TSTP Solution File: SWV664-1 by Bliksem---1.12

%------------------------------------------------------------------------------
% File     : Bliksem---1.12
% Problem  : SWV664-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : bliksem %s

% Computer : n020.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 0s
% DateTime : Wed Jul 20 16:27:36 EDT 2022

% Result   : Timeout 300.03s 300.43s
% Output   : None 
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : SWV664-1 : TPTP v8.1.0. Released v4.1.0.
% 0.12/0.13  % Command  : bliksem %s
% 0.13/0.34  % Computer : n020.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % DateTime : Wed Jun 15 08:23:34 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 1.42/1.81  *** allocated 10000 integers for termspace/termends
% 1.42/1.81  *** allocated 10000 integers for clauses
% 1.42/1.81  *** allocated 10000 integers for justifications
% 1.42/1.81  *** allocated 15000 integers for termspace/termends
% 1.42/1.81  *** allocated 22500 integers for termspace/termends
% 1.42/1.81  *** allocated 33750 integers for termspace/termends
% 1.42/1.81  *** allocated 50625 integers for termspace/termends
% 1.42/1.81  Bliksem 1.12
% 1.42/1.81  
% 1.42/1.81  
% 1.42/1.81  Automatic Strategy Selection
% 1.42/1.81  
% 1.42/1.81  Clauses:
% 1.42/1.81  [
% 1.42/1.81     [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), 'c_HOL_Oord__class_Oless'( 
% 1.42/1.81    Y, X, 'tc_nat' ), =( Y, X ) ],
% 1.42/1.81     [ =( X, Y ), ~( 'c_lessequals'( Y, X, 'tc_Int_Oint' ) ), ~( 
% 1.42/1.81    'c_lessequals'( X, Y, 'tc_Int_Oint' ) ) ],
% 1.42/1.81     [ =( X, Y ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ), ~( 'c_lessequals'( X
% 1.42/1.81    , Y, 'tc_nat' ) ) ],
% 1.42/1.81     [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Y, Z
% 1.42/1.81    , X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ],
% 1.42/1.81     [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.42/1.81    , X ), =( Z, Y ), 'c_HOL_Oord__class_Oless'( Z, Y, X ) ],
% 1.42/1.81     [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ), 
% 1.42/1.81    'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.42/1.81     ) ],
% 1.42/1.81     [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ), 
% 1.42/1.81    'c_HOL_Oord__class_Oless'( Z, Y, X ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.42/1.81     ) ],
% 1.42/1.81     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 
% 1.42/1.81    'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.42/1.81     ), =( Z, Y ) ],
% 1.42/1.81     [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =( hAPP( 
% 1.42/1.81    'c_HOL_Oabs__class_Oabs'( X ), Y ), Y ), ~( 'c_lessequals'( 
% 1.42/1.81    'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.42/1.81     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'( 
% 1.42/1.81    hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP( 
% 1.42/1.81    'c_Power_Opower__class_Opower'( X ), T ), Z ), X ), ~( 'c_lessequals'( 
% 1.42/1.81    hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Y ), hAPP( 'c_HOL_Oabs__class_Oabs'( 
% 1.42/1.81    X ), T ), X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ) ]
% 1.42/1.81    ,
% 1.42/1.81     [ 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ), ~( 
% 1.42/1.81    'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), ~( 
% 1.42/1.81    'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 1.42/1.81     [ 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', X ), 'tc_nat' ) ],
% 1.42/1.81     [ 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', X ), 'tc_nat' ) ],
% 1.42/1.81     [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint'
% 1.42/1.81     ), X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), X
% 1.42/1.81     ), Z ), 'tc_Int_Oint' ), ~( 'c_lessequals'( Y, Z, 'tc_Int_Oint' ) ) ]
% 1.42/1.81    ,
% 1.42/1.81     [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, Y ), T ) ), hAPP( hAPP( Z, Y ), 
% 1.42/1.81    hAPP( 'c_Suc', T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, Z, W
% 1.42/1.81    , V0, V1 ) ) ],
% 1.42/1.81     [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), Z ), hAPP( hAPP( Y, Z ), 
% 1.42/1.81    hAPP( 'c_Suc', T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, Y, W
% 1.42/1.81    , V0, V1 ) ) ],
% 1.42/1.81     [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ), =( Y, X ), 
% 1.42/1.81    'c_HOL_Oord__class_Oless'( Y, X, 'tc_Int_Oint' ) ],
% 1.42/1.81     [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =( Y, Z ), ~( 
% 1.42/1.81    'c_Deriv_Oderiv'( T, U, Z, X ) ), ~( 'c_Deriv_Oderiv'( T, U, Y, X ) ) ]
% 1.42/1.81    ,
% 1.42/1.81     [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), 'c_HOL_Oord__class_Oless'( Y, Z, 
% 1.42/1.81    'tc_nat' ), =( Z, Y ), 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ],
% 1.42/1.81     [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), 'c_HOL_Oord__class_Oless'( 
% 1.42/1.81    Y, X, 'tc_nat' ), =( Y, X ) ],
% 1.42/1.81     [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Z, Y
% 1.42/1.81    , X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.42/1.81     [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.42/1.81    , X ), 'c_HOL_Oord__class_Oless'( Z, Y, X ), =( Z, Y ) ],
% 1.42/1.81     [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Z, Y
% 1.42/1.81    , X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.42/1.81     [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), ~( =( hAPP( 
% 1.42/1.81    'c_HOL_Ouminus__class_Ouminus'( X ), Y ), hAPP( 
% 1.42/1.81    'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ), =( Y, Z ) ],
% 1.42/1.81     [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =( hAPP( 
% 1.42/1.81    'c_HOL_Ouminus__class_Ouminus'( X ), Y ), hAPP( 
% 1.42/1.81    'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ), =( Y, Z ) ],
% 1.42/1.81     [ ~( 'class_OrderedGroup_Olordered__ab__group__add__abs'( X ) ), 
% 1.42/1.81    'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( 
% 1.42/1.81    'c_HOL_Oabs__class_Oabs'( X ), T ) ), X ), ~( 'c_lessequals'( hAPP( hAPP( 
% 1.42/1.81    'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), Z, X ) ) ],
% 1.42/1.81     [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), X ), ~( 
% 1.42/1.81    'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.42/1.81     [ 'c_lessequals'( hAPP( 'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 
% 1.42/1.81    X ), hAPP( 'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), Y ), 'tc_nat'
% 1.42/1.81     ), ~( 'c_lessequals'( X, Y, 'tc_Int_Oint' ) ) ],
% 1.42/1.81     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( 
% 1.42/1.81    'class_Int_Onumber__ring'( X ) ), 'c_lessequals'( Y, Z, 'tc_Int_Oint' ), 
% 1.42/1.81    ~( 'c_lessequals'( hAPP( 'c_Int_Onumber__class_Onumber__of'( X ), Y ), 
% 1.42/1.81    hAPP( 'c_Int_Onumber__class_Onumber__of'( X ), Z ), X ) ) ],
% 1.42/1.81     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( 
% 1.42/1.81    'class_Int_Onumber__ring'( X ) ), 'c_lessequals'( hAPP( 
% 1.42/1.81    'c_Int_Onumber__class_Onumber__of'( X ), Y ), hAPP( 
% 1.42/1.81    'c_Int_Onumber__class_Onumber__of'( X ), Z ), X ), ~( 'c_lessequals'( Y, 
% 1.42/1.81    Z, 'tc_Int_Oint' ) ) ],
% 1.42/1.81     [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =( Y, 
% 1.42/1.81    'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'( hAPP( 
% 1.42/1.81    'c_HOL_Oabs__class_Oabs'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.42/1.81     ) ],
% 1.42/1.81     [ =( 'c_Fact_Ofact__class_Ofact'( hAPP( 'c_Suc', 
% 1.42/1.81    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ), hAPP( 'c_Suc', 
% 1.42/1.81    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.42/1.81     [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), 
% 1.42/1.81    'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y )
% 1.42/1.81    , hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), X ), ~( 
% 1.42/1.81    'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.42/1.81     [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), 
% 1.42/1.81    'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP( 
% 1.42/1.81    'c_HOL_Ouminus__class_Ouminus'( X ), Z ), hAPP( 
% 1.42/1.81    'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ) ) ],
% 1.42/1.81     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 
% 1.42/1.81    'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y )
% 1.42/1.81    , Z, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Oabs__class_Oabs'( X
% 1.42/1.81     ), Y ), Z, X ) ) ],
% 1.42/1.81     [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), 
% 1.42/1.81    'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 
% 1.42/1.81    'tc_nat' ), X ), Y ), Y, 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat'
% 1.42/1.81     ) ) ],
% 1.42/1.81     [ =( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ), hAPP( 'c_Suc', 
% 1.42/1.81    'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 
% 1.42/1.81    'tc_nat' ), X ), Y ), Y, 'tc_nat' ) ) ), 'c_HOL_Oord__class_Oless'( X, Y
% 1.42/1.81    , 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 
% 1.42/1.81    'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.42/1.81     [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_Complex_Ocomplex' ), 
% 1.42/1.81    'c_Complex_Oii' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.42/1.81    'tc_Complex_Ocomplex' ), 'c_Complex_Oii' ), X ) ), hAPP( 
% 1.42/1.81    'c_HOL_Ouminus__class_Ouminus'( 'tc_Complex_Ocomplex' ), X ) ) ],
% 1.42/1.81     [ hBOOL( hAPP( X, 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ) ), 
% 1.42/1.81    ~( hBOOL( hAPP( X, T ) ) ), ~( 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 
% 1.42/1.81    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), hAPP( 'c_Suc', T ) ), 
% 1.42/1.81    'tc_nat' ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.42/1.81    'tc_nat' ), Z ), T ), Y, 'tc_nat' ) ) ],
% 1.42/1.81     [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =( hAPP( 
% 1.42/1.81    'c_HOL_Oabs__class_Oabs'( X ), Y ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( 
% 1.42/1.81    X ), Y ) ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( 
% 1.42/1.81    X ), X ) ) ],
% 1.42/1.81     [ ~( 'class_Ring__and__Field_Oabs__if'( X ) ), =( hAPP( 
% 1.42/1.81    'c_HOL_Oabs__class_Oabs'( X ), Y ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( 
% 1.42/1.81    X ), Y ) ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( 
% 1.42/1.81    X ), X ) ) ],
% 1.42/1.81     [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 
% 1.42/1.81    'class_OrderedGroup_Olordered__ab__group__add__abs'( X ) ), =( hAPP( 
% 1.42/1.81    'c_HOL_Oabs__class_Oabs'( X ), Y ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( 
% 1.42/1.81    X ), Y ) ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( 
% 1.42/1.81    X ), X ) ) ],
% 1.42/1.81     [ =( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ), 
% 1.42/1.81    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X
% 1.42/1.81    , Y, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.42/1.81    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.42/1.81     [ ~( 'class_Nat_Osemiring__char__0'( X ) ), ~( =( hAPP( 
% 1.42/1.81    'c_Nat_Osemiring__1__class_Oof__nat'( X ), Y ), hAPP( 
% 1.42/1.81    'c_Nat_Osemiring__1__class_Oof__nat'( X ), Z ) ) ), =( Y, Z ) ],
% 1.42/1.81     [ 'c_lessequals'( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), Y, 
% 1.42/1.81    'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 
% 1.42/1.81    'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.42/1.81     [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( 
% 1.42/1.81    'c_Finite__Set_Osetsum'( Y, 'tc_nat', X ), 
% 1.42/1.81    'c_SetInterval_Oord__class_OatLeastAtMost'( Z, hAPP( 'c_Suc', T ), 
% 1.42/1.81    'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 
% 1.42/1.81    'c_Finite__Set_Osetsum'( Y, 'tc_nat', X ), 
% 1.42/1.81    'c_SetInterval_Oord__class_OatLeastAtMost'( Z, T, 'tc_nat' ) ) ), hAPP( Y
% 1.42/1.81    , hAPP( 'c_Suc', T ) ) ) ), 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', T )
% 1.42/1.81    , Z, 'tc_nat' ) ],
% 1.42/1.81     [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( 'c_Suc'
% 1.42/1.81    , X ) ), Y ), hAPP( 'c_Suc', hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 
% 1.42/1.81    'tc_nat' ), X ), Y ) ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.42/1.81     [ 'c_lessequals'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ), ~( 
% 1.42/1.81    'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.42/1.81     [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( hAPP( 
% 1.42/1.81    'c_Suc', X ), Y, 'tc_nat' ) ) ],
% 1.42/1.81     [ 'c_lessequals'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ), ~( 
% 1.42/1.81    'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.42/1.81     [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( hAPP( 
% 1.42/1.81    'c_Suc', X ), Y, 'tc_nat' ) ) ],
% 1.42/1.81     [ 'c_Fun_Oinj__on'( 'c_Suc', X, 'tc_nat', 'tc_nat' ) ],
% 1.42/1.81     [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), 
% 1.42/1.81    'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( 
% 1.42/1.81    'c_HOL_Oabs__class_Oabs'( X ), Y ) ), 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.42/1.81     ) ],
% 1.42/1.81     [ 'c_lessequals'( 'c_Int_OMin', 'c_Int_OBit0'( X ), 'tc_Int_Oint' ), ~( 
% 1.42/1.81    'c_HOL_Oord__class_Oless'( 'c_Int_OMin', X, 'tc_Int_Oint' ) ) ],
% 1.42/1.81     [ 'c_HOL_Oord__class_Oless'( 'c_Int_OMin', X, 'tc_Int_Oint' ), ~( 
% 1.42/1.81    'c_lessequals'( 'c_Int_OMin', 'c_Int_OBit0'( X ), 'tc_Int_Oint' ) ) ]
% 1.42/1.81    ,
% 1.42/1.81     [ 'c_lessequals'( 'c_Int_OMin', 'c_Int_OBit1'( X ), 'tc_Int_Oint' ), ~( 
% 1.42/1.81    'c_lessequals'( 'c_Int_OMin', X, 'tc_Int_Oint' ) ) ],
% 1.42/1.81     [ 'c_lessequals'( 'c_Int_OMin', X, 'tc_Int_Oint' ), ~( 'c_lessequals'( 
% 1.42/1.81    'c_Int_OMin', 'c_Int_OBit1'( X ), 'tc_Int_Oint' ) ) ],
% 1.42/1.81     [ 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', hAPP( hAPP( 
% 1.42/1.81    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), 'tc_nat' ) ],
% 1.42/1.81     [ 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', hAPP( hAPP( 
% 1.42/1.81    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ) ), 'tc_nat' ) ],
% 1.42/1.81     [ 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', hAPP( hAPP( 
% 1.42/1.81    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), 'tc_nat' ) ],
% 1.42/1.81     [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc'
% 1.42/1.81    , hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), 
% 1.42/1.81    'c_Divides_Odiv__class_Odiv'( X, hAPP( 'c_Suc', hAPP( 'c_Suc', 
% 1.42/1.81    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ) ), X ), ~( 
% 1.42/1.81    'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.42/1.81     [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), 
% 1.42/1.81    'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( 
% 1.42/1.81    'c_HOL_Ouminus__class_Ouminus'( X ), Z ), hAPP( 
% 1.42/1.81    'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ) ) ],
% 1.42/1.81     [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), 
% 1.42/1.81    'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), hAPP( 
% 1.42/1.81    'c_HOL_Ouminus__class_Ouminus'( X ), Z ), X ), ~( 'c_lessequals'( Z, Y, X
% 1.42/1.81     ) ) ],
% 1.42/1.81     [ ~( 'class_Ring__and__Field_Olordered__ring'( X ) ), 'c_lessequals'( 
% 1.42/1.81    hAPP( 'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP( 
% 1.42/1.81    'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP( 
% 1.42/1.81    'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Y
% 1.42/1.81     ) ), hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Z ) ), X ) ],
