
     => ! [V1__B] :
          ( cProp___24t(V1__B)
         => ( ( ( p(V0__A)
                & p(V1__B) )
             => p(c_24False) )
          <=> ( p(V0__A)
             => ( p(V1__B)
               => p(c_24False) ) ) ) ) ) ).

fof('Coq.Logic.Decidable.not_false_iff',axiom,
    ( ( p(c_24False)
     => p(c_24False) )
  <=> p(c_24True) ) ).

fof('Coq.Logic.Decidable.not_or_iff',axiom,
    ! [V0__A] :
      ( cProp___24t(V0__A)
     => ! [V1__B] :
          ( cProp___24t(V1__B)
         => ( ( ( p(V0__A)
                | p(V1__B) )
             => p(c_24False) )
          <=> ( ( p(V0__A)
               => p(c_24False) )
              & ( p(V1__B)
               => p(c_24False) ) ) ) ) ) ).

fof('Coq.Logic.Decidable.not_true_iff',axiom,
    ( ( p(c_24True)
     => p(c_24False) )
  <=> p(c_24False) ) ).

fof('Coq.Logic.EqdepFacts.eq_dep_intro',axiom,
    ! [V0__U] :
      ( cType___24t(V0__U)
     => ! [V1__P] :
          ( c_24__type__25011___24t(V0__U,V1__P)
         => ! [V2__p] :
              ( t(V2__p,V0__U)
             => ! [V3__x] :
                  ( t(V3__x,happ(V1__P,V2__p))
                 => cCoq_2eLogic_2eEqdepFacts_2eeq__dep___24a6(V0__U,V1__P,V2__p,V3__x,V2__p,V3__x) ) ) ) ) ).

fof('Coq.Logic.FunctionalExtensionality.equal_f',axiom,
    ! [V0__A] :
      ( cType___24t(V0__A)
     => ! [V1__B] :
          ( cType___24t(V1__B)
         => ! [V2__f] :
              ( c_24__type__32332___24t(V0__A,V1__B,V2__f)
             => ! [V3__g] :
                  ( c_24__type__32332___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__25011___24t(V0__A,V1__B)
         => ! [V2__f] :
              ( c_24__type__35420___24t(V0__A,V1__B,V2__f)
             => ! [V3__g] :
                  ( c_24__type__35425___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__32332___24t(V0__A,V1__B,V2__f)
             => V2__f = c_24__lam__32339___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__25011___24t(V0__A,V1__B)
         => ! [V2__f] :
              ( c_24__type__32321___24t(V0__A,V1__B,V2__f)
             => V2__f = c_24__lam__32329___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__32332___24t(V0__A,V1__B,V2__f)
             => ! [V3__g] :
                  ( c_24__type__32332___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__25011___24t(V0__A,V1__B)
         => ! [V2__f] :
              ( c_24__type__35431___24t(V0__A,V1__B,V2__f)
             => ! [V3__g] :
                  ( c_24__type__35436___24t(V0__A,V1__B,V3__g)
                 => ( ! [V4__x] :
                        ( t(V4__x,V0__A)
                       => happ(V2__f,V4__x) = happ(V3__g,V4__x) )
                   => V2__f = V3__g ) ) ) ) ) ).

fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.eq_refl',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
     => V0__x = V0__x ) ).

fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.eq_sym',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
         => ( V0__x = V1__y
           => V1__y = V0__x ) ) ) ).

fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.le_antisym',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
         => ( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__x,V1__y)
           => ( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V1__y,V0__x)
             => V0__x = V1__y ) ) ) ) ).

fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.le_refl',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
     => cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__x,V0__x) ) ).

fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.lt_irrefl',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
     => ~ cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__x,V0__x) ) ).

fof('Coq.NArith.BinNat.N.Private_OrderTac.Tac.not_gt_le',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
         => ( ~ cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V1__y,V0__x)
           => cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__x,V1__y) ) ) ) ).

fof('Coq.NArith.BinNat.N.Private_Tac.eq_refl',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
     => V0__x = V0__x ) ).

fof('Coq.NArith.BinNat.N.Private_Tac.eq_sym',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__y)
         => ( V0__x = V1__y
           => V1__y = V0__x ) ) ) ).

fof('Coq.NArith.BinNat.N.Private_Tac.le_refl',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
     => cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__x,V0__x) ) ).

fof('Coq.NArith.BinNat.N.Private_Tac.lt_irrefl',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__x)
     => ~ cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__x,V0__x) ) ).

fof('Coq.NArith.BinNat.N.add_comm',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
         => cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V0__n,V1__m) = cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V1__m,V0__n) ) ) ).

fof('Coq.NArith.BinNat.N.divide_refl',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
     => cCoq_2eNArith_2eBinNat_2eN_2edivide___24a2(V0__n,V0__n) ) ).

fof('Coq.NArith.BinNat.N.eq_equiv',axiom,
    cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(cCoq_2eNumbers_2eBinNums_2eN,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eN)) ).

fof('Coq.NArith.BinNat.N.le_0_l',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
     => cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eN0,V0__n) ) ).

fof('Coq.NArith.BinNat.N.le_ge_cases',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
         => ( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__n,V1__m)
            | cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V1__m,V0__n) ) ) ) ).

fof('Coq.NArith.BinNat.N.le_gt_cases',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
         => ( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__n,V1__m)
            | cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V1__m,V0__n) ) ) ) ).

fof('Coq.NArith.BinNat.N.le_refl',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
     => cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__n,V0__n) ) ).

fof('Coq.NArith.BinNat.N.le_trans',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
         => ! [V2__p] :
              ( cCoq_2eNumbers_2eBinNums_2eN___24t(V2__p)
             => ( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__n,V1__m)
               => ( cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V1__m,V2__p)
                 => cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__n,V2__p) ) ) ) ) ) ).

fof('Coq.NArith.BinNat.N.lt_ge_cases',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
         => ( cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__n,V1__m)
            | cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V1__m,V0__n) ) ) ) ).

fof('Coq.NArith.BinNat.N.lt_le_incl',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
         => ( cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__n,V1__m)
           => cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V0__n,V1__m) ) ) ) ).

fof('Coq.NArith.BinNat.N.lt_trichotomy',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
         => ( cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V0__n,V1__m)
            | V0__n = V1__m
            | cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V1__m,V0__n) ) ) ) ).

fof('Coq.NArith.BinNat.N.mul_comm',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eN___24t(V1__m)
         => cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V0__n,V1__m) = cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V1__m,V0__n) ) ) ).

fof('Coq.PArith.BinPos.Pos.Private_Tac.eq_refl',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
     => V0__x = V0__x ) ).

fof('Coq.PArith.BinPos.Pos.Private_Tac.eq_sym',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V1__y)
         => ( V0__x = V1__y
           => V1__y = V0__x ) ) ) ).

fof('Coq.PArith.BinPos.Pos.Private_Tac.le_refl',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
     => cCoq_2ePArith_2eBinPos_2ePos_2ele___24a2(V0__x,V0__x) ) ).

fof('Coq.PArith.BinPos.Pos.Private_Tac.lt_irrefl',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__x)
     => ~ cCoq_2ePArith_2eBinPos_2ePos_2elt___24a2(V0__x,V0__x) ) ).

fof('Coq.PArith.BinPos.Pos.le_refl',axiom,
    ! [V0__p] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V0__p)
     => cCoq_2ePArith_2eBinPos_2ePos_2ele___24a2(V0__p,V0__p) ) ).

fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.eq_refl',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
     => V0__x = V0__x ) ).

fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.eq_sym',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
         => ( V0__x = V1__y
           => V1__y = V0__x ) ) ) ).

fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.le_antisym',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
         => ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V1__y))
           => ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__y,V0__x))
             => V0__x = V1__y ) ) ) ) ).

fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.le_refl',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
     => p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V0__x)) ) ).

fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.lt_irrefl',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
     => ~ p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V0__x)) ) ).

fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.not_ge_lt',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
         => ( ~ p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__y,V0__x))
           => p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V1__y)) ) ) ) ).

fof('Coq.ZArith.BinInt.Z.Private_OrderTac.Tac.not_gt_le',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
         => ( ~ p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__y,V0__x))
           => p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V1__y)) ) ) ) ).

fof('Coq.ZArith.BinInt.Z.Private_Tac.eq_refl',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
     => V0__x = V0__x ) ).

fof('Coq.ZArith.BinInt.Z.Private_Tac.eq_sym',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
         => ( V0__x = V1__y
           => V1__y = V0__x ) ) ) ).

fof('Coq.ZArith.BinInt.Z.Private_Tac.le_refl',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
     => p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__x,V0__x)) ) ).

fof('Coq.ZArith.BinInt.Z.Private_Tac.lt_irrefl',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
     => ~ p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__x,V0__x)) ) ).

fof('Coq.ZArith.BinInt.Z.add_comm',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
         => cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V0__n,V1__m) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V1__m,V0__n) ) ) ).

fof('Coq.ZArith.BinInt.Z.divide_refl',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => cCoq_2eZArith_2eBinInt_2eZ_2edivide___24a2(V0__n,V0__n) ) ).

fof('Coq.ZArith.BinInt.Z.eq_decidable',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
         => cCoq_2eLogic_2eDecidable_2edecidable___24a1(c_24__prop__15792___24a2(V0__n,V1__m)) ) ) ).

fof('Coq.ZArith.BinInt.Z.eq_equiv',axiom,
    cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(cCoq_2eNumbers_2eBinNums_2eZ,c_3d___24a1(cCoq_2eNumbers_2eBinNums_2eZ)) ).

fof('Coq.ZArith.BinInt.Z.eq_stepl',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
     => ! [V1__y] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
         => ! [V2__z] :
              ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__z)
             => ( V0__x = V1__y
               => ( V0__x = V2__z
                 => V2__z = V1__y ) ) ) ) ) ).

fof('Coq.ZArith.BinInt.Z.le_decidable',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
         => cCoq_2eLogic_2eDecidable_2edecidable___24a1(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m)) ) ) ).

fof('Coq.ZArith.BinInt.Z.le_ge_cases',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
         => ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
            | p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m,V0__n)) ) ) ) ).

fof('Coq.ZArith.BinInt.Z.le_gt_cases',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
         => ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
            | p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__m,V0__n)) ) ) ) ).

fof('Coq.ZArith.BinInt.Z.le_refl',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V0__n)) ) ).

fof('Coq.ZArith.BinInt.Z.le_trans',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
         => ! [V2__p] :
              ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
             => ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m))
               => ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m,V2__p))
                 => p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V2__p)) ) ) ) ) ) ).

fof('Coq.ZArith.BinInt.Z.lt_0_1',axiom,
    p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,cCoq_2eNumbers_2eBinNums_2eZpos___24a1(cCoq_2eNumbers_2eBinNums_2exH))) ).

fof('Coq.ZArith.BinInt.Z.lt_decidable',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
         => cCoq_2eLogic_2eDecidable_2edecidable___24a1(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m)) ) ) ).

fof('Coq.ZArith.BinInt.Z.lt_ge_cases',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
         => ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
            | p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m,V0__n)) ) ) ) ).

fof('Coq.ZArith.BinInt.Z.lt_le_incl',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
         => ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
           => p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V0__n,V1__m)) ) ) ) ).

fof('Coq.ZArith.BinInt.Z.lt_le_trans',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
         => ! [V2__p] :
              ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
             => ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
               => ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V1__m,V2__p))
                 => p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V2__p)) ) ) ) ) ) ).

fof('Coq.ZArith.BinInt.Z.lt_trans',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
         => ! [V2__p] :
              ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V2__p)
             => ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
               => ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__m,V2__p))
                 => p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V2__p)) ) ) ) ) ) ).

fof('Coq.ZArith.BinInt.Z.lt_trichotomy',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
         => ( p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V0__n,V1__m))
            | V0__n = V1__m
            | p(cCoq_2eZArith_2eBinInt_2eZ_2elt___24a2(V1__m,V0__n)) ) ) ) ).

fof('Coq.ZArith.BinInt.Z.mul_comm',axiom,
    ! [V0__n] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__n)
     => ! [V1__m] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__m)
         => cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V0__n,V1__m) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V1__m,V0__n) ) ) ).

fof('Coq.micromega.OrderedRing.Rle_antisymm',axiom,
    ! [V0__R] :
      ( cType___24t(V0__R)
     => ! [V1__rO] :
          ( t(V1__rO,V0__R)
         => ! [V2__rI] :
              ( t(V2__rI,V0__R)
             => ! [V3__rplus] :
                  ( c_24__type__6582___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__6582___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__6582___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__6591___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__4775___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__4775___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__4775___24t(V0__R,V9__rlt)
                                         => ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
                                           => ! [V11__n] :
                                                ( t(V11__n,V0__R)
                                               => ! [V12__m] :
                                                    ( t(V12__m,V0__R)
                                                   => ( p(happ(happ(V8__rle,V11__n),V12__m))
                                                     => ( p(happ(happ(V8__rle,V12__m),V11__n))
                                                       => p(happ(happ(V7__req,V11__n),V12__m)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('Coq.micromega.OrderedRing.Rle_gt_cases',axiom,
    ! [V0__R] :
      ( cType___24t(V0__R)
     => ! [V1__rO] :
          ( t(V1__rO,V0__R)
         => ! [V2__rI] :
              ( t(V2__rI,V0__R)
             => ! [V3__rplus] :
                  ( c_24__type__6582___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__6582___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__6582___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__6591___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__4775___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__4775___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__4775___24t(V0__R,V9__rlt)
                                         => ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
                                           => ! [V11__n] :
                                                ( t(V11__n,V0__R)
                                               => ! [V12__m] :
                                                    ( t(V12__m,V0__R)
                                                   => ( p(happ(happ(V8__rle,V11__n),V12__m))
                                                      | p(happ(happ(V9__rlt,V12__m),V11__n)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('Coq.micromega.OrderedRing.Rle_lt_trans',axiom,
    ! [V0__R] :
      ( cType___24t(V0__R)
     => ! [V1__rO] :
          ( t(V1__rO,V0__R)
         => ! [V2__rI] :
              ( t(V2__rI,V0__R)
             => ! [V3__rplus] :
                  ( c_24__type__6582___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__6582___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__6582___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__6591___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__4775___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__4775___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__4775___24t(V0__R,V9__rlt)
                                         => ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
                                           => ! [V11__n] :
                                                ( t(V11__n,V0__R)
                                               => ! [V12__m] :
                                                    ( t(V12__m,V0__R)
                                                   => ! [V13__p] :
                                                        ( t(V13__p,V0__R)
                                                       => ( p(happ(happ(V8__rle,V11__n),V12__m))
                                                         => ( p(happ(happ(V9__rlt,V12__m),V13__p))
                                                           => p(happ(happ(V9__rlt,V11__n),V13__p)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('Coq.micromega.OrderedRing.Rle_refl',axiom,
    ! [V0__R] :
      ( cType___24t(V0__R)
     => ! [V1__rO] :
          ( t(V1__rO,V0__R)
         => ! [V2__rI] :
              ( t(V2__rI,V0__R)
             => ! [V3__rplus] :
                  ( c_24__type__6582___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__6582___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__6582___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__6591___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__4775___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__4775___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__4775___24t(V0__R,V9__rlt)
                                         => ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
                                           => ! [V11__n] :
                                                ( t(V11__n,V0__R)
                                               => p(happ(happ(V8__rle,V11__n),V11__n)) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('Coq.micromega.OrderedRing.Rle_trans',axiom,
    ! [V0__R] :
      ( cType___24t(V0__R)
     => ! [V1__rO] :
          ( t(V1__rO,V0__R)
         => ! [V2__rI] :
              ( t(V2__rI,V0__R)
             => ! [V3__rplus] :
                  ( c_24__type__6582___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__6582___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__6582___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__6591___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__4775___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__4775___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__4775___24t(V0__R,V9__rlt)
                                         => ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
                                           => ! [V11__n] :
                                                ( t(V11__n,V0__R)
                                               => ! [V12__m] :
                                                    ( t(V12__m,V0__R)
                                                   => ! [V13__p] :
                                                        ( t(V13__p,V0__R)
                                                       => ( p(happ(happ(V8__rle,V11__n),V12__m))
                                                         => ( p(happ(happ(V8__rle,V12__m),V13__p))
                                                           => p(happ(happ(V8__rle,V11__n),V13__p)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('Coq.micromega.OrderedRing.Rlt_0_1',axiom,
    ! [V0__R] :
      ( cType___24t(V0__R)
     => ! [V1__rO] :
          ( t(V1__rO,V0__R)
         => ! [V2__rI] :
              ( t(V2__rI,V0__R)
             => ! [V3__rplus] :
                  ( c_24__type__6582___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__6582___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__6582___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__6591___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__4775___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__4775___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__4775___24t(V0__R,V9__rlt)
                                         => ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
                                           => p(happ(happ(V9__rlt,V1__rO),V2__rI)) ) ) ) ) ) ) ) ) ) ) ) ).

fof('Coq.micromega.OrderedRing.Rlt_le_trans',axiom,
    ! [V0__R] :
      ( cType___24t(V0__R)
     => ! [V1__rO] :
          ( t(V1__rO,V0__R)
         => ! [V2__rI] :
              ( t(V2__rI,V0__R)
             => ! [V3__rplus] :
                  ( c_24__type__6582___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__6582___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__6582___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__6591___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__4775___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__4775___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__4775___24t(V0__R,V9__rlt)
                                         => ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
                                           => ! [V11__n] :
                                                ( t(V11__n,V0__R)
                                               => ! [V12__m] :
                                                    ( t(V12__m,V0__R)
                                                   => ! [V13__p] :
                                                        ( t(V13__p,V0__R)
                                                       => ( p(happ(happ(V9__rlt,V11__n),V12__m))
                                                         => ( p(happ(happ(V8__rle,V12__m),V13__p))
                                                           => p(happ(happ(V9__rlt,V11__n),V13__p)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('Coq.micromega.OrderedRing.Rlt_lt_succ',axiom,
    ! [V0__R] :
      ( cType___24t(V0__R)
     => ! [V1__rO] :
          ( t(V1__rO,V0__R)
         => ! [V2__rI] :
              ( t(V2__rI,V0__R)
             => ! [V3__rplus] :
                  ( c_24__type__6582___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__6582___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__6582___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__6591___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__4775___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__4775___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__4775___24t(V0__R,V9__rlt)
                                         => ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
                                           => ! [V11__n] :
                                                ( t(V11__n,V0__R)
                                               => ! [V12__m] :
                                                    ( t(V12__m,V0__R)
                                                   => ( p(happ(happ(V9__rlt,V11__n),V12__m))
                                                     => p(happ(happ(V9__rlt,V11__n),happ(happ(V3__rplus,V2__rI),V12__m))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('Coq.micromega.OrderedRing.Rlt_succ_r',axiom,
    ! [V0__R] :
      ( cType___24t(V0__R)
     => ! [V1__rO] :
          ( t(V1__rO,V0__R)
         => ! [V2__rI] :
              ( t(V2__rI,V0__R)
             => ! [V3__rplus] :
                  ( c_24__type__6582___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__6582___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__6582___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__6591___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__4775___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__4775___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__4775___24t(V0__R,V9__rlt)
                                         => ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
                                           => ! [V11__n] :
                                                ( t(V11__n,V0__R)
                                               => p(happ(happ(V9__rlt,V11__n),happ(happ(V3__rplus,V2__rI),V11__n))) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('Coq.micromega.OrderedRing.Rlt_trans',axiom,
    ! [V0__R] :
      ( cType___24t(V0__R)
     => ! [V1__rO] :
          ( t(V1__rO,V0__R)
         => ! [V2__rI] :
              ( t(V2__rI,V0__R)
             => ! [V3__rplus] :
                  ( c_24__type__6582___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__6582___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__6582___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__6591___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__4775___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__4775___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__4775___24t(V0__R,V9__rlt)
                                         => ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
                                           => ! [V11__n] :
                                                ( t(V11__n,V0__R)
                                               => ! [V12__m] :
                                                    ( t(V12__m,V0__R)
                                                   => ! [V13__p] :
                                                        ( t(V13__p,V0__R)
                                                       => ( p(happ(happ(V9__rlt,V11__n),V12__m))
                                                         => ( p(happ(happ(V9__rlt,V12__m),V13__p))
                                                           => p(happ(happ(V9__rlt,V11__n),V13__p)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('Coq.micromega.OrderedRing.Rlt_trichotomy',axiom,
    ! [V0__R] :
      ( cType___24t(V0__R)
     => ! [V1__rO] :
          ( t(V1__rO,V0__R)
         => ! [V2__rI] :
              ( t(V2__rI,V0__R)
             => ! [V3__rplus] :
                  ( c_24__type__6582___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__6582___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__6582___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__6591___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__4775___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__4775___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__4775___24t(V0__R,V9__rlt)
                                         => ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
                                           => ! [V11__n] :
                                                ( t(V11__n,V0__R)
                                               => ! [V12__m] :
                                                    ( t(V12__m,V0__R)
                                                   => ( p(happ(happ(V9__rlt,V11__n),V12__m))
                                                      | p(happ(happ(V7__req,V11__n),V12__m))
                                                      | p(happ(happ(V9__rlt,V12__m),V11__n)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('Coq.micromega.OrderedRing.Rplus_0_l',axiom,
    ! [V0__R] :
      ( cType___24t(V0__R)
     => ! [V1__rO] :
          ( t(V1__rO,V0__R)
         => ! [V2__rI] :
              ( t(V2__rI,V0__R)
             => ! [V3__rplus] :
                  ( c_24__type__6582___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__6582___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__6582___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__6591___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__4775___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__4775___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__4775___24t(V0__R,V9__rlt)
                                         => ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
                                           => ! [V11__n] :
                                                ( t(V11__n,V0__R)
                                               => p(happ(happ(V7__req,happ(happ(V3__rplus,V1__rO),V11__n)),V11__n)) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('Coq.micromega.OrderedRing.Rplus_0_r',axiom,
    ! [V0__R] :
      ( cType___24t(V0__R)
     => ! [V1__rO] :
          ( t(V1__rO,V0__R)
         => ! [V2__rI] :
              ( t(V2__rI,V0__R)
             => ! [V3__rplus] :
                  ( c_24__type__6582___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__6582___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__6582___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__6591___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__4775___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__4775___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__4775___24t(V0__R,V9__rlt)
                                         => ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
                                           => ! [V11__n] :
                                                ( t(V11__n,V0__R)
                                               => p(happ(happ(V7__req,happ(happ(V3__rplus,V11__n),V1__rO)),V11__n)) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('Coq.micromega.OrderedRing.Rplus_comm',axiom,
    ! [V0__R] :
      ( cType___24t(V0__R)
     => ! [V1__rO] :
          ( t(V1__rO,V0__R)
         => ! [V2__rI] :
              ( t(V2__rI,V0__R)
             => ! [V3__rplus] :
                  ( c_24__type__6582___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__6582___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__6582___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__6591___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__4775___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__4775___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__4775___24t(V0__R,V9__rlt)
                                         => ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
                                           => ! [V11__n] :
                                                ( t(V11__n,V0__R)
                                               => ! [V12__m] :
                                                    ( t(V12__m,V0__R)
                                                   => p(happ(happ(V7__req,happ(happ(V3__rplus,V11__n),V12__m)),happ(happ(V3__rplus,V12__m),V11__n))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('Coq.micromega.OrderedRing.Rplus_le_lt_mono',axiom,
    ! [V0__R] :
      ( cType___24t(V0__R)
     => ! [V1__rO] :
          ( t(V1__rO,V0__R)
         => ! [V2__rI] :
              ( t(V2__rI,V0__R)
             => ! [V3__rplus] :
                  ( c_24__type__6582___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__6582___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__6582___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__6591___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__4775___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__4775___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__4775___24t(V0__R,V9__rlt)
                                         => ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
                                           => ! [V11__n] :
                                                ( t(V11__n,V0__R)
                                               => ! [V12__m] :
                                                    ( t(V12__m,V0__R)
                                                   => ! [V13__p] :
                                                        ( t(V13__p,V0__R)
                                                       => ! [V14__q] :
                                                            ( t(V14__q,V0__R)
                                                           => ( p(happ(happ(V8__rle,V11__n),V12__m))
                                                             => ( p(happ(happ(V9__rlt,V13__p),V14__q))
                                                               => p(happ(happ(V9__rlt,happ(happ(V3__rplus,V11__n),V13__p)),happ(happ(V3__rplus,V12__m),V14__q))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('Coq.micromega.OrderedRing.Rplus_le_mono',axiom,
    ! [V0__R] :
      ( cType___24t(V0__R)
     => ! [V1__rO] :
          ( t(V1__rO,V0__R)
         => ! [V2__rI] :
              ( t(V2__rI,V0__R)
             => ! [V3__rplus] :
                  ( c_24__type__6582___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__6582___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__6582___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__6591___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__4775___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__4775___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__4775___24t(V0__R,V9__rlt)
                                         => ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
                                           => ! [V11__n] :
                                                ( t(V11__n,V0__R)
                                               => ! [V12__m] :
                                                    ( t(V12__m,V0__R)
                                                   => ! [V13__p] :
                                                        ( t(V13__p,V0__R)
                                                       => ! [V14__q] :
                                                            ( t(V14__q,V0__R)
                                                           => ( p(happ(happ(V8__rle,V11__n),V12__m))
                                                             => ( p(happ(happ(V8__rle,V13__p),V14__q))
                                                               => p(happ(happ(V8__rle,happ(happ(V3__rplus,V11__n),V13__p)),happ(happ(V3__rplus,V12__m),V14__q))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('Coq.micromega.OrderedRing.Rplus_lt_le_mono',axiom,
    ! [V0__R] :
      ( cType___24t(V0__R)
     => ! [V1__rO] :
          ( t(V1__rO,V0__R)
         => ! [V2__rI] :
              ( t(V2__rI,V0__R)
             => ! [V3__rplus] :
                  ( c_24__type__6582___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__6582___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__6582___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__6591___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__4775___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__4775___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__4775___24t(V0__R,V9__rlt)
                                         => ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
                                           => ! [V11__n] :
                                                ( t(V11__n,V0__R)
                                               => ! [V12__m] :
                                                    ( t(V12__m,V0__R)
                                                   => ! [V13__p] :
                                                        ( t(V13__p,V0__R)
                                                       => ! [V14__q] :
                                                            ( t(V14__q,V0__R)
                                                           => ( p(happ(happ(V9__rlt,V11__n),V12__m))
                                                             => ( p(happ(happ(V8__rle,V13__p),V14__q))
                                                               => p(happ(happ(V9__rlt,happ(happ(V3__rplus,V11__n),V13__p)),happ(happ(V3__rplus,V12__m),V14__q))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('Coq.micromega.OrderedRing.Rplus_lt_mono',axiom,
    ! [V0__R] :
      ( cType___24t(V0__R)
     => ! [V1__rO] :
          ( t(V1__rO,V0__R)
         => ! [V2__rI] :
              ( t(V2__rI,V0__R)
             => ! [V3__rplus] :
                  ( c_24__type__6582___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__6582___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__6582___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__6591___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__4775___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__4775___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__4775___24t(V0__R,V9__rlt)
                                         => ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
                                           => ! [V11__n] :
                                                ( t(V11__n,V0__R)
                                               => ! [V12__m] :
                                                    ( t(V12__m,V0__R)
                                                   => ! [V13__p] :
                                                        ( t(V13__p,V0__R)
                                                       => ! [V14__q] :
                                                            ( t(V14__q,V0__R)
                                                           => ( p(happ(happ(V9__rlt,V11__n),V12__m))
                                                             => ( p(happ(happ(V9__rlt,V13__p),V14__q))
                                                               => p(happ(happ(V9__rlt,happ(happ(V3__rplus,V11__n),V13__p)),happ(happ(V3__rplus,V12__m),V14__q))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('Coq.micromega.OrderedRing.Rplus_nonneg_nonneg',axiom,
    ! [V0__R] :
      ( cType___24t(V0__R)
     => ! [V1__rO] :
          ( t(V1__rO,V0__R)
         => ! [V2__rI] :
              ( t(V2__rI,V0__R)
             => ! [V3__rplus] :
                  ( c_24__type__6582___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__6582___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__6582___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__6591___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__4775___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__4775___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__4775___24t(V0__R,V9__rlt)
                                         => ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
                                           => ! [V11__n] :
                                                ( t(V11__n,V0__R)
                                               => ! [V12__m] :
                                                    ( t(V12__m,V0__R)
                                                   => ( p(happ(happ(V8__rle,V1__rO),V11__n))
                                                     => ( p(happ(happ(V8__rle,V1__rO),V12__m))
                                                       => p(happ(happ(V8__rle,V1__rO),happ(happ(V3__rplus,V11__n),V12__m))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('Coq.micromega.OrderedRing.Rplus_nonneg_pos',axiom,
    ! [V0__R] :
      ( cType___24t(V0__R)
     => ! [V1__rO] :
          ( t(V1__rO,V0__R)
         => ! [V2__rI] :
              ( t(V2__rI,V0__R)
             => ! [V3__rplus] :
                  ( c_24__type__6582___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__6582___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__6582___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__6591___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__4775___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__4775___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__4775___24t(V0__R,V9__rlt)
                                         => ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
                                           => ! [V11__n] :
                                                ( t(V11__n,V0__R)
                                               => ! [V12__m] :
                                                    ( t(V12__m,V0__R)
                                                   => ( p(happ(happ(V8__rle,V1__rO),V11__n))
                                                     => ( p(happ(happ(V9__rlt,V1__rO),V12__m))
                                                       => p(happ(happ(V9__rlt,V1__rO),happ(happ(V3__rplus,V11__n),V12__m))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('Coq.micromega.OrderedRing.Rplus_pos_nonneg',axiom,
    ! [V0__R] :
      ( cType___24t(V0__R)
     => ! [V1__rO] :
          ( t(V1__rO,V0__R)
         => ! [V2__rI] :
              ( t(V2__rI,V0__R)
             => ! [V3__rplus] :
                  ( c_24__type__6582___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__6582___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__6582___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__6591___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__4775___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__4775___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__4775___24t(V0__R,V9__rlt)
                                         => ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
                                           => ! [V11__n] :
                                                ( t(V11__n,V0__R)
                                               => ! [V12__m] :
                                                    ( t(V12__m,V0__R)
                                                   => ( p(happ(happ(V9__rlt,V1__rO),V11__n))
                                                     => ( p(happ(happ(V8__rle,V1__rO),V12__m))
                                                       => p(happ(happ(V9__rlt,V1__rO),happ(happ(V3__rplus,V11__n),V12__m))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('Coq.micromega.OrderedRing.Rplus_pos_pos',axiom,
    ! [V0__R] :
      ( cType___24t(V0__R)
     => ! [V1__rO] :
          ( t(V1__rO,V0__R)
         => ! [V2__rI] :
              ( t(V2__rI,V0__R)
             => ! [V3__rplus] :
                  ( c_24__type__6582___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__6582___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__6582___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__6591___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__4775___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__4775___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__4775___24t(V0__R,V9__rlt)
                                         => ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
                                           => ! [V11__n] :
                                                ( t(V11__n,V0__R)
                                               => ! [V12__m] :
                                                    ( t(V12__m,V0__R)
                                                   => ( p(happ(happ(V9__rlt,V1__rO),V11__n))
                                                     => ( p(happ(happ(V9__rlt,V1__rO),V12__m))
                                                       => p(happ(happ(V9__rlt,V1__rO),happ(happ(V3__rplus,V11__n),V12__m))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('Coq.micromega.OrderedRing.Rtimes_0_l',axiom,
    ! [V0__R] :
      ( cType___24t(V0__R)
     => ! [V1__rO] :
          ( t(V1__rO,V0__R)
         => ! [V2__rI] :
              ( t(V2__rI,V0__R)
             => ! [V3__rplus] :
                  ( c_24__type__6582___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__6582___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__6582___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__6591___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__4775___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__4775___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__4775___24t(V0__R,V9__rlt)
                                         => ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
                                           => ! [V11__n] :
                                                ( t(V11__n,V0__R)
                                               => p(happ(happ(V7__req,happ(happ(V4__rtimes,V1__rO),V11__n)),V1__rO)) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('Coq.micromega.OrderedRing.Rtimes_0_r',axiom,
    ! [V0__R] :
      ( cType___24t(V0__R)
     => ! [V1__rO] :
          ( t(V1__rO,V0__R)
         => ! [V2__rI] :
              ( t(V2__rI,V0__R)
             => ! [V3__rplus] :
                  ( c_24__type__6582___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__6582___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__6582___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__6591___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__4775___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__4775___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__4775___24t(V0__R,V9__rlt)
                                         => ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
                                           => ! [V11__n] :
                                                ( t(V11__n,V0__R)
                                               => p(happ(happ(V7__req,happ(happ(V4__rtimes,V11__n),V1__rO)),V1__rO)) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('Coq.micromega.OrderedRing.Rtimes_comm',axiom,
    ! [V0__R] :
      ( cType___24t(V0__R)
     => ! [V1__rO] :
          ( t(V1__rO,V0__R)
         => ! [V2__rI] :
              ( t(V2__rI,V0__R)
             => ! [V3__rplus] :
                  ( c_24__type__6582___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__6582___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__6582___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__6591___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__4775___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__4775___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__4775___24t(V0__R,V9__rlt)
                                         => ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
                                           => ! [V11__n] :
                                                ( t(V11__n,V0__R)
                                               => ! [V12__m] :
                                                    ( t(V12__m,V0__R)
                                                   => p(happ(happ(V7__req,happ(happ(V4__rtimes,V11__n),V12__m)),happ(happ(V4__rtimes,V12__m),V11__n))) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('Coq.micromega.OrderedRing.Rtimes_neg_neg',axiom,
    ! [V0__R] :
      ( cType___24t(V0__R)
     => ! [V1__rO] :
          ( t(V1__rO,V0__R)
         => ! [V2__rI] :
              ( t(V2__rI,V0__R)
             => ! [V3__rplus] :
                  ( c_24__type__6582___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__6582___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__6582___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__6591___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__4775___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__4775___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__4775___24t(V0__R,V9__rlt)
                                         => ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
                                           => ! [V11__n] :
                                                ( t(V11__n,V0__R)
                                               => ! [V12__m] :
                                                    ( t(V12__m,V0__R)
                                                   => ( p(happ(happ(V9__rlt,V11__n),V1__rO))
                                                     => ( p(happ(happ(V9__rlt,V12__m),V1__rO))
                                                       => p(happ(happ(V9__rlt,V1__rO),happ(happ(V4__rtimes,V11__n),V12__m))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('Coq.micromega.OrderedRing.Rtimes_nonneg_nonneg',axiom,
    ! [V0__R] :
      ( cType___24t(V0__R)
     => ! [V1__rO] :
          ( t(V1__rO,V0__R)
         => ! [V2__rI] :
              ( t(V2__rI,V0__R)
             => ! [V3__rplus] :
                  ( c_24__type__6582___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__6582___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__6582___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__6591___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__4775___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__4775___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__4775___24t(V0__R,V9__rlt)
                                         => ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
                                           => ! [V11__n] :
                                                ( t(V11__n,V0__R)
                                               => ! [V12__m] :
                                                    ( t(V12__m,V0__R)
                                                   => ( p(happ(happ(V8__rle,V1__rO),V11__n))
                                                     => ( p(happ(happ(V8__rle,V1__rO),V12__m))
                                                       => p(happ(happ(V8__rle,V1__rO),happ(happ(V4__rtimes,V11__n),V12__m))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('Coq.micromega.OrderedRing.Rtimes_pos_neg',axiom,
    ! [V0__R] :
      ( cType___24t(V0__R)
     => ! [V1__rO] :
          ( t(V1__rO,V0__R)
         => ! [V2__rI] :
              ( t(V2__rI,V0__R)
             => ! [V3__rplus] :
                  ( c_24__type__6582___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__6582___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__6582___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__6591___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__4775___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__4775___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__4775___24t(V0__R,V9__rlt)
                                         => ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
                                           => ! [V11__n] :
                                                ( t(V11__n,V0__R)
                                               => ! [V12__m] :
                                                    ( t(V12__m,V0__R)
                                                   => ( p(happ(happ(V9__rlt,V1__rO),V11__n))
                                                     => ( p(happ(happ(V9__rlt,V12__m),V1__rO))
                                                       => p(happ(happ(V9__rlt,happ(happ(V4__rtimes,V11__n),V12__m)),V1__rO)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('Coq.micromega.OrderedRing.Rtimes_pos_pos',axiom,
    ! [V0__R] :
      ( cType___24t(V0__R)
     => ! [V1__rO] :
          ( t(V1__rO,V0__R)
         => ! [V2__rI] :
              ( t(V2__rI,V0__R)
             => ! [V3__rplus] :
                  ( c_24__type__6582___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__6582___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__6582___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__6591___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__4775___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__4775___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__4775___24t(V0__R,V9__rlt)
                                         => ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
                                           => ! [V11__n] :
                                                ( t(V11__n,V0__R)
                                               => ! [V12__m] :
                                                    ( t(V12__m,V0__R)
                                                   => ( p(happ(happ(V9__rlt,V1__rO),V11__n))
                                                     => ( p(happ(happ(V9__rlt,V1__rO),V12__m))
                                                       => p(happ(happ(V9__rlt,V1__rO),happ(happ(V4__rtimes,V11__n),V12__m))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('Coq.micromega.OrderedRing.Rtimes_square_nonneg',axiom,
    ! [V0__R] :
      ( cType___24t(V0__R)
     => ! [V1__rO] :
          ( t(V1__rO,V0__R)
         => ! [V2__rI] :
              ( t(V2__rI,V0__R)
             => ! [V3__rplus] :
                  ( c_24__type__6582___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__6582___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__6582___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__6591___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__4775___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__4775___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__4775___24t(V0__R,V9__rlt)
                                         => ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
                                           => ! [V11__n] :
                                                ( t(V11__n,V0__R)
                                               => p(happ(happ(V8__rle,V1__rO),happ(happ(V4__rtimes,V11__n),V11__n))) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('Coq.micromega.ZCoeff.req_refl',axiom,
    ! [V0__R] :
      ( cType___24t(V0__R)
     => ! [V1__rO] :
          ( t(V1__rO,V0__R)
         => ! [V2__rI] :
              ( t(V2__rI,V0__R)
             => ! [V3__rplus] :
                  ( c_24__type__6582___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__6582___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__6582___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__6591___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__4775___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__4775___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__4775___24t(V0__R,V9__rlt)
                                         => ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
                                           => ! [V11__x] :
                                                ( t(V11__x,V0__R)
                                               => p(happ(happ(V7__req,V11__x),V11__x)) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('Coq.micromega.ZCoeff.req_sym',axiom,
    ! [V0__R] :
      ( cType___24t(V0__R)
     => ! [V1__rO] :
          ( t(V1__rO,V0__R)
         => ! [V2__rI] :
              ( t(V2__rI,V0__R)
             => ! [V3__rplus] :
                  ( c_24__type__6582___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__6582___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__6582___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__6591___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__4775___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__4775___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__4775___24t(V0__R,V9__rlt)
                                         => ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
                                           => ! [V11__x] :
                                                ( t(V11__x,V0__R)
                                               => ! [V12__y] :
                                                    ( t(V12__y,V0__R)
                                                   => ( p(happ(happ(V7__req,V11__x),V12__y))
                                                     => p(happ(happ(V7__req,V12__y),V11__x)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('Coq.micromega.ZCoeff.req_trans',axiom,
    ! [V0__R] :
      ( cType___24t(V0__R)
     => ! [V1__rO] :
          ( t(V1__rO,V0__R)
         => ! [V2__rI] :
              ( t(V2__rI,V0__R)
             => ! [V3__rplus] :
                  ( c_24__type__6582___24t(V0__R,V3__rplus)
                 => ! [V4__rtimes] :
                      ( c_24__type__6582___24t(V0__R,V4__rtimes)
                     => ! [V5__rminus] :
                          ( c_24__type__6582___24t(V0__R,V5__rminus)
                         => ! [V6__ropp] :
                              ( c_24__type__6591___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__4775___24t(V0__R,V7__req)
                                 => ! [V8__rle] :
                                      ( c_24__type__4775___24t(V0__R,V8__rle)
                                     => ! [V9__rlt] :
                                          ( c_24__type__4775___24t(V0__R,V9__rlt)
                                         => ( cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V0__R,V1__rO,V2__rI,V3__rplus,V4__rtimes,V5__rminus,V6__ropp,V7__req,V8__rle,V9__rlt)
                                           => ! [V11__x] :
                                                ( t(V11__x,V0__R)
                                               => ! [V12__y] :
                                                    ( t(V12__y,V0__R)
                                                   => ! [V13__z] :
                                                        ( t(V13__z,V0__R)
                                                       => ( p(happ(happ(V7__req,V11__x),V12__y))
                                                         => ( p(happ(happ(V7__req,V12__y),V13__z))
                                                           => p(happ(happ(V7__req,V11__x),V13__z)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('Coq.omega.OmegaLemmas.new_var',axiom,
    ! [V0__x] :
      ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V0__x)
     => ? [V1__y] :
          ( cCoq_2eNumbers_2eBinNums_2eZ___24t(V1__y)
          & V0__x = V1__y ) ) ).