% 1.42/1.81     [ =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( 'tc_nat' ), X ), 
% 1.42/1.81    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( 'c_Suc', 
% 1.42/1.81    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.42/1.81     [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), 
% 1.42/1.81    'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( 
% 1.42/1.81    'c_HOL_Oabs__class_Oabs'( X ), Y ), Z, X ) ) ],
% 1.42/1.81     [ 'c_lessequals'( 'c_Fact_Ofact__class_Ofact'( X, 'tc_nat' ), 
% 1.42/1.81    'c_Fact_Ofact__class_Ofact'( Y, 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'( 
% 1.42/1.81    X, Y, 'tc_nat' ) ) ],
% 1.42/1.81     [ 'c_lessequals'( 'c_Int_OBit0'( X ), 'c_Int_OMin', 'tc_Int_Oint' ), ~( 
% 1.42/1.81    'c_lessequals'( X, 'c_Int_OMin', 'tc_Int_Oint' ) ) ],
% 1.42/1.81     [ 'c_lessequals'( X, 'c_Int_OMin', 'tc_Int_Oint' ), ~( 'c_lessequals'( 
% 1.42/1.81    'c_Int_OBit0'( X ), 'c_Int_OMin', 'tc_Int_Oint' ) ) ],
% 1.42/1.81     [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'( 
% 1.42/1.81    hAPP( 'c_Nat_Osemiring__1__class_Oof__nat'( X ), Y ), hAPP( 
% 1.42/1.81    'c_Nat_Osemiring__1__class_Oof__nat'( X ), Z ), X ), ~( 'c_lessequals'( Y
% 1.42/1.81    , Z, 'tc_nat' ) ) ],
% 1.42/1.81     [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'( 
% 1.42/1.81    Y, Z, 'tc_nat' ), ~( 'c_lessequals'( hAPP( 
% 1.42/1.81    'c_Nat_Osemiring__1__class_Oof__nat'( X ), Y ), hAPP( 
% 1.42/1.81    'c_Nat_Osemiring__1__class_Oof__nat'( X ), Z ), X ) ) ],
% 1.42/1.81     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( 
% 1.42/1.81    'class_Int_Onumber__ring'( X ) ), =( hAPP( 'c_HOL_Oabs__class_Oabs'( X )
% 1.42/1.81    , hAPP( 'c_Int_Onumber__class_Onumber__of'( X ), Y ) ), hAPP( 
% 1.42/1.81    'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( 
% 1.42/1.81    'c_Int_Onumber__class_Onumber__of'( X ), Y ) ) ), ~( 
% 1.42/1.81    'c_HOL_Oord__class_Oless'( hAPP( 'c_Int_Onumber__class_Onumber__of'( X )
% 1.42/1.81    , Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.42/1.81     [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), 
% 1.42/1.81    'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y )
% 1.42/1.81    , 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.42/1.81    'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.42/1.81     [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), 
% 1.42/1.81    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 
% 1.42/1.81    'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y )
% 1.42/1.81    , 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.42/1.81     [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 
% 1.42/1.81    'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 
% 1.42/1.81    'tc_nat' ) ), 'tc_nat' ) ) ],
% 1.42/1.81     [ 'c_lessequals'( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ), X, 
% 1.42/1.81    'tc_nat' ) ],
% 1.42/1.81     [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), 
% 1.42/1.81    'c_lessequals'( hAPP( 'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP( 
% 1.42/1.81    'c_HOL_Ominus__class_Ominus'( X ), hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Y
% 1.42/1.81     ) ), hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Z ) ) ), hAPP( 
% 1.42/1.81    'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 
% 1.42/1.81    X ), Y ), Z ) ), X ) ],
% 1.42/1.81     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 
% 1.42/1.81    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.42/1.81    , hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Y ) ), hAPP( 
% 1.42/1.81    'c_HOL_Oabs__class_Oabs'( X ), Z ) ), hAPP( hAPP( 
% 1.42/1.81    'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X ), ~( 
% 1.42/1.81    'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Z ), U, X
% 1.42/1.81     ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Oabs__class_Oabs'( X ), 
% 1.42/1.81    Y ), T, X ) ) ],
% 1.42/1.81     [ =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ), 
% 1.42/1.81    hAPP( 'c_Suc', 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ) ), =( 
% 1.42/1.81    hAPP( 'c_Suc', 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), Y ) ]
% 1.42/1.81    ,
% 1.42/1.81     [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.42/1.81     ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 
% 1.42/1.81    'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 1.42/1.81     [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.42/1.81    , X ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 
% 1.42/1.81    'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.42/1.81     [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), hAPP( hAPP( 
% 1.42/1.81    'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), X ), Y ) ), Z ), hAPP( hAPP( 
% 1.42/1.81    'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), X ), hAPP( hAPP( 
% 1.42/1.81    'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), Y ), Z ) ) ) ],
% 1.42/1.81     [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), X ), hAPP( 
% 1.42/1.81    hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), Y ), Z ) ), hAPP( hAPP( 
% 1.42/1.81    'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), Y ), hAPP( hAPP( 
% 1.42/1.81    'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), X ), Z ) ) ) ],
% 1.42/1.81     [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), 
% 1.42/1.81    'c_lessequals'( hAPP( 'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP( 
% 1.42/1.81    'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP( 
% 1.42/1.81    'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Y )
% 1.42/1.81     ), hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Z ) ), X ) ],
% 1.42/1.81     [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 
% 1.42/1.81    'tc_nat' ), ~( 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP( 
% 1.42/1.81    'c_Power_Opower__class_Opower'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ],
% 1.42/1.81     [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_lessequals'( Y, Z, X ) )
% 1.42/1.81    , ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.42/1.81     [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.42/1.81    , X ), 'c_lessequals'( Z, Y, X ) ],
% 1.42/1.81     [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'( Y, Y, X ) )
% 1.42/1.81    , ~( 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ],
% 1.42/1.81     [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Y
% 1.42/1.81    , X ), 'c_lessequals'( Y, Y, X ) ],
% 1.42/1.81     [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.42/1.81    , Z, X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ],
% 1.42/1.81     [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ), 
% 1.42/1.81    'c_HOL_Oord__class_Oless'( Z, Y, X ) ],
% 1.42/1.81     [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.42/1.81    , X ), 'c_lessequals'( Z, Y, X ) ],
% 1.42/1.81     [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'( Y, Z, X ) )
% 1.42/1.81    , ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.42/1.81     [ =( 'c_Fact_Ofact__class_Ofact'( hAPP( hAPP( 
% 1.42/1.81    'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( 'c_Suc', X ) ), Y ), 
% 1.42/1.81    'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 
% 1.42/1.81    hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( 'c_Suc', X ) ), Y )
% 1.42/1.81     ), 'c_Fact_Ofact__class_Ofact'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 
% 1.42/1.81    'tc_nat' ), X ), Y ), 'tc_nat' ) ) ), ~( 'c_HOL_Oord__class_Oless'( Y, 
% 1.42/1.81    hAPP( 'c_Suc', X ), 'tc_nat' ) ) ],
% 1.42/1.81     [ ~( =( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), U ) ), hAPP( hAPP( X, Y
% 1.42/1.81     ), hAPP( hAPP( Z, T ), W ) ) ) ), =( U, W ), =( T, V0 ), ~( 
% 1.42/1.81    'c_Groebner__Basis_Osemiringb'( X, Z, V1, V0, V2, V3 ) ) ],
% 1.42/1.81     [ ~( =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), hAPP( hAPP( Y, U ), W
% 1.42/1.81     ) ), hAPP( hAPP( X, hAPP( hAPP( Y, Z ), W ) ), hAPP( hAPP( Y, U ), T ) )
% 1.42/1.81     ) ), ~( 'c_Groebner__Basis_Osemiringb'( X, Y, V0, V1, V2, V3 ) ), =( T, 
% 1.42/1.81    W ), =( Z, U ) ],
% 1.42/1.81     [ ~( =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), hAPP( hAPP( Y, U ), W
% 1.42/1.81     ) ), hAPP( hAPP( X, hAPP( hAPP( Y, Z ), W ) ), hAPP( hAPP( Y, U ), T ) )
% 1.42/1.81     ) ), =( T, W ), =( Z, U ), ~( 'c_Groebner__Basis_Osemiringb'( X, Y, V0, 
% 1.42/1.81    V1, V2, V3 ) ) ],
% 1.42/1.81     [ =( X, hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X
% 1.42/1.81    , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.42/1.81    X, hAPP( 'c_Suc', hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 1.42/1.81     ), 'tc_nat' ) ) ],
% 1.42/1.81     [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 
% 1.42/1.81    hAPP( 'c_Suc', X ), 'tc_nat' ) ],
% 1.42/1.81     [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 
% 1.42/1.81    hAPP( 'c_Suc', X ), 'tc_nat' ) ],
% 1.42/1.81     [ ~( 'class_Orderings_Olinorder'( X ) ), ~( =( 
% 1.42/1.81    'c_SetInterval_Oord__class_OlessThan'( Y, X ), 
% 1.42/1.81    'c_SetInterval_Oord__class_OlessThan'( Z, X ) ) ), =( Y, Z ) ],
% 1.42/1.81     [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 
% 1.42/1.81    'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat'
% 1.42/1.81     ), Z ), Y ), 'tc_nat' ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ), ~( 
% 1.42/1.81    'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 1.42/1.81     [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~( 
% 1.42/1.81    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.42/1.81    'tc_nat' ), hAPP( 'c_Suc', Z ) ), X ), hAPP( hAPP( 
% 1.42/1.81    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc', Z ) ), Y ), 
% 1.42/1.81    'tc_nat' ) ) ],
% 1.42/1.81     [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.42/1.81    'tc_nat' ), hAPP( 'c_Suc', X ) ), Y ), hAPP( hAPP( 
% 1.42/1.81    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc', X ) ), Z ), 
% 1.42/1.81    'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 1.42/1.81     [ 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ), =( hAPP( 
% 1.42/1.81    'c_Suc', X ), Y ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ]
% 1.42/1.81    ,
% 1.42/1.81     [ 'c_lessequals'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ), 'c_lessequals'( Y, 
% 1.42/1.81    X, 'tc_nat' ) ],
% 1.42/1.81     [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), ~( 'c_lessequals'( hAPP( 
% 1.42/1.81    'c_Suc', Y ), X, 'tc_nat' ) ) ],
% 1.42/1.81     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP( hAPP( 
% 1.42/1.81    'c_Power_Opower__class_Opower'( X ), hAPP( 'c_HOL_Oabs__class_Oabs'( X )
% 1.42/1.81    , Y ) ), Z ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ) )
% 1.42/1.81    , ~( 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ) ],
% 1.42/1.81     [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 
% 1.42/1.81    'tc_nat' ), 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.42/1.81     [ 'c_lessequals'( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), X, 
% 1.42/1.81    'tc_nat' ) ],
% 1.42/1.81     [ ~( =( hAPP( 'c_Suc', 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) )
% 1.42/1.81    , Y ) ), =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', X ), Y, 'tc_nat'
% 1.42/1.81     ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.42/1.81     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 
% 1.42/1.81    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X )
% 1.42/1.81    , Y ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP( 
% 1.42/1.81    'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 
% 1.42/1.81    X ), T ), Y ) ), Z, X ) ) ],
% 1.42/1.81     [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =( hAPP( 
% 1.42/1.81    'c_HOL_Oabs__class_Oabs'( X ), Y ), Y ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.42/1.81    'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.42/1.81     [ 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OMin', 
% 1.42/1.81    'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Int_OMin', 
% 1.42/1.81    'tc_Int_Oint' ) ) ],
% 1.42/1.81     [ 'c_HOL_Oord__class_Oless'( X, 'c_Int_OMin', 'tc_Int_Oint' ), ~( 
% 1.42/1.81    'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OMin', 
% 1.42/1.81    'tc_Int_Oint' ) ) ],
% 1.42/1.81     [ 'c_lessequals'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.42/1.81     ), 'c_Fact_Ofact__class_Ofact'( X, 'tc_nat' ), 'tc_nat' ) ],
% 1.42/1.81     [ =( hAPP( hAPP( X, Y ), hAPP( 'c_Suc', Z ) ), hAPP( hAPP( T, Y ), hAPP( 
% 1.42/1.81    hAPP( X, Y ), Z ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, T, X, W, 
% 1.42/1.81    V0, V1 ) ) ],
% 1.42/1.81     [ =( hAPP( hAPP( X, Y ), hAPP( 'c_Suc', Z ) ), hAPP( hAPP( T, Y ), hAPP( 
% 1.42/1.81    hAPP( X, Y ), Z ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, T, X, W, 
% 1.42/1.81    V0, V1 ) ) ],
% 1.42/1.81     [ =( 'c_Fact_Ofact__class_Ofact'( hAPP( 'c_Suc', X ), 'tc_nat' ), hAPP( 
% 1.42/1.81    hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc', X ) ), 
% 1.42/1.81    'c_Fact_Ofact__class_Ofact'( X, 'tc_nat' ) ) ) ],
% 1.42/1.81     [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), 
% 1.42/1.81    'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 
% 1.42/1.81    'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), 
% 1.42/1.81    'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.42/1.81     [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), 
% 1.42/1.81    'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), 
% 1.42/1.81    'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( 
% 1.42/1.81    'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.42/1.81     [ ~( =( 'c_Divides_Odiv__class_Omod'( X, hAPP( 'c_Suc', hAPP( 'c_Suc', 
% 1.42/1.81    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ), 
% 1.42/1.81    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 
% 1.42/1.81    'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.42/1.81     [ =( 'c_Divides_Odiv__class_Omod'( X, hAPP( 'c_Suc', hAPP( 'c_Suc', 
% 1.42/1.81    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ), 
% 1.42/1.81    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 
% 1.42/1.81    'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.42/1.81     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 
% 1.42/1.81    'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Y ), Z, X
% 1.42/1.81     ), ~( 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.42/1.81     ), Y ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.42/1.81     [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), 
% 1.42/1.81    'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Z, X ), 
% 1.42/1.81    ~( 'c_lessequals'( hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Y ), Z, X ) ) ]
% 1.42/1.81    ,
% 1.42/1.81     [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), 
% 1.42/1.81    'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 
% 1.42/1.81    'tc_nat' ), X ), Y ), Y, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( X, Y, 
% 1.42/1.81    'tc_nat' ) ],
% 1.42/1.81     [ =( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ), hAPP( 'c_Suc', 
% 1.42/1.81    'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 
% 1.42/1.81    'tc_nat' ), X ), Y ), Y, 'tc_nat' ) ) ), ~( 'c_lessequals'( Y, X, 
% 1.42/1.81    'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 
% 1.42/1.81    'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.42/1.81     [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 
% 1.42/1.81    'c_Fact_Ofact__class_Ofact'( X, 'tc_nat' ), 'tc_nat' ) ],
% 1.42/1.81     [ ~( =( X, hAPP( 'c_Suc', X ) ) ) ],
% 1.42/1.81     [ ~( =( hAPP( 'c_Suc', X ), X ) ) ],
% 1.42/1.81     [ 'c_lessequals'( 'c_Int_OMin', 'c_Int_OMin', 'tc_Int_Oint' ) ],
% 1.42/1.81     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'( 
% 1.42/1.81    hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP( 
% 1.42/1.81    'c_Power_Opower__class_Opower'( X ), T ), Z ), X ), ~( 'c_lessequals'( Y
% 1.42/1.81    , T, X ) ), 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.42/1.81     [ 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', Y ), 'tc_nat' ), ~( 
% 1.42/1.81    'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.42/1.81     [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~( 
% 1.42/1.81    'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ) ) ],
% 1.42/1.81     [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 
% 1.42/1.81    'tc_nat' ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 
% 1.42/1.81    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( 
% 1.42/1.81    hAPP( 'c_Power_Opower__class_Opower'( 'tc_nat' ), X ), Y ), 'tc_nat' ) )
% 1.42/1.81     ],
% 1.42/1.81     [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 
% 1.42/1.81    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 
% 1.42/1.81    'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 
% 1.42/1.81    'tc_nat' ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( 'tc_nat' ), Y ), 
% 1.42/1.81    X ), 'tc_nat' ) ) ],
% 1.42/1.81     [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.42/1.81     ), =( Y, Z ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.42/1.81     [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), 
% 1.42/1.81    'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 1.42/1.81    ,
% 1.42/1.81     [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), =( X, Y ), ~( 
% 1.42/1.81    'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.42/1.81     [ =( X, Y ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~( 
% 1.42/1.81    'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.42/1.81     [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), =( X, Y ), ~( 
% 1.42/1.81    'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.42/1.81     [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ), =( X, Y ), ~( 
% 1.42/1.81    'c_lessequals'( X, Y, 'tc_Int_Oint' ) ) ],
% 1.42/1.81     [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.42/1.81     ), =( Y, Z ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.42/1.81     [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.42/1.81     ), ~( 'c_lessequals'( Y, Z, X ) ), =( Y, Z ) ],
% 1.42/1.81     [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Y
% 1.42/1.81    , Z, X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ) ],
% 1.42/1.81     [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ), 
% 1.42/1.81    'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 1.42/1.81    ,
% 1.42/1.81     [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.42/1.81     ), ~( 'c_lessequals'( Y, Z, X ) ), =( Z, Y ) ],
% 1.42/1.81     [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.42/1.81     ), =( Z, Y ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.42/1.81     [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 
% 1.42/1.81    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( 
% 1.42/1.81    'c_Nat_Osemiring__1__class_Oof__nat'( X ), 'c_Fact_Ofact__class_Ofact'( Y
% 1.42/1.81    , 'tc_nat' ) ), X ) ],
% 1.42/1.81     [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), 
% 1.42/1.81    'c_lessequals'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), hAPP( 
% 1.42/1.81    'c_HOL_Oabs__class_Oabs'( X ), Y ) ), hAPP( 'c_HOL_Oabs__class_Oabs'( X )
% 1.42/1.81    , Z ) ), hAPP( 'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP( 
% 1.42/1.81    'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ), X ) ],
% 1.42/1.81     [ ~( 'c_lessequals'( 'c_Int_OPls', 'c_Int_OMin', 'tc_Int_Oint' ) ) ]
% 1.42/1.81    ,
% 1.42/1.81     [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'( 
% 1.42/1.81    Y, Z, 'tc_nat' ), ~( 'c_lessequals'( hAPP( hAPP( 
% 1.42/1.81    'c_Power_Opower__class_Opower'( X ), T ), Y ), hAPP( hAPP( 
% 1.42/1.81    'c_Power_Opower__class_Opower'( X ), T ), Z ), X ) ), ~( 
% 1.42/1.81    'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), T, X ) ) ],
% 1.42/1.81     [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'( 
% 1.42/1.81    Y, Z, 'tc_nat' ), ~( 'c_lessequals'( hAPP( hAPP( 
% 1.42/1.81    'c_Power_Opower__class_Opower'( X ), T ), Y ), hAPP( hAPP( 
% 1.42/1.81    'c_Power_Opower__class_Opower'( X ), T ), Z ), X ) ), ~( 
% 1.42/1.81    'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), T, X ) ) ],
% 1.42/1.81     [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'( 
% 1.42/1.81    hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP( 
% 1.42/1.81    'c_Power_Opower__class_Opower'( X ), Y ), T ), X ), ~( 'c_lessequals'( Z
% 1.42/1.81    , T, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( 
% 1.42/1.81    X ), Y, X ) ) ],
% 1.42/1.81     [ =( 'c_Divides_Odiv__class_Odiv'( X, hAPP( 'c_Suc', 
% 1.42/1.81    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ), X ) ],
% 1.42/1.81     [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 
% 1.42/1.81    hAPP( hAPP( 'c_Power_Opower__class_Opower'( 'tc_nat' ), X ), 
% 1.42/1.81    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ],
% 1.42/1.81     [ ~( =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Y ), T ) ) ), ~( 
% 1.42/1.81    'c_Groebner__Basis_Osemiringb'( X, U, W, V0, V1, V2 ) ), =( Z, T ) ],
% 1.42/1.81     [ ~( =( X, hAPP( hAPP( Y, X ), Z ) ) ), ~( 
% 1.42/1.81    'c_Groebner__Basis_Osemiringb'( Y, T, U, W, V0, V1 ) ), =( Z, W ) ],
% 1.42/1.81     [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 
% 1.42/1.81    X, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 
% 1.42/1.81    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), hAPP( 'c_Suc', 
% 1.42/1.81    'c_Divides_Odiv__class_Odiv'( Y, X, 'tc_nat' ) ) ), 'tc_nat' ) ],
% 1.42/1.81     [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 
% 1.42/1.81    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), Z, 'tc_nat' ), hAPP( 
% 1.42/1.81    hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP( 
% 1.42/1.81    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( X, 
% 1.42/1.81    Z, 'tc_nat' ) ), 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ) ), 
% 1.42/1.81    'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 
% 1.42/1.81    'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X, Z, 'tc_nat' ) ), 
% 1.42/1.81    'c_Divides_Odiv__class_Omod'( Y, Z, 'tc_nat' ) ), Z, 'tc_nat' ) ) ) ]
% 1.42/1.81    ,
% 1.42/1.81     [ 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ), 'c_HOL_Oord__class_Oless'( 
% 1.42/1.81    X, hAPP( 'c_Suc', X ), 'tc_nat' ) ],
% 1.42/1.81     [ ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), ~( 
% 1.42/1.81    'c_HOL_Oord__class_Oless'( Y, hAPP( 'c_Suc', X ), 'tc_nat' ) ) ],
% 1.42/1.81     [ 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', Y ), 'tc_nat' ), 
% 1.42/1.81    'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ],
% 1.42/1.81     [ =( X, hAPP( 'c_Suc', Y ) ), 'c_lessequals'( X, Y, 'tc_nat' ), ~( 
% 1.42/1.81    'c_lessequals'( X, hAPP( 'c_Suc', Y ), 'tc_nat' ) ) ],
% 1.42/1.81     [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( 'c_Suc', X ), hAPP( 'c_Suc', 
% 1.42/1.81    hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ), 
% 1.42/1.81    hAPP( 'c_Suc', 'c_Divides_Odiv__class_Odiv'( X, hAPP( 'c_Suc', hAPP( 
% 1.42/1.81    'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ) ) ), 
% 1.42/1.81    'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.42/1.81     [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'( 
% 1.42/1.81    hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Z, X ), 
% 1.42/1.81    'c_Divides_Odiv__class_Omod'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), 
% 1.42/1.81    'c_Divides_Odiv__class_Omod'( Y, Z, X ) ), Z, X ) ) ],
% 1.42/1.81     [ =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( 'tc_nat' ), hAPP( 
% 1.42/1.81    'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), X ), hAPP( 'c_Suc', 
% 1.42/1.81    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.42/1.81     [ =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( 'tc_nat' ), hAPP( 
% 1.42/1.81    'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), X ), hAPP( 'c_Suc', 
% 1.42/1.81    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.42/1.81     [ ~( =( 'c_Divides_Odiv__class_Omod'( X, hAPP( 'c_Suc', hAPP( 'c_Suc', 
% 1.42/1.81    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ), hAPP( 'c_Suc', 
% 1.42/1.81    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), ~( 
% 1.42/1.81    'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.42/1.81     [ =( 'c_Divides_Odiv__class_Omod'( X, hAPP( 'c_Suc', hAPP( 'c_Suc', 
% 1.42/1.81    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ), hAPP( 'c_Suc', 
% 1.42/1.81    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 
% 1.42/1.81    'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.42/1.81     [ 'c_lessequals'( X, 'c_Int_OMin', 'tc_Int_Oint' ), ~( 'c_lessequals'( 
% 1.42/1.81    'c_Int_OBit1'( X ), 'c_Int_OMin', 'tc_Int_Oint' ) ) ],
% 1.42/1.81     [ 'c_lessequals'( 'c_Int_OBit1'( X ), 'c_Int_OMin', 'tc_Int_Oint' ), ~( 
% 1.42/1.81    'c_lessequals'( X, 'c_Int_OMin', 'tc_Int_Oint' ) ) ],
% 1.42/1.81     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( 
% 1.42/1.81    'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( 
% 1.42/1.81    'c_Int_Onumber__class_Onumber__of'( X ), Y ), hAPP( 
% 1.42/1.81    'c_Int_Onumber__class_Onumber__of'( X ), Z ), X ), ~( 
% 1.42/1.81    'c_HOL_Oord__class_Oless'( Y, Z, 'tc_Int_Oint' ) ) ],
% 1.42/1.81     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( 
% 1.42/1.81    'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, 
% 1.42/1.81    'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( hAPP( 
% 1.42/1.81    'c_Int_Onumber__class_Onumber__of'( X ), Y ), hAPP( 
% 1.42/1.81    'c_Int_Onumber__class_Onumber__of'( X ), Z ), X ) ) ],
% 1.42/1.81     [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ), ~( 
% 1.42/1.81    'c_HOL_Oord__class_Oless'( hAPP( 'c_Int_Onumber__class_Onumber__of'( 
% 1.42/1.81    'tc_nat' ), X ), hAPP( 'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), Y
% 1.42/1.81     ), 'tc_nat' ) ) ],
% 1.42/1.81     [ 'c_lessequals'( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ), 
% 1.42/1.81    'c_Divides_Odiv__class_Odiv'( Z, Y, 'tc_nat' ), 'tc_nat' ), ~( 
% 1.42/1.81    'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 1.42/1.81     [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP( 
% 1.42/1.81    'c_Power_Opower__class_Opower'( 'tc_nat' ), X ), Y ), 'tc_nat' ), ~( 
% 1.42/1.81    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 
% 1.42/1.81    'tc_nat' ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ]
% 1.42/1.81    ,
% 1.42/1.81     [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), hAPP( hAPP( Y, U ), T ) )
% 1.42/1.81    , hAPP( hAPP( Y, hAPP( hAPP( X, Z ), U ) ), T ) ), ~( 
% 1.42/1.81    'c_Groebner__Basis_Ogb__semiring'( X, Y, W, V0, V1, V2 ) ) ],
% 1.42/1.81     [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), T ), hAPP( hAPP( Y, hAPP( 
% 1.42/1.81    hAPP( X, Z ), U ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, Y, W
% 1.42/1.81    , V0, U, V1 ) ) ],
% 1.42/1.81     [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), Y ) ), hAPP( hAPP( Z, hAPP( 
% 1.42/1.81    hAPP( X, T ), U ) ), Y ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, Z, W
% 1.42/1.81    , V0, U, V1 ) ) ],
% 1.42/1.81     [ =( hAPP( hAPP( X, Y ), Y ), hAPP( hAPP( Z, hAPP( hAPP( X, T ), T ) ), 
% 1.42/1.81    Y ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, Z, U, W, T, V0 ) ) ],
% 1.42/1.81     [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'( 
% 1.42/1.81    X, T, U, Y, W, V0 ) ) ],
% 1.42/1.81     [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'( 
% 1.42/1.81    X, T, U, Z, W, V0 ) ) ],
% 1.42/1.81     [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~( 
% 1.42/1.81    'c_Groebner__Basis_Ogb__semiring'( T, X, U, W, V0, V1 ) ) ],
% 1.42/1.81     [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), U ), hAPP( hAPP( Y, hAPP( 
% 1.42/1.81    hAPP( X, Z ), U ) ), hAPP( hAPP( X, T ), U ) ) ), ~( 
% 1.42/1.81    'c_Groebner__Basis_Ogb__semiring'( Y, X, W, V0, V1, V2 ) ) ],
% 1.42/1.81     [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'( 
% 1.42/1.81    T, X, U, Y, W, V0 ) ) ],
% 1.42/1.81     [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'( 
% 1.42/1.81    T, X, U, Z, W, V0 ) ) ],
% 1.42/1.81     [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'( 
% 1.42/1.81    T, X, U, W, Y, V0 ) ) ],
% 1.42/1.81     [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'( 
% 1.42/1.81    T, X, U, W, Z, V0 ) ) ],
% 1.42/1.81     [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 1.42/1.81    , hAPP( hAPP( X, hAPP( hAPP( X, Y ), T ) ), hAPP( hAPP( X, Z ), U ) ) ), 
% 1.42/1.81    ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, V0, V1, V2, V3 ) ) ],
% 1.42/1.81     [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 1.42/1.81    , hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), hAPP( hAPP( X, T ), U ) ) ) ), 
% 1.42/1.81    ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, V0, V1, V2, V3 ) ) ],
% 1.42/1.81     [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 1.42/1.81    , hAPP( hAPP( X, T ), hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), U ) ) ), 
% 1.42/1.81    ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, V0, V1, V2, V3 ) ) ],
% 1.42/1.81     [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, hAPP( 
% 1.42/1.81    hAPP( X, Y ), T ) ), Z ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, W
% 1.42/1.81    , V0, V1, V2 ) ) ],
% 1.42/1.81     [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, Y ), 
% 1.42/1.81    hAPP( hAPP( X, Z ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, 
% 1.42/1.81    W, V0, V1, V2 ) ) ],
% 1.42/1.81     [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP( 
% 1.42/1.81    hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, W
% 1.42/1.81    , V0, V1, V2 ) ) ],
% 1.42/1.81     [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, Z ), 
% 1.42/1.81    hAPP( hAPP( X, Y ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, 
% 1.42/1.81    W, V0, V1, V2 ) ) ],
% 1.42/1.81     [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 1.42/1.81    , hAPP( hAPP( X, hAPP( hAPP( X, Y ), T ) ), hAPP( hAPP( X, Z ), U ) ) ), 
% 1.42/1.81    ~( 'c_Groebner__Basis_Ogb__semiring'( X, W, V0, V1, V2, V3 ) ) ],
% 1.42/1.81     [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, Y ), 
% 1.42/1.81    hAPP( hAPP( X, Z ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U, 
% 1.42/1.81    W, V0, V1, V2 ) ) ],
% 1.42/1.81     [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, Z ), 
% 1.42/1.81    hAPP( hAPP( X, Y ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U, 
% 1.42/1.81    W, V0, V1, V2 ) ) ],
% 1.42/1.81     [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, hAPP( 
% 1.42/1.81    hAPP( X, Y ), T ) ), Z ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U, W
% 1.42/1.81    , V0, V1, V2 ) ) ],
% 1.42/1.81     [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~( 
% 1.42/1.81    'c_Groebner__Basis_Ogb__semiring'( X, T, U, W, V0, V1 ) ) ],
% 1.42/1.81     [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP( 
% 1.42/1.81    hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U, W
% 1.42/1.81    , V0, V1, V2 ) ) ],
% 1.42/1.81     [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'( 
% 1.42/1.81    X, T, U, Y, W, V0 ) ) ],