fof('Coq.setoid_ring.Ring_theory.ARadd_0_l',axiom,
    ! [V0__R] :
      ( cType___24t(V0__R)
     => ! [V1__rO] :
          ( t(V1__rO,V0__R)
         => ! [V2__rI] :
              ( t(V2__rI,V0__R)
             => ! [V3__radd] :
                  ( c_24__type__6582___24t(V0__R,V3__radd)
                 => ! [V4__rmul] :
                      ( c_24__type__6582___24t(V0__R,V4__rmul)
                     => ! [V5__rsub] :
                          ( c_24__type__6582___24t(V0__R,V5__rsub)
                         => ! [V6__ropp] :
                              ( c_24__type__6591___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__4775___24t(V0__R,V7__req)
                                 => ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
                                   => ! [V9__x] :
                                        ( t(V9__x,V0__R)
                                       => p(happ(happ(V7__req,happ(happ(V3__radd,V1__rO),V9__x)),V9__x)) ) ) ) ) ) ) ) ) ) ) ).

fof('Coq.setoid_ring.Ring_theory.ARadd_assoc',axiom,
    ! [V0__R] :
      ( cType___24t(V0__R)
     => ! [V1__rO] :
          ( t(V1__rO,V0__R)
         => ! [V2__rI] :
              ( t(V2__rI,V0__R)
             => ! [V3__radd] :
                  ( c_24__type__6582___24t(V0__R,V3__radd)
                 => ! [V4__rmul] :
                      ( c_24__type__6582___24t(V0__R,V4__rmul)
                     => ! [V5__rsub] :
                          ( c_24__type__6582___24t(V0__R,V5__rsub)
                         => ! [V6__ropp] :
                              ( c_24__type__6591___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__4775___24t(V0__R,V7__req)
                                 => ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
                                   => ! [V9__x] :
                                        ( t(V9__x,V0__R)
                                       => ! [V10__y] :
                                            ( t(V10__y,V0__R)
                                           => ! [V11__z] :
                                                ( t(V11__z,V0__R)
                                               => p(happ(happ(V7__req,happ(happ(V3__radd,V9__x),happ(happ(V3__radd,V10__y),V11__z))),happ(happ(V3__radd,happ(happ(V3__radd,V9__x),V10__y)),V11__z))) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('Coq.setoid_ring.Ring_theory.ARmul_0_l',axiom,
    ! [V0__R] :
      ( cType___24t(V0__R)
     => ! [V1__rO] :
          ( t(V1__rO,V0__R)
         => ! [V2__rI] :
              ( t(V2__rI,V0__R)
             => ! [V3__radd] :
                  ( c_24__type__6582___24t(V0__R,V3__radd)
                 => ! [V4__rmul] :
                      ( c_24__type__6582___24t(V0__R,V4__rmul)
                     => ! [V5__rsub] :
                          ( c_24__type__6582___24t(V0__R,V5__rsub)
                         => ! [V6__ropp] :
                              ( c_24__type__6591___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__4775___24t(V0__R,V7__req)
                                 => ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
                                   => ! [V9__x] :
                                        ( t(V9__x,V0__R)
                                       => p(happ(happ(V7__req,happ(happ(V4__rmul,V1__rO),V9__x)),V1__rO)) ) ) ) ) ) ) ) ) ) ) ).

fof('Coq.setoid_ring.Ring_theory.ARmul_0_r',axiom,
    ! [V0__R] :
      ( cType___24t(V0__R)
     => ! [V1__rO] :
          ( t(V1__rO,V0__R)
         => ! [V2__rI] :
              ( t(V2__rI,V0__R)
             => ! [V3__radd] :
                  ( c_24__type__6582___24t(V0__R,V3__radd)
                 => ! [V4__rmul] :
                      ( c_24__type__6582___24t(V0__R,V4__rmul)
                     => ! [V5__rsub] :
                          ( c_24__type__6582___24t(V0__R,V5__rsub)
                         => ! [V6__ropp] :
                              ( c_24__type__6591___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__4775___24t(V0__R,V7__req)
                                 => ( cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V0__R,V7__req)
                                   => ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
                                     => ! [V10__x] :
                                          ( t(V10__x,V0__R)
                                         => p(happ(happ(V7__req,happ(happ(V4__rmul,V10__x),V1__rO)),V1__rO)) ) ) ) ) ) ) ) ) ) ) ) ).

fof('Coq.setoid_ring.Ring_theory.ARmul_1_l',axiom,
    ! [V0__R] :
      ( cType___24t(V0__R)
     => ! [V1__rO] :
          ( t(V1__rO,V0__R)
         => ! [V2__rI] :
              ( t(V2__rI,V0__R)
             => ! [V3__radd] :
                  ( c_24__type__6582___24t(V0__R,V3__radd)
                 => ! [V4__rmul] :
                      ( c_24__type__6582___24t(V0__R,V4__rmul)
                     => ! [V5__rsub] :
                          ( c_24__type__6582___24t(V0__R,V5__rsub)
                         => ! [V6__ropp] :
                              ( c_24__type__6591___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__4775___24t(V0__R,V7__req)
                                 => ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
                                   => ! [V9__x] :
                                        ( t(V9__x,V0__R)
                                       => p(happ(happ(V7__req,happ(happ(V4__rmul,V2__rI),V9__x)),V9__x)) ) ) ) ) ) ) ) ) ) ) ).

fof('Coq.setoid_ring.Ring_theory.ARmul_assoc',axiom,
    ! [V0__R] :
      ( cType___24t(V0__R)
     => ! [V1__rO] :
          ( t(V1__rO,V0__R)
         => ! [V2__rI] :
              ( t(V2__rI,V0__R)
             => ! [V3__radd] :
                  ( c_24__type__6582___24t(V0__R,V3__radd)
                 => ! [V4__rmul] :
                      ( c_24__type__6582___24t(V0__R,V4__rmul)
                     => ! [V5__rsub] :
                          ( c_24__type__6582___24t(V0__R,V5__rsub)
                         => ! [V6__ropp] :
                              ( c_24__type__6591___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__4775___24t(V0__R,V7__req)
                                 => ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
                                   => ! [V9__x] :
                                        ( t(V9__x,V0__R)
                                       => ! [V10__y] :
                                            ( t(V10__y,V0__R)
                                           => ! [V11__z] :
                                                ( t(V11__z,V0__R)
                                               => p(happ(happ(V7__req,happ(happ(V4__rmul,V9__x),happ(happ(V4__rmul,V10__y),V11__z))),happ(happ(V4__rmul,happ(happ(V4__rmul,V9__x),V10__y)),V11__z))) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('Coq.setoid_ring.Ring_theory.ARmul_comm',axiom,
    ! [V0__R] :
      ( cType___24t(V0__R)
     => ! [V1__rO] :
          ( t(V1__rO,V0__R)
         => ! [V2__rI] :
              ( t(V2__rI,V0__R)
             => ! [V3__radd] :
                  ( c_24__type__6582___24t(V0__R,V3__radd)
                 => ! [V4__rmul] :
                      ( c_24__type__6582___24t(V0__R,V4__rmul)
                     => ! [V5__rsub] :
                          ( c_24__type__6582___24t(V0__R,V5__rsub)
                         => ! [V6__ropp] :
                              ( c_24__type__6591___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__4775___24t(V0__R,V7__req)
                                 => ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
                                   => ! [V9__x] :
                                        ( t(V9__x,V0__R)
                                       => ! [V10__y] :
                                            ( t(V10__y,V0__R)
                                           => p(happ(happ(V7__req,happ(happ(V4__rmul,V9__x),V10__y)),happ(happ(V4__rmul,V10__y),V9__x))) ) ) ) ) ) ) ) ) ) ) ) ).

fof('Coq.setoid_ring.Ring_theory.ARopp_mul_l',axiom,
    ! [V0__R] :
      ( cType___24t(V0__R)
     => ! [V1__rO] :
          ( t(V1__rO,V0__R)
         => ! [V2__rI] :
              ( t(V2__rI,V0__R)
             => ! [V3__radd] :
                  ( c_24__type__6582___24t(V0__R,V3__radd)
                 => ! [V4__rmul] :
                      ( c_24__type__6582___24t(V0__R,V4__rmul)
                     => ! [V5__rsub] :
                          ( c_24__type__6582___24t(V0__R,V5__rsub)
                         => ! [V6__ropp] :
                              ( c_24__type__6591___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__4775___24t(V0__R,V7__req)
                                 => ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
                                   => ! [V9__x] :
                                        ( t(V9__x,V0__R)
                                       => ! [V10__y] :
                                            ( t(V10__y,V0__R)
                                           => p(happ(happ(V7__req,happ(V6__ropp,happ(happ(V4__rmul,V9__x),V10__y))),happ(happ(V4__rmul,happ(V6__ropp,V9__x)),V10__y))) ) ) ) ) ) ) ) ) ) ) ) ).

fof('Coq.setoid_ring.Ring_theory.ARsub_def',axiom,
    ! [V0__R] :
      ( cType___24t(V0__R)
     => ! [V1__rO] :
          ( t(V1__rO,V0__R)
         => ! [V2__rI] :
              ( t(V2__rI,V0__R)
             => ! [V3__radd] :
                  ( c_24__type__6582___24t(V0__R,V3__radd)
                 => ! [V4__rmul] :
                      ( c_24__type__6582___24t(V0__R,V4__rmul)
                     => ! [V5__rsub] :
                          ( c_24__type__6582___24t(V0__R,V5__rsub)
                         => ! [V6__ropp] :
                              ( c_24__type__6591___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__4775___24t(V0__R,V7__req)
                                 => ( cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req)
                                   => ! [V9__x] :
                                        ( t(V9__x,V0__R)
                                       => ! [V10__y] :
                                            ( t(V10__y,V0__R)
                                           => p(happ(happ(V7__req,happ(happ(V5__rsub,V9__x),V10__y)),happ(happ(V3__radd,V9__x),happ(V6__ropp,V10__y)))) ) ) ) ) ) ) ) ) ) ) ) ).

fof('Coq.setoid_ring.Ring_theory.mk_art',axiom,
    ! [V0__R] :
      ( cType___24t(V0__R)
     => ! [V1__rO] :
          ( t(V1__rO,V0__R)
         => ! [V2__rI] :
              ( t(V2__rI,V0__R)
             => ! [V3__radd] :
                  ( c_24__type__6582___24t(V0__R,V3__radd)
                 => ! [V4__rmul] :
                      ( c_24__type__6582___24t(V0__R,V4__rmul)
                     => ! [V5__rsub] :
                          ( c_24__type__6582___24t(V0__R,V5__rsub)
                         => ! [V6__ropp] :
                              ( c_24__type__6591___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__4775___24t(V0__R,V7__req)
                                 => ( ! [V8__x] :
                                        ( t(V8__x,V0__R)
                                       => p(happ(happ(V7__req,happ(happ(V3__radd,V1__rO),V8__x)),V8__x)) )
                                   => ( ! [V9__x] :
                                          ( t(V9__x,V0__R)
                                         => ! [V10__y] :
                                              ( t(V10__y,V0__R)
                                             => p(happ(happ(V7__req,happ(happ(V3__radd,V9__x),V10__y)),happ(happ(V3__radd,V10__y),V9__x))) ) )
                                     => ( ! [V10__x] :
                                            ( t(V10__x,V0__R)
                                           => ! [V11__y] :
                                                ( t(V11__y,V0__R)
                                               => ! [V12__z] :
                                                    ( t(V12__z,V0__R)
                                                   => p(happ(happ(V7__req,happ(happ(V3__radd,V10__x),happ(happ(V3__radd,V11__y),V12__z))),happ(happ(V3__radd,happ(happ(V3__radd,V10__x),V11__y)),V12__z))) ) ) )
                                       => ( ! [V11__x] :
                                              ( t(V11__x,V0__R)
                                             => p(happ(happ(V7__req,happ(happ(V4__rmul,V2__rI),V11__x)),V11__x)) )
                                         => ( ! [V12__x] :
                                                ( t(V12__x,V0__R)
                                               => p(happ(happ(V7__req,happ(happ(V4__rmul,V1__rO),V12__x)),V1__rO)) )
                                           => ( ! [V13__x] :
                                                  ( t(V13__x,V0__R)
                                                 => ! [V14__y] :
                                                      ( t(V14__y,V0__R)
                                                     => p(happ(happ(V7__req,happ(happ(V4__rmul,V13__x),V14__y)),happ(happ(V4__rmul,V14__y),V13__x))) ) )
                                             => ( ! [V14__x] :
                                                    ( t(V14__x,V0__R)
                                                   => ! [V15__y] :
                                                        ( t(V15__y,V0__R)
                                                       => ! [V16__z] :
                                                            ( t(V16__z,V0__R)
                                                           => p(happ(happ(V7__req,happ(happ(V4__rmul,V14__x),happ(happ(V4__rmul,V15__y),V16__z))),happ(happ(V4__rmul,happ(happ(V4__rmul,V14__x),V15__y)),V16__z))) ) ) )
                                               => ( ! [V15__x] :
                                                      ( t(V15__x,V0__R)
                                                     => ! [V16__y] :
                                                          ( t(V16__y,V0__R)
                                                         => ! [V17__z] :
                                                              ( t(V17__z,V0__R)
                                                             => p(happ(happ(V7__req,happ(happ(V4__rmul,happ(happ(V3__radd,V15__x),V16__y)),V17__z)),happ(happ(V3__radd,happ(happ(V4__rmul,V15__x),V17__z)),happ(happ(V4__rmul,V16__y),V17__z)))) ) ) )
                                                 => ( ! [V16__x] :
                                                        ( t(V16__x,V0__R)
                                                       => ! [V17__y] :
                                                            ( t(V17__y,V0__R)
                                                           => p(happ(happ(V7__req,happ(V6__ropp,happ(happ(V4__rmul,V16__x),V17__y))),happ(happ(V4__rmul,happ(V6__ropp,V16__x)),V17__y))) ) )
                                                   => ( ! [V17__x] :
                                                          ( t(V17__x,V0__R)
                                                         => ! [V18__y] :
                                                              ( t(V18__y,V0__R)
                                                             => p(happ(happ(V7__req,happ(V6__ropp,happ(happ(V3__radd,V17__x),V18__y))),happ(happ(V3__radd,happ(V6__ropp,V17__x)),happ(V6__ropp,V18__y)))) ) )
                                                     => ( ! [V18__x] :
                                                            ( t(V18__x,V0__R)
                                                           => ! [V19__y] :
                                                                ( t(V19__y,V0__R)
                                                               => p(happ(happ(V7__req,happ(happ(V5__rsub,V18__x),V19__y)),happ(happ(V3__radd,V18__x),happ(V6__ropp,V19__y)))) ) )
                                                       => cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('Coq.setoid_ring.Ring_theory.mk_rt',axiom,
    ! [V0__R] :
      ( cType___24t(V0__R)
     => ! [V1__rO] :
          ( t(V1__rO,V0__R)
         => ! [V2__rI] :
              ( t(V2__rI,V0__R)
             => ! [V3__radd] :
                  ( c_24__type__6582___24t(V0__R,V3__radd)
                 => ! [V4__rmul] :
                      ( c_24__type__6582___24t(V0__R,V4__rmul)
                     => ! [V5__rsub] :
                          ( c_24__type__6582___24t(V0__R,V5__rsub)
                         => ! [V6__ropp] :
                              ( c_24__type__6591___24t(V0__R,V6__ropp)
                             => ! [V7__req] :
                                  ( c_24__type__4775___24t(V0__R,V7__req)
                                 => ( ! [V8__x] :
                                        ( t(V8__x,V0__R)
                                       => p(happ(happ(V7__req,happ(happ(V3__radd,V1__rO),V8__x)),V8__x)) )
                                   => ( ! [V9__x] :
                                          ( t(V9__x,V0__R)
                                         => ! [V10__y] :
                                              ( t(V10__y,V0__R)
                                             => p(happ(happ(V7__req,happ(happ(V3__radd,V9__x),V10__y)),happ(happ(V3__radd,V10__y),V9__x))) ) )
                                     => ( ! [V10__x] :
                                            ( t(V10__x,V0__R)
                                           => ! [V11__y] :
                                                ( t(V11__y,V0__R)
                                               => ! [V12__z] :
                                                    ( t(V12__z,V0__R)
                                                   => p(happ(happ(V7__req,happ(happ(V3__radd,V10__x),happ(happ(V3__radd,V11__y),V12__z))),happ(happ(V3__radd,happ(happ(V3__radd,V10__x),V11__y)),V12__z))) ) ) )
                                       => ( ! [V11__x] :
                                              ( t(V11__x,V0__R)
                                             => p(happ(happ(V7__req,happ(happ(V4__rmul,V2__rI),V11__x)),V11__x)) )
                                         => ( ! [V12__x] :
                                                ( t(V12__x,V0__R)
                                               => ! [V13__y] :
                                                    ( t(V13__y,V0__R)
                                                   => p(happ(happ(V7__req,happ(happ(V4__rmul,V12__x),V13__y)),happ(happ(V4__rmul,V13__y),V12__x))) ) )
                                           => ( ! [V13__x] :
                                                  ( t(V13__x,V0__R)
                                                 => ! [V14__y] :
                                                      ( t(V14__y,V0__R)
                                                     => ! [V15__z] :
                                                          ( t(V15__z,V0__R)
                                                         => p(happ(happ(V7__req,happ(happ(V4__rmul,V13__x),happ(happ(V4__rmul,V14__y),V15__z))),happ(happ(V4__rmul,happ(happ(V4__rmul,V13__x),V14__y)),V15__z))) ) ) )
                                             => ( ! [V14__x] :
                                                    ( t(V14__x,V0__R)
                                                   => ! [V15__y] :
                                                        ( t(V15__y,V0__R)
                                                       => ! [V16__z] :
                                                            ( t(V16__z,V0__R)
                                                           => p(happ(happ(V7__req,happ(happ(V4__rmul,happ(happ(V3__radd,V14__x),V15__y)),V16__z)),happ(happ(V3__radd,happ(happ(V4__rmul,V14__x),V16__z)),happ(happ(V4__rmul,V15__y),V16__z)))) ) ) )
                                               => ( ! [V15__x] :
                                                      ( t(V15__x,V0__R)
                                                     => ! [V16__y] :
                                                          ( t(V16__y,V0__R)
                                                         => p(happ(happ(V7__req,happ(happ(V5__rsub,V15__x),V16__y)),happ(happ(V3__radd,V15__x),happ(V6__ropp,V16__y)))) ) )
                                                 => ( ! [V16__x] :
                                                        ( t(V16__x,V0__R)
                                                       => p(happ(happ(V7__req,happ(happ(V3__radd,V16__x),happ(V6__ropp,V16__x))),V1__rO)) )
                                                   => cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(V0__R,V1__rO,V2__rI,V3__radd,V4__rmul,V5__rsub,V6__ropp,V7__req) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('Norm.ST_App1',axiom,
    ! [V0__t1] :
      ( cNorm_2etm___24t(V0__t1)
     => ! [V1__t1_27] :
          ( cNorm_2etm___24t(V1__t1_27)
         => ! [V2__t2] :
              ( cNorm_2etm___24t(V2__t2)
             => ( cNorm_2estep___24a2(V0__t1,V1__t1_27)
               => cNorm_2estep___24a2(cNorm_2eapp___24a2(V0__t1,V2__t2),cNorm_2eapp___24a2(V1__t1_27,V2__t2)) ) ) ) ) ).