% 1.42/1.81     [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP( 
% 1.42/1.81    hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U, W
% 1.42/1.81    , V0, V1, V2 ) ) ],
% 1.42/1.81     [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~( 
% 1.42/1.81    'c_Groebner__Basis_Ogb__semiring'( X, T, U, W, V0, V1 ) ) ],
% 1.42/1.81     [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'( 
% 1.42/1.81    T, X, U, Y, W, V0 ) ) ],
% 1.42/1.81     [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'( 
% 1.42/1.81    T, X, U, W, Y, V0 ) ) ],
% 1.42/1.81     [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP( 
% 1.42/1.81    hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, W
% 1.42/1.81    , V0, V1, V2 ) ) ],
% 1.42/1.81     [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~( 
% 1.42/1.81    'c_Groebner__Basis_Ogb__semiring'( T, X, U, W, V0, V1 ) ) ],
% 1.42/1.81     [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), U ) ), hAPP( hAPP( Z, hAPP( 
% 1.42/1.81    hAPP( X, Y ), T ) ), hAPP( hAPP( X, Y ), U ) ) ), ~( 
% 1.42/1.81    'c_Groebner__Basis_Ogb__semiring'( Z, X, W, V0, V1, V2 ) ) ],
% 1.42/1.81     [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), U ), hAPP( hAPP( Y, hAPP( 
% 1.42/1.81    hAPP( X, Z ), U ) ), hAPP( hAPP( X, T ), U ) ) ), ~( 
% 1.42/1.81    'c_Groebner__Basis_Ogb__semiring'( W, Y, X, V0, V1, V2 ) ) ],
% 1.42/1.81     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP( 
% 1.42/1.81    'c_HOL_Oabs__class_Oabs'( X ), hAPP( 'c_Nat_Osemiring__1__class_Oof__nat'( 
% 1.42/1.81    X ), Y ) ), hAPP( 'c_Nat_Osemiring__1__class_Oof__nat'( X ), Y ) ) ],
% 1.42/1.81     [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), 
% 1.42/1.81    'c_lessequals'( hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Y ), Z, X ), ~( 
% 1.42/1.81    'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Z, X ) )
% 1.42/1.81    , ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.42/1.81     [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), 
% 1.42/1.81    'c_lessequals'( hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Y ), Z, X ), ~( 
% 1.42/1.81    'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Z, X ) )
% 1.42/1.81    , ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.42/1.81     [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =( hAPP( 
% 1.42/1.81    'c_HOL_Oabs__class_Oabs'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X )
% 1.42/1.81    , Y ) ), hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Y ) ) ],
% 1.42/1.81     [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), 
% 1.42/1.81    'c_lessequals'( hAPP( 'c_HOL_Oabs__class_Oabs'( X ), 
% 1.42/1.81    'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ]
% 1.42/1.81    ,
% 1.42/1.81     [ 'c_lessequals'( 'c_Int_OMin', 'c_Int_OPls', 'tc_Int_Oint' ) ],
% 1.42/1.81     [ =( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ), 
% 1.42/1.81    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X
% 1.42/1.81    , Y, 'tc_nat' ) ) ],
% 1.42/1.81     [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( hAPP( hAPP( 
% 1.42/1.81    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc', Z ) ), X ), hAPP( 
% 1.42/1.81    hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc', Z ) ), Y )
% 1.42/1.81    , 'tc_nat' ) ) ],
% 1.42/1.81     [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 
% 1.42/1.81    hAPP( 'c_Suc', X ) ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.42/1.81    'tc_nat' ), hAPP( 'c_Suc', X ) ), Z ), 'tc_nat' ), ~( 'c_lessequals'( Y, 
% 1.42/1.82    Z, 'tc_nat' ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( hAPP( 'c_Nat_Osemiring__1__class_Oof__nat'( X
% 1.42/1.82     ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.42/1.82     [ 'c_lessequals'( hAPP( 'c_Suc', X ), hAPP( 'c_Suc', X ), 'tc_nat' ) ]
% 1.42/1.82    ,
% 1.42/1.82     [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ), ~( 
% 1.42/1.82    'c_Parity_Oeven__odd__class_Oeven'( hAPP( 'c_Suc', X ), 'tc_nat' ) ) ]
% 1.42/1.82    ,
% 1.42/1.82     [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( 'c_Suc', X ), 'tc_nat' ), 
% 1.42/1.82    'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.42/1.82     [ =( 'c_Fact_Ofact__class_Ofact'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.42/1.82    , 'tc_nat' ), hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ]
% 1.42/1.82    ,
% 1.42/1.82     [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ), 'tc_nat' ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.42/1.82     [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =( hAPP( 
% 1.42/1.82    'c_HOL_Oabs__class_Oabs'( X ), Y ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( 
% 1.42/1.82    X ), Y ) ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.42/1.82     ],
% 1.42/1.82     [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( 
% 1.42/1.82    'tc_nat' ), Z ), X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( 
% 1.42/1.82    'tc_nat' ), Z ), Y ), 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_nat' ) ) ],
% 1.42/1.82     [ ~( 'class_Nat_Osemiring__char__0'( X ) ), ~( =( hAPP( 
% 1.42/1.82    'c_Nat_Osemiring__1__class_Oof__nat'( X ), 'c_Fact_Ofact__class_Ofact'( Y
% 1.42/1.82    , 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'( 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), hAPP( 
% 1.42/1.82    'c_Nat_Osemiring__1__class_Oof__nat'( X ), Y ), X ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'( 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), hAPP( 
% 1.42/1.82    'c_Nat_Osemiring__1__class_Oof__nat'( X ), Y ), X ) ],
% 1.42/1.82     [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( 
% 1.42/1.82    'c_Finite__Set_Osetsum'( Y, 'tc_nat', X ), 
% 1.42/1.82    'c_SetInterval_Oord__class_OatLeastAtMost'( Z, T, 'tc_nat' ) ), hAPP( 
% 1.42/1.82    hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( Y, Z ) ), hAPP( 
% 1.42/1.82    'c_Finite__Set_Osetsum'( Y, 'tc_nat', X ), 
% 1.42/1.82    'c_SetInterval_Oord__class_OatLeastAtMost'( hAPP( 'c_Suc', Z ), T, 
% 1.42/1.82    'tc_nat' ) ) ) ), ~( 'c_lessequals'( Z, T, 'tc_nat' ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'( 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), hAPP( 
% 1.42/1.82    'c_Nat_Osemiring__1__class_Oof__nat'( X ), 'c_Fact_Ofact__class_Ofact'( Y
% 1.42/1.82    , 'tc_nat' ) ), X ) ],
% 1.42/1.82     [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( 
% 1.42/1.82    'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( 
% 1.42/1.82    X ), Y ) ), Y ) ],
% 1.42/1.82     [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( Y, hAPP( 
% 1.42/1.82    'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( 
% 1.42/1.82    X ), Y ) ) ) ],
% 1.42/1.82     [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( Y, hAPP( 
% 1.42/1.82    'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( 
% 1.42/1.82    X ), Y ) ) ) ],
% 1.42/1.82     [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), =( hAPP( 
% 1.42/1.82    'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( 
% 1.42/1.82    X ), Y ) ), Y ) ],
% 1.42/1.82     [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( 
% 1.42/1.82    'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( 
% 1.42/1.82    X ), Y ) ), Y ) ],
% 1.42/1.82     [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ), 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.42/1.82     ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~( 
% 1.42/1.82    'c_lessequals'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ]
% 1.42/1.82    ,
% 1.42/1.82     [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ), 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.42/1.82     ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ]
% 1.42/1.82    ,
% 1.42/1.82     [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 
% 1.42/1.82    'tc_Int_Oint' ), X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 
% 1.42/1.82    'tc_Int_Oint' ), Z ), T ), 'tc_Int_Oint' ), ~( 'c_lessequals'( Y, T, 
% 1.42/1.82    'tc_Int_Oint' ) ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_Int_Oint' ) )
% 1.42/1.82     ],
% 1.42/1.82     [ 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', X ), hAPP( 'c_Suc', Y ), 
% 1.42/1.82    'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.42/1.82     [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', X ), hAPP( 'c_Suc', Y ), 
% 1.42/1.82    'tc_nat' ) ) ],
% 1.42/1.82     [ 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', X ), hAPP( 'c_Suc', Y ), 
% 1.42/1.82    'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.42/1.82     [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y )
% 1.42/1.82    , Z, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP( 
% 1.42/1.82    'c_HOL_Ouminus__class_Ouminus'( X ), Z ), Y, X ) ) ],
% 1.42/1.82     [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y )
% 1.42/1.82    , Z, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP( 
% 1.42/1.82    'c_HOL_Ouminus__class_Ouminus'( X ), Z ), Y, X ) ) ],
% 1.42/1.82     [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( Y, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), 
% 1.42/1.82    Z ), X ), ~( 'c_HOL_Oord__class_Oless'( Z, hAPP( 
% 1.42/1.82    'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ) ) ],
% 1.42/1.82     [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( Y, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), 
% 1.42/1.82    Z ), X ), ~( 'c_HOL_Oord__class_Oless'( Z, hAPP( 
% 1.42/1.82    'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ) ) ],
% 1.42/1.82     [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), 
% 1.42/1.82    'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Z, X ), 
% 1.42/1.82    ~( 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), Y, X )
% 1.42/1.82     ) ],
% 1.42/1.82     [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), 
% 1.42/1.82    'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Z, X ), 
% 1.42/1.82    ~( 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), Y, X )
% 1.42/1.82     ) ],
% 1.42/1.82     [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), 
% 1.42/1.82    'c_lessequals'( Y, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), X ), 
% 1.42/1.82    ~( 'c_lessequals'( Z, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X )
% 1.42/1.82     ) ],
% 1.42/1.82     [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), 
% 1.42/1.82    'c_lessequals'( Y, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), X ), 
% 1.42/1.82    ~( 'c_lessequals'( Z, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X )
% 1.42/1.82     ) ],
% 1.42/1.82     [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), ~( =( 
% 1.42/1.82    hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.42/1.82     ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.82     [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ), =( hAPP( 
% 1.42/1.82    'c_HOL_Ouminus__class_Ouminus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.82     [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( 
% 1.42/1.82    'c_HOL_Ouminus__class_Ouminus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.82     [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.42/1.82     ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.42/1.82     [ ~( 'class_Divides_Osemiring__div'( X ) ), =( 
% 1.42/1.82    'c_Divides_Odiv__class_Omod'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.42/1.82     ) ],
% 1.42/1.82     [ ~( 'class_Divides_Osemiring__div'( X ) ), =( 
% 1.42/1.82    'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 1.42/1.82     ) ],
% 1.42/1.82     [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ), ~( =( hAPP( 
% 1.42/1.82    'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Y ) ), =( Y, 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.82     [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =( hAPP( 
% 1.42/1.82    'c_HOL_Ouminus__class_Ouminus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.42/1.82     ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.82     [ ~( 'class_Divides_Osemiring__div'( X ) ), =( 
% 1.42/1.82    'c_Divides_Odiv__class_Odiv'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.82     [ ~( 'class_Divides_Osemiring__div'( X ) ), =( 
% 1.42/1.82    'c_Divides_Odiv__class_Odiv'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.82     [ ~( 'class_Divides_Osemiring__div'( X ) ), =( 
% 1.42/1.82    'c_Divides_Odiv__class_Omod'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.82     [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =( hAPP( 
% 1.42/1.82    'c_HOL_Oabs__class_Oabs'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.82     [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =( 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.42/1.82     ), Y ) ) ), =( 'c_HOL_Ozero__class_Ozero'( X ), Y ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.42/1.82    , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X )
% 1.42/1.82    , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) )
% 1.42/1.82    , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 
% 1.42/1.82    'c_lessequals'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ]
% 1.42/1.82    ,
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.42/1.82    , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X )
% 1.42/1.82    , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ]
% 1.42/1.82    ,
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Y
% 1.42/1.82     ) ), Z ), hAPP( 'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ), ~( 'c_lessequals'( 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.42/1.82    , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X )
% 1.42/1.82    , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 
% 1.42/1.82    'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, 
% 1.42/1.82    T, X ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Opordered__ring__abs'( X ) ), =( hAPP( 
% 1.42/1.82    'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.42/1.82    X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 
% 1.42/1.82    'c_HOL_Oabs__class_Oabs'( X ), Y ) ), hAPP( 'c_HOL_Oabs__class_Oabs'( X )
% 1.42/1.82    , Z ) ) ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 
% 1.42/1.82    ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Opordered__ring__abs'( X ) ), =( hAPP( 
% 1.42/1.82    'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.42/1.82    X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 
% 1.42/1.82    'c_HOL_Oabs__class_Oabs'( X ), Y ) ), hAPP( 'c_HOL_Oabs__class_Oabs'( X )
% 1.42/1.82    , Z ) ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), 
% 1.42/1.82    ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Opordered__ring__abs'( X ) ), =( hAPP( 
% 1.42/1.82    'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.42/1.82    X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 
% 1.42/1.82    'c_HOL_Oabs__class_Oabs'( X ), Y ) ), hAPP( 'c_HOL_Oabs__class_Oabs'( X )
% 1.42/1.82    , Z ) ) ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 
% 1.42/1.82    ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Opordered__ring__abs'( X ) ), =( hAPP( 
% 1.42/1.82    'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.42/1.82    X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 
% 1.42/1.82    'c_HOL_Oabs__class_Oabs'( X ), Y ) ), hAPP( 'c_HOL_Oabs__class_Oabs'( X )
% 1.42/1.82    , Z ) ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), 
% 1.42/1.82    ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.42/1.82    hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.42/1.82    hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ), 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.42/1.82    hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ), 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.42/1.82    hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.42/1.82    , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X )
% 1.42/1.82    , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, 
% 1.42/1.82    T, X ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), 
% 1.42/1.82    'c_lessequals'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), 
% 1.42/1.82    'c_lessequals'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), 
% 1.42/1.82    'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), 
% 1.42/1.82    hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~( 
% 1.42/1.82    'c_lessequals'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), 
% 1.42/1.82    'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ]
% 1.42/1.82    ,
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), 
% 1.42/1.82    'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), 
% 1.42/1.82    hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~( 
% 1.42/1.82    'c_lessequals'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), 
% 1.42/1.82    'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.42/1.82    ,
% 1.42/1.82     [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.42/1.82    , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.42/1.82    , Z ), T ), X ), ~( 'c_lessequals'( Y, T, X ) ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 1.42/1.82    ,
% 1.42/1.82     [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~( 'c_lessequals'( 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.42/1.82     [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 
% 1.42/1.82    'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.42/1.82     [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), 
% 1.42/1.82    'c_lessequals'( Y, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), X ), 
% 1.42/1.82    ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z )
% 1.42/1.82    , 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.42/1.82     [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), 
% 1.42/1.82    'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y, hAPP( 
% 1.42/1.82    'c_HOL_Ouminus__class_Ouminus'( X ), Z ), X ) ) ],
% 1.42/1.82     [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.42/1.82     ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 
% 1.42/1.82    'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.42/1.82     [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.42/1.82     ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z, 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.42/1.82     [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP( 
% 1.42/1.82    'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ), 
% 1.42/1.82    'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), hAPP( 'c_Suc', Z ) ), hAPP( 
% 1.42/1.82    hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP( 
% 1.42/1.82    'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ), 
% 1.42/1.82    'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), Z ) ) ) ],
% 1.42/1.82     [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP( 
% 1.42/1.82    'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ), 
% 1.42/1.82    'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), hAPP( 'c_Suc', Z ) ), hAPP( 
% 1.42/1.82    hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 
% 1.42/1.82    'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ), 
% 1.42/1.82    'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), Z ) ), Y ) ) ],
% 1.42/1.82     [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.42/1.82    , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.42/1.82    , Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 
% 1.42/1.82    'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( 
% 1.42/1.82    'class_Int_Onumber__ring'( X ) ), =( hAPP( 'c_HOL_Oabs__class_Oabs'( X )
% 1.42/1.82    , hAPP( 'c_Int_Onumber__class_Onumber__of'( X ), Y ) ), hAPP( 
% 1.42/1.82    'c_Int_Onumber__class_Onumber__of'( X ), Y ) ), 'c_HOL_Oord__class_Oless'( 
% 1.42/1.82    hAPP( 'c_Int_Onumber__class_Onumber__of'( X ), Y ), 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.42/1.82     [ ~( 'class_Divides_Osemiring__div'( X ) ), =( 
% 1.42/1.82    'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.42/1.82     ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X
% 1.42/1.82     ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), 
% 1.42/1.82    'c_Divides_Odiv__class_Omod'( Y, T, X ) ), Z ) ) ],
% 1.42/1.82     [ ~( 'class_Divides_Osemiring__div'( X ) ), =( 
% 1.42/1.82    'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.42/1.82     ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X
% 1.42/1.82     ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), 
% 1.42/1.82    'c_Divides_Odiv__class_Omod'( Z, T, X ) ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( 
% 1.42/1.82    X ), Y ) ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( 
% 1.42/1.82    'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ) ],
% 1.42/1.82     [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =( 
% 1.42/1.82    'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.42/1.82    , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ), 
% 1.42/1.82    'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =( 
% 1.42/1.82    'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.42/1.82     ), U ), Y ), Z, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Otimes__class_Otimes'( X ), W ), T ), Z, X ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Y
% 1.42/1.82     ) ), hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Y ) ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ) ],
% 1.42/1.82     [ ~( 'class_Divides_Osemiring__div'( X ) ), =( 
% 1.42/1.82    'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.42/1.82     ), Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Otimes__class_Otimes'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X
% 1.42/1.82     ) ), 'c_Divides_Odiv__class_Omod'( Z, T, X ) ), T, X ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.42/1.82     ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.42/1.82     ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( 
% 1.42/1.82    X ), Y ) ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oidom'( X ) ), =( hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( 
% 1.42/1.82    X ), Y ) ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ) ],
% 1.42/1.82     [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( 
% 1.42/1.82    'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ), hAPP( 
% 1.42/1.82    'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ) ],
% 1.42/1.82     [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( 
% 1.42/1.82    'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ), hAPP( 
% 1.42/1.82    'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ) ],
% 1.42/1.82     [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( 
% 1.42/1.82    X ), Y ) ), Z ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ) ],
% 1.42/1.82     [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( 
% 1.42/1.82    X ), Y ) ), Z ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP( 
% 1.42/1.82    'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( 
% 1.42/1.82    'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP( 
% 1.42/1.82    'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( 
% 1.42/1.82    X ), Y ) ), Z ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP( 
% 1.42/1.82    'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.42/1.82    X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 
% 1.42/1.82    'c_HOL_Oabs__class_Oabs'( X ), Y ) ), hAPP( 'c_HOL_Oabs__class_Oabs'( X )
% 1.42/1.82    , Z ) ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( =( hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ) ), =( Y, hAPP( 
% 1.42/1.82    'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ), =( Y, Z ) ],
% 1.42/1.82     [ ~( 'class_Divides_Osemiring__div'( X ) ), =( 
% 1.42/1.82    'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.42/1.82     ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ), T ), Z, X ), 
% 1.42/1.82    'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.42/1.82     ), Y ), T ), Z, X ) ) ],
% 1.42/1.82     [ ~( 'class_Divides_Osemiring__div'( X ) ), =( 
% 1.42/1.82    'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.42/1.82     ), Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_Divides_Odiv__class_Omod'( Z, 
% 1.42/1.82    T, X ) ), T, X ) ) ],
% 1.42/1.82     [ ~( 'class_Divides_Osemiring__div'( X ) ), =( 
% 1.42/1.82    'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.42/1.82     ), Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Otimes__class_Otimes'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X
% 1.42/1.82     ) ), Z ), T, X ) ) ],
% 1.42/1.82     [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), 
% 1.42/1.82    'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 
% 1.42/1.82    'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( 
% 1.42/1.82    'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ) ) ],
% 1.42/1.82     [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), 
% 1.42/1.82    'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( 
% 1.42/1.82    'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ), ~( 'c_lessequals'( Y, 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.42/1.82     [ 'c_HOL_Oord__class_Oless'( 'c_Divides_Odiv__class_Omod'( X, Y, 
% 1.42/1.82    'tc_nat' ), Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.42/1.82     [ =( hAPP( 'c_Suc', hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' )
% 1.42/1.82    , hAPP( 'c_Suc', hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 1.42/1.82     ) ), 'c_Divides_Odiv__class_Odiv'( X, hAPP( 'c_Suc', hAPP( 'c_Suc', 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ) ) ), X ), 
% 1.42/1.82    'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.42/1.82     [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 
% 1.42/1.82    'tc_nat' ), X ), Y ), hAPP( 'c_Suc', X ), 'tc_nat' ) ],
% 1.42/1.82     [ 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', Y ), 'tc_nat' ), ~( 
% 1.42/1.82    'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.42/1.82     [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, 
% 1.42/1.82    hAPP( 'c_Suc', Y ), 'tc_nat' ) ) ],
% 1.42/1.82     [ ~( 'c_lessequals'( X, X, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( X, 
% 1.42/1.82    hAPP( 'c_Suc', X ), 'tc_nat' ) ],
% 1.42/1.82     [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ), 
% 1.42/1.82    hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( X, 
% 1.42/1.82    Y, 'tc_nat' ) ), 'c_Divides_Odiv__class_Odiv'( hAPP( 'c_Suc', 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ) ), 
% 1.42/1.82    'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 
% 1.42/1.82    'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), 
% 1.42/1.82    'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 
% 1.42/1.82    'tc_nat' ) ), Y, 'tc_nat' ) ), Y, 'tc_nat' ) ) ) ],
% 1.42/1.82     [ ~( 'class_Divides_Osemiring__div'( X ) ), =( 
% 1.42/1.82    'c_Divides_Odiv__class_Omod'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), Z
% 1.42/1.82    , X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =( hAPP( 
% 1.42/1.82    'c_Nat_Osemiring__1__class_Oof__nat'( X ), hAPP( hAPP( 
% 1.42/1.82    'c_Power_Opower__class_Opower'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP( 
% 1.42/1.82    'c_Power_Opower__class_Opower'( X ), hAPP( 
% 1.42/1.82    'c_Nat_Osemiring__1__class_Oof__nat'( X ), Y ) ), Z ) ) ],
% 1.42/1.82     [ 'c_HOL_Oord__class_Oless'( 'c_Int_OMin', 'c_Int_OPls', 'tc_Int_Oint' )
% 1.42/1.82     ],
% 1.42/1.82     [ 'c_lessequals'( X, 'c_Int_OMin', 'tc_Int_Oint' ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( 'c_Int_OBit0'( X ), 'c_Int_OMin', 
% 1.42/1.82    'tc_Int_Oint' ) ) ],
% 1.42/1.82     [ 'c_HOL_Oord__class_Oless'( 'c_Int_OBit0'( X ), 'c_Int_OMin', 
% 1.42/1.82    'tc_Int_Oint' ), ~( 'c_lessequals'( X, 'c_Int_OMin', 'tc_Int_Oint' ) ) ]
% 1.42/1.82    ,
% 1.42/1.82     [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), 
% 1.42/1.82    'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 
% 1.42/1.82    'c_lessequals'( Y, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ) )
% 1.42/1.82     ],
% 1.42/1.82     [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), 
% 1.42/1.82    'c_lessequals'( Y, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ), 
% 1.42/1.82    ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.42/1.82     [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), 
% 1.42/1.82    'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 
% 1.42/1.82    'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Y, X ) )
% 1.42/1.82     ],
% 1.42/1.82     [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), 
% 1.42/1.82    'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Y, X ), 
% 1.42/1.82    ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.42/1.82     [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ), 
% 1.42/1.82    'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 
% 1.42/1.82    'c_lessequals'( Y, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ) )
% 1.42/1.82     ],
% 1.42/1.82     [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ), 
% 1.42/1.82    'c_lessequals'( Y, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ), 
% 1.42/1.82    ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.42/1.82     [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ), 
% 1.42/1.82    'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 
% 1.42/1.82    'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Y, X ) )
% 1.42/1.82     ],
% 1.42/1.82     [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ), 
% 1.42/1.82    'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Y, X ), 
% 1.42/1.82    ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =( hAPP( hAPP( 
% 1.42/1.82    'c_Power_Opower__class_Opower'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( 
% 1.42/1.82    X ), Y ) ), Z ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z
% 1.42/1.82     ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ) ],
% 1.42/1.82     [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =( hAPP( 
% 1.42/1.82    'c_HOL_Oabs__class_Oabs'( X ), hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Y ) )
% 1.42/1.82    , hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Y ) ) ],
% 1.42/1.82     [ =( X, 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.42/1.82    'tc_nat' ), Z ), hAPP( 'c_Suc', X ) ), 'tc_nat' ) ), ~( 'c_lessequals'( 
% 1.42/1.82    hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), X ), Y, 
% 1.42/1.82    'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 
% 1.42/1.82    'tc_nat' ), Z, 'tc_nat' ) ) ],
% 1.42/1.82     [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( 
% 1.42/1.82    'c_HOL_Oabs__class_Oabs'( X ), Y ), X ), =( Y, 'c_HOL_Ozero__class_Ozero'( 
% 1.42/1.82    X ) ) ],
% 1.42/1.82     [ 'c_HOL_Oord__class_Oless'( 'c_Int_OMin', X, 'tc_Int_Oint' ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( 'c_Int_OMin', 'c_Int_OBit0'( X ), 
% 1.42/1.82    'tc_Int_Oint' ) ) ],
% 1.42/1.82     [ 'c_HOL_Oord__class_Oless'( 'c_Int_OMin', 'c_Int_OBit0'( X ), 
% 1.42/1.82    'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( 'c_Int_OMin', X, 
% 1.42/1.82    'tc_Int_Oint' ) ) ],
% 1.42/1.82     [ 'c_HOL_Oord__class_Oless'( 'c_Int_OMin', X, 'tc_Int_Oint' ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( 'c_Int_OMin', 'c_Int_OBit1'( X ), 
% 1.42/1.82    'tc_Int_Oint' ) ) ],