fof('Norm.ST_App2',axiom,
    ! [V0__v1] :
      ( cNorm_2etm___24t(V0__v1)
     => ! [V1__t2] :
          ( cNorm_2etm___24t(V1__t2)
         => ! [V2__t2_27] :
              ( cNorm_2etm___24t(V2__t2_27)
             => ( cNorm_2evalue___24a1(V0__v1)
               => ( cNorm_2estep___24a2(V1__t2,V2__t2_27)
                 => cNorm_2estep___24a2(cNorm_2eapp___24a2(V0__v1,V1__t2),cNorm_2eapp___24a2(V0__v1,V2__t2_27)) ) ) ) ) ) ).

fof('Norm.ST_AppAbs',axiom,
    ! [V0__x] :
      ( cCoq_2eStrings_2eString_2estring___24t(V0__x)
     => ! [V1__T11] :
          ( cNorm_2ety___24t(V1__T11)
         => ! [V2__t12] :
              ( cNorm_2etm___24t(V2__t12)
             => ! [V3__v2] :
                  ( cNorm_2etm___24t(V3__v2)
                 => ( cNorm_2evalue___24a1(V3__v2)
                   => cNorm_2estep___24a2(cNorm_2eapp___24a2(cNorm_2eabs___24a3(V0__x,V1__T11,V2__t12),V3__v2),cNorm_2esubst___24a3(V0__x,V3__v2,V2__t12)) ) ) ) ) ) ).

fof('Norm.ST_Fst',axiom,
    ! [V0__t1] :
      ( cNorm_2etm___24t(V0__t1)
     => ! [V1__t1_27] :
          ( cNorm_2etm___24t(V1__t1_27)
         => ( cNorm_2estep___24a2(V0__t1,V1__t1_27)
           => cNorm_2estep___24a2(cNorm_2efst___24a1(V0__t1),cNorm_2efst___24a1(V1__t1_27)) ) ) ) ).

fof('Norm.ST_FstPair',axiom,
    ! [V0__v1] :
      ( cNorm_2etm___24t(V0__v1)
     => ! [V1__v2] :
          ( cNorm_2etm___24t(V1__v2)
         => ( cNorm_2evalue___24a1(V0__v1)
           => ( cNorm_2evalue___24a1(V1__v2)
             => cNorm_2estep___24a2(cNorm_2efst___24a1(cNorm_2epair___24a2(V0__v1,V1__v2)),V0__v1) ) ) ) ) ).

fof('Norm.ST_Pair1',axiom,
    ! [V0__t1] :
      ( cNorm_2etm___24t(V0__t1)
     => ! [V1__t1_27] :
          ( cNorm_2etm___24t(V1__t1_27)
         => ! [V2__t2] :
              ( cNorm_2etm___24t(V2__t2)
             => ( cNorm_2estep___24a2(V0__t1,V1__t1_27)
               => cNorm_2estep___24a2(cNorm_2epair___24a2(V0__t1,V2__t2),cNorm_2epair___24a2(V1__t1_27,V2__t2)) ) ) ) ) ).

fof('Norm.ST_Pair2',axiom,
    ! [V0__v1] :
      ( cNorm_2etm___24t(V0__v1)
     => ! [V1__t2] :
          ( cNorm_2etm___24t(V1__t2)
         => ! [V2__t2_27] :
              ( cNorm_2etm___24t(V2__t2_27)
             => ( cNorm_2evalue___24a1(V0__v1)
               => ( cNorm_2estep___24a2(V1__t2,V2__t2_27)
                 => cNorm_2estep___24a2(cNorm_2epair___24a2(V0__v1,V1__t2),cNorm_2epair___24a2(V0__v1,V2__t2_27)) ) ) ) ) ) ).

fof('Norm.ST_Snd',axiom,
    ! [V0__t1] :
      ( cNorm_2etm___24t(V0__t1)
     => ! [V1__t1_27] :
          ( cNorm_2etm___24t(V1__t1_27)
         => ( cNorm_2estep___24a2(V0__t1,V1__t1_27)
           => cNorm_2estep___24a2(cNorm_2esnd___24a1(V0__t1),cNorm_2esnd___24a1(V1__t1_27)) ) ) ) ).

fof('Norm.ST_SndPair',axiom,
    ! [V0__v1] :
      ( cNorm_2etm___24t(V0__v1)
     => ! [V1__v2] :
          ( cNorm_2etm___24t(V1__v2)
         => ( cNorm_2evalue___24a1(V0__v1)
           => ( cNorm_2evalue___24a1(V1__v2)
             => cNorm_2estep___24a2(cNorm_2esnd___24a1(cNorm_2epair___24a2(V0__v1,V1__v2)),V1__v2) ) ) ) ) ).

fof('Norm.ST_Test',axiom,
    ! [V0__t0] :
      ( cNorm_2etm___24t(V0__t0)
     => ! [V1__t0_27] :
          ( cNorm_2etm___24t(V1__t0_27)
         => ! [V2__t1] :
              ( cNorm_2etm___24t(V2__t1)
             => ! [V3__t2] :
                  ( cNorm_2etm___24t(V3__t2)
                 => ( cNorm_2estep___24a2(V0__t0,V1__t0_27)
                   => cNorm_2estep___24a2(cNorm_2etest___24a3(V0__t0,V2__t1,V3__t2),cNorm_2etest___24a3(V1__t0_27,V2__t1,V3__t2)) ) ) ) ) ) ).

fof('Norm.ST_TestFalse',axiom,
    ! [V0__t1] :
      ( cNorm_2etm___24t(V0__t1)
     => ! [V1__t2] :
          ( cNorm_2etm___24t(V1__t2)
         => cNorm_2estep___24a2(cNorm_2etest___24a3(cNorm_2efls,V0__t1,V1__t2),V1__t2) ) ) ).

fof('Norm.ST_TestTrue',axiom,
    ! [V0__t1] :
      ( cNorm_2etm___24t(V0__t1)
     => ! [V1__t2] :
          ( cNorm_2etm___24t(V1__t2)
         => cNorm_2estep___24a2(cNorm_2etest___24a3(cNorm_2etru,V0__t1,V1__t2),V0__t1) ) ) ).

fof('Norm.step_ind',axiom,
    ! [V0__P] :
      ( c_24__type__211___24t(V0__P)
     => ( ! [V1__x] :
            ( cCoq_2eStrings_2eString_2estring___24t(V1__x)
           => ! [V2__T11] :
                ( cNorm_2ety___24t(V2__T11)
               => ! [V3__t12] :
                    ( cNorm_2etm___24t(V3__t12)
                   => ! [V4__v2] :
                        ( cNorm_2etm___24t(V4__v2)
                       => ( cNorm_2evalue___24a1(V4__v2)
                         => p(happ(happ(V0__P,cNorm_2eapp___24a2(cNorm_2eabs___24a3(V1__x,V2__T11,V3__t12),V4__v2)),cNorm_2esubst___24a3(V1__x,V4__v2,V3__t12))) ) ) ) ) )
       => ( ! [V2__t1] :
              ( cNorm_2etm___24t(V2__t1)
             => ! [V3__t1_27] :
                  ( cNorm_2etm___24t(V3__t1_27)
                 => ! [V4__t2] :
                      ( cNorm_2etm___24t(V4__t2)
                     => ( cNorm_2estep___24a2(V2__t1,V3__t1_27)
                       => ( p(happ(happ(V0__P,V2__t1),V3__t1_27))
                         => p(happ(happ(V0__P,cNorm_2eapp___24a2(V2__t1,V4__t2)),cNorm_2eapp___24a2(V3__t1_27,V4__t2))) ) ) ) ) )
         => ( ! [V3__v1] :
                ( cNorm_2etm___24t(V3__v1)
               => ! [V4__t2] :
                    ( cNorm_2etm___24t(V4__t2)
                   => ! [V5__t2_27] :
                        ( cNorm_2etm___24t(V5__t2_27)
                       => ( cNorm_2evalue___24a1(V3__v1)
                         => ( cNorm_2estep___24a2(V4__t2,V5__t2_27)
                           => ( p(happ(happ(V0__P,V4__t2),V5__t2_27))
                             => p(happ(happ(V0__P,cNorm_2eapp___24a2(V3__v1,V4__t2)),cNorm_2eapp___24a2(V3__v1,V5__t2_27))) ) ) ) ) ) )
           => ( ! [V4__t1] :
                  ( cNorm_2etm___24t(V4__t1)
                 => ! [V5__t1_27] :
                      ( cNorm_2etm___24t(V5__t1_27)
                     => ! [V6__t2] :
                          ( cNorm_2etm___24t(V6__t2)
                         => ( cNorm_2estep___24a2(V4__t1,V5__t1_27)
                           => ( p(happ(happ(V0__P,V4__t1),V5__t1_27))
                             => p(happ(happ(V0__P,cNorm_2epair___24a2(V4__t1,V6__t2)),cNorm_2epair___24a2(V5__t1_27,V6__t2))) ) ) ) ) )
             => ( ! [V5__v1] :
                    ( cNorm_2etm___24t(V5__v1)
                   => ! [V6__t2] :
                        ( cNorm_2etm___24t(V6__t2)
                       => ! [V7__t2_27] :
                            ( cNorm_2etm___24t(V7__t2_27)
                           => ( cNorm_2evalue___24a1(V5__v1)
                             => ( cNorm_2estep___24a2(V6__t2,V7__t2_27)
                               => ( p(happ(happ(V0__P,V6__t2),V7__t2_27))
                                 => p(happ(happ(V0__P,cNorm_2epair___24a2(V5__v1,V6__t2)),cNorm_2epair___24a2(V5__v1,V7__t2_27))) ) ) ) ) ) )
               => ( ! [V6__t1] :
                      ( cNorm_2etm___24t(V6__t1)
                     => ! [V7__t1_27] :
                          ( cNorm_2etm___24t(V7__t1_27)
                         => ( cNorm_2estep___24a2(V6__t1,V7__t1_27)
                           => ( p(happ(happ(V0__P,V6__t1),V7__t1_27))
                             => p(happ(happ(V0__P,cNorm_2efst___24a1(V6__t1)),cNorm_2efst___24a1(V7__t1_27))) ) ) ) )
                 => ( ! [V7__v1] :
                        ( cNorm_2etm___24t(V7__v1)
                       => ! [V8__v2] :
                            ( cNorm_2etm___24t(V8__v2)
                           => ( cNorm_2evalue___24a1(V7__v1)
                             => ( cNorm_2evalue___24a1(V8__v2)
                               => p(happ(happ(V0__P,cNorm_2efst___24a1(cNorm_2epair___24a2(V7__v1,V8__v2))),V7__v1)) ) ) ) )
                   => ( ! [V8__t1] :
                          ( cNorm_2etm___24t(V8__t1)
                         => ! [V9__t1_27] :
                              ( cNorm_2etm___24t(V9__t1_27)
                             => ( cNorm_2estep___24a2(V8__t1,V9__t1_27)
                               => ( p(happ(happ(V0__P,V8__t1),V9__t1_27))
                                 => p(happ(happ(V0__P,cNorm_2esnd___24a1(V8__t1)),cNorm_2esnd___24a1(V9__t1_27))) ) ) ) )
                     => ( ! [V9__v1] :
                            ( cNorm_2etm___24t(V9__v1)
                           => ! [V10__v2] :
                                ( cNorm_2etm___24t(V10__v2)
                               => ( cNorm_2evalue___24a1(V9__v1)
                                 => ( cNorm_2evalue___24a1(V10__v2)
                                   => p(happ(happ(V0__P,cNorm_2esnd___24a1(cNorm_2epair___24a2(V9__v1,V10__v2))),V10__v2)) ) ) ) )
                       => ( ! [V10__t1] :
                              ( cNorm_2etm___24t(V10__t1)
                             => ! [V11__t2] :
                                  ( cNorm_2etm___24t(V11__t2)
                                 => p(happ(happ(V0__P,cNorm_2etest___24a3(cNorm_2etru,V10__t1,V11__t2)),V10__t1)) ) )
                         => ( ! [V11__t1] :
                                ( cNorm_2etm___24t(V11__t1)
                               => ! [V12__t2] :
                                    ( cNorm_2etm___24t(V12__t2)
                                   => p(happ(happ(V0__P,cNorm_2etest___24a3(cNorm_2efls,V11__t1,V12__t2)),V12__t2)) ) )
                           => ( ! [V12__t0] :
                                  ( cNorm_2etm___24t(V12__t0)
                                 => ! [V13__t0_27] :
                                      ( cNorm_2etm___24t(V13__t0_27)
                                     => ! [V14__t1] :
                                          ( cNorm_2etm___24t(V14__t1)
                                         => ! [V15__t2] :
                                              ( cNorm_2etm___24t(V15__t2)
                                             => ( cNorm_2estep___24a2(V12__t0,V13__t0_27)
                                               => ( p(happ(happ(V0__P,V12__t0),V13__t0_27))
                                                 => p(happ(happ(V0__P,cNorm_2etest___24a3(V12__t0,V14__t1,V15__t2)),cNorm_2etest___24a3(V13__t0_27,V14__t1,V15__t2))) ) ) ) ) ) )
                             => ! [V13__t] :
                                  ( cNorm_2etm___24t(V13__t)
                                 => ! [V14__t] :
                                      ( cNorm_2etm___24t(V14__t)
                                     => ( cNorm_2estep___24a2(V13__t,V14__t)
                                       => p(happ(happ(V0__P,V13__t),V14__t)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

fof('Norm.v_abs',axiom,
    ! [V0__x] :
      ( cCoq_2eStrings_2eString_2estring___24t(V0__x)
     => ! [V1__T11] :
          ( cNorm_2ety___24t(V1__T11)
         => ! [V2__t12] :
              ( cNorm_2etm___24t(V2__t12)
             => cNorm_2evalue___24a1(cNorm_2eabs___24a3(V0__x,V1__T11,V2__t12)) ) ) ) ).

fof('Norm.v_fls',axiom,
    cNorm_2evalue___24a1(cNorm_2efls) ).

fof('Norm.v_pair',axiom,
    ! [V0__v1] :
      ( cNorm_2etm___24t(V0__v1)
     => ! [V1__v2] :
          ( cNorm_2etm___24t(V1__v2)
         => ( cNorm_2evalue___24a1(V0__v1)
           => ( cNorm_2evalue___24a1(V1__v2)
             => cNorm_2evalue___24a1(cNorm_2epair___24a2(V0__v1,V1__v2)) ) ) ) ) ).

fof('Norm.v_tru',axiom,
    cNorm_2evalue___24a1(cNorm_2etru) ).

fof('Norm.value_ind',axiom,
    ! [V0__P] :
      ( c_24__type__4524___24t(V0__P)
     => ( ! [V1__x] :
            ( cCoq_2eStrings_2eString_2estring___24t(V1__x)
           => ! [V2__T11] :
                ( cNorm_2ety___24t(V2__T11)
               => ! [V3__t12] :
                    ( cNorm_2etm___24t(V3__t12)
                   => p(happ(V0__P,cNorm_2eabs___24a3(V1__x,V2__T11,V3__t12))) ) ) )
       => ( ! [V2__v1] :
              ( cNorm_2etm___24t(V2__v1)
             => ! [V3__v2] :
                  ( cNorm_2etm___24t(V3__v2)
                 => ( cNorm_2evalue___24a1(V2__v1)
                   => ( p(happ(V0__P,V2__v1))
                     => ( cNorm_2evalue___24a1(V3__v2)
                       => ( p(happ(V0__P,V3__v2))
                         => p(happ(V0__P,cNorm_2epair___24a2(V2__v1,V3__v2))) ) ) ) ) ) )
         => ( p(happ(V0__P,cNorm_2etru))
           => ( p(happ(V0__P,cNorm_2efls))
             => ! [V5__t] :
                  ( cNorm_2etm___24t(V5__t)
                 => ( cNorm_2evalue___24a1(V5__t)
                   => p(happ(V0__P,V5__t)) ) ) ) ) ) ) ) ).

fof('PLF.Imp.AExp.silly2',axiom,
    ! [V0__P] :
      ( cProp___24t(V0__P)
     => ( p(V0__P)
       => p(V0__P) ) ) ).

fof('PLF.Smallstep.Temp1.value_not_same_as_normal_form',axiom,
    ? [V0__v] :
      ( cPLF_2eSmallstep_2etm___24t(V0__v)
      & cPLF_2eSmallstep_2eTemp1_2evalue___24a1(V0__v)
      & ~ cPLF_2eSmallstep_2enormal__form___24a3(cPLF_2eSmallstep_2etm,cPLF_2eSmallstep_2eTemp1_2estep,V0__v) ) ).

fof('PLF.Smallstep.Temp2.value_not_same_as_normal_form',axiom,
    ? [V0__v] :
      ( cPLF_2eSmallstep_2etm___24t(V0__v)
      & cPLF_2eSmallstep_2eTemp2_2evalue___24a1(V0__v)
      & ~ cPLF_2eSmallstep_2enormal__form___24a3(cPLF_2eSmallstep_2etm,cPLF_2eSmallstep_2eTemp2_2estep,V0__v) ) ).

fof('PLF.Smallstep.Temp3.value_not_same_as_normal_form',axiom,
    ? [V0__t] :
      ( cPLF_2eSmallstep_2etm___24t(V0__t)
      & ~ cPLF_2eSmallstep_2eTemp3_2evalue___24a1(V0__t)
      & cPLF_2eSmallstep_2enormal__form___24a3(cPLF_2eSmallstep_2etm,cPLF_2eSmallstep_2eTemp3_2estep,V0__t) ) ).

fof('PLF.Smallstep.Temp4.Temp5.bool_step_prop4_holds',axiom,
    p(cPLF_2eSmallstep_2eTemp4_2eTemp5_2ebool__step__prop4) ).

fof('PLF.Smallstep.compiler_is_correct',axiom,
    p(cPLF_2eSmallstep_2ecompiler__is__correct__statement) ).

fof('PLF.Smallstep.nf_is_value',axiom,
    ! [V0__t] :
      ( cPLF_2eSmallstep_2etm___24t(V0__t)
     => ( cPLF_2eSmallstep_2enormal__form___24a3(cPLF_2eSmallstep_2etm,cPLF_2eSmallstep_2estep,V0__t)
       => cPLF_2eSmallstep_2evalue___24a1(V0__t) ) ) ).

fof('PLF.Smallstep.nf_same_as_value',axiom,
    ! [V0__t] :
      ( cPLF_2eSmallstep_2etm___24t(V0__t)
     => ( cPLF_2eSmallstep_2enormal__form___24a3(cPLF_2eSmallstep_2etm,cPLF_2eSmallstep_2estep,V0__t)
      <=> cPLF_2eSmallstep_2evalue___24a1(V0__t) ) ) ).

fof('PLF.Smallstep.strong_progress',axiom,
    ! [V0__t] :
      ( cPLF_2eSmallstep_2etm___24t(V0__t)
     => ( cPLF_2eSmallstep_2evalue___24a1(V0__t)
        | ? [V1__t_27] :
            ( cPLF_2eSmallstep_2etm___24t(V1__t_27)
            & cPLF_2eSmallstep_2estep___24a2(V0__t,V1__t_27) ) ) ) ).

fof('PLF.Smallstep.value_is_nf',axiom,
    ! [V0__v] :
      ( cPLF_2eSmallstep_2etm___24t(V0__v)
     => ( cPLF_2eSmallstep_2evalue___24a1(V0__v)
       => cPLF_2eSmallstep_2enormal__form___24a3(cPLF_2eSmallstep_2etm,cPLF_2eSmallstep_2estep,V0__v) ) ) ).

fof('$adef_Coq.PArith.BinPos.Pos.le_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2ePArith_2eBinPos_2ePos_2ele,V_24X1),V_24X2))
    <=> cCoq_2ePArith_2eBinPos_2ePos_2ele___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.micromega.ZMicromega.CutProof_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eZMicromega_2eCutProof,V_24X1),V_24X2) = cCoq_2emicromega_2eZMicromega_2eCutProof___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.ZArith.BinIntDef.Z.max_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2emax,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2emax___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Structures.GenericMinMax.gmin_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eStructures_2eGenericMinMax_2egmin,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eStructures_2eGenericMinMax_2egmin___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.Arith.PeanoNat.Nat.eqf_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eArith_2ePeanoNat_2eNat_2eeqf,V_24X1),V_24X2))
    <=> cCoq_2eArith_2ePeanoNat_2eNat_2eeqf___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.Init.Nat.mul_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2emul,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2emul___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Init.Peano.le_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eInit_2ePeano_2ele,V_24X1),V_24X2))
    <=> cCoq_2eInit_2ePeano_2ele___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.Init.Decimal.D7_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD7,V_24X1) = cCoq_2eInit_2eDecimal_2eD7___24a1(V_24X1) ).

fof('$adef_Coq.FSets.FSetPositive.PositiveSet.Node_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode,V_24X1),V_24X2),V_24X3) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eNode___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.Arith.PeanoNat.Nat.divide_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eArith_2ePeanoNat_2eNat_2edivide,V_24X1),V_24X2))
    <=> cCoq_2eArith_2ePeanoNat_2eNat_2edivide___24a2(V_24X1,V_24X2) ) ).

fof('$adef_PLF.Smallstep.Temp4.step_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cPLF_2eSmallstep_2eTemp4_2estep,V_24X1),V_24X2))
    <=> cPLF_2eSmallstep_2eTemp4_2estep___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.setoid_ring.Field_theory.rsplit_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2esetoid__ring_2eField__theory_2ersplit,V_24X1) = cCoq_2esetoid__ring_2eField__theory_2ersplit___24a1(V_24X1) ).

fof('$adef_PLF.Smallstep.P_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cPLF_2eSmallstep_2eP,V_24X1),V_24X2) = cPLF_2eSmallstep_2eP___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Init.Decimal.D2_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD2,V_24X1) = cCoq_2eInit_2eDecimal_2eD2___24a1(V_24X1) ).

fof('$adef_Coq.NArith.Ndigits.eqf_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eNArith_2eNdigits_2eeqf,V_24X1),V_24X2))
    <=> cCoq_2eNArith_2eNdigits_2eeqf___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.Classes.RelationClasses.Equivalence_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eClasses_2eRelationClasses_2eEquivalence,V_24X1),V_24X2))
    <=> cCoq_2eClasses_2eRelationClasses_2eEquivalence___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.Arith.Even.even_$a1',axiom,
    ! [V_24X1] :
      ( p(happ(cCoq_2eArith_2eEven_2eeven,V_24X1))
    <=> cCoq_2eArith_2eEven_2eeven___24a1(V_24X1) ) ).

fof('$adef_Coq.micromega.Tauto.TT_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eTT,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eTauto_2eTT___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.PArith.BinPos.Pos.PeanoSucc_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPos_2ePos_2ePeanoSucc,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPos_2ePos_2ePeanoSucc___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.setoid_ring.Ring_theory.SRopp_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2esetoid__ring_2eRing__theory_2eSRopp,V_24X1) = cCoq_2esetoid__ring_2eRing__theory_2eSRopp___24a1(V_24X1) ).

fof('$adef_Coq.Logic.Decidable.decidable_$a1',axiom,
    ! [V_24X1] :
      ( p(happ(cCoq_2eLogic_2eDecidable_2edecidable,V_24X1))
    <=> cCoq_2eLogic_2eDecidable_2edecidable___24a1(V_24X1) ) ).

fof('$adef_Coq.Relations.Relation_Operators.clos_trans_n1_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eclos__trans__n1,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> cCoq_2eRelations_2eRelation__Operators_2eclos__trans__n1___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).

fof('$adef_Coq.Relations.Relation_Definitions.PER_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eRelations_2eRelation__Definitions_2ePER,V_24X1),V_24X2))
    <=> cCoq_2eRelations_2eRelation__Definitions_2ePER___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.micromega.EnvRing.PEmul_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePEmul,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eEnvRing_2ePEmul___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.Reals.Rdefinitions.IZR_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eReals_2eRdefinitions_2eIZR,V_24X1) = cCoq_2eReals_2eRdefinitions_2eIZR___24a1(V_24X1) ).

fof('$adef_$_lam_44633_$a1',axiom,
    ! [V_24X1] : happ(c_24__lam__44633,V_24X1) = c_24__lam__44633___24a1(V_24X1) ).

fof('$adef_Coq.Init.Datatypes.snd_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2esnd,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2esnd___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.ZArith.BinInt.Z.eqf_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2eeqf,V_24X1),V_24X2))
    <=> cCoq_2eZArith_2eBinInt_2eZ_2eeqf___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.Relations.Relation_Definitions.preorder_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eRelations_2eRelation__Definitions_2epreorder,V_24X1),V_24X2))
    <=> cCoq_2eRelations_2eRelation__Definitions_2epreorder___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.Init.Datatypes.None_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2eNone,V_24X1) = cCoq_2eInit_2eDatatypes_2eNone___24a1(V_24X1) ).

fof('$adef_Coq.ZArith.BinIntDef.Z.to_nat_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eto__nat,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eto__nat___24a1(V_24X1) ).

fof('$adef_Coq.PArith.BinPos.Pos.lt_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2ePArith_2eBinPos_2ePos_2elt,V_24X1),V_24X2))
    <=> cCoq_2ePArith_2eBinPos_2ePos_2elt___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.NArith.BinNat.N.lt_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eNArith_2eBinNat_2eN_2elt,V_24X1),V_24X2))
    <=> cCoq_2eNArith_2eBinNat_2eN_2elt___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.NArith.BinNatDef.N.testbit_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2etestbit,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2etestbit___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Vectors.VectorDef.cons_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eVectors_2eVectorDef_2econs,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eVectors_2eVectorDef_2econs___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.ZArith.BinIntDef.Z.of_N_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eof__N___24a1(V_24X1) ).

fof('$adef_Coq.PArith.BinPosDef.Pos.to_nat_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2eto__nat___24a1(V_24X1) ).

fof('$adef_Coq.Init.Decimal.D0_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD0,V_24X1) = cCoq_2eInit_2eDecimal_2eD0___24a1(V_24X1) ).

fof('$adef_Coq.Relations.Relation_Definitions.antisymmetric_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eRelations_2eRelation__Definitions_2eantisymmetric,V_24X1),V_24X2))
    <=> cCoq_2eRelations_2eRelation__Definitions_2eantisymmetric___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.ZArith.BinIntDef.Z.modulo_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2emodulo___24a2(V_24X1,V_24X2) ).

fof('$adef_$_fix_35183_v_CANONICAL_0_$a1',axiom,
    ! [V_24X1] : happ(c_24__fix__35183__v__CANONICAL__0,V_24X1) = c_24__fix__35183__v__CANONICAL__0___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('$adef_Coq.ZArith.BinIntDef.Z.abs_N_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__N,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__N___24a1(V_24X1) ).

fof('$adef_PLF.Imp.BreakImp.CAss_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cPLF_2eImp_2eBreakImp_2eCAss,V_24X1),V_24X2) = cPLF_2eImp_2eBreakImp_2eCAss___24a2(V_24X1,V_24X2) ).

fof('$adef_PLF.Imp.beval_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cPLF_2eImp_2ebeval,V_24X1),V_24X2) = cPLF_2eImp_2ebeval___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.setoid_ring.Ring_theory.SRopp_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__theory_2eSRopp,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__theory_2eSRopp___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.PArith.BinPosDef.Pos.size_nat_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2esize__nat,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2esize__nat___24a1(V_24X1) ).

fof('$adef_Coq.Init.Datatypes.CompLtT_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2eCompLtT,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2eCompLtT___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.micromega.VarMap.t_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2emicromega_2eVarMap_2et,V_24X1) = cCoq_2emicromega_2eVarMap_2et___24a1(V_24X1) ).

fof('$adef_Coq.Lists.List.nth_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eLists_2eList_2enth,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eLists_2eList_2enth___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.Lists.SetoidList.transpose_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(cCoq_2eLists_2eSetoidList_2etranspose,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> cCoq_2eLists_2eSetoidList_2etranspose___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).

fof('$adef_Coq.PArith.BinPosDef.Pos.of_nat_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__nat,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2eof__nat___24a1(V_24X1) ).

fof('$adef_Coq.Init.Datatypes.nat_rect_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2enat__rect,V_24X1) = cCoq_2eInit_2eDatatypes_2enat__rect___24a1(V_24X1) ).

fof('$adef_$_case_Coq.Init.Datatypes.nat$45451_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2enat_2445451,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__case__Coq_2eInit_2eDatatypes_2enat_2445451___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.Init.Decimal.nzhead_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2enzhead,V_24X1) = cCoq_2eInit_2eDecimal_2enzhead___24a1(V_24X1) ).

fof('$adef_PLF.Smallstep.Combined.step_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cPLF_2eSmallstep_2eCombined_2estep,V_24X1),V_24X2))
    <=> cPLF_2eSmallstep_2eCombined_2estep___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('$adef_Coq.Lists.List.Exists_$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('$adef_PLF.Smallstep.CImp.CIf_$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('$adef_PLF.Imp.aevalR_division.AMinus_$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('$adef_Coq.micromega.RingMicromega.PsatzMulC_$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('$adef_Coq.Init.Datatypes.inr_$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('$adef_$_let_var_6_p_32782_32784_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__let__var__6__p__32782__32784,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__let__var__6__p__32782__32784___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.micromega.VarMap.Branch_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eVarMap_2eBranch,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eVarMap_2eBranch___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.setoid_ring.Ring_theory.sring_eq_ext_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2esring__eq__ext,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> cCoq_2esetoid__ring_2eRing__theory_2esring__eq__ext___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).

fof('$adef_Coq.Reals.RIneq.mkposreal_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eReals_2eRIneq_2emkposreal,V_24X1) = cCoq_2eReals_2eRIneq_2emkposreal___24a1(V_24X1) ).

fof('$adef_Coq.setoid_ring.Ring_polynom.PEc_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEc,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEc___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Vectors.Fin.F1_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eVectors_2eFin_2eF1,V_24X1) = cCoq_2eVectors_2eFin_2eF1___24a1(V_24X1) ).

fof('$adef_PLF.Smallstep.SimpleArith1.step_$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('$adef_Coq.Vectors.VectorDef.Forall_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(cCoq_2eVectors_2eVectorDef_2eForall,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> cCoq_2eVectors_2eVectorDef_2eForall___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).

fof('$adef_Coq.QArith.QArith_base.Qnum_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eQArith_2eQArith__base_2eQnum,V_24X1) = cCoq_2eQArith_2eQArith__base_2eQnum___24a1(V_24X1) ).

fof('$adef_Coq.Init.Datatypes.implb_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2eimplb,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2eimplb___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.micromega.EnvRing.Pol_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2emicromega_2eEnvRing_2ePol,V_24X1) = cCoq_2emicromega_2eEnvRing_2ePol___24a1(V_24X1) ).

fof('$adef_$_lam_32339_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__32339,V_24X1),V_24X2),V_24X3) = c_24__lam__32339___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.micromega.Tauto.Cj_$a6',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eCj,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2emicromega_2eTauto_2eCj___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).

fof('$adef_Norm.app_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cNorm_2eapp,V_24X1),V_24X2) = cNorm_2eapp___24a2(V_24X1,V_24X2) ).