% 1.42/1.82     [ 'c_HOL_Oord__class_Oless'( 'c_Int_OMin', 'c_Int_OBit1'( X ), 
% 1.42/1.82    'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( 'c_Int_OMin', X, 
% 1.42/1.82    'tc_Int_Oint' ) ) ],
% 1.42/1.82     [ =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), X, 'tc_nat' ), 
% 1.42/1.82    'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.42/1.82    'c_HOL_Oone__class_Oone'( 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.42/1.82     [ 'c_lessequals'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.42/1.82     ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( 'tc_nat' ), X ), Y ), 
% 1.42/1.82    'tc_nat' ), ~( 'c_lessequals'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 
% 1.42/1.82    'tc_nat' ) ), X, 'tc_nat' ) ) ],
% 1.42/1.82     [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), X ), Y ), 
% 1.42/1.82    hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), Y ), X ) ) ]
% 1.42/1.82    ,
% 1.42/1.82     [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ), ~( 
% 1.42/1.82    'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP( 
% 1.42/1.82    'c_Power_Opower__class_Opower'( 'tc_nat' ), X ), Y ), 'tc_nat' ) ) ],
% 1.42/1.82     [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ), hAPP( 'c_Suc'
% 1.42/1.82    , U ) ), hAPP( hAPP( Y, T ), hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z
% 1.42/1.82     ), T ), U ) ) ) ],
% 1.42/1.82     [ 'c_lessequals'( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ), 
% 1.42/1.82    'c_Divides_Odiv__class_Odiv'( X, Z, 'tc_nat' ), 'tc_nat' ), ~( 
% 1.42/1.82    'c_lessequals'( Z, Y, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_nat' ) ) ],
% 1.42/1.82     [ ~( 'class_Divides_Osemiring__div'( X ) ), =( 
% 1.42/1.82    'c_Divides_Odiv__class_Odiv'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), Z
% 1.42/1.82    , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.82     [ ~( 'class_Divides_Oring__div'( X ) ), ~( =( 
% 1.42/1.82    'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.42/1.82    , Z, X ) ) ), =( 'c_Divides_Odiv__class_Omod'( hAPP( 
% 1.42/1.82    'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Z, X ), 
% 1.42/1.82    'c_Divides_Odiv__class_Omod'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), 
% 1.42/1.82    T ), Z, X ) ) ],
% 1.42/1.82     [ ~( =( hAPP( 'c_Suc', X ), hAPP( 'c_Suc', Y ) ) ), =( X, Y ) ],
% 1.42/1.82     [ ~( =( hAPP( 'c_Suc', X ), hAPP( 'c_Suc', Y ) ) ), =( X, Y ) ],
% 1.42/1.82     [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), 
% 1.42/1.82    'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), hAPP( 
% 1.42/1.82    'c_HOL_Oabs__class_Oabs'( X ), Y ), X ) ],
% 1.42/1.82     [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), 
% 1.42/1.82    'c_lessequals'( Y, hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Y ), X ) ],
% 1.42/1.82     [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 
% 1.42/1.82    hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ]
% 1.42/1.82    ,
% 1.42/1.82     [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 
% 1.42/1.82    hAPP( hAPP( 'c_Power_Opower__class_Opower'( 'tc_nat' ), X ), Y ), 
% 1.42/1.82    'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 
% 1.42/1.82    'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP( 
% 1.42/1.82    'c_HOL_Oabs__class_Oabs'( X ), Y ), Z, X ) ) ],
% 1.42/1.82     [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), 'c_Deriv_Oderiv'( 
% 1.42/1.82    'c_COMBB'( 'c_HOL_Ouminus__class_Ouminus'( X ), Y, X, X, X ), Z, hAPP( 
% 1.42/1.82    'c_HOL_Ouminus__class_Ouminus'( X ), T ), X ), ~( 'c_Deriv_Oderiv'( Y, Z
% 1.42/1.82    , T, X ) ) ],
% 1.42/1.82     [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', Y ), 
% 1.42/1.82    'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ],
% 1.42/1.82     [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( Y, hAPP( 'c_Suc', X ), 
% 1.42/1.82    'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ],
% 1.42/1.82     [ =( X, Y ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', Y ), 'tc_nat' ) ) ],
% 1.42/1.82     [ 'c_lessequals'( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 
% 1.42/1.82    'c_Fact_Ofact__class_Ofact'( X, 'tc_nat' ), 'tc_nat' ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP( 
% 1.42/1.82    'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( 
% 1.42/1.82    X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ), Z ) ), hAPP( 
% 1.42/1.82    'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( 
% 1.42/1.82    X ), Y ), Z ) ) ) ],
% 1.42/1.82     [ =( 'c_Divides_Odiv__class_Omod'( X, hAPP( 'c_Suc', 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ), 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.42/1.82     [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Y
% 1.42/1.82    , X ) ) ],
% 1.42/1.82     [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ],
% 1.42/1.82     [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ],
% 1.42/1.82     [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_Int_Oint' ) ) ],
% 1.42/1.82     [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.42/1.82    , Y, X ) ) ],
% 1.42/1.82     [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.42/1.82    , Y, X ) ) ],
% 1.42/1.82     [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.42/1.82    , X ), 'c_lessequals'( Z, Y, X ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.42/1.82     [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.42/1.82     [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 
% 1.42/1.82    'tc_nat' ) ) ],
% 1.42/1.82     [ 'c_lessequals'( X, Y, 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X
% 1.42/1.82    , Y, 'tc_Int_Oint' ) ) ],
% 1.42/1.82     [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.42/1.82     [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 
% 1.42/1.82    'tc_nat' ) ) ],
% 1.42/1.82     [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Y ), 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.42/1.82    hAPP( 'c_Nat_Osemiring__1__class_Oof__nat'( X ), Y ), hAPP( 
% 1.42/1.82    'c_Nat_Osemiring__1__class_Oof__nat'( X ), Z ), X ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( hAPP( 'c_Nat_Osemiring__1__class_Oof__nat'( X
% 1.42/1.82     ), Y ), hAPP( 'c_Nat_Osemiring__1__class_Oof__nat'( X ), Z ), X ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 1.42/1.82     [ ~( 'c_Groebner__Basis_Osemiringb'( X, Y, Z, T, U, W ) ), =( V0, hAPP( 
% 1.42/1.82    hAPP( X, V0 ), T ) ) ],
% 1.42/1.82     [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), hAPP( hAPP( Y, Z ), U ) )
% 1.42/1.82    , hAPP( hAPP( X, hAPP( hAPP( Y, Z ), U ) ), hAPP( hAPP( Y, Z ), T ) ) ), 
% 1.42/1.82    ~( 'c_Groebner__Basis_Osemiringb'( X, Y, W, V0, V1, V2 ) ) ],
% 1.42/1.82     [ ~( 'c_Groebner__Basis_Osemiringb'( X, Y, Z, T, U, W ) ), =( hAPP( hAPP( 
% 1.42/1.82    X, hAPP( hAPP( Y, V0 ), V1 ) ), hAPP( hAPP( Y, V0 ), V2 ) ), hAPP( hAPP( 
% 1.42/1.82    X, hAPP( hAPP( Y, V0 ), V2 ) ), hAPP( hAPP( Y, V0 ), V1 ) ) ) ],
% 1.42/1.82     [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), =( Y, 
% 1.42/1.82    'c_Series_Osuminf'( Z, X ) ), ~( 'c_Series_Osums'( Z, Y, X ) ) ],
% 1.42/1.82     [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), =( 
% 1.42/1.82    'c_Series_Osuminf'( Y, X ), Z ), ~( 'c_Series_Osums'( Y, Z, X ) ) ],
% 1.42/1.82     [ ~( 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', 'c_Int_OMin', 
% 1.42/1.82    'tc_Int_Oint' ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 
% 1.42/1.82    'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X )
% 1.42/1.82    , hAPP( 'c_Nat_Osemiring__1__class_Oof__nat'( X ), Y ), X ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( 
% 1.42/1.82    'c_Nat_Osemiring__1__class_Oof__nat'( X ), Y ), X ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 
% 1.42/1.82    'tc_nat' ) ) ],
% 1.42/1.82     [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'class_Int_Onumber'( X ) ), 
% 1.42/1.82    ~( 'c_HOL_Oord__class_Oless'( hAPP( 'c_Int_Onumber__class_Onumber__of'( X
% 1.42/1.82     ), Y ), hAPP( 'c_Int_Onumber__class_Onumber__of'( X ), Z ), X ) ), ~( 
% 1.42/1.82    'c_lessequals'( hAPP( 'c_Int_Onumber__class_Onumber__of'( X ), Z ), hAPP( 
% 1.42/1.82    'c_Int_Onumber__class_Onumber__of'( X ), Y ), X ) ) ],
% 1.42/1.82     [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'class_Int_Onumber'( X ) ), 
% 1.42/1.82    'c_lessequals'( hAPP( 'c_Int_Onumber__class_Onumber__of'( X ), Y ), hAPP( 
% 1.42/1.82    'c_Int_Onumber__class_Onumber__of'( X ), Z ), X ), 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( hAPP( 'c_Int_Onumber__class_Onumber__of'( X )
% 1.42/1.82    , Z ), hAPP( 'c_Int_Onumber__class_Onumber__of'( X ), Y ), X ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =( hAPP( hAPP( 
% 1.42/1.82    'c_Power_Opower__class_Opower'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( 
% 1.42/1.82    X ), Y ) ), Z ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP( 
% 1.42/1.82    'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ), 
% 1.42/1.82    'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.42/1.82     [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), 'c_Series_Osums'( 
% 1.42/1.82    'c_COMBB'( 'c_HOL_Ouminus__class_Ouminus'( X ), Y, X, X, 'tc_nat' ), hAPP( 
% 1.42/1.82    'c_HOL_Ouminus__class_Ouminus'( X ), Z ), X ), ~( 'c_Series_Osums'( Y, Z
% 1.42/1.82    , X ) ) ],
% 1.42/1.82     [ 'c_lessequals'( X, hAPP( 'c_Suc', Y ), 'tc_nat' ), ~( 'c_lessequals'( 
% 1.42/1.82    X, Y, 'tc_nat' ) ) ],
% 1.42/1.82     [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( hAPP( 'c_Suc', X
% 1.42/1.82     ), Y, 'tc_nat' ) ) ],
% 1.42/1.82     [ 'c_HOL_Oord__class_Oless'( 'c_Fact_Ofact__class_Ofact'( X, 'tc_nat' )
% 1.42/1.82    , 'c_Fact_Ofact__class_Ofact'( Y, 'tc_nat' ), 'tc_nat' ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 
% 1.42/1.82    'tc_nat' ) ) ],
% 1.42/1.82     [ ~( 'c_lessequals'( hAPP( 'c_Suc', X ), X, 'tc_nat' ) ) ],
% 1.42/1.82     [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 
% 1.42/1.82    'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat'
% 1.42/1.82     ), Z ), Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' )
% 1.42/1.82     ), ~( 'c_lessequals'( Y, Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 
% 1.42/1.82    'tc_nat' ) ) ],
% 1.42/1.82     [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 
% 1.42/1.82    'tc_nat' ), X ), Z ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat'
% 1.42/1.82     ), Y ), Z ), 'tc_nat' ) ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ), ~( 
% 1.42/1.82    'c_lessequals'( Z, X, 'tc_nat' ) ) ],
% 1.42/1.82     [ ~( =( 'c_Complex_Oii', 'c_HOL_Ozero__class_Ozero'( 
% 1.42/1.82    'tc_Complex_Ocomplex' ) ) ) ],
% 1.42/1.82     [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( 'c_Suc', X ), hAPP( 'c_Suc', 
% 1.42/1.82    hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ), 
% 1.42/1.82    'c_Divides_Odiv__class_Odiv'( X, hAPP( 'c_Suc', hAPP( 'c_Suc', 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ) ), ~( 
% 1.42/1.82    'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.42/1.82     [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 
% 1.42/1.82    'class_OrderedGroup_Olordered__ab__group__add__abs'( X ) ), =( hAPP( 
% 1.42/1.82    'c_HOL_Oabs__class_Oabs'( X ), Y ), Y ), 'c_HOL_Oord__class_Oless'( Y, 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oabs__if'( X ) ), =( hAPP( 
% 1.42/1.82    'c_HOL_Oabs__class_Oabs'( X ), Y ), Y ), 'c_HOL_Oord__class_Oless'( Y, 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.42/1.82     [ ~( =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( 'tc_nat' ), X ), Y )
% 1.42/1.82    , hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X, hAPP( 
% 1.42/1.82    'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y, 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.42/1.82     [ ~( 'c_HOL_Oord__class_Oless'( 'c_Int_OMin', 'c_Int_OMin', 
% 1.42/1.82    'tc_Int_Oint' ) ) ],
% 1.42/1.82     [ =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ), 
% 1.42/1.82    'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', 'c_Divides_Odiv__class_Omod'( 
% 1.42/1.82    X, Y, 'tc_nat' ) ), Y, 'tc_nat' ) ) ],
% 1.42/1.82     [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( 
% 1.42/1.82    'c_HOL_Oabs__class_Oabs'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), X ) ) ]
% 1.42/1.82    ,
% 1.42/1.82     [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 
% 1.42/1.82    'tc_Int_Oint' ), X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 
% 1.42/1.82    'tc_Int_Oint' ), Z ), Y ), 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.42/1.82    X, Z, 'tc_Int_Oint' ) ) ],
% 1.42/1.82     [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Y, X ) ]
% 1.42/1.82    ,
% 1.42/1.82     [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Y, X ) ],
% 1.42/1.82     [ 'c_lessequals'( X, X, 'tc_nat' ) ],
% 1.42/1.82     [ 'c_lessequals'( X, Y, 'tc_Int_Oint' ), ~( 'c_lessequals'( Z, Y, 
% 1.42/1.82    'tc_Int_Oint' ) ), ~( 'c_lessequals'( X, Z, 'tc_Int_Oint' ) ) ],
% 1.42/1.82     [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( Z, Y, 'tc_nat' )
% 1.42/1.82     ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 1.42/1.82     [ 'c_lessequals'( X, X, 'tc_Int_Oint' ) ],
% 1.42/1.82     [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), 'c_Deriv_Oderiv'( 
% 1.42/1.82    hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z, Y, X ) ],
% 1.42/1.82     [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oplus__class_Oplus'( X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X )
% 1.42/1.82     ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), 
% 1.42/1.82    'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ), Z ) ), Y ) ],
% 1.42/1.82     [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 
% 1.42/1.82    X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), 
% 1.42/1.82    'c_Divides_Odiv__class_Odiv'( Z, Y, X ) ) ), 'c_Divides_Odiv__class_Omod'( 
% 1.42/1.82    Z, Y, X ) ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T )
% 1.42/1.82     ) ],
% 1.42/1.82     [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 
% 1.42/1.82    X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), 
% 1.42/1.82    'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ), Z ) ), 
% 1.42/1.82    'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ), T ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ],
% 1.42/1.82     [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.42/1.82    X ), Y ), 'c_Divides_Odiv__class_Odiv'( Z, Y, X ) ) ), 
% 1.42/1.82    'c_Divides_Odiv__class_Omod'( Z, Y, X ) ), Z ) ],
% 1.42/1.82     [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.42/1.82    X ), 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ), Z ) ), 
% 1.42/1.82    'c_Divides_Odiv__class_Omod'( Y, Z, X ) ), Y ) ],
% 1.42/1.82     [ ~( 'class_Divides_Osemiring__div'( X ) ), =( Y, hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.42/1.82    X ), 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ), Z ) ), 
% 1.42/1.82    'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ) ],
% 1.42/1.82     [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( 
% 1.42/1.82    'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.42/1.82     ), Y ) ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ) ],
% 1.42/1.82     [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( 
% 1.42/1.82    'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.42/1.82     ), Z ) ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ) ) ],
% 1.42/1.82     [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), 
% 1.42/1.82    'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T )