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('$adef_PLF.Smallstep.normalizing_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cPLF_2eSmallstep_2enormalizing,V_24X1),V_24X2))
    <=> cPLF_2eSmallstep_2enormalizing___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.Relations.Relation_Operators.clos_refl_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eclos__refl,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).

fof('$adef_Coq.setoid_ring.Ring_polynom.Pc_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePc,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__polynom_2ePc___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Structures.OrderedTypeEx.PositiveOrderedTypeBits.bits_lt_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt,V_24X1),V_24X2))
    <=> cCoq_2eStructures_2eOrderedTypeEx_2ePositiveOrderedTypeBits_2ebits__lt___24a2(V_24X1,V_24X2) ) ).

fof('$adef_PLF.Smallstep.Combined.C_$a1',axiom,
    ! [V_24X1] : happ(cPLF_2eSmallstep_2eCombined_2eC,V_24X1) = cPLF_2eSmallstep_2eCombined_2eC___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('$adef_Coq.Init.Nat.log2_iter_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eInit_2eNat_2elog2__iter,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eInit_2eNat_2elog2__iter___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_PLF.Smallstep.Temp1.step_$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('$adef_Coq.Relations.Relation_Definitions.symmetric_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eRelations_2eRelation__Definitions_2esymmetric,V_24X1),V_24X2))
    <=> cCoq_2eRelations_2eRelation__Definitions_2esymmetric___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.Init.Nat.even_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eNat_2eeven,V_24X1) = cCoq_2eInit_2eNat_2eeven___24a1(V_24X1) ).

fof('$adef_Coq.Sorting.Sorted.LocallySorted_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] :
      ( p(happ(happ(happ(cCoq_2eSorting_2eSorted_2eLocallySorted,V_24X1),V_24X2),V_24X3))
    <=> cCoq_2eSorting_2eSorted_2eLocallySorted___24a3(V_24X1,V_24X2,V_24X3) ) ).

fof('$adef_Coq.setoid_ring.Ring_polynom.vmon_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2evmon,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__polynom_2evmon___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.PArith.BinPosDef.Pos.succ_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2esucc,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2esucc___24a1(V_24X1) ).

fof('$adef_$_lam_44640_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__lam__44640,V_24X1),V_24X2) = c_24__lam__44640___24a2(V_24X1,V_24X2) ).

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('$adef_$_fix_26837_v_CANONICAL_1_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__fix__26837__v__CANONICAL__1,V_24X1),V_24X2),V_24X3) = c_24__fix__26837__v__CANONICAL__1___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.Relations.Relation_Operators.Desc_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] :
      ( p(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eDesc,V_24X1),V_24X2),V_24X3))
    <=> cCoq_2eRelations_2eRelation__Operators_2eDesc___24a3(V_24X1,V_24X2,V_24X3) ) ).

fof('$adef_Coq.Init.Decimal.Pos_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2ePos,V_24X1) = cCoq_2eInit_2eDecimal_2ePos___24a1(V_24X1) ).

fof('$adef_Coq.setoid_ring.Ring_polynom.Pol_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2esetoid__ring_2eRing__polynom_2ePol,V_24X1) = cCoq_2esetoid__ring_2eRing__polynom_2ePol___24a1(V_24X1) ).

fof('$adef_Coq.FSets.FSetPositive.PositiveSet.mem_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem,V_24X1),V_24X2) = cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2emem___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.micromega.Tauto.D_$a6',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eD,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2emicromega_2eTauto_2eD___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).

fof('$adef_PLF.Smallstep.Temp2.step_$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('$adef_Coq.Arith.Between.P_nth_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
      ( p(happ(happ(happ(happ(happ(cCoq_2eArith_2eBetween_2eP__nth,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
    <=> cCoq_2eArith_2eBetween_2eP__nth___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).

fof('$adef_Coq.Init.Datatypes.prod_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2eprod,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2eprod___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Relations.Relation_Operators.clos_refl_sym_trans_n1_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__n1,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__n1___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).

fof('$adef_Coq.Reals.Rdefinitions.IPR_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eReals_2eRdefinitions_2eIPR,V_24X1) = cCoq_2eReals_2eRdefinitions_2eIPR___24a1(V_24X1) ).

fof('$adef_PLF.Maps.eqb_string_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cPLF_2eMaps_2eeqb__string,V_24X1),V_24X2) = cPLF_2eMaps_2eeqb__string___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.micromega.Env.Env_$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('$adef_Coq.Init.Specif.Exc_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eSpecif_2eExc,V_24X1) = cCoq_2eInit_2eSpecif_2eExc___24a1(V_24X1) ).

fof('$adef_Coq.Init.Datatypes.CompareSpecT_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eInit_2eDatatypes_2eCompareSpecT,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eInit_2eDatatypes_2eCompareSpecT___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.ZArith.BinIntDef.Z.pred_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2epred,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2epred___24a1(V_24X1) ).

fof('$adef_Coq.micromega.ZMicromega.Vars.Facts.MP.Dec.FSetDecideAuxiliary.FSet_elt_Prop_$a1',axiom,
    ! [V_24X1] :
      ( p(happ(cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop,V_24X1))
    <=> cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__elt__Prop___24a1(V_24X1) ) ).

fof('$adef_Coq.Vectors.VectorDef.Forall2_$a6',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] :
      ( p(happ(happ(happ(happ(happ(happ(cCoq_2eVectors_2eVectorDef_2eForall2,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6))
    <=> cCoq_2eVectors_2eVectorDef_2eForall2___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ) ).

fof('$adef_Coq.micromega.DeclConstant.DeclaredConstant_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2emicromega_2eDeclConstant_2eDeclaredConstant,V_24X1),V_24X2))
    <=> cCoq_2emicromega_2eDeclConstant_2eDeclaredConstant___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.setoid_ring.Field_theory.FEdiv_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEdiv,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eField__theory_2eFEdiv___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.ZArith.BinIntDef.Z.compare_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2ecompare___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Init.Nat.compare_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2ecompare,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2ecompare___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.setoid_ring.Ring_theory.ring_theory_$a8',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8] :
      ( p(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2ering__theory,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8))
    <=> cCoq_2esetoid__ring_2eRing__theory_2ering__theory___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8) ) ).

fof('$adef_$_prop_4765_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__prop__4765,V_24X1),V_24X2) = c_24__prop__4765___24a2(V_24X1,V_24X2) ).

fof('$adef_$_case_Coq.Init.Datatypes.nat$45654_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2enat_2445654,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__case__Coq_2eInit_2eDatatypes_2enat_2445654___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_PLF.Imp.AExp.aevalR_first_try.TooHardToRead.aevalR_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cPLF_2eImp_2eAExp_2eaevalR__first__try_2eTooHardToRead_2eaevalR,V_24X1),V_24X2))
    <=> cPLF_2eImp_2eAExp_2eaevalR__first__try_2eTooHardToRead_2eaevalR___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.setoid_ring.Ring_theory.almost_ring_theory_$a8',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8] :
      ( p(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8))
    <=> cCoq_2esetoid__ring_2eRing__theory_2ealmost__ring__theory___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8) ) ).

fof('$adef_Coq.QArith.QArith_base.Qden_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eQArith_2eQArith__base_2eQden,V_24X1) = cCoq_2eQArith_2eQArith__base_2eQden___24a1(V_24X1) ).

fof('$adef_PLF.Imp.BreakImp.CWhile_$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('$adef_$_case_Coq.Init.Datatypes.nat$44389_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2enat_2444389,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__case__Coq_2eInit_2eDatatypes_2enat_2444389___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.setoid_ring.InitialRing.gen_phiPOS_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_Coq.Init.Peano.IsSucc_$a1',axiom,
    ! [V_24X1] :
      ( p(happ(cCoq_2eInit_2ePeano_2eIsSucc,V_24X1))
    <=> cCoq_2eInit_2ePeano_2eIsSucc___24a1(V_24X1) ) ).

fof('$adef_Coq.Init.Datatypes.app_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2eapp,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2eapp___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.NArith.BinNatDef.N.div2_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2ediv2,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2ediv2___24a1(V_24X1) ).

fof('$adef_Coq.Init.Datatypes.eq_true_$a1',axiom,
    ! [V_24X1] :
      ( p(happ(cCoq_2eInit_2eDatatypes_2eeq__true,V_24X1))
    <=> cCoq_2eInit_2eDatatypes_2eeq__true___24a1(V_24X1) ) ).

fof('$adef_Coq.Init.Specif.existT_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eInit_2eSpecif_2eexistT,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eInit_2eSpecif_2eexistT___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.Init.Decimal.D6_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD6,V_24X1) = cCoq_2eInit_2eDecimal_2eD6___24a1(V_24X1) ).

fof('$adef_Coq.micromega.VarMap.Elt_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eVarMap_2eElt,V_24X1),V_24X2) = cCoq_2emicromega_2eVarMap_2eElt___24a2(V_24X1,V_24X2) ).

fof('$adef_Norm.value_$a1',axiom,
    ! [V_24X1] :
      ( p(happ(cNorm_2evalue,V_24X1))
    <=> cNorm_2evalue___24a1(V_24X1) ) ).

fof('$adef_$_lam_32339_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__32339,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__32339___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

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('$adef_Coq.Init.Specif.sig_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eSpecif_2esig,V_24X1),V_24X2) = cCoq_2eInit_2eSpecif_2esig___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Init.Decimal.Decimal_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDecimal_2eDecimal,V_24X1),V_24X2) = cCoq_2eInit_2eDecimal_2eDecimal___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Init.Nat.tail_add_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2etail__add,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2etail__add___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Strings.Ascii.nat_of_ascii_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eStrings_2eAscii_2enat__of__ascii,V_24X1) = cCoq_2eStrings_2eAscii_2enat__of__ascii___24a1(V_24X1) ).

fof('$adef_$_case_Coq.Init.Datatypes.nat$42879_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2enat_2442879,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__case__Coq_2eInit_2eDatatypes_2enat_2442879___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_Coq.Relations.Relation_Operators.lexprod_$a6',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] :
      ( p(happ(happ(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2elexprod,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6))
    <=> cCoq_2eRelations_2eRelation__Operators_2elexprod___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ) ).

fof('$adef_PLF.Smallstep.step_$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('$adef_Coq.setoid_ring.Field_theory.FEmul_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEmul,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eField__theory_2eFEmul___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.NArith.BinNat.N.peano_rect_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eNArith_2eBinNat_2eN_2epeano__rect,V_24X1) = cCoq_2eNArith_2eBinNat_2eN_2epeano__rect___24a1(V_24X1) ).

fof('$adef_Coq.Vectors.VectorDef.t_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eVectors_2eVectorDef_2et,V_24X1) = cCoq_2eVectors_2eVectorDef_2et___24a1(V_24X1) ).

fof('$adef_Coq.ZArith.BinIntDef.Z.mul_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2emul,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(V_24X1,V_24X2) ).

fof('$adef_PLF.Smallstep.Temp3.value_$a1',axiom,
    ! [V_24X1] :
      ( p(happ(cPLF_2eSmallstep_2eTemp3_2evalue,V_24X1))
    <=> cPLF_2eSmallstep_2eTemp3_2evalue___24a1(V_24X1) ) ).

fof('$adef_Coq.micromega.ZMicromega.EnumProof_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eZMicromega_2eEnumProof,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eZMicromega_2eEnumProof___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.PArith.BinPosDef.Pos.iter_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eiter,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2ePArith_2eBinPosDef_2ePos_2eiter___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.Bool.Bool.eqb_$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('$adef_$_lam_42274_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(c_24__lam__42274,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> c_24__lam__42274___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).

fof('$adef_PLF.Imp.AExp.aevalR_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cPLF_2eImp_2eAExp_2eaevalR,V_24X1),V_24X2))
    <=> cPLF_2eImp_2eAExp_2eaevalR___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.Relations.Relation_Operators.symprod_$a6',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] :
      ( p(happ(happ(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2esymprod,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6))
    <=> cCoq_2eRelations_2eRelation__Operators_2esymprod___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ) ).

fof('$adef_Coq.micromega.RMicromega.CZ_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2emicromega_2eRMicromega_2eCZ,V_24X1) = cCoq_2emicromega_2eRMicromega_2eCZ___24a1(V_24X1) ).

fof('$adef_$_fix_43374_v_CANONICAL_0_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__fix__43374__v__CANONICAL__0,V_24X1),V_24X2) = c_24__fix__43374__v__CANONICAL__0___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('$adef_Coq.Init.Decimal.D4_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD4,V_24X1) = cCoq_2eInit_2eDecimal_2eD4___24a1(V_24X1) ).

fof('$adef_Coq.FSets.FSetPositive.PositiveSet.Equal_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eEqual,V_24X1),V_24X2))
    <=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eEqual___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.setoid_ring.Field_theory.linear_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2esetoid__ring_2eField__theory_2elinear,V_24X1) = cCoq_2esetoid__ring_2eField__theory_2elinear___24a1(V_24X1) ).

fof('$adef_Coq.micromega.RingMicromega.Build_Formula_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2eBuild__Formula,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eRingMicromega_2eBuild__Formula___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.setoid_ring.Ring_polynom.mkmult_pow_$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('$adef_$_prop_35093_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__35093,V_24X1),V_24X2),V_24X3) = c_24__prop__35093___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.Arith.PeanoNat.Nat.b2n_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eArith_2ePeanoNat_2eNat_2eb2n,V_24X1) = cCoq_2eArith_2ePeanoNat_2eNat_2eb2n___24a1(V_24X1) ).

fof('$adef_Coq.Init.Specif.sumbool_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eSpecif_2esumbool,V_24X1),V_24X2) = cCoq_2eInit_2eSpecif_2esumbool___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Arith.PeanoNat.Nat.recursion_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eArith_2ePeanoNat_2eNat_2erecursion,V_24X1) = cCoq_2eArith_2ePeanoNat_2eNat_2erecursion___24a1(V_24X1) ).

fof('$adef_PLF.Smallstep.CImp.CPar_$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('$adef_Coq.PArith.BinPosDef.Pos.eqb_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2eeqb___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Structures.OrderedTypeEx.String_as_OT.lts_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2elts,V_24X1),V_24X2))
    <=> cCoq_2eStructures_2eOrderedTypeEx_2eString__as__OT_2elts___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.ZArith.Zlogarithm.Is_power_$a1',axiom,
    ! [V_24X1] :
      ( p(happ(cCoq_2eZArith_2eZlogarithm_2eIs__power,V_24X1))
    <=> cCoq_2eZArith_2eZlogarithm_2eIs__power___24a1(V_24X1) ) ).

fof('$adef_$_fix_120_v_CANONICAL_0_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__fix__120__v__CANONICAL__0,V_24X1),V_24X2) = c_24__fix__120__v__CANONICAL__0___24a2(V_24X1,V_24X2) ).

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_29551_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__29551,V_24X1),V_24X2),V_24X3) = c_24__prop__29551___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_$_prop_29550_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__29550,V_24X1),V_24X2),V_24X3) = c_24__prop__29550___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.setoid_ring.Field_theory.mk_rsplit_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2emk__rsplit,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eField__theory_2emk__rsplit___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_PLF.Imp.BLe_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cPLF_2eImp_2eBLe,V_24X1),V_24X2) = cPLF_2eImp_2eBLe___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Lists.List.last_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eLists_2eList_2elast,V_24X1),V_24X2),V_24X3) = cCoq_2eLists_2eList_2elast___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.Sets.Relations_1.Relation_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eSets_2eRelations__1_2eRelation,V_24X1) = cCoq_2eSets_2eRelations__1_2eRelation___24a1(V_24X1) ).

fof('$adef_Coq.Numbers.BinNums.Zneg_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2eZneg,V_24X1) = cCoq_2eNumbers_2eBinNums_2eZneg___24a1(V_24X1) ).

fof('$adef_$_prop_15792_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__prop__15792,V_24X1),V_24X2) = c_24__prop__15792___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.setoid_ring.Ring_theory.semi_ring_theory_$a6',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] :
      ( p(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2esemi__ring__theory,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6))
    <=> cCoq_2esetoid__ring_2eRing__theory_2esemi__ring__theory___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ) ).

fof('$adef_Coq.Reals.RIneq.mknonposreal_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eReals_2eRIneq_2emknonposreal,V_24X1) = cCoq_2eReals_2eRIneq_2emknonposreal___24a1(V_24X1) ).

fof('$adef_Coq.micromega.RingMicromega.ge_bool_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRingMicromega_2ege__bool,V_24X1),V_24X2) = cCoq_2emicromega_2eRingMicromega_2ege__bool___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Reals.RIneq.mknonnegreal_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eReals_2eRIneq_2emknonnegreal,V_24X1) = cCoq_2eReals_2eRIneq_2emknonnegreal___24a1(V_24X1) ).

fof('$adef_$_lam_44570_$a1',axiom,
    ! [V_24X1] : happ(c_24__lam__44570,V_24X1) = c_24__lam__44570___24a1(V_24X1) ).

fof('$adef_PLF.Imp.aeval_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cPLF_2eImp_2eaeval,V_24X1),V_24X2) = cPLF_2eImp_2eaeval___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Reals.Rdefinitions.Rgt_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eReals_2eRdefinitions_2eRgt,V_24X1),V_24X2))
    <=> cCoq_2eReals_2eRdefinitions_2eRgt___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.setoid_ring.Ring_polynom.PEpow_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEpow,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eRing__polynom_2ePEpow___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.NArith.BinNatDef.N.to_nat_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2eto__nat___24a1(V_24X1) ).

fof('$adef_Coq.Lists.SetoidList.transpose_restr2_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
      ( p(happ(happ(happ(happ(happ(cCoq_2eLists_2eSetoidList_2etranspose__restr2,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
    <=> cCoq_2eLists_2eSetoidList_2etranspose__restr2___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).

fof('$adef_$_lam_42298_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(c_24__lam__42298,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> c_24__lam__42298___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).

fof('$adef_PLF.Imp.ceval_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] :
      ( p(happ(happ(happ(cPLF_2eImp_2eceval,V_24X1),V_24X2),V_24X3))
    <=> cPLF_2eImp_2eceval___24a3(V_24X1,V_24X2,V_24X3) ) ).

fof('$adef_Coq.ZArith.Zeven.Zeven_$a1',axiom,
    ! [V_24X1] :
      ( p(happ(cCoq_2eZArith_2eZeven_2eZeven,V_24X1))
    <=> cCoq_2eZArith_2eZeven_2eZeven___24a1(V_24X1) ) ).

fof('$adef_PLF.Imp.AMinus_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cPLF_2eImp_2eAMinus,V_24X1),V_24X2) = cPLF_2eImp_2eAMinus___24a2(V_24X1,V_24X2) ).

fof('$adef_$_case_Coq.Init.Datatypes.list$26792_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2elist_2426792,V_24X1),V_24X2),V_24X3) = c_24__case__Coq_2eInit_2eDatatypes_2elist_2426792___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.Init.Specif.proj1_sig_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2eproj1__sig,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2eproj1__sig___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_$_case_Coq.Numbers.BinNums.positive$35167_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__case__Coq_2eNumbers_2eBinNums_2epositive_2435167,V_24X1),V_24X2) = c_24__case__Coq_2eNumbers_2eBinNums_2epositive_2435167___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.setoid_ring.Ring_polynom.PEsub_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEsub,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eRing__polynom_2ePEsub___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.Bool.Bool.reflect_$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('$adef_Coq.FSets.FSetPositive.PositiveSet.ct_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] :
      ( p(happ(happ(happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2ect,V_24X1),V_24X2),V_24X3))
    <=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2ect___24a3(V_24X1,V_24X2,V_24X3) ) ).

fof('$adef_Coq.setoid_ring.Ring_polynom.PX_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePX,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eRing__polynom_2ePX___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.Init.Nat.max_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2emax,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2emax___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.PArith.BinPosDef.Pos.pred_N_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2epred__N,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2epred__N___24a1(V_24X1) ).

fof('$adef_PLF.Imp.BreakImp.CIf_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cPLF_2eImp_2eBreakImp_2eCIf,V_24X1),V_24X2),V_24X3) = cPLF_2eImp_2eBreakImp_2eCIf___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.Structures.OrderedTypeEx.Z_as_OT.lt_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2elt,V_24X1),V_24X2))
    <=> cCoq_2eStructures_2eOrderedTypeEx_2eZ__as__OT_2elt___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.Lists.List.hd_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eLists_2eList_2ehd,V_24X1),V_24X2),V_24X3) = cCoq_2eLists_2eList_2ehd___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.Arith.Between.between_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] :
      ( p(happ(happ(happ(cCoq_2eArith_2eBetween_2ebetween,V_24X1),V_24X2),V_24X3))
    <=> cCoq_2eArith_2eBetween_2ebetween___24a3(V_24X1,V_24X2,V_24X3) ) ).

fof('$adef_Coq.micromega.RingMicromega.PsatzIn_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRingMicromega_2ePsatzIn,V_24X1),V_24X2) = cCoq_2emicromega_2eRingMicromega_2ePsatzIn___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Init.Datatypes.option_$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('$adef_Coq.PArith.BinPosDef.Pos.sub_mask_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2esub__mask___24a2(V_24X1,V_24X2) ).

fof('$adef_PLF.Imp.AExp.ANum_$a1',axiom,
    ! [V_24X1] : happ(cPLF_2eImp_2eAExp_2eANum,V_24X1) = cPLF_2eImp_2eAExp_2eANum___24a1(V_24X1) ).

fof('$adef_Coq.setoid_ring.Ring_polynom.PEI_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEI,V_24X1) = cCoq_2esetoid__ring_2eRing__polynom_2ePEI___24a1(V_24X1) ).

fof('$adef_Coq.Init.Specif.inright_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eSpecif_2einright,V_24X1),V_24X2) = cCoq_2eInit_2eSpecif_2einright___24a2(V_24X1,V_24X2) ).

fof('$adef_PLF.Imp.AExp.BEq_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cPLF_2eImp_2eAExp_2eBEq,V_24X1),V_24X2) = cPLF_2eImp_2eAExp_2eBEq___24a2(V_24X1,V_24X2) ).

fof('$adef_$_case_Coq.Init.Datatypes.nat$42617_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2enat_2442617,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__case__Coq_2eInit_2eDatatypes_2enat_2442617___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Norm.subst_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cNorm_2esubst,V_24X1),V_24X2),V_24X3) = cNorm_2esubst___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_PLF.Imp.BNot_$a1',axiom,
    ! [V_24X1] : happ(cPLF_2eImp_2eBNot,V_24X1) = cPLF_2eImp_2eBNot___24a1(V_24X1) ).

fof('$adef_PLF.Imp.BAnd_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cPLF_2eImp_2eBAnd,V_24X1),V_24X2) = cPLF_2eImp_2eBAnd___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.setoid_ring.Ring_polynom.Peq_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePeq,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eRing__polynom_2ePeq___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_$_lam_42290_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__42290,V_24X1),V_24X2),V_24X3) = c_24__lam__42290___24a3(V_24X1,V_24X2,V_24X3) ).

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('$adef_$_fix_42920_v_CANONICAL_0_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__fix__42920__v__CANONICAL__0,V_24X1),V_24X2) = c_24__fix__42920__v__CANONICAL__0___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Vectors.VectorDef.t_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eVectors_2eVectorDef_2et,V_24X1),V_24X2) = cCoq_2eVectors_2eVectorDef_2et___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.setoid_ring.Ring_polynom.PExpr_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2esetoid__ring_2eRing__polynom_2ePExpr,V_24X1) = cCoq_2esetoid__ring_2eRing__polynom_2ePExpr___24a1(V_24X1) ).

fof('$adef_Coq.Init.Datatypes.orb_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2eorb,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2eorb___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.setoid_ring.Ring_polynom.PEadd_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEadd,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eRing__polynom_2ePEadd___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.Arith.Plus.tail_plus_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eArith_2ePlus_2etail__plus,V_24X1),V_24X2) = cCoq_2eArith_2ePlus_2etail__plus___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.setoid_ring.Ring_theory.ring_morph_$a17',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17] :
      ( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2ering__morph,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14),V_24X15),V_24X16),V_24X17))
    <=> cCoq_2esetoid__ring_2eRing__theory_2ering__morph___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17) ) ).

fof('$adef_Coq.Init.Datatypes.CompOpp_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2eCompOpp,V_24X1) = cCoq_2eInit_2eDatatypes_2eCompOpp___24a1(V_24X1) ).

fof('$adef_Coq.setoid_ring.Field_theory.FEopp_$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('$adef_Coq.micromega.EnvRing.PEopp_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eEnvRing_2ePEopp,V_24X1),V_24X2) = cCoq_2emicromega_2eEnvRing_2ePEopp___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Init.Specif.exist2_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eInit_2eSpecif_2eexist2,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eInit_2eSpecif_2eexist2___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.Init.Datatypes.CompareSpec_$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('$adef_Norm.Arrow_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cNorm_2eArrow,V_24X1),V_24X2) = cNorm_2eArrow___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Init.Datatypes.xorb_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2exorb,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2exorb___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.micromega.RingMicromega.SORaddon_$a22',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22] :
      ( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2eSORaddon,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14),V_24X15),V_24X16),V_24X17),V_24X18),V_24X19),V_24X20),V_24X21),V_24X22))
    <=> cCoq_2emicromega_2eRingMicromega_2eSORaddon___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22) ) ).

fof('$adef_Coq.ZArith.Zpower.two_power_pos_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eZArith_2eZpower_2etwo__power__pos,V_24X1) = cCoq_2eZArith_2eZpower_2etwo__power__pos___24a1(V_24X1) ).

fof('$adef_Coq.Arith.Between.exists_between_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] :
      ( p(happ(happ(happ(cCoq_2eArith_2eBetween_2eexists__between,V_24X1),V_24X2),V_24X3))
    <=> cCoq_2eArith_2eBetween_2eexists__between___24a3(V_24X1,V_24X2,V_24X3) ) ).

fof('$adef_Coq.Strings.String.String_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eStrings_2eString_2eString,V_24X1),V_24X2) = cCoq_2eStrings_2eString_2eString___24a2(V_24X1,V_24X2) ).

fof('$adef_$_case_Coq.Init.Datatypes.nat$45341_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2enat_2445341,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__case__Coq_2eInit_2eDatatypes_2enat_2445341___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

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('$adef_$_prop_29554_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__prop__29554,V_24X1),V_24X2) = c_24__prop__29554___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Relations.Relation_Definitions.equivalence_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eRelations_2eRelation__Definitions_2eequivalence,V_24X1),V_24X2))
    <=> cCoq_2eRelations_2eRelation__Definitions_2eequivalence___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.ZArith.Znumtheory.Euclid_intro_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eZArith_2eZnumtheory_2eEuclid__intro,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eZArith_2eZnumtheory_2eEuclid__intro___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_Coq.Init.Datatypes.CompEqT_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2eCompEqT,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2eCompEqT___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.Init.Nat.square_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eNat_2esquare,V_24X1) = cCoq_2eInit_2eNat_2esquare___24a1(V_24X1) ).

fof('$adef_Coq.setoid_ring.Field_theory.FExpr_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2esetoid__ring_2eField__theory_2eFExpr,V_24X1) = cCoq_2esetoid__ring_2eField__theory_2eFExpr___24a1(V_24X1) ).

fof('$adef_Coq.micromega.RingMicromega.PsatzMulE_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2ePsatzMulE,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eRingMicromega_2ePsatzMulE___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.Classes.Morphisms.respectful_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eClasses_2eMorphisms_2erespectful,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eClasses_2eMorphisms_2erespectful___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.micromega.RingMicromega.PolEnv_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2emicromega_2eRingMicromega_2ePolEnv,V_24X1) = cCoq_2emicromega_2eRingMicromega_2ePolEnv___24a1(V_24X1) ).

fof('$adef_$_lam_44644_$a1',axiom,
    ! [V_24X1] : happ(c_24__lam__44644,V_24X1) = c_24__lam__44644___24a1(V_24X1) ).

fof('$adef_$_lam_42274_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__42274,V_24X1),V_24X2),V_24X3) = c_24__lam__42274___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.micromega.Refl.make_impl_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(cCoq_2emicromega_2eRefl_2emake__impl,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> cCoq_2emicromega_2eRefl_2emake__impl___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).

fof('$adef_Coq.micromega.Tauto.FF_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eFF,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eTauto_2eFF___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.ZArith.BinIntDef.Z.abs_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eabs,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eabs___24a1(V_24X1) ).

fof('$adef_Coq.PArith.BinPosDef.Pos.min_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2emin,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2emin___24a2(V_24X1,V_24X2) ).

fof('$adef_Norm.test_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cNorm_2etest,V_24X1),V_24X2),V_24X3) = cNorm_2etest___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.FSets.FSetPositive.PositiveSet.In_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn,V_24X1),V_24X2))
    <=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eIn___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.Init.Datatypes.identity_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] :
      ( p(happ(happ(happ(cCoq_2eInit_2eDatatypes_2eidentity,V_24X1),V_24X2),V_24X3))
    <=> cCoq_2eInit_2eDatatypes_2eidentity___24a3(V_24X1,V_24X2,V_24X3) ) ).

fof('$adef_PLF.Imp.ANum_$a1',axiom,
    ! [V_24X1] : happ(cPLF_2eImp_2eANum,V_24X1) = cPLF_2eImp_2eANum___24a1(V_24X1) ).

fof('$adef_Coq.Init.Nat.leb_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2eleb,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2eleb___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Init.Datatypes.id_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2eid,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2eid___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.NArith.BinNatDef.N.succ_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2esucc,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2esucc___24a1(V_24X1) ).

fof('$adef_Coq.Relations.Relation_Definitions.transitive_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eRelations_2eRelation__Definitions_2etransitive,V_24X1),V_24X2))
    <=> cCoq_2eRelations_2eRelation__Definitions_2etransitive___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.Structures.OrderedType.GT_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eStructures_2eOrderedType_2eGT,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eStructures_2eOrderedType_2eGT___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_Coq.Reals.Rdefinitions.Rle_$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('$adef_PLF.Imp.AExp.aevalR_first_try.aevalR_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cPLF_2eImp_2eAExp_2eaevalR__first__try_2eaevalR,V_24X1),V_24X2))
    <=> cPLF_2eImp_2eAExp_2eaevalR__first__try_2eaevalR___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Hammer.Tactics.Tactics.rdone_$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_42282_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__42282,V_24X1),V_24X2),V_24X3) = c_24__lam__42282___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_$_case_Coq.Init.Datatypes.bool$4574_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2ebool_244574,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_244574___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.Relations.Relation_Definitions.order_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eRelations_2eRelation__Definitions_2eorder,V_24X1),V_24X2))
    <=> cCoq_2eRelations_2eRelation__Definitions_2eorder___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.micromega.Tauto.TFormula_$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('$adef_PLF.Imp.aevalR_division.ADiv_$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('$adef_PLF.Imp.aevalR_extended.APlus_$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('$adef_Coq.setoid_ring.Ring_theory.id_phi_N_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2esetoid__ring_2eRing__theory_2eid__phi__N,V_24X1) = cCoq_2esetoid__ring_2eRing__theory_2eid__phi__N___24a1(V_24X1) ).

fof('$adef_Coq.micromega.EnvRing.zmon_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eEnvRing_2ezmon,V_24X1),V_24X2) = cCoq_2emicromega_2eEnvRing_2ezmon___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Vectors.Fin.FS_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eVectors_2eFin_2eFS,V_24X1),V_24X2) = cCoq_2eVectors_2eFin_2eFS___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Bool.Zerob.zerob_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eBool_2eZerob_2ezerob,V_24X1) = cCoq_2eBool_2eZerob_2ezerob___24a1(V_24X1) ).

fof('$adef_$_case_Norm.tm$2929_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__case__Norm_2etm_242929,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__case__Norm_2etm_242929___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

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('$adef_PLF.Smallstep.multi_$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('$adef_Coq.micromega.EnvRing.PExpr_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2emicromega_2eEnvRing_2ePExpr,V_24X1) = cCoq_2emicromega_2eEnvRing_2ePExpr___24a1(V_24X1) ).

fof('$adef_Coq.Init.Nat.eqb_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2eeqb,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2eeqb___24a2(V_24X1,V_24X2) ).

fof('$adef_$_lam_44633_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__lam__44633,V_24X1),V_24X2) = c_24__lam__44633___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.setoid_ring.Ring_theory.div_theory_$a7',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] :
      ( p(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2ediv__theory,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7))
    <=> cCoq_2esetoid__ring_2eRing__theory_2ediv__theory___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ) ).

fof('$adef_$_lam_32329_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__32329,V_24X1),V_24X2),V_24X3) = c_24__lam__32329___24a3(V_24X1,V_24X2,V_24X3) ).

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('$adef_Coq.Sorting.Sorted.HdRel_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(cCoq_2eSorting_2eSorted_2eHdRel,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> cCoq_2eSorting_2eSorted_2eHdRel___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).

fof('$adef_Coq.Init.Peano.ge_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eInit_2ePeano_2ege,V_24X1),V_24X2))
    <=> cCoq_2eInit_2ePeano_2ege___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Hammer.Tactics.Reconstr.rdone_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cHammer_2eTactics_2eReconstr_2erdone,V_24X1),V_24X2))
    <=> cHammer_2eTactics_2eReconstr_2erdone___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.Reals.Rfunctions.Z_spec_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRfunctions_2eZ__spec,V_24X1),V_24X2) = cCoq_2eReals_2eRfunctions_2eZ__spec___24a2(V_24X1,V_24X2) ).

fof('$adef_$_lam_42282_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(c_24__lam__42282,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> c_24__lam__42282___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).

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('$adef_Norm.step_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cNorm_2estep,V_24X1),V_24X2))
    <=> cNorm_2estep___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.Relations.Relation_Operators.clos_refl_trans_1n_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__1n,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__1n___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).

fof('$adef_Coq.Init.Decimal.Neg_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eNeg,V_24X1) = cCoq_2eInit_2eDecimal_2eNeg___24a1(V_24X1) ).

fof('$adef_Coq.NArith.BinNat.N.divide_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eNArith_2eBinNat_2eN_2edivide,V_24X1),V_24X2))
    <=> cCoq_2eNArith_2eBinNat_2eN_2edivide___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.Lists.SetoidList.transpose2_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(cCoq_2eLists_2eSetoidList_2etranspose2,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> cCoq_2eLists_2eSetoidList_2etranspose2___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).

fof('$adef_Coq.Lists.SetoidList.NoDupA_$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('$adef_Coq.PArith.BinPosDef.Pos.testbit_nat_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat___24a1(V_24X1) ).

fof('$adef_$_case_Coq.Init.Datatypes.prod$15423_$a9',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9] :
      ( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2eprod_2415423,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9))
    <=> c_24__case__Coq_2eInit_2eDatatypes_2eprod_2415423___24a9(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9) ) ).

fof('$adef_$_fix_43676_v_CANONICAL_0_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__fix__43676__v__CANONICAL__0,V_24X1),V_24X2) = c_24__fix__43676__v__CANONICAL__0___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.setoid_ring.Ring_theory.ring_eq_ext_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
      ( p(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
    <=> cCoq_2esetoid__ring_2eRing__theory_2ering__eq__ext___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).

fof('$adef_Coq.micromega.RingMicromega.eval_op1_$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('$adef_$_lam_42290_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(c_24__lam__42290,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> c_24__lam__42290___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('$adef_Coq.Logic.EqdepFacts.UIP_on__$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] :
      ( p(happ(happ(happ(cCoq_2eLogic_2eEqdepFacts_2eUIP__on__,V_24X1),V_24X2),V_24X3))
    <=> cCoq_2eLogic_2eEqdepFacts_2eUIP__on_____24a3(V_24X1,V_24X2,V_24X3) ) ).

fof('$adef_$_lam_44640_$a1',axiom,
    ! [V_24X1] : happ(c_24__lam__44640,V_24X1) = c_24__lam__44640___24a1(V_24X1) ).

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('$adef_Coq.Init.Byte.byte_of_byte_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eByte_2ebyte__of__byte,V_24X1) = cCoq_2eInit_2eByte_2ebyte__of__byte___24a1(V_24X1) ).

fof('$adef_PLF.Imp.AExp.BAnd_$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_4768_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__prop__4768,V_24X1),V_24X2) = c_24__prop__4768___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.ZArith.BinIntDef.Z.to_N_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eto__N,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eto__N___24a1(V_24X1) ).

fof('$adef_Coq.Arith.EqNat.eq_nat_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eArith_2eEqNat_2eeq__nat,V_24X1),V_24X2))
    <=> cCoq_2eArith_2eEqNat_2eeq__nat___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.Init.Datatypes.nat_rect_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eInit_2eDatatypes_2enat__rect,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eInit_2eDatatypes_2enat__rect___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.Lists.List.Forall2_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
      ( p(happ(happ(happ(happ(happ(cCoq_2eLists_2eList_2eForall2,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
    <=> cCoq_2eLists_2eList_2eForall2___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).

fof('$adef_Coq.micromega.Tauto.A_$a6',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eA,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = cCoq_2emicromega_2eTauto_2eA___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).

fof('$adef_Coq.Relations.Relation_Definitions.reflexive_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eRelations_2eRelation__Definitions_2ereflexive,V_24X1),V_24X2))
    <=> cCoq_2eRelations_2eRelation__Definitions_2ereflexive___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.micromega.EnvRing.vmon_$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('$adef_Coq.Init.Datatypes.nil_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2enil,V_24X1) = cCoq_2eInit_2eDatatypes_2enil___24a1(V_24X1) ).

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('$adef_$_case_Coq.Numbers.BinNums.Z$32710_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2432710,V_24X1),V_24X2),V_24X3) = c_24__case__Coq_2eNumbers_2eBinNums_2eZ_2432710___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.Logic.EqdepFacts.eq_dep1_$a6',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] :
      ( p(happ(happ(happ(happ(happ(happ(cCoq_2eLogic_2eEqdepFacts_2eeq__dep1,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6))
    <=> cCoq_2eLogic_2eEqdepFacts_2eeq__dep1___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ) ).

fof('$adef_Coq.setoid_ring.Field_theory.almost_field_theory_$a10',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10] :
      ( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10))
    <=> cCoq_2esetoid__ring_2eField__theory_2ealmost__field__theory___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10) ) ).

fof('$adef_Coq.Arith.Wf_nat.ltof_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(cCoq_2eArith_2eWf__nat_2eltof,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> cCoq_2eArith_2eWf__nat_2eltof___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).

fof('$adef_$_lam_44548_$a1',axiom,
    ! [V_24X1] : happ(c_24__lam__44548,V_24X1) = c_24__lam__44548___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('$adef_Coq.NArith.BinNatDef.N.max_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2emax,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2emax___24a2(V_24X1,V_24X2) ).

fof('$adef_$_case_Coq.Init.Datatypes.nat$32693_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2enat_2432693,V_24X1),V_24X2),V_24X3) = c_24__case__Coq_2eInit_2eDatatypes_2enat_2432693___24a3(V_24X1,V_24X2,V_24X3) ).

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('$adef_PLF.Imp.aevalR_division.ANum_$a1',axiom,
    ! [V_24X1] : happ(cPLF_2eImp_2eaevalR__division_2eANum,V_24X1) = cPLF_2eImp_2eaevalR__division_2eANum___24a1(V_24X1) ).

fof('$adef_Coq.Reals.Rdefinitions.Rge_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eReals_2eRdefinitions_2eRge,V_24X1),V_24X2))
    <=> cCoq_2eReals_2eRdefinitions_2eRge___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.PArith.BinPosDef.Pos.mul_$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('$adef_$_case_Coq.Init.Datatypes.nat$45560_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2enat_2445560,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__case__Coq_2eInit_2eDatatypes_2enat_2445560___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.Init.Datatypes.CompGtT_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2eCompGtT,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2eCompGtT___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.PArith.BinPosDef.Pos.testbit_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Reals.Rdefinitions.Rmult_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRdefinitions_2eRmult,V_24X1),V_24X2) = cCoq_2eReals_2eRdefinitions_2eRmult___24a2(V_24X1,V_24X2) ).

fof('$adef_PLF.Smallstep.eval_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cPLF_2eSmallstep_2eeval,V_24X1),V_24X2))
    <=> cPLF_2eSmallstep_2eeval___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.Reals.Rfunctions.ZintNeg_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eReals_2eRfunctions_2eZintNeg,V_24X1),V_24X2) = cCoq_2eReals_2eRfunctions_2eZintNeg___24a2(V_24X1,V_24X2) ).

fof('$adef_$_case_Coq.Init.Datatypes.bool$43239_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2ebool_2443239,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_2443239___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_Coq.ZArith.Znumtheory.rel_prime_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eZArith_2eZnumtheory_2erel__prime,V_24X1),V_24X2))
    <=> cCoq_2eZArith_2eZnumtheory_2erel__prime___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.NArith.BinNatDef.N.mul_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2emul,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2emul___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Init.Nat.pred_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eNat_2epred,V_24X1) = cCoq_2eInit_2eNat_2epred___24a1(V_24X1) ).

fof('$adef_Coq.ZArith.Znumtheory.Bezout_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] :
      ( p(happ(happ(happ(cCoq_2eZArith_2eZnumtheory_2eBezout,V_24X1),V_24X2),V_24X3))
    <=> cCoq_2eZArith_2eZnumtheory_2eBezout___24a3(V_24X1,V_24X2,V_24X3) ) ).

fof('$adef_Coq.micromega.Tauto.GFormula_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eGFormula,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eTauto_2eGFormula___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.Numbers.BinNums.Npos_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2eNpos,V_24X1) = cCoq_2eNumbers_2eBinNums_2eNpos___24a1(V_24X1) ).

fof('$adef_Coq.setoid_ring.Ring_theory.Morphism_$a17',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17] : happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2eMorphism,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13),V_24X14),V_24X15),V_24X16),V_24X17) = cCoq_2esetoid__ring_2eRing__theory_2eMorphism___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17) ).

fof('$adef_Coq.setoid_ring.Ring_theory.IDphi_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__theory_2eIDphi,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__theory_2eIDphi___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Init.Specif.exist_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2eexist,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2eexist___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.ZArith.BinInt.Z.le_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2ele,V_24X1),V_24X2) = cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Init.Specif.projT1_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2eprojT1,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2eprojT1___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_PLF.Smallstep.bstep_$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('$adef_Coq.Numbers.BinNums.xI_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2exI,V_24X1) = cCoq_2eNumbers_2eBinNums_2exI___24a1(V_24X1) ).

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('$adef_$_prop_29553_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__29553,V_24X1),V_24X2),V_24X3) = c_24__prop__29553___24a3(V_24X1,V_24X2,V_24X3) ).

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('$adef_Coq.ZArith.Zeven.Zodd_$a1',axiom,
    ! [V_24X1] :
      ( p(happ(cCoq_2eZArith_2eZeven_2eZodd,V_24X1))
    <=> cCoq_2eZArith_2eZeven_2eZodd___24a1(V_24X1) ) ).

fof('$adef_PLF.Imp.BEq_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cPLF_2eImp_2eBEq,V_24X1),V_24X2) = cPLF_2eImp_2eBEq___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Init.Specif.inleft_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2einleft,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2einleft___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_PLF.Imp.BreakImp.CSeq_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cPLF_2eImp_2eBreakImp_2eCSeq,V_24X1),V_24X2) = cPLF_2eImp_2eBreakImp_2eCSeq___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.micromega.EnvRing.Pinj_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePinj,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eEnvRing_2ePinj___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.Structures.GenericMinMax.gmax_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eStructures_2eGenericMinMax_2egmax,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eStructures_2eGenericMinMax_2egmax___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.Init.Wf.well_founded_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eInit_2eWf_2ewell__founded,V_24X1),V_24X2))
    <=> cCoq_2eInit_2eWf_2ewell__founded___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.micromega.RMicromega.CPow_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRMicromega_2eCPow,V_24X1),V_24X2) = cCoq_2emicromega_2eRMicromega_2eCPow___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.ZArith.BinIntDef.Z.abs_nat_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__nat,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eabs__nat___24a1(V_24X1) ).

fof('$adef_Coq.micromega.RMicromega.CPlus_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRMicromega_2eCPlus,V_24X1),V_24X2) = cCoq_2emicromega_2eRMicromega_2eCPlus___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Init.Datatypes.cons_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDatatypes_2econs,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDatatypes_2econs___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.setoid_ring.Field_theory.field_theory_$a10',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10] :
      ( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2efield__theory,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10))
    <=> cCoq_2esetoid__ring_2eField__theory_2efield__theory___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10) ) ).

fof('$adef_Coq.setoid_ring.Ring_theory.Computational_$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('$adef_Coq.Init.Decimal.D1_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD1,V_24X1) = cCoq_2eInit_2eDecimal_2eD1___24a1(V_24X1) ).

fof('$adef_Coq.NArith.BinNat.N.recursion_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eNArith_2eBinNat_2eN_2erecursion,V_24X1) = cCoq_2eNArith_2eBinNat_2eN_2erecursion___24a1(V_24X1) ).

fof('$adef_Coq.ZArith.BinIntDef.Z.to_pos_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eto__pos,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eto__pos___24a1(V_24X1) ).

fof('$adef_Coq.ZArith.BinIntDef.Z.of_nat_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eof__nat___24a1(V_24X1) ).

fof('$adef_Coq.Init.Nat.div2_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eNat_2ediv2,V_24X1) = cCoq_2eInit_2eNat_2ediv2___24a1(V_24X1) ).

fof('$adef_Norm.var_$a1',axiom,
    ! [V_24X1] : happ(cNorm_2evar,V_24X1) = cNorm_2evar___24a1(V_24X1) ).

fof('$adef_Coq.Init.Datatypes.pair_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eInit_2eDatatypes_2epair,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eInit_2eDatatypes_2epair___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.Init.Decimal.int_of_int_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eint__of__int,V_24X1) = cCoq_2eInit_2eDecimal_2eint__of__int___24a1(V_24X1) ).

fof('$adef_Coq.Init.Datatypes.negb_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2enegb,V_24X1) = cCoq_2eInit_2eDatatypes_2enegb___24a1(V_24X1) ).

fof('$adef_Coq.micromega.RMicromega.COpp_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2emicromega_2eRMicromega_2eCOpp,V_24X1) = cCoq_2emicromega_2eRMicromega_2eCOpp___24a1(V_24X1) ).

fof('$adef_Coq.Init.Nat.testbit_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2etestbit,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2etestbit___24a2(V_24X1,V_24X2) ).

fof('$adef_PLF.Imp.CIf_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cPLF_2eImp_2eCIf,V_24X1),V_24X2),V_24X3) = cPLF_2eImp_2eCIf___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.PArith.BinPosDef.Pos.IsPos_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2eIsPos___24a1(V_24X1) ).

fof('$adef_Coq.PArith.BinPosDef.Pos.div2_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2ediv2,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2ediv2___24a1(V_24X1) ).

fof('$adef_$_case_Coq.Init.Datatypes.nat$45138_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2enat_2445138,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__case__Coq_2eInit_2eDatatypes_2enat_2445138___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_$_case_Coq.Init.Datatypes.nat$43635_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2enat_2443635,V_24X1),V_24X2) = c_24__case__Coq_2eInit_2eDatatypes_2enat_2443635___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Reals.Rdefinitions.Ropp_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eReals_2eRdefinitions_2eRopp,V_24X1) = cCoq_2eReals_2eRdefinitions_2eRopp___24a1(V_24X1) ).

fof('$adef_$_case_Coq.Init.Datatypes.nat$43322_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2enat_2443322,V_24X1),V_24X2) = c_24__case__Coq_2eInit_2eDatatypes_2enat_2443322___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.PArith.BinPosDef.Pos.max_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2emax,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2emax___24a2(V_24X1,V_24X2) ).

fof('$adef_$_lam_44570_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__lam__44570,V_24X1),V_24X2) = c_24__lam__44570___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.ZArith.BinIntDef.Z.pow_pos_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2epow__pos,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2epow__pos___24a2(V_24X1,V_24X2) ).

fof('$adef_Norm.snd_$a1',axiom,
    ! [V_24X1] : happ(cNorm_2esnd,V_24X1) = cNorm_2esnd___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('$adef_Coq.micromega.RingMicromega.Psatz_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2emicromega_2eRingMicromega_2ePsatz,V_24X1) = cCoq_2emicromega_2eRingMicromega_2ePsatz___24a1(V_24X1) ).

fof('$adef_$_lam_32329_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__lam__32329,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__lam__32329___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

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('$adef_PLF.Smallstep.Combined.P_$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('$adef_Coq.Structures.OrderedType.EQ_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eStructures_2eOrderedType_2eEQ,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eStructures_2eOrderedType_2eEQ___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_Coq.Numbers.BinNums.Zpos_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2eZpos,V_24X1) = cCoq_2eNumbers_2eBinNums_2eZpos___24a1(V_24X1) ).

fof('$adef_Coq.Arith.Even.odd_$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('$adef_Coq.Lists.List.ForallOrdPairs_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] :
      ( p(happ(happ(happ(cCoq_2eLists_2eList_2eForallOrdPairs,V_24X1),V_24X2),V_24X3))
    <=> cCoq_2eLists_2eList_2eForallOrdPairs___24a3(V_24X1,V_24X2,V_24X3) ) ).

fof('$adef_PLF.Smallstep.normal_form_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cPLF_2eSmallstep_2enormal__form,V_24X1),V_24X2) = cPLF_2eSmallstep_2enormal__form___24a2(V_24X1,V_24X2) ).

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('$adef_PLF.Smallstep.Temp4.value_$a1',axiom,
    ! [V_24X1] :
      ( p(happ(cPLF_2eSmallstep_2eTemp4_2evalue,V_24X1))
    <=> cPLF_2eSmallstep_2eTemp4_2evalue___24a1(V_24X1) ) ).

fof('$adef_Coq.Relations.Relation_Operators.clos_trans_1n_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eclos__trans__1n,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> cCoq_2eRelations_2eRelation__Operators_2eclos__trans__1n___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).

fof('$adef_Coq.Init.Logic_Type.notT_$a1',axiom,
    ! [V_24X1] :
      ( p(happ(cCoq_2eInit_2eLogic__Type_2enotT,V_24X1))
    <=> cCoq_2eInit_2eLogic__Type_2enotT___24a1(V_24X1) ) ).

fof('$adef_Coq.Init.Datatypes.list_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2elist,V_24X1) = cCoq_2eInit_2eDatatypes_2elist___24a1(V_24X1) ).

fof('$adef_Coq.Init.Nat.add_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2eadd,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2eadd___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Init.Specif.sigT2_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eSpecif_2esigT2,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eSpecif_2esigT2___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.Init.Nat.sub_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2esub,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2esub___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Structures.OrderedType.Compare_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eStructures_2eOrderedType_2eCompare,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eStructures_2eOrderedType_2eCompare___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_Coq.PArith.BinPos.Pos.SubMaskSpec_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] :
      ( p(happ(happ(happ(cCoq_2ePArith_2eBinPos_2ePos_2eSubMaskSpec,V_24X1),V_24X2),V_24X3))
    <=> cCoq_2ePArith_2eBinPos_2ePos_2eSubMaskSpec___24a3(V_24X1,V_24X2,V_24X3) ) ).

fof('$adef_Coq.micromega.Tauto.clause_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eTauto_2eclause,V_24X1),V_24X2) = cCoq_2emicromega_2eTauto_2eclause___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.NArith.BinNatDef.N.add_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2eadd,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2eadd___24a2(V_24X1,V_24X2) ).

fof('$adef_PLF.Imp.AId_$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('$adef_Coq.setoid_ring.Field_theory.FEc_$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('$adef_Coq.Bool.Bool.ReflectF_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eBool_2eBool_2eReflectF,V_24X1) = cCoq_2eBool_2eBool_2eReflectF___24a1(V_24X1) ).

fof('$adef_Coq.micromega.ZMicromega.Vars.Facts.MP.Dec.FSetDecideAuxiliary.FSet_Prop_$a1',axiom,
    ! [V_24X1] :
      ( p(happ(cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__Prop,V_24X1))
    <=> cCoq_2emicromega_2eZMicromega_2eVars_2eFacts_2eMP_2eDec_2eFSetDecideAuxiliary_2eFSet__Prop___24a1(V_24X1) ) ).

fof('$adef_Coq.Reals.Rfunctions.ZintNull_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eReals_2eRfunctions_2eZintNull,V_24X1) = cCoq_2eReals_2eRfunctions_2eZintNull___24a1(V_24X1) ).

fof('$adef_Coq.setoid_ring.Field_theory.FEI_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2esetoid__ring_2eField__theory_2eFEI,V_24X1) = cCoq_2esetoid__ring_2eField__theory_2eFEI___24a1(V_24X1) ).

fof('$adef_Coq.micromega.EnvRing.PEX_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eEnvRing_2ePEX,V_24X1),V_24X2) = cCoq_2emicromega_2eEnvRing_2ePEX___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.ZArith.BinIntDef.Z.pos_sub_$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_35549_$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__35549,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = c_24__lam__35549___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).

fof('$adef_Coq.Bool.Bool.ReflectT_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eBool_2eBool_2eReflectT,V_24X1) = cCoq_2eBool_2eBool_2eReflectT___24a1(V_24X1) ).

fof('$adef_Coq.ZArith.Znumtheory.Euclid_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eZnumtheory_2eEuclid,V_24X1),V_24X2) = cCoq_2eZArith_2eZnumtheory_2eEuclid___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Init.Specif.right_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eSpecif_2eright,V_24X1),V_24X2) = cCoq_2eInit_2eSpecif_2eright___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.setoid_ring.Ring_theory.power_theory_$a7',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] :
      ( p(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2epower__theory,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7))
    <=> cCoq_2esetoid__ring_2eRing__theory_2epower__theory___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ) ).

fof('$adef_PLF.Imp.AExp.AMinus_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cPLF_2eImp_2eAExp_2eAMinus,V_24X1),V_24X2) = cPLF_2eImp_2eAExp_2eAMinus___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Lists.List.fold_left_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eLists_2eList_2efold__left,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eLists_2eList_2efold__left___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_Coq.Lists.List.Forall_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] :
      ( p(happ(happ(happ(cCoq_2eLists_2eList_2eForall,V_24X1),V_24X2),V_24X3))
    <=> cCoq_2eLists_2eList_2eForall___24a3(V_24X1,V_24X2,V_24X3) ) ).

fof('$adef_Coq.setoid_ring.Ring_polynom.Pinj_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePinj,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eRing__polynom_2ePinj___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_$_case_Coq.Init.Datatypes.nat$44186_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2enat_2444186,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__case__Coq_2eInit_2eDatatypes_2enat_2444186___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.Sorting.Sorted.StronglySorted_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] :
      ( p(happ(happ(happ(cCoq_2eSorting_2eSorted_2eStronglySorted,V_24X1),V_24X2),V_24X3))
    <=> cCoq_2eSorting_2eSorted_2eStronglySorted___24a3(V_24X1,V_24X2,V_24X3) ) ).

fof('$adef_PLF.Smallstep.value_$a1',axiom,
    ! [V_24X1] :
      ( p(happ(cPLF_2eSmallstep_2evalue,V_24X1))
    <=> cPLF_2eSmallstep_2evalue___24a1(V_24X1) ) ).

fof('$adef_Coq.NArith.BinNatDef.N.lxor_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2elxor,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2elxor___24a2(V_24X1,V_24X2) ).

fof('$adef_$_case_Coq.Init.Datatypes.nat$45247_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2enat_2445247,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__case__Coq_2eInit_2eDatatypes_2enat_2445247___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_PLF.Smallstep.Combined.value_$a1',axiom,
    ! [V_24X1] :
      ( p(happ(cPLF_2eSmallstep_2eCombined_2evalue,V_24X1))
    <=> cPLF_2eSmallstep_2eCombined_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('$adef_Coq.Lists.List.Add_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(cCoq_2eLists_2eList_2eAdd,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> cCoq_2eLists_2eList_2eAdd___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).

fof('$adef_Coq.micromega.RMicromega.CMinus_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRMicromega_2eCMinus,V_24X1),V_24X2) = cCoq_2emicromega_2eRMicromega_2eCMinus___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.ZArith.Zlogarithm.log_inf_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eZArith_2eZlogarithm_2elog__inf,V_24X1) = cCoq_2eZArith_2eZlogarithm_2elog__inf___24a1(V_24X1) ).

fof('$adef_PLF.Smallstep.C_$a1',axiom,
    ! [V_24X1] : happ(cPLF_2eSmallstep_2eC,V_24X1) = cPLF_2eSmallstep_2eC___24a1(V_24X1) ).

fof('$adef_Coq.Bool.Bool.ifb_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eBool_2eBool_2eifb,V_24X1),V_24X2),V_24X3) = cCoq_2eBool_2eBool_2eifb___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.Init.Decimal.D5_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD5,V_24X1) = cCoq_2eInit_2eDecimal_2eD5___24a1(V_24X1) ).

fof('$adef_Coq.PArith.BinPosDef.Pos.sub_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2esub,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2esub___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.NArith.BinNatDef.N.compare_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2ecompare,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2ecompare___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.setoid_ring.Field_theory.FEadd_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEadd,V_24X1),V_24X2),V_24X3) = cCoq_2esetoid__ring_2eField__theory_2eFEadd___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.Init.Decimal.uint_of_uint_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2euint__of__uint,V_24X1) = cCoq_2eInit_2eDecimal_2euint__of__uint___24a1(V_24X1) ).

fof('$adef_$_let_var_6_p_32780_32783_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__let__var__6__p__32780__32783,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__let__var__6__p__32780__32783___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.ZArith.BinIntDef.Z.odd_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eodd,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eodd___24a1(V_24X1) ).

fof('$adef_Coq.PArith.BinPosDef.Pos.lxor_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2elxor,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2elxor___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Init.Datatypes.fst_$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('$adef_$_fix_3546_v_CANONICAL_0_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__fix__3546__v__CANONICAL__0,V_24X1),V_24X2),V_24X3) = c_24__fix__3546__v__CANONICAL__0___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_$_prop_4766_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__prop__4766,V_24X1),V_24X2) = c_24__prop__4766___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Init.Datatypes.S_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eDatatypes_2eS,V_24X1) = cCoq_2eInit_2eDatatypes_2eS___24a1(V_24X1) ).

fof('$adef_PLF.Imp.aevalR_extended.aevalR_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cPLF_2eImp_2eaevalR__extended_2eaevalR,V_24X1),V_24X2))
    <=> cPLF_2eImp_2eaevalR__extended_2eaevalR___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.Strings.Ascii.Ascii_$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('$adef_Norm.fst_$a1',axiom,
    ! [V_24X1] : happ(cNorm_2efst,V_24X1) = cNorm_2efst___24a1(V_24X1) ).

fof('$adef_Coq.micromega.EnvRing.PEpow_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePEpow,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eEnvRing_2ePEpow___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.setoid_ring.Ring_polynom.zmon_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ezmon,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__polynom_2ezmon___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.setoid_ring.Ring_theory.semi_morph_$a13',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13] :
      ( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2esemi__morph,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10),V_24X11),V_24X12),V_24X13))
    <=> cCoq_2esetoid__ring_2eRing__theory_2esemi__morph___24a13(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13) ) ).

fof('$adef_Coq.micromega.VarMap.Empty_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2emicromega_2eVarMap_2eEmpty,V_24X1) = cCoq_2emicromega_2eVarMap_2eEmpty___24a1(V_24X1) ).

fof('$adef_Coq.micromega.RingMicromega.PsatzAdd_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eRingMicromega_2ePsatzAdd,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eRingMicromega_2ePsatzAdd___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_PLF.Smallstep.CImp.CAss_$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('$adef_Coq.PArith.BinPos.Pos.PeanoView_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2ePArith_2eBinPos_2ePos_2ePeanoView,V_24X1) = cCoq_2ePArith_2eBinPos_2ePos_2ePeanoView___24a1(V_24X1) ).

fof('$adef_Coq.ZArith.BinIntDef.Z.add_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eadd,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2eadd___24a2(V_24X1,V_24X2) ).

fof('$adef_$_case_Coq.Init.Datatypes.bool$3843_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2ebool_243843,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_243843___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.Init.Decimal.DecimalExp_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2eInit_2eDecimal_2eDecimalExp,V_24X1),V_24X2),V_24X3) = cCoq_2eInit_2eDecimal_2eDecimalExp___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.ZArith.BinIntDef.Z.min_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2emin,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2emin___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.micromega.Tauto.N_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eN,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2emicromega_2eTauto_2eN___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_$_case_Coq.Init.Datatypes.list$26705_$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_2426705,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__case__Coq_2eInit_2eDatatypes_2elist_2426705___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).