% 1.42/1.82    , X ), ~( 'c_lessequals'( U, T, X ) ), ~( 'c_lessequals'( Y, hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oplus__class_Oplus'( X ), Z ), U ), X ) ) ],
% 1.42/1.82     [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ), 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.42/1.82     ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.42/1.82     [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.42/1.82    , 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.42/1.82    , Y ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), 
% 1.42/1.82    ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.42/1.82     [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.42/1.82    , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.42/1.82    hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ],
% 1.42/1.82     [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ), 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.42/1.82     ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.42/1.82     [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.42/1.82    , 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.42/1.82    , Y ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), 
% 1.42/1.82    ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.42/1.82     [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.42/1.82    , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.42/1.82    hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Y ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ) ) ],
% 1.42/1.82     [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =( hAPP( 
% 1.42/1.82    'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.42/1.82     ), hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Y ) ), hAPP( 
% 1.42/1.82    'c_HOL_Oabs__class_Oabs'( X ), Z ) ) ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Y )
% 1.42/1.82     ), hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Z ) ) ) ],
% 1.42/1.82     [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.42/1.82     ), Y ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), Z ) ]
% 1.42/1.82    ,
% 1.42/1.82     [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.42/1.82     ), Y ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ), Z ) ]
% 1.42/1.82    ,
% 1.42/1.82     [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ), 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.42/1.82     ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, 
% 1.42/1.82    T, X ) ) ],
% 1.42/1.82     [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =( 
% 1.42/1.82    'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.42/1.82    , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ), 
% 1.42/1.82    'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =( 
% 1.42/1.82    'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.42/1.82    , U ), Y ), Z, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oplus__class_Oplus'( X ), W ), T ), Z, X ) ) ],
% 1.42/1.82     [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ), 
% 1.42/1.82    'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), 
% 1.42/1.82    hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~( 
% 1.42/1.82    'c_lessequals'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.42/1.82     [ ~( 'class_Divides_Osemiring__div'( X ) ), =( 
% 1.42/1.82    'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.42/1.82    , 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ), T ), Z, X ), 
% 1.42/1.82    'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.42/1.82    , Y ), T ), Z, X ) ) ],
% 1.42/1.82     [ ~( 'class_Divides_Osemiring__div'( X ) ), =( 
% 1.42/1.82    'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.42/1.82    , Y ), 'c_Divides_Odiv__class_Omod'( Z, T, X ) ), T, X ), 
% 1.42/1.82    'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.42/1.82    , Y ), Z ), T, X ) ) ],
% 1.42/1.82     [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.42/1.82     ), Y ) ), Z ) ), Z ) ],
% 1.42/1.82     [ ~( 'class_Divides_Osemiring__div'( X ) ), =( 
% 1.42/1.82    'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.42/1.82    , Y ), Z ), Z, X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 1.42/1.82     [ ~( 'class_Divides_Osemiring__div'( X ) ), =( 
% 1.42/1.82    'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.42/1.82    , Y ), Z ), Y, X ), 'c_Divides_Odiv__class_Omod'( Z, Y, X ) ) ],
% 1.42/1.82     [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.42/1.82    , 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), 
% 1.42/1.82    hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~( 
% 1.42/1.82    'c_lessequals'( Y, T, X ) ) ],
% 1.42/1.82     [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.42/1.82    , 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ],
% 1.42/1.82     [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.42/1.82    , 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), 
% 1.42/1.82    hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~( 
% 1.42/1.82    'c_lessequals'( Z, T, X ) ) ],
% 1.42/1.82     [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.42/1.82    , 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oplus__class_Oplus'( X ), T ), Y ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ) ) ],
% 1.42/1.82     [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ), 
% 1.42/1.82    'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), 
% 1.42/1.82    hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~( 
% 1.42/1.82    'c_lessequals'( Y, T, X ) ) ],
% 1.42/1.82     [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ), 
% 1.42/1.82    'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), 
% 1.42/1.82    hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~( 
% 1.42/1.82    'c_lessequals'( Z, T, X ) ) ],
% 1.42/1.82     [ ~( 'class_Divides_Osemiring__div'( X ) ), =( 
% 1.42/1.82    'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.42/1.82    , Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oplus__class_Oplus'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X )
% 1.42/1.82     ), 'c_Divides_Odiv__class_Omod'( Z, T, X ) ), T, X ) ) ],
% 1.42/1.82     [ ~( 'class_Divides_Osemiring__div'( X ) ), =( 
% 1.42/1.82    'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.42/1.82    , Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_Divides_Odiv__class_Omod'( Z, T
% 1.42/1.82    , X ) ), T, X ) ) ],
% 1.42/1.82     [ ~( 'class_Divides_Osemiring__div'( X ) ), =( 
% 1.42/1.82    'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.42/1.82    , Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oplus__class_Oplus'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X )
% 1.42/1.82     ), Z ), T, X ) ) ],
% 1.42/1.82     [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =( hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), Z ) ), =( Y, hAPP( 
% 1.42/1.82    'c_HOL_Ouminus__class_Ouminus'( X ), T ) ) ],
% 1.42/1.82     [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Otimes__class_Otimes'( X ), hAPP( 
% 1.42/1.82    'c_Int_Onumber__class_Onumber__of'( X ), 'c_Int_OMin' ) ), Y ), hAPP( 
% 1.42/1.82    'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ) ],
% 1.42/1.82     [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( 
% 1.42/1.82    'c_Int_Onumber__class_Onumber__of'( X ), 'c_Int_OMin' ) ), hAPP( 
% 1.42/1.82    'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.42/1.82    , Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( hAPP( 
% 1.42/1.82    'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 
% 1.42/1.82    X ), Y ), Z ) ), T, X ) ) ],
% 1.42/1.82     [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), 
% 1.42/1.82    'c_lessequals'( hAPP( 'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Y )
% 1.42/1.82     ), hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Z ) ), X ) ],
% 1.42/1.82     [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), 
% 1.42/1.82    'c_lessequals'( hAPP( 'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 
% 1.42/1.82    X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) )
% 1.42/1.82     ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 
% 1.42/1.82    'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 
% 1.42/1.82    X ), Y ), T ) ) ), hAPP( 'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Ominus__class_Ominus'( X ), Z ), U ) ) ), X ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Oabs__class_Oabs'( X ), hAPP( 
% 1.42/1.82    hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ), T, X ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.42/1.82    , Z ), T ), X ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Ominus__class_Ominus'( X ), Z ), T ), Y, X ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =( hAPP( 
% 1.42/1.82    'c_Nat_Osemiring__1__class_Oof__nat'( X ), hAPP( 'c_Suc', Y ) ), hAPP( 
% 1.42/1.82    hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ), 
% 1.42/1.82    hAPP( 'c_Nat_Osemiring__1__class_Oof__nat'( X ), Y ) ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'( 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 
% 1.42/1.82    'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ), ~( 'c_lessequals'( 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 
% 1.42/1.82    'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'( 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 
% 1.42/1.82    'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~( 'c_lessequals'( 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), 
% 1.42/1.82    'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'( 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'( 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 
% 1.42/1.82    'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ) ), 
% 1.42/1.82    'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'( 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 
% 1.42/1.82    'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~( 'c_lessequals'( 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), 
% 1.42/1.82    'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 
% 1.42/1.82    'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), 'c_lessequals'( 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'( 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 
% 1.42/1.82    'c_Power_Opower__class_Opower'( X ), Z ), Y ), X ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'( 
% 1.42/1.82    Y, Z, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), 
% 1.42/1.82    ~( 'c_lessequals'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), 
% 1.42/1.82    hAPP( 'c_Suc', T ) ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Z
% 1.42/1.82     ), hAPP( 'c_Suc', T ) ), X ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 
% 1.42/1.82    'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), 'c_lessequals'( Z, 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP( 
% 1.42/1.82    'c_Power_Opower__class_Opower'( X ), Z ), Y ), 'c_HOL_Ozero__class_Ozero'( 
% 1.42/1.82    X ), X ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'( 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 
% 1.42/1.82    'c_Power_Opower__class_Opower'( X ), hAPP( 'c_HOL_Oabs__class_Oabs'( X )
% 1.42/1.82    , Y ) ), Z ), X ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 
% 1.42/1.82    'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), =( Y, 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'( 
% 1.42/1.82    Z, 'tc_nat' ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =( hAPP( hAPP( 
% 1.42/1.82    'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ), hAPP( 
% 1.42/1.82    hAPP( 'c_Power_Opower__class_Opower'( X ), T ), hAPP( 'c_Suc', Z ) ) ) )
% 1.42/1.82    , =( Y, T ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) )
% 1.42/1.82    , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 
% 1.42/1.82    'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), 
% 1.42/1.82    'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y, 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'( 
% 1.42/1.82    Z, 'tc_nat' ) ), ~( 'c_lessequals'( hAPP( hAPP( 
% 1.42/1.82    'c_Power_Opower__class_Opower'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( 
% 1.42/1.82    X ), X ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.42/1.82     ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 
% 1.42/1.82    'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.42/1.82    hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), T ), hAPP( hAPP( 
% 1.42/1.82    'c_Power_Opower__class_Opower'( X ), Z ), T ), X ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( 
% 1.42/1.82    'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.42/1.82     ), Z ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'( 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 
% 1.42/1.82    'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~( 
% 1.42/1.82    'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'( 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 
% 1.42/1.82    'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~( 
% 1.42/1.82    'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( 
% 1.42/1.82    'class_OrderedGroup_Omonoid__mult'( X ) ), 'c_lessequals'( 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 
% 1.42/1.82    'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~( 
% 1.42/1.82    'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ) ],
% 1.42/1.82     [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Ominus__class_Ominus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( 
% 1.42/1.82    X ), Y ) ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ), hAPP( 
% 1.42/1.82    'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ) ) ],
% 1.42/1.82     [ ~( 'class_Divides_Oring__div'( X ) ), ~( =( 
% 1.42/1.82    'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.42/1.82    , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ), 
% 1.42/1.82    'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =( 
% 1.42/1.82    'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X
% 1.42/1.82     ), U ), Y ), Z, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Ominus__class_Ominus'( X ), W ), T ), Z, X ) ) ],
% 1.42/1.82     [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'( 
% 1.42/1.82    hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), T, X ), 
% 1.42/1.82    'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X
% 1.42/1.82     ), Y ), 'c_Divides_Odiv__class_Omod'( Z, T, X ) ), T, X ) ) ],
% 1.42/1.82     [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'( 
% 1.42/1.82    hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), T, X ), 
% 1.42/1.82    'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X
% 1.42/1.82     ), 'c_Divides_Odiv__class_Omod'( Y, T, X ) ), Z ), T, X ) ) ],
% 1.42/1.82     [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'( 
% 1.42/1.82    hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), T, X ), 
% 1.42/1.82    'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X
% 1.42/1.82     ), 'c_Divides_Odiv__class_Omod'( Y, T, X ) ), 
% 1.42/1.82    'c_Divides_Odiv__class_Omod'( Z, T, X ) ), T, X ) ) ],
% 1.42/1.82     [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =( hAPP( 
% 1.42/1.82    'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 
% 1.42/1.82    X ), Y ), Z ) ), hAPP( 'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Ominus__class_Ominus'( X ), Z ), Y ) ) ) ],
% 1.42/1.82     [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =( hAPP( 
% 1.42/1.82    hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Ominus__class_Ominus'( X ), T ), U ) ) ), 'c_lessequals'( U, T, X
% 1.42/1.82     ), ~( 'c_lessequals'( Z, Y, X ) ) ],
% 1.42/1.82     [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =( hAPP( 