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('$adef_$_case_Coq.Init.Datatypes.bool$3576_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2ebool_243576,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_243576___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.micromega.RingMicromega.Formula_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2emicromega_2eRingMicromega_2eFormula,V_24X1) = cCoq_2emicromega_2eRingMicromega_2eFormula___24a1(V_24X1) ).

fof('$adef_Coq.Reals.RIneq.mknegreal_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eReals_2eRIneq_2emknegreal,V_24X1) = cCoq_2eReals_2eRIneq_2emknegreal___24a1(V_24X1) ).

fof('$adef_Coq.setoid_ring.Ring_theory.SRsub_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2eSRsub,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eRing__theory_2eSRsub___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_PLF.Imp.CAss_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cPLF_2eImp_2eCAss,V_24X1),V_24X2) = cPLF_2eImp_2eCAss___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.setoid_ring.InitialRing.gen_phiPOS1_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2esetoid__ring_2eInitialRing_2egen__phiPOS1___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_Coq.micromega.ZMicromega.RatProof_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eZMicromega_2eRatProof,V_24X1),V_24X2) = cCoq_2emicromega_2eZMicromega_2eRatProof___24a2(V_24X1,V_24X2) ).

fof('$adef_PLF.Smallstep.relation_$a1',axiom,
    ! [V_24X1] : happ(cPLF_2eSmallstep_2erelation,V_24X1) = cPLF_2eSmallstep_2erelation___24a1(V_24X1) ).

fof('$adef_Coq.micromega.RingMicromega.PolC_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2emicromega_2eRingMicromega_2ePolC,V_24X1) = cCoq_2emicromega_2eRingMicromega_2ePolC___24a1(V_24X1) ).

fof('$adef_$_fix_43006_v_CANONICAL_0_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__fix__43006__v__CANONICAL__0,V_24X1),V_24X2) = c_24__fix__43006__v__CANONICAL__0___24a2(V_24X1,V_24X2) ).

fof('$adef_$_case_Coq.Init.Datatypes.nat$42757_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2enat_2442757,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__case__Coq_2eInit_2eDatatypes_2enat_2442757___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

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('$adef_PLF.Imp.AMult_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cPLF_2eImp_2eAMult,V_24X1),V_24X2) = cPLF_2eImp_2eAMult___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.micromega.RingMicromega.PsatzC_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2emicromega_2eRingMicromega_2ePsatzC,V_24X1),V_24X2) = cCoq_2emicromega_2eRingMicromega_2ePsatzC___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.ZArith.BinInt.Zne_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eZArith_2eBinInt_2eZne,V_24X1),V_24X2))
    <=> cCoq_2eZArith_2eBinInt_2eZne___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.Reals.RIneq.Rsqr_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eReals_2eRIneq_2eRsqr,V_24X1) = cCoq_2eReals_2eRIneq_2eRsqr___24a1(V_24X1) ).

fof('$adef_Coq.PArith.BinPosDef.Pos.compare_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2ecompare___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Lists.SetoidList.InA_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(cCoq_2eLists_2eSetoidList_2eInA,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> cCoq_2eLists_2eSetoidList_2eInA___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).

fof('$adef_$_prop_29548_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__prop__29548,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__prop__29548___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.setoid_ring.InitialRing.mkhypo_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eInitialRing_2emkhypo,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eInitialRing_2emkhypo___24a2(V_24X1,V_24X2) ).

fof('$adef_Norm.abs_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cNorm_2eabs,V_24X1),V_24X2),V_24X3) = cNorm_2eabs___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_$_case_Coq.Init.Datatypes.nat$32715_$a1',axiom,
    ! [V_24X1] : happ(c_24__case__Coq_2eInit_2eDatatypes_2enat_2432715,V_24X1) = c_24__case__Coq_2eInit_2eDatatypes_2enat_2432715___24a1(V_24X1) ).

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('$adef_Coq.Reals.Rdefinitions.Rlt_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eReals_2eRdefinitions_2eRlt,V_24X1),V_24X2))
    <=> cCoq_2eReals_2eRdefinitions_2eRlt___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.Reals.RIneq.mknonzeroreal_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eReals_2eRIneq_2emknonzeroreal,V_24X1) = cCoq_2eReals_2eRIneq_2emknonzeroreal___24a1(V_24X1) ).

fof('$adef_Coq.ZArith.BinIntDef.Z.sub_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2esub,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2esub___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.ZArith.BinIntDef.Z.div_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2ediv,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2ediv___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.setoid_ring.Ring_polynom.PEopp_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEopp,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eRing__polynom_2ePEopp___24a2(V_24X1,V_24X2) ).

fof('$adef_$_prop_35094_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__35094,V_24X1),V_24X2),V_24X3) = c_24__prop__35094___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.micromega.RingMicromega.PsatzZ_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2emicromega_2eRingMicromega_2ePsatzZ,V_24X1) = cCoq_2emicromega_2eRingMicromega_2ePsatzZ___24a1(V_24X1) ).

fof('$adef_Coq.Bool.Bool.Is_true_$a1',axiom,
    ! [V_24X1] :
      ( p(happ(cCoq_2eBool_2eBool_2eIs__true,V_24X1))
    <=> cCoq_2eBool_2eBool_2eIs__true___24a1(V_24X1) ) ).

fof('$adef_$_lam_35549_$a6',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6] : happ(happ(happ(happ(happ(happ(c_24__lam__35549,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6) = c_24__lam__35549___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6) ).

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('$adef_Coq.Lists.List.fold_right_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eLists_2eList_2efold__right,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eLists_2eList_2efold__right___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_Coq.setoid_ring.Ring_theory.pow_pos_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2epow__pos,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2esetoid__ring_2eRing__theory_2epow__pos___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_$_prop_35092_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__prop__35092,V_24X1),V_24X2) = c_24__prop__35092___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Relations.Relation_Operators.Ltl_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eLtl,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> cCoq_2eRelations_2eRelation__Operators_2eLtl___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).

fof('$adef_Coq.Init.Nat.pow_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eNat_2epow,V_24X1),V_24X2) = cCoq_2eInit_2eNat_2epow___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.micromega.Tauto.I_$a7',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7] : happ(happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eTauto_2eI,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7) = cCoq_2emicromega_2eTauto_2eI___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7) ).

fof('$adef_Coq.micromega.Refl.make_conj_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] :
      ( p(happ(happ(happ(cCoq_2emicromega_2eRefl_2emake__conj,V_24X1),V_24X2),V_24X3))
    <=> cCoq_2emicromega_2eRefl_2emake__conj___24a3(V_24X1,V_24X2,V_24X3) ) ).

fof('$adef_PLF.Imp.AExp.APlus_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cPLF_2eImp_2eAExp_2eAPlus,V_24X1),V_24X2) = cPLF_2eImp_2eAExp_2eAPlus___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.PArith.BinPos.Pos.switch_Eq_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPos_2ePos_2eswitch__Eq,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPos_2ePos_2eswitch__Eq___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Init.Nat.odd_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eNat_2eodd,V_24X1) = cCoq_2eInit_2eNat_2eodd___24a1(V_24X1) ).

fof('$adef_PLF.Imp.SPush_$a1',axiom,
    ! [V_24X1] : happ(cPLF_2eImp_2eSPush,V_24X1) = cPLF_2eImp_2eSPush___24a1(V_24X1) ).

fof('$adef_Coq.ZArith.BinIntDef.Z.even_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eZArith_2eBinIntDef_2eZ_2eeven,V_24X1) = cCoq_2eZArith_2eBinIntDef_2eZ_2eeven___24a1(V_24X1) ).

fof('$adef_Coq.ZArith.BinInt.Z.gt_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2egt,V_24X1),V_24X2))
    <=> cCoq_2eZArith_2eBinInt_2eZ_2egt___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.Init.Logic.eq_rect_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2eInit_2eLogic_2eeq__rect,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2eInit_2eLogic_2eeq__rect___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_Coq.setoid_ring.Ring_polynom.PEO_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2esetoid__ring_2eRing__polynom_2ePEO,V_24X1) = cCoq_2esetoid__ring_2eRing__polynom_2ePEO___24a1(V_24X1) ).

fof('$adef_$_case_Coq.Init.Datatypes.nat$44509_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2enat_2444509,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__case__Coq_2eInit_2eDatatypes_2enat_2444509___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.setoid_ring.Ring_theory.sign_theory_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2esign__theory,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> cCoq_2esetoid__ring_2eRing__theory_2esign__theory___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).

fof('$adef_Coq.Numbers.BinNums.xO_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eNumbers_2eBinNums_2exO,V_24X1) = cCoq_2eNumbers_2eBinNums_2exO___24a1(V_24X1) ).

fof('$adef_Coq.NArith.BinNatDef.N.even_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2eeven,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2eeven___24a1(V_24X1) ).

fof('$adef_Coq.setoid_ring.Field_theory.FEX_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEX,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2eFEX___24a2(V_24X1,V_24X2) ).

fof('$adef_PLF.Imp.APlus_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cPLF_2eImp_2eAPlus,V_24X1),V_24X2) = cPLF_2eImp_2eAPlus___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Lists.List.NoDup_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eLists_2eList_2eNoDup,V_24X1),V_24X2))
    <=> cCoq_2eLists_2eList_2eNoDup___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.Vectors.VectorDef.nil_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eVectors_2eVectorDef_2enil,V_24X1) = cCoq_2eVectors_2eVectorDef_2enil___24a1(V_24X1) ).

fof('$adef_PLF.Maps.total_map_$a1',axiom,
    ! [V_24X1] : happ(cPLF_2eMaps_2etotal__map,V_24X1) = cPLF_2eMaps_2etotal__map___24a1(V_24X1) ).

fof('$adef_Coq.Lists.SetoidList.transpose_restr_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] :
      ( p(happ(happ(happ(happ(happ(cCoq_2eLists_2eSetoidList_2etranspose__restr,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5))
    <=> cCoq_2eLists_2eSetoidList_2etranspose__restr___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ) ).

fof('$adef_PLF.Smallstep.Temp4.Temp5.step_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cPLF_2eSmallstep_2eTemp4_2eTemp5_2estep,V_24X1),V_24X2))
    <=> cPLF_2eSmallstep_2eTemp4_2eTemp5_2estep___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.Init.Specif.left_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eSpecif_2eleft,V_24X1),V_24X2) = cCoq_2eInit_2eSpecif_2eleft___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.setoid_ring.Field_theory.FEinv_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2esetoid__ring_2eField__theory_2eFEinv,V_24X1),V_24X2) = cCoq_2esetoid__ring_2eField__theory_2eFEinv___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.ZArith.Zpower.Zdiv_rest_proof_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2eZArith_2eZpower_2eZdiv__rest__proof,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2eZArith_2eZpower_2eZdiv__rest__proof___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.Init.Wf.Acc_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] :
      ( p(happ(happ(happ(cCoq_2eInit_2eWf_2eAcc,V_24X1),V_24X2),V_24X3))
    <=> cCoq_2eInit_2eWf_2eAcc___24a3(V_24X1,V_24X2,V_24X3) ) ).

fof('$adef_Coq.setoid_ring.Ring_theory.pow_N_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(cCoq_2esetoid__ring_2eRing__theory_2epow__N,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = cCoq_2esetoid__ring_2eRing__theory_2epow__N___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_Coq.Init.Specif.sigT_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eSpecif_2esigT,V_24X1),V_24X2) = cCoq_2eInit_2eSpecif_2esigT___24a2(V_24X1,V_24X2) ).

fof('$adef_PLF.Smallstep.Temp4.test_$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('$adef_Coq.Init.Decimal.D3_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eDecimal_2eD3,V_24X1) = cCoq_2eInit_2eDecimal_2eD3___24a1(V_24X1) ).

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('$adef_$_prop_29552_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__29552,V_24X1),V_24X2),V_24X3) = c_24__prop__29552___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_Coq.Relations.Relation_Operators.swapprod_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eswapprod,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> cCoq_2eRelations_2eRelation__Operators_2eswapprod___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).

fof('$adef_Coq.ZArith.BinInt.Z.ge_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2ege,V_24X1),V_24X2))
    <=> cCoq_2eZArith_2eBinInt_2eZ_2ege___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.ZArith.Zbool.Zeq_bool_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eZbool_2eZeq__bool,V_24X1),V_24X2) = cCoq_2eZArith_2eZbool_2eZeq__bool___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.micromega.RMicromega.CQ_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2emicromega_2eRMicromega_2eCQ,V_24X1) = cCoq_2emicromega_2eRMicromega_2eCQ___24a1(V_24X1) ).

fof('$adef_Coq.ZArith.BinIntDef.Z.pow_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eBinIntDef_2eZ_2epow,V_24X1),V_24X2) = cCoq_2eZArith_2eBinIntDef_2eZ_2epow___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.QArith.QArith_base.Qmake_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eQArith_2eQArith__base_2eQmake,V_24X1),V_24X2) = cCoq_2eQArith_2eQArith__base_2eQmake___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Relations.Relation_Operators.clos_refl_trans_n1_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__n1,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans__n1___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).

fof('$adef_Coq.setoid_ring.Ring_polynom.PEX_$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('$adef_PLF.Smallstep.CImp.CSeq_$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('$adef_$_case_Coq.Init.Datatypes.bool$43570_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2ebool_2443570,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__case__Coq_2eInit_2eDatatypes_2ebool_2443570___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_$_lam_44548_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__lam__44548,V_24X1),V_24X2) = c_24__lam__44548___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.NArith.BinNatDef.N.pred_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eNArith_2eBinNatDef_2eN_2epred,V_24X1) = cCoq_2eNArith_2eBinNatDef_2eN_2epred___24a1(V_24X1) ).

fof('$adef_$_case_Coq.Init.Datatypes.nat$44295_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2enat_2444295,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__case__Coq_2eInit_2eDatatypes_2enat_2444295___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.micromega.OrderedRing.SOR_$a10',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10] :
      ( p(happ(happ(happ(happ(happ(happ(happ(happ(happ(happ(cCoq_2emicromega_2eOrderedRing_2eSOR,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5),V_24X6),V_24X7),V_24X8),V_24X9),V_24X10))
    <=> cCoq_2emicromega_2eOrderedRing_2eSOR___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10) ) ).

fof('$adef_Coq.Relations.Relation_Operators.clos_refl_trans_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__trans___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).

fof('$adef_Coq.micromega.EnvRing.PX_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePX,V_24X1),V_24X2),V_24X3),V_24X4) = cCoq_2emicromega_2eEnvRing_2ePX___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

fof('$adef_Coq.Init.Datatypes.sum_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2esum,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2esum___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.micromega.EnvRing.PEadd_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePEadd,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eEnvRing_2ePEadd___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_$_lam_42298_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__lam__42298,V_24X1),V_24X2),V_24X3) = c_24__lam__42298___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_PLF.Imp.aevalR_division.aevalR_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cPLF_2eImp_2eaevalR__division_2eaevalR,V_24X1),V_24X2))
    <=> cPLF_2eImp_2eaevalR__division_2eaevalR___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.NArith.BinNatDef.N.min_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eNArith_2eBinNatDef_2eN_2emin,V_24X1),V_24X2) = cCoq_2eNArith_2eBinNatDef_2eN_2emin___24a2(V_24X1,V_24X2) ).

fof('$adef_$_prop_29549_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(c_24__prop__29549,V_24X1),V_24X2),V_24X3) = c_24__prop__29549___24a3(V_24X1,V_24X2,V_24X3) ).

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('$adef_$_case_Coq.Init.Datatypes.nat$101_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] : happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2enat_24101,V_24X1),V_24X2),V_24X3),V_24X4) = c_24__case__Coq_2eInit_2eDatatypes_2enat_24101___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ).

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('$adef_$_prop_4767_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(c_24__prop__4767,V_24X1),V_24X2) = c_24__prop__4767___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Init.Datatypes.length_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eInit_2eDatatypes_2elength,V_24X1),V_24X2) = cCoq_2eInit_2eDatatypes_2elength___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.NArith.BinNat.N.eqf_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eNArith_2eBinNat_2eN_2eeqf,V_24X1),V_24X2))
    <=> cCoq_2eNArith_2eBinNat_2eN_2eeqf___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.Relations.Relation_Operators.clos_trans_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eclos__trans,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> cCoq_2eRelations_2eRelation__Operators_2eclos__trans___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).

fof('$adef_Coq.Relations.Relation_Operators.clos_refl_sym_trans_1n_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__1n,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> cCoq_2eRelations_2eRelation__Operators_2eclos__refl__sym__trans__1n___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).

fof('$adef_Coq.micromega.ZMicromega.is_diff_env_elt_$a4',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4] :
      ( p(happ(happ(happ(happ(cCoq_2emicromega_2eZMicromega_2eis__diff__env__elt,V_24X1),V_24X2),V_24X3),V_24X4))
    <=> cCoq_2emicromega_2eZMicromega_2eis__diff__env__elt___24a4(V_24X1,V_24X2,V_24X3,V_24X4) ) ).

fof('$adef_Coq.Vectors.Fin.t_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eVectors_2eFin_2et,V_24X1) = cCoq_2eVectors_2eFin_2et___24a1(V_24X1) ).

fof('$adef_Coq.NArith.BinNat.N.le_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eNArith_2eBinNat_2eN_2ele,V_24X1),V_24X2))
    <=> cCoq_2eNArith_2eBinNat_2eN_2ele___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.setoid_ring.Field_theory.FEO_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2esetoid__ring_2eField__theory_2eFEO,V_24X1) = cCoq_2esetoid__ring_2eField__theory_2eFEO___24a1(V_24X1) ).

fof('$adef_Coq.PArith.BinPosDef.Pos.testbit_nat_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2etestbit__nat___24a2(V_24X1,V_24X2) ).

fof('$adef_Norm.Prod_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cNorm_2eProd,V_24X1),V_24X2) = cNorm_2eProd___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Lists.List.In_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] :
      ( p(happ(happ(happ(cCoq_2eLists_2eList_2eIn,V_24X1),V_24X2),V_24X3))
    <=> cCoq_2eLists_2eList_2eIn___24a3(V_24X1,V_24X2,V_24X3) ) ).

fof('$adef_Coq.ZArith.Zpower.Zdiv_rest_proofs_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2eZArith_2eZpower_2eZdiv__rest__proofs,V_24X1),V_24X2) = cCoq_2eZArith_2eZpower_2eZdiv__rest__proofs___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.PArith.BinPosDef.Pos.of_succ_nat_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat,V_24X1) = cCoq_2ePArith_2eBinPosDef_2ePos_2eof__succ__nat___24a1(V_24X1) ).

fof('$adef_$_case_Coq.Init.Datatypes.nat$42987_$a5',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5] : happ(happ(happ(happ(happ(c_24__case__Coq_2eInit_2eDatatypes_2enat_2442987,V_24X1),V_24X2),V_24X3),V_24X4),V_24X5) = c_24__case__Coq_2eInit_2eDatatypes_2enat_2442987___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5) ).

fof('$adef_Coq.micromega.EnvRing.PEsub_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] : happ(happ(happ(cCoq_2emicromega_2eEnvRing_2ePEsub,V_24X1),V_24X2),V_24X3) = cCoq_2emicromega_2eEnvRing_2ePEsub___24a3(V_24X1,V_24X2,V_24X3) ).

fof('$adef_PLF.Imp.aevalR_extended.ANum_$a1',axiom,
    ! [V_24X1] : happ(cPLF_2eImp_2eaevalR__extended_2eANum,V_24X1) = cPLF_2eImp_2eaevalR__extended_2eANum___24a1(V_24X1) ).

fof('$adef_Coq.PArith.BinPosDef.Pos.add_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cCoq_2ePArith_2eBinPosDef_2ePos_2eadd,V_24X1),V_24X2) = cCoq_2ePArith_2eBinPosDef_2ePos_2eadd___24a2(V_24X1,V_24X2) ).

fof('$adef_Coq.Init.Nat.double_$a1',axiom,
    ! [V_24X1] : happ(cCoq_2eInit_2eNat_2edouble,V_24X1) = cCoq_2eInit_2eNat_2edouble___24a1(V_24X1) ).

fof('$adef_PLF.Smallstep.normal_form_$a3',axiom,
    ! [V_24X1,V_24X2,V_24X3] :
      ( p(happ(happ(happ(cPLF_2eSmallstep_2enormal__form,V_24X1),V_24X2),V_24X3))
    <=> cPLF_2eSmallstep_2enormal__form___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('$adef_Coq.Init.Peano.gt_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eInit_2ePeano_2egt,V_24X1),V_24X2))
    <=> cCoq_2eInit_2ePeano_2egt___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Coq.Init.Peano.lt_$a2',axiom,
    ! [V_24X1,V_24X2] :
      ( p(happ(happ(cCoq_2eInit_2ePeano_2elt,V_24X1),V_24X2))
    <=> cCoq_2eInit_2ePeano_2elt___24a2(V_24X1,V_24X2) ) ).

fof('$adef_Norm.pair_$a2',axiom,
    ! [V_24X1,V_24X2] : happ(happ(cNorm_2epair,V_24X1),V_24X2) = cNorm_2epair___24a2(V_24X1,V_24X2) ).

fof('$tdef_$_type_35486',axiom,
    ! [V_24Y] :
      ( c_24__type__35486___24t(V_24Y)
    <=> t(V_24Y,c_24__type__35486) ) ).

fof('$tdef_$_type_29987',axiom,
    ! [V_24Y] :
      ( c_24__type__29987___24t(V_24Y)
    <=> t(V_24Y,c_24__type__29987) ) ).

fof('$tdef_$_type_211',axiom,
    ! [V_24Y] :
      ( c_24__type__211___24t(V_24Y)
    <=> t(V_24Y,c_24__type__211) ) ).

fof('$tdef_$_type_33195',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__33195___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__33195___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_$_type_13393',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__13393___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__13393___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.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_44582',axiom,
    ! [V_24Y] :
      ( c_24__type__44582___24t(V_24Y)
    <=> t(V_24Y,c_24__type__44582) ) ).

fof('$tdef_$_type_35681',axiom,
    ! [V_24Y] :
      ( c_24__type__35681___24t(V_24Y)
    <=> t(V_24Y,c_24__type__35681) ) ).

fof('$tdef_$_type_30297',axiom,
    ! [V_24Y] :
      ( c_24__type__30297___24t(V_24Y)
    <=> t(V_24Y,c_24__type__30297) ) ).

fof('$tdef_$_type_44412',axiom,
    ! [V_24Y] :
      ( c_24__type__44412___24t(V_24Y)
    <=> t(V_24Y,c_24__type__44412) ) ).

fof('$tdef_$_type_30586',axiom,
    ! [V_24Y] :
      ( c_24__type__30586___24t(V_24Y)
    <=> t(V_24Y,c_24__type__30586) ) ).

fof('$tdef_Coq.Structures.OrderedTypeEx.Nat_as_OT.t',axiom,
    ! [V_24Y] :
      ( cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2et___24t(V_24Y)
    <=> t(V_24Y,cCoq_2eStructures_2eOrderedTypeEx_2eNat__as__OT_2et) ) ).

fof('$tdef_$_type_13819',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__13819___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__13819___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_6427',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__6427___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__6427___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_$_type_32433',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__32433___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__32433___24a1(V_24X1)) ) ).

fof('$tdef_$_type_8921',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__8921___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__8921___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_30593',axiom,
    ! [V_24Y] :
      ( c_24__type__30593___24t(V_24Y)
    <=> t(V_24Y,c_24__type__30593) ) ).

fof('$tdef_$_type_29147',axiom,
    ! [V_24Y] :
      ( c_24__type__29147___24t(V_24Y)
    <=> t(V_24Y,c_24__type__29147) ) ).

fof('$tdef_$_type_34038',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__34038___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__34038___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_15310',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
      ( c_24__type__15310___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
    <=> t(V_24Y,c_24__type__15310___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).

fof('$tdef_$_type_31646',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__31646___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__31646___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.EnvRing.Mon',axiom,
    ! [V_24Y] :
      ( cCoq_2emicromega_2eEnvRing_2eMon___24t(V_24Y)
    <=> t(V_24Y,cCoq_2emicromega_2eEnvRing_2eMon) ) ).

fof('$tdef_$_type_34284',axiom,
    ! [V_24Y] :
      ( c_24__type__34284___24t(V_24Y)
    <=> t(V_24Y,c_24__type__34284) ) ).

fof('$tdef_$_type_33788',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__33788___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__33788___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_4733',axiom,
    ! [V_24Y] :
      ( c_24__type__4733___24t(V_24Y)
    <=> t(V_24Y,c_24__type__4733) ) ).

fof('$tdef_$_type_32665',axiom,
    ! [V_24Y] :
      ( c_24__type__32665___24t(V_24Y)
    <=> t(V_24Y,c_24__type__32665) ) ).

fof('$tdef_$_type_30799',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__30799___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__30799___24a1(V_24X1)) ) ).

fof('$tdef_$_type_32535',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
      ( c_24__type__32535___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
    <=> t(V_24Y,c_24__type__32535___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).

fof('$tdef_$_type_30033',axiom,
    ! [V_24Y] :
      ( c_24__type__30033___24t(V_24Y)
    <=> t(V_24Y,c_24__type__30033) ) ).

fof('$tdef_$_type_14848',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__14848___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__14848___24a17(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17)) ) ).

fof('$tdef_Coq.micromega.VarMap.t',axiom,
    ! [V_24X1,V_24Y] :
      ( cCoq_2emicromega_2eVarMap_2et___24t(V_24X1,V_24Y)
    <=> t(V_24Y,cCoq_2emicromega_2eVarMap_2et___24a1(V_24X1)) ) ).

fof('$tdef_Coq.Reals.RIneq.nonposreal',axiom,
    ! [V_24Y] :
      ( cCoq_2eReals_2eRIneq_2enonposreal___24t(V_24Y)
    <=> t(V_24Y,cCoq_2eReals_2eRIneq_2enonposreal) ) ).

fof('$tdef_$_type_4725',axiom,
    ! [V_24Y] :
      ( c_24__type__4725___24t(V_24Y)
    <=> t(V_24Y,c_24__type__4725) ) ).

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_26216',axiom,
    ! [V_24Y] :
      ( c_24__type__26216___24t(V_24Y)
    <=> t(V_24Y,c_24__type__26216) ) ).

fof('$tdef_$_type_35480',axiom,
    ! [V_24Y] :
      ( c_24__type__35480___24t(V_24Y)
    <=> t(V_24Y,c_24__type__35480) ) ).

fof('$tdef_$_type_27',axiom,
    ! [V_24Y] :
      ( c_24__type__27___24t(V_24Y)
    <=> t(V_24Y,c_24__type__27) ) ).

fof('$tdef_$_type_23773',axiom,
    ! [V_24Y] :
      ( c_24__type__23773___24t(V_24Y)
    <=> t(V_24Y,c_24__type__23773) ) ).

fof('$tdef_$_type_7685',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__7685___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__7685___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_$_type_35407',axiom,
    ! [V_24Y] :
      ( c_24__type__35407___24t(V_24Y)
    <=> t(V_24Y,c_24__type__35407) ) ).

fof('$tdef_$_type_27807',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__27807___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__27807___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_Coq.Reals.RIneq.posreal',axiom,
    ! [V_24Y] :
      ( cCoq_2eReals_2eRIneq_2eposreal___24t(V_24Y)
    <=> t(V_24Y,cCoq_2eReals_2eRIneq_2eposreal) ) ).

fof('$tdef_$_type_9774',axiom,
    ! [V_24Y] :
      ( c_24__type__9774___24t(V_24Y)
    <=> t(V_24Y,c_24__type__9774) ) ).

fof('$tdef_$_type_4730',axiom,
    ! [V_24Y] :
      ( c_24__type__4730___24t(V_24Y)
    <=> t(V_24Y,c_24__type__4730) ) ).

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_31821',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__31821___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__31821___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.list',axiom,
    ! [V_24X1,V_24Y] :
      ( cCoq_2eInit_2eDatatypes_2elist___24t(V_24X1,V_24Y)
    <=> t(V_24Y,cCoq_2eInit_2eDatatypes_2elist___24a1(V_24X1)) ) ).

fof('$tdef_$_type_45000',axiom,
    ! [V_24Y] :
      ( c_24__type__45000___24t(V_24Y)
    <=> t(V_24Y,c_24__type__45000) ) ).

fof('$tdef_$_type_35124',axiom,
    ! [V_24Y] :
      ( c_24__type__35124___24t(V_24Y)
    <=> t(V_24Y,c_24__type__35124) ) ).

fof('$tdef_$_type_7119',axiom,
    ! [V_24Y] :
      ( c_24__type__7119___24t(V_24Y)
    <=> t(V_24Y,c_24__type__7119) ) ).

fof('$tdef_$_type_11447',axiom,
    ! [V_24Y] :
      ( c_24__type__11447___24t(V_24Y)
    <=> t(V_24Y,c_24__type__11447) ) ).

fof('$tdef_$_type_15023',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__15023___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__15023___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_$_type_40575',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__40575___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__40575___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).

fof('$tdef_Coq.Init.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.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_35293',axiom,
    ! [V_24Y] :
      ( c_24__type__35293___24t(V_24Y)
    <=> t(V_24Y,c_24__type__35293) ) ).

fof('$tdef_$_type_32194',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
      ( c_24__type__32194___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__32194___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).

fof('$tdef_Coq.Structures.OrdersTac.ord',axiom,
    ! [V_24Y] :
      ( cCoq_2eStructures_2eOrdersTac_2eord___24t(V_24Y)
    <=> t(V_24Y,cCoq_2eStructures_2eOrdersTac_2eord) ) ).

fof('$tdef_$_type_35737',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__35737___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__35737___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_27368',axiom,
    ! [V_24Y] :
      ( c_24__type__27368___24t(V_24Y)
    <=> t(V_24Y,c_24__type__27368) ) ).

fof('$tdef_Coq.micromega.EnvRing.PExpr',axiom,
    ! [V_24X1,V_24Y] :
      ( cCoq_2emicromega_2eEnvRing_2ePExpr___24t(V_24X1,V_24Y)
    <=> t(V_24Y,cCoq_2emicromega_2eEnvRing_2ePExpr___24a1(V_24X1)) ) ).

fof('$tdef_Coq.Init.Datatypes.option',axiom,
    ! [V_24X1,V_24Y] :
      ( cCoq_2eInit_2eDatatypes_2eoption___24t(V_24X1,V_24Y)
    <=> t(V_24Y,cCoq_2eInit_2eDatatypes_2eoption___24a1(V_24X1)) ) ).

fof('$tdef_$_type_26231',axiom,
    ! [V_24Y] :
      ( c_24__type__26231___24t(V_24Y)
    <=> t(V_24Y,c_24__type__26231) ) ).

fof('$tdef_$_type_32321',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__32321___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__32321___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_34723',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__34723___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__34723___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_44753',axiom,
    ! [V_24Y] :
      ( c_24__type__44753___24t(V_24Y)
    <=> t(V_24Y,c_24__type__44753) ) ).

fof('$tdef_$_type_33149',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__33149___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__33149___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_$_type_15009',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__15009___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__15009___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_$_type_14653',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__14653___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__14653___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.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_6135',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__6135___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__6135___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_$_type_36879',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
      ( c_24__type__36879___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
    <=> t(V_24Y,c_24__type__36879___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).

fof('$tdef_$_type_35396',axiom,
    ! [V_24Y] :
      ( c_24__type__35396___24t(V_24Y)
    <=> t(V_24Y,c_24__type__35396) ) ).

fof('$tdef_$_type_31081',axiom,
    ! [V_24Y] :
      ( c_24__type__31081___24t(V_24Y)
    <=> t(V_24Y,c_24__type__31081) ) ).

fof('$tdef_$_type_15168',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
      ( c_24__type__15168___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
    <=> t(V_24Y,c_24__type__15168___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).

fof('$tdef_$_type_43822',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__43822___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__43822___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_12235',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
      ( c_24__type__12235___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
    <=> t(V_24Y,c_24__type__12235___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).

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_31071',axiom,
    ! [V_24Y] :
      ( c_24__type__31071___24t(V_24Y)
    <=> t(V_24Y,c_24__type__31071) ) ).

fof('$tdef_$_type_29560',axiom,
    ! [V_24Y] :
      ( c_24__type__29560___24t(V_24Y)
    <=> t(V_24Y,c_24__type__29560) ) ).

fof('$tdef_$_type_44647',axiom,
    ! [V_24Y] :
      ( c_24__type__44647___24t(V_24Y)
    <=> t(V_24Y,c_24__type__44647) ) ).

fof('$tdef_$_type_39214',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__39214___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__39214___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_34569',axiom,
    ! [V_24Y] :
      ( c_24__type__34569___24t(V_24Y)
    <=> t(V_24Y,c_24__type__34569) ) ).

fof('$tdef_$_type_7035',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
      ( c_24__type__7035___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__7035___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).

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_35364',axiom,
    ! [V_24Y] :
      ( c_24__type__35364___24t(V_24Y)
    <=> t(V_24Y,c_24__type__35364) ) ).

fof('$tdef_PLF.Smallstep.tm',axiom,
    ! [V_24Y] :
      ( cPLF_2eSmallstep_2etm___24t(V_24Y)
    <=> t(V_24Y,cPLF_2eSmallstep_2etm) ) ).

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_30716',axiom,
    ! [V_24Y] :
      ( c_24__type__30716___24t(V_24Y)
    <=> t(V_24Y,c_24__type__30716) ) ).

fof('$tdef_$_type_32794',axiom,
    ! [V_24Y] :
      ( c_24__type__32794___24t(V_24Y)
    <=> t(V_24Y,c_24__type__32794) ) ).

fof('$tdef_$_type_7953',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__7953___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__7953___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_$_type_9',axiom,
    ! [V_24Y] :
      ( c_24__type__9___24t(V_24Y)
    <=> t(V_24Y,c_24__type__9) ) ).

fof('$tdef_$_type_28026',axiom,
    ! [V_24Y] :
      ( c_24__type__28026___24t(V_24Y)
    <=> t(V_24Y,c_24__type__28026) ) ).

fof('$tdef_$_type_31739',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__31739___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__31739___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.state',axiom,
    ! [V_24Y] :
      ( cPLF_2eImp_2estate___24t(V_24Y)
    <=> t(V_24Y,cPLF_2eImp_2estate) ) ).

fof('$tdef_$_type_26507',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__26507___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__26507___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_Coq.setoid_ring.Ring_polynom.Mon',axiom,
    ! [V_24Y] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2eMon___24t(V_24Y)
    <=> t(V_24Y,cCoq_2esetoid__ring_2eRing__polynom_2eMon) ) ).

fof('$tdef_Coq.Init.Datatypes.comparison',axiom,
    ! [V_24Y] :
      ( cCoq_2eInit_2eDatatypes_2ecomparison___24t(V_24Y)
    <=> t(V_24Y,cCoq_2eInit_2eDatatypes_2ecomparison) ) ).

fof('$tdef_$_type_35255',axiom,
    ! [V_24Y] :
      ( c_24__type__35255___24t(V_24Y)
    <=> t(V_24Y,c_24__type__35255) ) ).

fof('$tdef_$_type_33045',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
      ( c_24__type__33045___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
    <=> t(V_24Y,c_24__type__33045___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).

fof('$tdef_$_type_7381',axiom,
    ! [V_24Y] :
      ( c_24__type__7381___24t(V_24Y)
    <=> t(V_24Y,c_24__type__7381) ) ).

fof('$tdef_$_type_30965',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__30965___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__30965___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_35291',axiom,
    ! [V_24Y] :
      ( c_24__type__35291___24t(V_24Y)
    <=> t(V_24Y,c_24__type__35291) ) ).

fof('$tdef_$_type_29964',axiom,
    ! [V_24Y] :
      ( c_24__type__29964___24t(V_24Y)
    <=> t(V_24Y,c_24__type__29964) ) ).

fof('$tdef_PLF.Imp.BreakImp.com',axiom,
    ! [V_24Y] :
      ( cPLF_2eImp_2eBreakImp_2ecom___24t(V_24Y)
    <=> t(V_24Y,cPLF_2eImp_2eBreakImp_2ecom) ) ).

fof('$tdef_$_type_25840',axiom,
    ! [V_24Y] :
      ( c_24__type__25840___24t(V_24Y)
    <=> t(V_24Y,c_24__type__25840) ) ).

fof('$tdef_PLF.Imp.aexp',axiom,
    ! [V_24Y] :
      ( cPLF_2eImp_2eaexp___24t(V_24Y)
    <=> t(V_24Y,cPLF_2eImp_2eaexp) ) ).

fof('$tdef_$_type_42550',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__42550___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__42550___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_$_type_44560',axiom,
    ! [V_24Y] :
      ( c_24__type__44560___24t(V_24Y)
    <=> t(V_24Y,c_24__type__44560) ) ).

fof('$tdef_$_type_32722',axiom,
    ! [V_24Y] :
      ( c_24__type__32722___24t(V_24Y)
    <=> t(V_24Y,c_24__type__32722) ) ).

fof('$tdef_Coq.micromega.Tauto.GFormula',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( cCoq_2emicromega_2eTauto_2eGFormula___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,cCoq_2emicromega_2eTauto_2eGFormula___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_Coq.Numbers.BinNums.N',axiom,
    ! [V_24Y] :
      ( cCoq_2eNumbers_2eBinNums_2eN___24t(V_24Y)
    <=> t(V_24Y,cCoq_2eNumbers_2eBinNums_2eN) ) ).

fof('$tdef_PLF.Imp.BreakImp.result',axiom,
    ! [V_24Y] :
      ( cPLF_2eImp_2eBreakImp_2eresult___24t(V_24Y)
    <=> t(V_24Y,cPLF_2eImp_2eBreakImp_2eresult) ) ).

fof('$tdef_$_type_7778',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__7778___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__7778___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_Coq.Init.Specif.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_15824',axiom,
    ! [V_24Y] :
      ( c_24__type__15824___24t(V_24Y)
    <=> t(V_24Y,c_24__type__15824) ) ).

fof('$tdef_$_type_34536',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__34536___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__34536___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_$_type_35567',axiom,
    ! [V_24Y] :
      ( c_24__type__35567___24t(V_24Y)
    <=> t(V_24Y,c_24__type__35567) ) ).

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_5474',axiom,
    ! [V_24Y] :
      ( c_24__type__5474___24t(V_24Y)
    <=> t(V_24Y,c_24__type__5474) ) ).

fof('$tdef_$_type_7176',axiom,
    ! [V_24Y] :
      ( c_24__type__7176___24t(V_24Y)
    <=> t(V_24Y,c_24__type__7176) ) ).

fof('$tdef_$_type_4775',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__4775___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__4775___24a1(V_24X1)) ) ).

fof('$tdef_Coq.Init.Specif.sumbool',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( cCoq_2eInit_2eSpecif_2esumbool___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,cCoq_2eInit_2eSpecif_2esumbool___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_36487',axiom,
    ! [V_24Y] :
      ( c_24__type__36487___24t(V_24Y)
    <=> t(V_24Y,c_24__type__36487) ) ).

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_35299',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__35299___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__35299___24a1(V_24X1)) ) ).

fof('$tdef_$_type_6629',axiom,
    ! [V_24Y] :
      ( c_24__type__6629___24t(V_24Y)
    <=> t(V_24Y,c_24__type__6629) ) ).

fof('$tdef_$_type_6225',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__6225___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__6225___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_Coq.Reals.Rdefinitions.R',axiom,
    ! [V_24Y] :
      ( cCoq_2eReals_2eRdefinitions_2eR___24t(V_24Y)
    <=> t(V_24Y,cCoq_2eReals_2eRdefinitions_2eR) ) ).

fof('$tdef_$_type_44001',axiom,
    ! [V_24Y] :
      ( c_24__type__44001___24t(V_24Y)
    <=> t(V_24Y,c_24__type__44001) ) ).

fof('$tdef_$_type_31026',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__31026___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__31026___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_44587',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__44587___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__44587___24a1(V_24X1)) ) ).

fof('$tdef_$_type_41913',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__41913___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__41913___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_7408',axiom,
    ! [V_24Y] :
      ( c_24__type__7408___24t(V_24Y)
    <=> t(V_24Y,c_24__type__7408) ) ).

fof('$tdef_$_type_23749',axiom,
    ! [V_24Y] :
      ( c_24__type__23749___24t(V_24Y)
    <=> t(V_24Y,c_24__type__23749) ) ).

fof('$tdef_$_type_23684',axiom,
    ! [V_24Y] :
      ( c_24__type__23684___24t(V_24Y)
    <=> t(V_24Y,c_24__type__23684) ) ).

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_35604',axiom,
    ! [V_24Y] :
      ( c_24__type__35604___24t(V_24Y)
    <=> t(V_24Y,c_24__type__35604) ) ).

fof('$tdef_$_type_27790',axiom,
    ! [V_24Y] :
      ( c_24__type__27790___24t(V_24Y)
    <=> t(V_24Y,c_24__type__27790) ) ).

fof('$tdef_$_type_43995',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
      ( c_24__type__43995___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
    <=> t(V_24Y,c_24__type__43995___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).

fof('$tdef_$_type_44677',axiom,
    ! [V_24Y] :
      ( c_24__type__44677___24t(V_24Y)
    <=> t(V_24Y,c_24__type__44677) ) ).

fof('$tdef_$_type_29752',axiom,
    ! [V_24Y] :
      ( c_24__type__29752___24t(V_24Y)
    <=> t(V_24Y,c_24__type__29752) ) ).

fof('$tdef_$_type_35334',axiom,
    ! [V_24Y] :
      ( c_24__type__35334___24t(V_24Y)
    <=> t(V_24Y,c_24__type__35334) ) ).

fof('$tdef_$_type_31564',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__31564___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__31564___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_$_type_41267',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__41267___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__41267___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_44654',axiom,
    ! [V_24Y] :
      ( c_24__type__44654___24t(V_24Y)
    <=> t(V_24Y,c_24__type__44654) ) ).

fof('$tdef_$_type_6326',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__6326___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__6326___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_$_type_43787',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__43787___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__43787___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_44565',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__44565___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__44565___24a1(V_24X1)) ) ).

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_35317',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__35317___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__35317___24a1(V_24X1)) ) ).

fof('$tdef_$_type_33236',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__33236___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__33236___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_$_type_23739',axiom,
    ! [V_24Y] :
      ( c_24__type__23739___24t(V_24Y)
    <=> t(V_24Y,c_24__type__23739) ) ).

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_39906',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__39906___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__39906___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_27970',axiom,
    ! [V_24Y] :
      ( c_24__type__27970___24t(V_24Y)
    <=> t(V_24Y,c_24__type__27970) ) ).

fof('$tdef_$_type_23770',axiom,
    ! [V_24Y] :
      ( c_24__type__23770___24t(V_24Y)
    <=> t(V_24Y,c_24__type__23770) ) ).

fof('$tdef_$_type_7398',axiom,
    ! [V_24Y] :
      ( c_24__type__7398___24t(V_24Y)
    <=> t(V_24Y,c_24__type__7398) ) ).

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_40252',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__40252___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__40252___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).

fof('$tdef_Coq.Reals.RIneq.nonnegreal',axiom,
    ! [V_24Y] :
      ( cCoq_2eReals_2eRIneq_2enonnegreal___24t(V_24Y)
    <=> t(V_24Y,cCoq_2eReals_2eRIneq_2enonnegreal) ) ).

fof('$tdef_$_type_42341',axiom,
    ! [V_24Y] :
      ( c_24__type__42341___24t(V_24Y)
    <=> t(V_24Y,c_24__type__42341) ) ).

fof('$tdef_$_type_13198',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__13198___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__13198___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.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_44593',axiom,
    ! [V_24Y] :
      ( c_24__type__44593___24t(V_24Y)
    <=> t(V_24Y,c_24__type__44593) ) ).

fof('$tdef_$_type_43910',axiom,
    ! [V_24Y] :
      ( c_24__type__43910___24t(V_24Y)
    <=> t(V_24Y,c_24__type__43910) ) ).

fof('$tdef_$_type_29802',axiom,
    ! [V_24Y] :
      ( c_24__type__29802___24t(V_24Y)
    <=> t(V_24Y,c_24__type__29802) ) ).

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_35552',axiom,
    ! [V_24Y] :
      ( c_24__type__35552___24t(V_24Y)
    <=> t(V_24Y,c_24__type__35552) ) ).

fof('$tdef_$_type_32773',axiom,
    ! [V_24Y] :
      ( c_24__type__32773___24t(V_24Y)
    <=> t(V_24Y,c_24__type__32773) ) ).

fof('$tdef_$_type_28937',axiom,
    ! [V_24Y] :
      ( c_24__type__28937___24t(V_24Y)
    <=> t(V_24Y,c_24__type__28937) ) ).

fof('$tdef_$_type_15545',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
      ( c_24__type__15545___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
    <=> t(V_24Y,c_24__type__15545___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).

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_12181',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
      ( c_24__type__12181___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
    <=> t(V_24Y,c_24__type__12181___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).

fof('$tdef_$_type_4777',axiom,
    ! [V_24Y] :
      ( c_24__type__4777___24t(V_24Y)
    <=> t(V_24Y,c_24__type__4777) ) ).

fof('$tdef_$_type_7488',axiom,
    ! [V_24Y] :
      ( c_24__type__7488___24t(V_24Y)
    <=> t(V_24Y,c_24__type__7488) ) ).

fof('$tdef_$_type_23706',axiom,
    ! [V_24Y] :
      ( c_24__type__23706___24t(V_24Y)
    <=> t(V_24Y,c_24__type__23706) ) ).

fof('$tdef_$_type_15669',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
      ( c_24__type__15669___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
    <=> t(V_24Y,c_24__type__15669___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).

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_29990',axiom,
    ! [V_24Y] :
      ( c_24__type__29990___24t(V_24Y)
    <=> t(V_24Y,c_24__type__29990) ) ).

fof('$tdef_$_type_36716',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
      ( c_24__type__36716___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
    <=> t(V_24Y,c_24__type__36716___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).

fof('$tdef_$_type_34163',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__34163___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__34163___24a13(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13)) ) ).

fof('$tdef_Coq.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_30796',axiom,
    ! [V_24Y] :
      ( c_24__type__30796___24t(V_24Y)
    <=> t(V_24Y,c_24__type__30796) ) ).

fof('$tdef_$_type_27772',axiom,
    ! [V_24Y] :
      ( c_24__type__27772___24t(V_24Y)
    <=> t(V_24Y,c_24__type__27772) ) ).

fof('$tdef_$_type_29192',axiom,
    ! [V_24Y] :
      ( c_24__type__29192___24t(V_24Y)
    <=> t(V_24Y,c_24__type__29192) ) ).

fof('$tdef_$_type_33913',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__33913___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__33913___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_35436',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__35436___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__35436___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_32555',axiom,
    ! [V_24Y] :
      ( c_24__type__32555___24t(V_24Y)
    <=> t(V_24Y,c_24__type__32555) ) ).

fof('$tdef_$_type_25910',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__25910___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__25910___24a1(V_24X1)) ) ).

fof('$tdef_$_type_35550',axiom,
    ! [V_24Y] :
      ( c_24__type__35550___24t(V_24Y)
    <=> t(V_24Y,c_24__type__35550) ) ).

fof('$tdef_$_type_23815',axiom,
    ! [V_24Y] :
      ( c_24__type__23815___24t(V_24Y)
    <=> t(V_24Y,c_24__type__23815) ) ).

fof('$tdef_$_type_14245',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__14245___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__14245___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.Strings.Ascii.ascii',axiom,
    ! [V_24Y] :
      ( cCoq_2eStrings_2eAscii_2eascii___24t(V_24Y)
    <=> t(V_24Y,cCoq_2eStrings_2eAscii_2eascii) ) ).

fof('$tdef_$_type_33538',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__33538___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__33538___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_4802',axiom,
    ! [V_24Y] :
      ( c_24__type__4802___24t(V_24Y)
    <=> t(V_24Y,c_24__type__4802) ) ).

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_12151',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
      ( c_24__type__12151___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
    <=> t(V_24Y,c_24__type__12151___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).

fof('$tdef_$_type_31471',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__31471___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__31471___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_$_type_42360',axiom,
    ! [V_24Y] :
      ( c_24__type__42360___24t(V_24Y)
    <=> t(V_24Y,c_24__type__42360) ) ).

fof('$tdef_$_type_35475',axiom,
    ! [V_24Y] :
      ( c_24__type__35475___24t(V_24Y)
    <=> t(V_24Y,c_24__type__35475) ) ).

fof('$tdef_$_type_37853',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__37853___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__37853___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.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_35420',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__35420___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__35420___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_45037',axiom,
    ! [V_24Y] :
      ( c_24__type__45037___24t(V_24Y)
    <=> t(V_24Y,c_24__type__45037) ) ).

fof('$tdef_$_type_30910',axiom,
    ! [V_24Y] :
      ( c_24__type__30910___24t(V_24Y)
    <=> t(V_24Y,c_24__type__30910) ) ).

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_15436',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__15436___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__15436___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_34667',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__34667___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__34667___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_35402',axiom,
    ! [V_24Y] :
      ( c_24__type__35402___24t(V_24Y)
    <=> t(V_24Y,c_24__type__35402) ) ).

fof('$tdef_$_type_35367',axiom,
    ! [V_24Y] :
      ( c_24__type__35367___24t(V_24Y)
    <=> t(V_24Y,c_24__type__35367) ) ).

fof('$tdef_$_type_35322',axiom,
    ! [V_24Y] :
      ( c_24__type__35322___24t(V_24Y)
    <=> t(V_24Y,c_24__type__35322) ) ).

fof('$tdef_$_type_32967',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
      ( c_24__type__32967___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
    <=> t(V_24Y,c_24__type__32967___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).

fof('$tdef_$_type_32248',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
      ( c_24__type__32248___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__32248___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).

fof('$tdef_$_type_31174',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
      ( c_24__type__31174___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
    <=> t(V_24Y,c_24__type__31174___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).

fof('$tdef_$_type_15625',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
      ( c_24__type__15625___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
    <=> t(V_24Y,c_24__type__15625___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).

fof('$tdef_$_type_9779',axiom,
    ! [V_24Y] :
      ( c_24__type__9779___24t(V_24Y)
    <=> t(V_24Y,c_24__type__9779) ) ).

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_36782',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
      ( c_24__type__36782___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
    <=> t(V_24Y,c_24__type__36782___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).

fof('$tdef_$_type_43893',axiom,
    ! [V_24Y] :
      ( c_24__type__43893___24t(V_24Y)
    <=> t(V_24Y,c_24__type__43893) ) ).

fof('$tdef_$_type_33280',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__33280___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__33280___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_PLF.Imp.com',axiom,
    ! [V_24Y] :
      ( cPLF_2eImp_2ecom___24t(V_24Y)
    <=> t(V_24Y,cPLF_2eImp_2ecom) ) ).

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_40921',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__40921___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__40921___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_25835',axiom,
    ! [V_24Y] :
      ( c_24__type__25835___24t(V_24Y)
    <=> t(V_24Y,c_24__type__25835) ) ).

fof('$tdef_$_type_4770',axiom,
    ! [V_24Y] :
      ( c_24__type__4770___24t(V_24Y)
    <=> t(V_24Y,c_24__type__4770) ) ).

fof('$tdef_$_type_43875',axiom,
    ! [V_24Y] :
      ( c_24__type__43875___24t(V_24Y)
    <=> t(V_24Y,c_24__type__43875) ) ).

fof('$tdef_$_type_44101',axiom,
    ! [V_24Y] :
      ( c_24__type__44101___24t(V_24Y)
    <=> t(V_24Y,c_24__type__44101) ) ).

fof('$tdef_$_type_44016',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__44016___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__44016___24a1(V_24X1)) ) ).

fof('$tdef_$_type_35556',axiom,
    ! [V_24Y] :
      ( c_24__type__35556___24t(V_24Y)
    <=> t(V_24Y,c_24__type__35556) ) ).

fof('$tdef_$_type_23747',axiom,
    ! [V_24Y] :
      ( c_24__type__23747___24t(V_24Y)
    <=> t(V_24Y,c_24__type__23747) ) ).

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_6855',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
      ( c_24__type__6855___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__6855___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).

fof('$tdef_Coq.micromega.RingMicromega.Op2',axiom,
    ! [V_24Y] :
      ( cCoq_2emicromega_2eRingMicromega_2eOp2___24t(V_24Y)
    <=> t(V_24Y,cCoq_2emicromega_2eRingMicromega_2eOp2) ) ).

fof('$tdef_$_type_35370',axiom,
    ! [V_24Y] :
      ( c_24__type__35370___24t(V_24Y)
    <=> t(V_24Y,c_24__type__35370) ) ).

fof('$tdef_$_type_38522',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__38522___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__38522___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_35109',axiom,
    ! [V_24Y] :
      ( c_24__type__35109___24t(V_24Y)
    <=> t(V_24Y,c_24__type__35109) ) ).

fof('$tdef_$_type_27359',axiom,
    ! [V_24Y] :
      ( c_24__type__27359___24t(V_24Y)
    <=> t(V_24Y,c_24__type__27359) ) ).

fof('$tdef_$_type_36854',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
      ( c_24__type__36854___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
    <=> t(V_24Y,c_24__type__36854___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).

fof('$tdef_$_type_35399',axiom,
    ! [V_24Y] :
      ( c_24__type__35399___24t(V_24Y)
    <=> t(V_24Y,c_24__type__35399) ) ).

fof('$tdef_$_type_9352',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__9352___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__9352___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_7344',axiom,
    ! [V_24Y] :
      ( c_24__type__7344___24t(V_24Y)
    <=> t(V_24Y,c_24__type__7344) ) ).

fof('$tdef_$_type_4524',axiom,
    ! [V_24Y] :
      ( c_24__type__4524___24t(V_24Y)
    <=> t(V_24Y,c_24__type__4524) ) ).

fof('$tdef_$_type_30597',axiom,
    ! [V_24Y] :
      ( c_24__type__30597___24t(V_24Y)
    <=> t(V_24Y,c_24__type__30597) ) ).

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_Coq.Init.Byte.byte',axiom,
    ! [V_24Y] :
      ( cCoq_2eInit_2eByte_2ebyte___24t(V_24Y)
    <=> t(V_24Y,cCoq_2eInit_2eByte_2ebyte) ) ).

fof('$tdef_$_type_42365',axiom,
    ! [V_24Y] :
      ( c_24__type__42365___24t(V_24Y)
    <=> t(V_24Y,c_24__type__42365) ) ).

fof('$tdef_$_type_12205',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
      ( c_24__type__12205___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
    <=> t(V_24Y,c_24__type__12205___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).

fof('$tdef_Coq.Reals.Rfunctions.Z_spec',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( cCoq_2eReals_2eRfunctions_2eZ__spec___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,cCoq_2eReals_2eRfunctions_2eZ__spec___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_38199',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__38199___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__38199___24a22(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10,V_24X11,V_24X12,V_24X13,V_24X14,V_24X15,V_24X16,V_24X17,V_24X18,V_24X19,V_24X20,V_24X21,V_24X22)) ) ).

fof('$tdef_Coq.Init.Decimal.int',axiom,
    ! [V_24Y] :
      ( cCoq_2eInit_2eDecimal_2eint___24t(V_24Y)
    <=> t(V_24Y,cCoq_2eInit_2eDecimal_2eint) ) ).

fof('$tdef_$_type_32332',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__32332___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__32332___24a2(V_24X1,V_24X2)) ) ).

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_35361',axiom,
    ! [V_24Y] :
      ( c_24__type__35361___24t(V_24Y)
    <=> t(V_24Y,c_24__type__35361) ) ).

fof('$tdef_$_type_27362',axiom,
    ! [V_24Y] :
      ( c_24__type__27362___24t(V_24Y)
    <=> t(V_24Y,c_24__type__27362) ) ).

fof('$tdef_$_type_34274',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__34274___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__34274___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_11764',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
      ( c_24__type__11764___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__11764___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).

fof('$tdef_$_type_32311',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
      ( c_24__type__32311___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__32311___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).

fof('$tdef_$_type_36921',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__36921___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__36921___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_$_type_42376',axiom,
    ! [V_24Y] :
      ( c_24__type__42376___24t(V_24Y)
    <=> t(V_24Y,c_24__type__42376) ) ).

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_23960',axiom,
    ! [V_24Y] :
      ( c_24__type__23960___24t(V_24Y)
    <=> t(V_24Y,c_24__type__23960) ) ).

fof('$tdef_$_type_25826',axiom,
    ! [V_24Y] :
      ( c_24__type__25826___24t(V_24Y)
    <=> t(V_24Y,c_24__type__25826) ) ).

fof('$tdef_$_type_33218',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__33218___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__33218___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_$_type_26014',axiom,
    ! [V_24Y] :
      ( c_24__type__26014___24t(V_24Y)
    <=> t(V_24Y,c_24__type__26014) ) ).

fof('$tdef_$_type_23687',axiom,
    ! [V_24Y] :
      ( c_24__type__23687___24t(V_24Y)
    <=> t(V_24Y,c_24__type__23687) ) ).

fof('$tdef_$_type_42510',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__42510___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__42510___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_6582',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__6582___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__6582___24a1(V_24X1)) ) ).

fof('$tdef_$_type_30551',axiom,
    ! [V_24Y] :
      ( c_24__type__30551___24t(V_24Y)
    <=> t(V_24Y,c_24__type__30551) ) ).

fof('$tdef_$_type_7426',axiom,
    ! [V_24Y] :
      ( c_24__type__7426___24t(V_24Y)
    <=> t(V_24Y,c_24__type__7426) ) ).

fof('$tdef_$_type_26239',axiom,
    ! [V_24Y] :
      ( c_24__type__26239___24t(V_24Y)
    <=> t(V_24Y,c_24__type__26239) ) ).

fof('$tdef_$_type_15268',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
      ( c_24__type__15268___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
    <=> t(V_24Y,c_24__type__15268___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).

fof('$tdef_$_type_125',axiom,
    ! [V_24Y] :
      ( c_24__type__125___24t(V_24Y)
    <=> t(V_24Y,c_24__type__125) ) ).

fof('$tdef_$_type_43944',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__43944___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__43944___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_Coq.Init.Datatypes.CompareSpecT',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( cCoq_2eInit_2eDatatypes_2eCompareSpecT___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,cCoq_2eInit_2eDatatypes_2eCompareSpecT___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_Coq.micromega.RingMicromega.Op1',axiom,
    ! [V_24Y] :
      ( cCoq_2emicromega_2eRingMicromega_2eOp1___24t(V_24Y)
    <=> t(V_24Y,cCoq_2emicromega_2eRingMicromega_2eOp1) ) ).

fof('$tdef_$_type_7396',axiom,
    ! [V_24Y] :
      ( c_24__type__7396___24t(V_24Y)
    <=> t(V_24Y,c_24__type__7396) ) ).

fof('$tdef_Coq.micromega.ZMicromega.coneMember',axiom,
    ! [V_24Y] :
      ( cCoq_2emicromega_2eZMicromega_2econeMember___24t(V_24Y)
    <=> t(V_24Y,cCoq_2emicromega_2eZMicromega_2econeMember) ) ).

fof('$tdef_Coq.Init.Specif.sigT',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( cCoq_2eInit_2eSpecif_2esigT___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,cCoq_2eInit_2eSpecif_2esigT___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_4794',axiom,
    ! [V_24Y] :
      ( c_24__type__4794___24t(V_24Y)
    <=> t(V_24Y,c_24__type__4794) ) ).

fof('$tdef_PLF.Imp.sinstr',axiom,
    ! [V_24Y] :
      ( cPLF_2eImp_2esinstr___24t(V_24Y)
    <=> t(V_24Y,cPLF_2eImp_2esinstr) ) ).

fof('$tdef_$_type_6591',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__6591___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__6591___24a1(V_24X1)) ) ).

fof('$tdef_$_type_36745',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
      ( c_24__type__36745___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
    <=> t(V_24Y,c_24__type__36745___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).

fof('$tdef_$_type_5493',axiom,
    ! [V_24Y] :
      ( c_24__type__5493___24t(V_24Y)
    <=> t(V_24Y,c_24__type__5493) ) ).

fof('$tdef_$_type_25997',axiom,
    ! [V_24Y] :
      ( c_24__type__25997___24t(V_24Y)
    <=> t(V_24Y,c_24__type__25997) ) ).

fof('$tdef_$_type_31378',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__31378___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__31378___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_$_type_27745',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__27745___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__27745___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_$_type_27353',axiom,
    ! [V_24Y] :
      ( c_24__type__27353___24t(V_24Y)
    <=> t(V_24Y,c_24__type__27353) ) ).

fof('$tdef_$_type_25493',axiom,
    ! [V_24Y] :
      ( c_24__type__25493___24t(V_24Y)
    <=> t(V_24Y,c_24__type__25493) ) ).

fof('$tdef_$_type_24094',axiom,
    ! [V_24Y] :
      ( c_24__type__24094___24t(V_24Y)
    <=> t(V_24Y,c_24__type__24094) ) ).

fof('$tdef_$_type_41590',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__41590___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__41590___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_12289',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
      ( c_24__type__12289___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
    <=> t(V_24Y,c_24__type__12289___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).

fof('$tdef_$_type_27653',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__27653___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__27653___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_12772',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__12772___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__12772___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_6034',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__6034___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__6034___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_$_type_4797',axiom,
    ! [V_24Y] :
      ( c_24__type__4797___24t(V_24Y)
    <=> t(V_24Y,c_24__type__4797) ) ).

fof('$tdef_$_type_4578',axiom,
    ! [V_24Y] :
      ( c_24__type__4578___24t(V_24Y)
    <=> t(V_24Y,c_24__type__4578) ) ).

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_5479',axiom,
    ! [V_24Y] :
      ( c_24__type__5479___24t(V_24Y)
    <=> t(V_24Y,c_24__type__5479) ) ).

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_35410',axiom,
    ! [V_24Y] :
      ( c_24__type__35410___24t(V_24Y)
    <=> t(V_24Y,c_24__type__35410) ) ).

fof('$tdef_$_type_33663',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__33663___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__33663___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_7148',axiom,
    ! [V_24Y] :
      ( c_24__type__7148___24t(V_24Y)
    <=> t(V_24Y,c_24__type__7148) ) ).

fof('$tdef_$_type_44426',axiom,
    ! [V_24Y] :
      ( c_24__type__44426___24t(V_24Y)
    <=> t(V_24Y,c_24__type__44426) ) ).

fof('$tdef_$_type_14440',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__14440___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__14440___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_36443',axiom,
    ! [V_24Y] :
      ( c_24__type__36443___24t(V_24Y)
    <=> t(V_24Y,c_24__type__36443) ) ).

fof('$tdef_$_type_33262',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__33262___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__33262___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_$_type_6918',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
      ( c_24__type__6918___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__6918___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).

fof('$tdef_$_type_8046',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__8046___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__8046___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_$_type_12322',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
      ( c_24__type__12322___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
    <=> t(V_24Y,c_24__type__12322___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).

fof('$tdef_$_type_34731',axiom,
    ! [V_24Y] :
      ( c_24__type__34731___24t(V_24Y)
    <=> t(V_24Y,c_24__type__34731) ) ).

fof('$tdef_$_type_33006',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
      ( c_24__type__33006___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
    <=> t(V_24Y,c_24__type__33006___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).

fof('$tdef_$_type_35808',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
      ( c_24__type__35808___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
    <=> t(V_24Y,c_24__type__35808___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).

fof('$tdef_$_type_29240',axiom,
    ! [V_24Y] :
      ( c_24__type__29240___24t(V_24Y)
    <=> t(V_24Y,c_24__type__29240) ) ).

fof('$tdef_$_type_32068',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
      ( c_24__type__32068___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__32068___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).

fof('$tdef_$_type_5933',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__5933___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__5933___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_$_type_44421',axiom,
    ! [V_24Y] :
      ( c_24__type__44421___24t(V_24Y)
    <=> t(V_24Y,c_24__type__44421) ) ).

fof('$tdef_$_type_35386',axiom,
    ! [V_24Y] :
      ( c_24__type__35386___24t(V_24Y)
    <=> t(V_24Y,c_24__type__35386) ) ).

fof('$tdef_$_type_27811',axiom,
    ! [V_24Y] :
      ( c_24__type__27811___24t(V_24Y)
    <=> t(V_24Y,c_24__type__27811) ) ).

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_35431',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__35431___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__35431___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_35891',axiom,
    ! [V_24Y] :
      ( c_24__type__35891___24t(V_24Y)
    <=> t(V_24Y,c_24__type__35891) ) ).

fof('$tdef_$_type_12985',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__12985___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__12985___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_32131',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
      ( c_24__type__32131___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__32131___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).

fof('$tdef_$_type_35628',axiom,
    ! [V_24Y] :
      ( c_24__type__35628___24t(V_24Y)
    <=> t(V_24Y,c_24__type__35628) ) ).

fof('$tdef_$_type_8128',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__8128___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__8128___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_Coq.Structures.OrderedTypeEx.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_34872',axiom,
    ! [V_24Y] :
      ( c_24__type__34872___24t(V_24Y)
    <=> t(V_24Y,c_24__type__34872) ) ).

fof('$tdef_$_type_44098',axiom,
    ! [V_24Y] :
      ( c_24__type__44098___24t(V_24Y)
    <=> t(V_24Y,c_24__type__44098) ) ).

fof('$tdef_$_type_31005',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__31005___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__31005___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_29675',axiom,
    ! [V_24Y] :
      ( c_24__type__29675___24t(V_24Y)
    <=> t(V_24Y,c_24__type__29675) ) ).

fof('$tdef_$_type_23704',axiom,
    ! [V_24Y] :
      ( c_24__type__23704___24t(V_24Y)
    <=> t(V_24Y,c_24__type__23704) ) ).

fof('$tdef_$_type_35652',axiom,
    ! [V_24Y] :
      ( c_24__type__35652___24t(V_24Y)
    <=> t(V_24Y,c_24__type__35652) ) ).

fof('$tdef_$_type_8221',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__8221___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__8221___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_$_type_44418',axiom,
    ! [V_24Y] :
      ( c_24__type__44418___24t(V_24Y)
    <=> t(V_24Y,c_24__type__44418) ) ).

fof('$tdef_Coq.Bool.Bool.reflect',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( cCoq_2eBool_2eBool_2ereflect___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,cCoq_2eBool_2eBool_2ereflect___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_9338',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__9338___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__9338___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_12265',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
      ( c_24__type__12265___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
    <=> t(V_24Y,c_24__type__12265___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).

fof('$tdef_Coq.setoid_ring.Ring_polynom.Pol',axiom,
    ! [V_24X1,V_24Y] :
      ( cCoq_2esetoid__ring_2eRing__polynom_2ePol___24t(V_24X1,V_24Y)
    <=> t(V_24Y,cCoq_2esetoid__ring_2eRing__polynom_2ePol___24a1(V_24X1)) ) ).

fof('$tdef_$_type_35879',axiom,
    ! [V_24Y] :
      ( c_24__type__35879___24t(V_24Y)
    <=> t(V_24Y,c_24__type__35879) ) ).

fof('$tdef_$_type_29237',axiom,
    ! [V_24Y] :
      ( c_24__type__29237___24t(V_24Y)
    <=> t(V_24Y,c_24__type__29237) ) ).

fof('$tdef_$_type_42259',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__42259___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__42259___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_27842',axiom,
    ! [V_24Y] :
      ( c_24__type__27842___24t(V_24Y)
    <=> t(V_24Y,c_24__type__27842) ) ).

fof('$tdef_$_type_42472',axiom,
    ! [V_24Y] :
      ( c_24__type__42472___24t(V_24Y)
    <=> t(V_24Y,c_24__type__42472) ) ).

fof('$tdef_$_type_35285',axiom,
    ! [V_24Y] :
      ( c_24__type__35285___24t(V_24Y)
    <=> t(V_24Y,c_24__type__35285) ) ).

fof('$tdef_$_type_13606',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__13606___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__13606___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_29683',axiom,
    ! [V_24Y] :
      ( c_24__type__29683___24t(V_24Y)
    <=> t(V_24Y,c_24__type__29683) ) ).

fof('$tdef_$_type_27643',axiom,
    ! [V_24Y] :
      ( c_24__type__27643___24t(V_24Y)
    <=> t(V_24Y,c_24__type__27643) ) ).

fof('$tdef_$_type_7098',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
      ( c_24__type__7098___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__7098___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).

fof('$tdef_$_type_7401',axiom,
    ! [V_24Y] :
      ( c_24__type__7401___24t(V_24Y)
    <=> t(V_24Y,c_24__type__7401) ) ).

fof('$tdef_$_type_15822',axiom,
    ! [V_24Y] :
      ( c_24__type__15822___24t(V_24Y)
    <=> t(V_24Y,c_24__type__15822) ) ).

fof('$tdef_$_type_11881',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
      ( c_24__type__11881___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__11881___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).

fof('$tdef_$_type_35425',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__35425___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__35425___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_26173',axiom,
    ! [V_24Y] :
      ( c_24__type__26173___24t(V_24Y)
    <=> t(V_24Y,c_24__type__26173) ) ).

fof('$tdef_$_type_38868',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__38868___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__38868___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_34748',axiom,
    ! [V_24Y] :
      ( c_24__type__34748___24t(V_24Y)
    <=> t(V_24Y,c_24__type__34748) ) ).

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_27768',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__27768___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__27768___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_30891',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y] :
      ( c_24__type__30891___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24Y)
    <=> t(V_24Y,c_24__type__30891___24a6(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6)) ) ).

fof('$tdef_Coq.QArith.QArith_base.Q',axiom,
    ! [V_24Y] :
      ( cCoq_2eQArith_2eQArith__base_2eQ___24t(V_24Y)
    <=> t(V_24Y,cCoq_2eQArith_2eQArith__base_2eQ) ) ).

fof('$tdef_$_type_6981',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
      ( c_24__type__6981___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__6981___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).

fof('$tdef_Coq.PArith.BinPos.Pos.PeanoView',axiom,
    ! [V_24X1,V_24Y] :
      ( cCoq_2ePArith_2eBinPos_2ePos_2ePeanoView___24t(V_24X1,V_24Y)
    <=> t(V_24Y,cCoq_2ePArith_2eBinPos_2ePos_2ePeanoView___24a1(V_24X1)) ) ).

fof('$tdef_Coq.Numbers.BinNums.positive',axiom,
    ! [V_24Y] :
      ( cCoq_2eNumbers_2eBinNums_2epositive___24t(V_24Y)
    <=> t(V_24Y,cCoq_2eNumbers_2eBinNums_2epositive) ) ).

fof('$tdef_$_type_45363',axiom,
    ! [V_24Y] :
      ( c_24__type__45363___24t(V_24Y)
    <=> t(V_24Y,c_24__type__45363) ) ).

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_44013',axiom,
    ! [V_24Y] :
      ( c_24__type__44013___24t(V_24Y)
    <=> t(V_24Y,c_24__type__44013) ) ).

fof('$tdef_$_type_36436',axiom,
    ! [V_24Y] :
      ( c_24__type__36436___24t(V_24Y)
    <=> t(V_24Y,c_24__type__36436) ) ).

fof('$tdef_$_type_34579',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__34579___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__34579___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_31069',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
      ( c_24__type__31069___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
    <=> t(V_24Y,c_24__type__31069___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).

fof('$tdef_$_type_45004',axiom,
    ! [V_24Y] :
      ( c_24__type__45004___24t(V_24Y)
    <=> t(V_24Y,c_24__type__45004) ) ).

fof('$tdef_$_type_35688',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__35688___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__35688___24a2(V_24X1,V_24X2)) ) ).

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_7171',axiom,
    ! [V_24Y] :
      ( c_24__type__7171___24t(V_24Y)
    <=> t(V_24Y,c_24__type__7171) ) ).

fof('$tdef_$_type_39560',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__39560___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__39560___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_35375',axiom,
    ! [V_24Y] :
      ( c_24__type__35375___24t(V_24Y)
    <=> t(V_24Y,c_24__type__35375) ) ).

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_36439',axiom,
    ! [V_24Y] :
      ( c_24__type__36439___24t(V_24Y)
    <=> t(V_24Y,c_24__type__36439) ) ).

fof('$tdef_$_type_9359',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__9359___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__9359___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_7871',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__7871___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__7871___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_Coq.micromega.RingMicromega.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_35863',axiom,
    ! [V_24Y] :
      ( c_24__type__35863___24t(V_24Y)
    <=> t(V_24Y,c_24__type__35863) ) ).

fof('$tdef_$_type_23754',axiom,
    ! [V_24Y] :
      ( c_24__type__23754___24t(V_24Y)
    <=> t(V_24Y,c_24__type__23754) ) ).

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_35579',axiom,
    ! [V_24Y] :
      ( c_24__type__35579___24t(V_24Y)
    <=> t(V_24Y,c_24__type__35579) ) ).

fof('$tdef_$_type_29800',axiom,
    ! [V_24Y] :
      ( c_24__type__29800___24t(V_24Y)
    <=> t(V_24Y,c_24__type__29800) ) ).

fof('$tdef_PLF.Smallstep.Combined.tm',axiom,
    ! [V_24Y] :
      ( cPLF_2eSmallstep_2eCombined_2etm___24t(V_24Y)
    <=> t(V_24Y,cPLF_2eSmallstep_2eCombined_2etm) ) ).

fof('$tdef_$_type_14990',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__14990___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__14990___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_$_type_11944',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
      ( c_24__type__11944___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__11944___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).

fof('$tdef_$_type_31914',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__31914___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__31914___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_Coq.NArith.BinNatDef.N.t',axiom,
    ! [V_24Y] :
      ( cCoq_2eNArith_2eBinNatDef_2eN_2et___24t(V_24Y)
    <=> t(V_24Y,cCoq_2eNArith_2eBinNatDef_2eN_2et) ) ).

fof('$tdef_Coq.Init.Datatypes.ID',axiom,
    ! [V_24Y] :
      ( cCoq_2eInit_2eDatatypes_2eID___24t(V_24Y)
    <=> t(V_24Y,cCoq_2eInit_2eDatatypes_2eID) ) ).

fof('$tdef_$_type_32430',axiom,
    ! [V_24Y] :
      ( c_24__type__32430___24t(V_24Y)
    <=> t(V_24Y,c_24__type__32430) ) ).

fof('$tdef_PLF.Imp.bexp',axiom,
    ! [V_24Y] :
      ( cPLF_2eImp_2ebexp___24t(V_24Y)
    <=> t(V_24Y,cPLF_2eImp_2ebexp) ) ).

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_4800',axiom,
    ! [V_24Y] :
      ( c_24__type__4800___24t(V_24Y)
    <=> t(V_24Y,c_24__type__4800) ) ).

fof('$tdef_$_type_34715',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__34715___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__34715___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_29075',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__29075___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__29075___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_Norm.ty',axiom,
    ! [V_24Y] :
      ( cNorm_2ety___24t(V_24Y)
    <=> t(V_24Y,cNorm_2ety) ) ).

fof('$tdef_$_type_45900',axiom,
    ! [V_24Y] :
      ( c_24__type__45900___24t(V_24Y)
    <=> t(V_24Y,c_24__type__45900) ) ).

fof('$tdef_$_type_45041',axiom,
    ! [V_24Y] :
      ( c_24__type__45041___24t(V_24Y)
    <=> t(V_24Y,c_24__type__45041) ) ).

fof('$tdef_$_type_30490',axiom,
    ! [V_24Y] :
      ( c_24__type__30490___24t(V_24Y)
    <=> t(V_24Y,c_24__type__30490) ) ).

fof('$tdef_Norm.tm',axiom,
    ! [V_24Y] :
      ( cNorm_2etm___24t(V_24Y)
    <=> t(V_24Y,cNorm_2etm) ) ).

fof('$tdef_Coq.setoid_ring.Ring_theory.ring_kind',axiom,
    ! [V_24Y] :
      ( cCoq_2esetoid__ring_2eRing__theory_2ering__kind___24t(V_24Y)
    <=> t(V_24Y,cCoq_2esetoid__ring_2eRing__theory_2ering__kind) ) ).

fof('$tdef_$_type_29084',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__29084___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__29084___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_$_type_36972',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__36972___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__36972___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_PLF.Smallstep.stack',axiom,
    ! [V_24Y] :
      ( cPLF_2eSmallstep_2estack___24t(V_24Y)
    <=> t(V_24Y,cPLF_2eSmallstep_2estack) ) ).

fof('$tdef_$_type_35489',axiom,
    ! [V_24Y] :
      ( c_24__type__35489___24t(V_24Y)
    <=> t(V_24Y,c_24__type__35489) ) ).

fof('$tdef_$_type_35348',axiom,
    ! [V_24Y] :
      ( c_24__type__35348___24t(V_24Y)
    <=> t(V_24Y,c_24__type__35348) ) ).

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_35761',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__35761___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__35761___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_34659',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__34659___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__34659___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_12373',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
      ( c_24__type__12373___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
    <=> t(V_24Y,c_24__type__12373___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).

fof('$tdef_$_type_15218',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
      ( c_24__type__15218___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
    <=> t(V_24Y,c_24__type__15218___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).

fof('$tdef_$_type_36461',axiom,
    ! [V_24Y] :
      ( c_24__type__36461___24t(V_24Y)
    <=> t(V_24Y,c_24__type__36461) ) ).

fof('$tdef_$_type_32516',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
      ( c_24__type__32516___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
    <=> t(V_24Y,c_24__type__32516___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).

fof('$tdef_$_type_32380',axiom,
    ! [V_24Y] :
      ( c_24__type__32380___24t(V_24Y)
    <=> t(V_24Y,c_24__type__32380) ) ).

fof('$tdef_$_type_14032',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__14032___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__14032___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_6528',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__6528___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__6528___24a10(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24X9,V_24X10)) ) ).

fof('$tdef_$_type_7450',axiom,
    ! [V_24Y] :
      ( c_24__type__7450___24t(V_24Y)
    <=> t(V_24Y,c_24__type__7450) ) ).

fof('$tdef_$_type_23699',axiom,
    ! [V_24Y] :
      ( c_24__type__23699___24t(V_24Y)
    <=> t(V_24Y,c_24__type__23699) ) ).

fof('$tdef_$_type_35483',axiom,
    ! [V_24Y] :
      ( c_24__type__35483___24t(V_24Y)
    <=> t(V_24Y,c_24__type__35483) ) ).

fof('$tdef_$_type_31061',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
      ( c_24__type__31061___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
    <=> t(V_24Y,c_24__type__31061___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).

fof('$tdef_$_type_25011',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__25011___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__25011___24a1(V_24X1)) ) ).

fof('$tdef_$_type_15688',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__15688___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__15688___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_45360',axiom,
    ! [V_24Y] :
      ( c_24__type__45360___24t(V_24Y)
    <=> t(V_24Y,c_24__type__45360) ) ).

fof('$tdef_$_type_24',axiom,
    ! [V_24Y] :
      ( c_24__type__24___24t(V_24Y)
    <=> t(V_24Y,c_24__type__24) ) ).

fof('$tdef_$_type_10078',axiom,
    ! [V_24Y] :
      ( c_24__type__10078___24t(V_24Y)
    <=> t(V_24Y,c_24__type__10078) ) ).

fof('$tdef_Type',axiom,
    ! [V_24Y] :
      ( cType___24t(V_24Y)
    <=> t(V_24Y,cType) ) ).

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_7406',axiom,
    ! [V_24Y] :
      ( c_24__type__7406___24t(V_24Y)
    <=> t(V_24Y,c_24__type__7406) ) ).

fof('$tdef_$_type_44599',axiom,
    ! [V_24Y] :
      ( c_24__type__44599___24t(V_24Y)
    <=> t(V_24Y,c_24__type__44599) ) ).

fof('$tdef_$_type_34675',axiom,
    ! [V_24Y] :
      ( c_24__type__34675___24t(V_24Y)
    <=> t(V_24Y,c_24__type__34675) ) ).

fof('$tdef_$_type_35843',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__35843___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__35843___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_43857',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24Y] :
      ( c_24__type__43857___24t(V_24X1,V_24X2,V_24X3,V_24Y)
    <=> t(V_24Y,c_24__type__43857___24a3(V_24X1,V_24X2,V_24X3)) ) ).

fof('$tdef_$_type_42379',axiom,
    ! [V_24Y] :
      ( c_24__type__42379___24t(V_24Y)
    <=> t(V_24Y,c_24__type__42379) ) ).

fof('$tdef_$_type_33172',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24Y] :
      ( c_24__type__33172___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24Y)
    <=> t(V_24Y,c_24__type__33172___24a4(V_24X1,V_24X2,V_24X3,V_24X4)) ) ).

fof('$tdef_$_type_26196',axiom,
    ! [V_24Y] :
      ( c_24__type__26196___24t(V_24Y)
    <=> t(V_24Y,c_24__type__26196) ) ).

fof('$tdef_Coq.Vectors.Fin.t',axiom,
    ! [V_24X1,V_24Y] :
      ( cCoq_2eVectors_2eFin_2et___24t(V_24X1,V_24Y)
    <=> t(V_24Y,cCoq_2eVectors_2eFin_2et___24a1(V_24X1)) ) ).

fof('$tdef_Coq.Reals.RIneq.nonzeroreal',axiom,
    ! [V_24Y] :
      ( cCoq_2eReals_2eRIneq_2enonzeroreal___24t(V_24Y)
    <=> t(V_24Y,cCoq_2eReals_2eRIneq_2enonzeroreal) ) ).

fof('$tdef_$_type_35312',axiom,
    ! [V_24Y] :
      ( c_24__type__35312___24t(V_24Y)
    <=> t(V_24Y,c_24__type__35312) ) ).

fof('$tdef_$_type_15360',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
      ( c_24__type__15360___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
    <=> t(V_24Y,c_24__type__15360___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).

fof('$tdef_$_type_11827',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
      ( c_24__type__11827___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__11827___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).

fof('$tdef_$_type_9314',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__9314___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__9314___24a1(V_24X1)) ) ).

fof('$tdef_$_type_42373',axiom,
    ! [V_24Y] :
      ( c_24__type__42373___24t(V_24Y)
    <=> t(V_24Y,c_24__type__42373) ) ).

fof('$tdef_$_type_12346',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y] :
      ( c_24__type__12346___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24Y)
    <=> t(V_24Y,c_24__type__12346___24a5(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5)) ) ).

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_37507',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__37507___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__37507___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_35346',axiom,
    ! [V_24Y] :
      ( c_24__type__35346___24t(V_24Y)
    <=> t(V_24Y,c_24__type__35346) ) ).

fof('$tdef_$_type_29998',axiom,
    ! [V_24Y] :
      ( c_24__type__29998___24t(V_24Y)
    <=> t(V_24Y,c_24__type__29998) ) ).

fof('$tdef_$_type_35383',axiom,
    ! [V_24Y] :
      ( c_24__type__35383___24t(V_24Y)
    <=> t(V_24Y,c_24__type__35383) ) ).

fof('$tdef_$_type_25490',axiom,
    ! [V_24Y] :
      ( c_24__type__25490___24t(V_24Y)
    <=> t(V_24Y,c_24__type__25490) ) ).

fof('$tdef_$_type_11701',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8,V_24Y] :
      ( c_24__type__11701___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__11701___24a8(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24X8)) ) ).

fof('$tdef_Coq.setoid_ring.InitialRing.Nword',axiom,
    ! [V_24Y] :
      ( cCoq_2esetoid__ring_2eInitialRing_2eNword___24t(V_24Y)
    <=> t(V_24Y,cCoq_2esetoid__ring_2eInitialRing_2eNword) ) ).

fof('$tdef_$_type_35458',axiom,
    ! [V_24Y] :
      ( c_24__type__35458___24t(V_24Y)
    <=> t(V_24Y,c_24__type__35458) ) ).

fof('$tdef_$_type_27866',axiom,
    ! [V_24Y] :
      ( c_24__type__27866___24t(V_24Y)
    <=> t(V_24Y,c_24__type__27866) ) ).

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_43866',axiom,
    ! [V_24Y] :
      ( c_24__type__43866___24t(V_24Y)
    <=> t(V_24Y,c_24__type__43866) ) ).

fof('$tdef_$_type_44415',axiom,
    ! [V_24Y] :
      ( c_24__type__44415___24t(V_24Y)
    <=> t(V_24Y,c_24__type__44415) ) ).

fof('$tdef_$_type_15589',axiom,
    ! [V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y] :
      ( c_24__type__15589___24t(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7,V_24Y)
    <=> t(V_24Y,c_24__type__15589___24a7(V_24X1,V_24X2,V_24X3,V_24X4,V_24X5,V_24X6,V_24X7)) ) ).

fof('$tdef_$_type_35447',axiom,
    ! [V_24X1,V_24Y] :
      ( c_24__type__35447___24t(V_24X1,V_24Y)
    <=> t(V_24Y,c_24__type__35447___24a1(V_24X1)) ) ).

fof('$tdef_$_type_27836',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__27836___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__27836___24a2(V_24X1,V_24X2)) ) ).

fof('$tdef_$_type_27860',axiom,
    ! [V_24X1,V_24X2,V_24Y] :
      ( c_24__type__27860___24t(V_24X1,V_24X2,V_24Y)
    <=> t(V_24Y,c_24__type__27860___24a2(V_24X1,V_24X2)) ) ).

fof('_HAMMER_GOAL',conjecture,
    ! [V0__t] :
      ( cNorm_2etm___24t(V0__t)
     => ( cNorm_2evalue___24a1(V0__t)
       => cPLF_2eSmallstep_2enormal__form___24a3(cNorm_2etm,cNorm_2estep,V0__t) ) ) ).

%------------------------------------------------------------------------------