% 1.42/1.82    hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Ominus__class_Ominus'( X ), T ), U ) ) ), 'c_lessequals'( Z, Y, X
% 1.42/1.82     ), ~( 'c_lessequals'( U, T, X ) ) ],
% 1.42/1.82     [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =( hAPP( 
% 1.42/1.82    hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Ominus__class_Ominus'( X ), T ), U ) ) ), 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( T, U, X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z
% 1.42/1.82    , X ) ) ],
% 1.42/1.82     [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =( hAPP( 
% 1.42/1.82    hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Ominus__class_Ominus'( X ), T ), U ) ) ), 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( T, U
% 1.42/1.82    , X ) ) ],
% 1.42/1.82     [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( 
% 1.42/1.82    'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Ominus__class_Ominus'( X ), Z ), Y ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'( 
% 1.42/1.82    hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oinverse__class_Odivide'( X ), T ), U ), X ), ~( 'c_lessequals'( U
% 1.42/1.82    , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X )
% 1.42/1.82    , U, X ) ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'( 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), X ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 
% 1.42/1.82    'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'( 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), X ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 
% 1.42/1.82    'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.42/1.82     ), Y ), Z ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), T ), U )
% 1.42/1.82    , X ), ~( 'c_lessequals'( U, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), U, X ) ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.42/1.82    Y, T, X ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) )
% 1.42/1.82     ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'( 
% 1.42/1.82    hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y, 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'( 
% 1.42/1.82    hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z, 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.82    'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oinverse__class_Odivide'( X ), hAPP( 'c_HOL_Oabs__class_Oabs'( X )
% 1.42/1.82    , Y ) ), Z ), hAPP( 'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ) ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 1.42/1.82    ,
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.42/1.82     ), Y ), Z ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), T ), U )
% 1.42/1.82    , X ), ~( 'c_HOL_Oord__class_Oless'( U, Z, X ) ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), U, X ) ), ~( 
% 1.42/1.82    'c_lessequals'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.82    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y, 
% 1.42/1.82    hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~( 
% 1.42/1.82    'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ), 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.82    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y, 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'( Z, 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'( 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'( Y, hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ), X ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.82    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP( 
% 1.42/1.82    hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), T, X ), ~( 
% 1.42/1.82    'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.82    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Oord__class_Oless'( Z, 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'( 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'( hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ), Y, X ) ) ],
% 1.42/1.82     [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( 
% 1.42/1.82    'c_Int_Onumber__class_Onumber__of'( X ), 'c_Int_OMin' ), hAPP( 
% 1.42/1.82    'c_HOL_Ouminus__class_Ouminus'( X ), 'c_HOL_Oone__class_Oone'( X ) ) ) ]
% 1.42/1.82    ,
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( 
% 1.42/1.82    'class_Int_Onumber__ring'( X ) ), =( hAPP( 'c_HOL_Oabs__class_Oabs'( X )
% 1.42/1.82    , hAPP( 'c_Int_Onumber__class_Onumber__of'( X ), 'c_Int_OMin' ) ), 
% 1.42/1.82    'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.42/1.82     [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( 
% 1.42/1.82    'c_HOL_Ouminus__class_Ouminus'( X ), 'c_HOL_Oone__class_Oone'( X ) ), 
% 1.42/1.82    hAPP( 'c_Int_Onumber__class_Onumber__of'( X ), 'c_Int_OMin' ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.42/1.82     ), Y ), Z ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), T ), Z ), 
% 1.42/1.82    X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.42/1.82    , Z, 'tc_nat' ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y
% 1.42/1.82    , X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP( 
% 1.42/1.82    'c_HOL_Oabs__class_Oabs'( X ), 'c_HOL_Oone__class_Oone'( X ) ), 
% 1.42/1.82    'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.42/1.82     [ ~( 'class_Divides_Osemiring__div'( X ) ), =( 
% 1.42/1.82    'c_Divides_Odiv__class_Odiv'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y )
% 1.42/1.82     ],
% 1.42/1.82     [ ~( hBOOL( hAPP( X, 'c_Divides_Odiv__class_Omod'( Y, 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ) ), hBOOL( hAPP( X
% 1.42/1.82    , Y ) ) ],
% 1.42/1.82     [ ~( hBOOL( hAPP( X, Y ) ) ), hBOOL( hAPP( X, 
% 1.42/1.82    'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 
% 1.42/1.82    'tc_nat' ) ) ) ],
% 1.42/1.82     [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ), 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ],
% 1.42/1.82     [ 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ],
% 1.42/1.82     [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 1.42/1.82     [ ~( hBOOL( hAPP( X, 'c_Divides_Odiv__class_Odiv'( Y, 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ) ), hBOOL( hAPP( X
% 1.42/1.82    , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.42/1.82     [ ~( hBOOL( hAPP( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), hBOOL( 
% 1.42/1.82    hAPP( X, 'c_Divides_Odiv__class_Odiv'( Y, 'c_HOL_Ozero__class_Ozero'( 
% 1.42/1.82    'tc_nat' ), 'tc_nat' ) ) ) ],
% 1.42/1.82     [ hBOOL( hAPP( X, 'c_Divides_Odiv__class_Odiv'( Y, 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ), ~( hBOOL( hAPP( X
% 1.42/1.82    , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.42/1.82     [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 
% 1.42/1.82    'tc_nat' ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.42/1.82     [ 'c_lessequals'( X, X, 'tc_nat' ) ],
% 1.42/1.82     [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.42/1.82    , X ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_lessequals'( Y, T
% 1.42/1.82    , X ) ) ],
% 1.42/1.82     [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.42/1.82    , X ), ~( 'c_lessequals'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T
% 1.42/1.82    , X ) ) ],
% 1.42/1.82     [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~( 
% 1.42/1.82    'c_lessequals'( T, Z, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.42/1.82     [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.42/1.82     ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_lessequals'( T, Z, X
% 1.42/1.82     ) ) ],
% 1.42/1.82     [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.42/1.82     ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X
% 1.42/1.82     ) ) ],
% 1.42/1.82     [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~( 
% 1.42/1.82    'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( T, Z, X ) ) ],
% 1.42/1.82     [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', Y ), 
% 1.42/1.82    'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.42/1.82     [ =( hAPP( 'c_SetInterval_Oord__class_OatLeastLessThan'( X, 'tc_nat' ), 
% 1.42/1.82    hAPP( 'c_Suc', Y ) ), 'c_SetInterval_Oord__class_OatLeastAtMost'( X, Y, 
% 1.42/1.82    'tc_nat' ) ) ],
% 1.42/1.82     [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ), 
% 1.42/1.82    'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ), ~( 
% 1.42/1.82    'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ],
% 1.42/1.82     [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ), 
% 1.42/1.82    'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~( 
% 1.42/1.82    'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ), 'tc_nat' ) ) ],
% 1.42/1.82     [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( 
% 1.42/1.82    'c_Finite__Set_Osetsum'( Y, 'tc_nat', X ), 
% 1.42/1.82    'c_SetInterval_Oord__class_OatLeastAtMost'( Z, hAPP( 'c_Suc', T ), 
% 1.42/1.82    'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', T ), Z, 'tc_nat' ) ) ],
% 1.42/1.82     [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( 
% 1.42/1.82    'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ) ) ],
% 1.42/1.82     [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( 
% 1.42/1.82    'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.42/1.82    ,
% 1.42/1.82     [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 
% 1.42/1.82    X, 'tc_nat' ) ), 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.42/1.82    'tc_nat' ), X ), 'c_Divides_Odiv__class_Odiv'( Y, X, 'tc_nat' ) ), Y, 
% 1.42/1.82    'tc_nat' ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( Y, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), 
% 1.42/1.82    Y ), X ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( Y, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), 
% 1.42/1.82    Y ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.42/1.82     ), X ) ) ],
% 1.42/1.82     [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), 
% 1.42/1.82    'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( 
% 1.42/1.82    'c_HOL_Oabs__class_Oabs'( X ), Y ), X ) ],
% 1.42/1.82     [ 'c_lessequals'( hAPP( 'c_Suc', X ), hAPP( 'c_Suc', Y ), 'tc_nat' ), 
% 1.42/1.82    ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.42/1.82     [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( hAPP( 'c_Suc', X
% 1.42/1.82     ), hAPP( 'c_Suc', Y ), 'tc_nat' ) ) ],
% 1.42/1.82     [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.42/1.82    , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.42/1.82     [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ), 
% 1.42/1.82    'c_lessequals'( Z, Y, X ) ],
% 1.42/1.82     [ 'c_lessequals'( X, Y, 'tc_nat' ), 'c_lessequals'( Y, X, 'tc_nat' ) ]
% 1.42/1.82    ,
% 1.42/1.82     [ 'c_lessequals'( X, Y, 'tc_Int_Oint' ), 'c_lessequals'( Y, X, 
% 1.42/1.82    'tc_Int_Oint' ) ],
% 1.42/1.82     [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.42/1.82    , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.42/1.82     [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.42/1.82    , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.42/1.82     [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Z
% 1.42/1.82    , X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( 
% 1.42/1.82    'class_Int_Onumber__ring'( X ) ), =( hAPP( 'c_HOL_Oabs__class_Oabs'( X )
% 1.42/1.82    , hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), hAPP( 
% 1.42/1.82    'c_Int_Onumber__class_Onumber__of'( X ), 'c_Int_OMin' ) ), Y ) ), 
% 1.42/1.82    'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.42/1.82     [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP( 
% 1.42/1.82    'c_Power_Opower__class_Opower'( X ), hAPP( 
% 1.42/1.82    'c_Int_Onumber__class_Onumber__of'( X ), 'c_Int_OMin' ) ), Y ), 
% 1.42/1.82    'c_HOL_Oone__class_Oone'( X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'( Y
% 1.42/1.82    , 'tc_nat' ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 
% 1.42/1.82    'c_Parity_Oeven__odd__class_Oeven'( hAPP( 
% 1.42/1.82    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), Y ), 'tc_nat' ), 
% 1.42/1.82    'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 
% 1.42/1.82    'c_lessequals'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Z ), 
% 1.42/1.82    hAPP( 'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), Y ) ), 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.42/1.82     ), Y ), hAPP( 'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), Z ) ), 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), X ) ), 
% 1.42/1.82    'c_Parity_Oeven__odd__class_Oeven'( hAPP( 
% 1.42/1.82    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), Z ), 'tc_nat' ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'( 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 
% 1.42/1.82    'c_Parity_Oeven__odd__class_Oeven'( hAPP( 
% 1.42/1.82    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), Z ), 'tc_nat' ), ~( 
% 1.42/1.82    'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 
% 1.42/1.82    'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 
% 1.42/1.82    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), Z ) ), X ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'( 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 
% 1.42/1.82    'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 
% 1.42/1.82    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), Z ) ), X ), ~( 
% 1.42/1.82    'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), 
% 1.42/1.82    'c_Parity_Oeven__odd__class_Oeven'( hAPP( 
% 1.42/1.82    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), Z ), 'tc_nat' ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( 
% 1.42/1.82    'c_Parity_Oeven__odd__class_Oeven'( hAPP( 
% 1.42/1.82    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), Y ), 'tc_nat' ) ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.42/1.82     ), Z ), hAPP( 'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), Y ) ), 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'( 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 
% 1.42/1.82    'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 
% 1.42/1.82    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), Z ) ), X ), ~( 
% 1.42/1.82    'c_Parity_Oeven__odd__class_Oeven'( hAPP( 
% 1.42/1.82    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), Z ), 'tc_nat' ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y, 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'( 
% 1.42/1.82    hAPP( 'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), Z ), 'tc_nat' ) ), 
% 1.42/1.82    ~( 'c_lessequals'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), 
% 1.42/1.82    hAPP( 'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), Z ) ), 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 
% 1.42/1.82    'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 
% 1.42/1.82    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), Z ) ), X ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), 
% 1.42/1.82    'c_Parity_Oeven__odd__class_Oeven'( hAPP( 
% 1.42/1.82    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), Z ), 'tc_nat' ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 
% 1.42/1.82    'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 
% 1.42/1.82    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), Z ) ), X ), =( Y, 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'( 
% 1.42/1.82    hAPP( 'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), Z ), 'tc_nat' ) ) ]
% 1.42/1.82    ,
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( 
% 1.42/1.82    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.42/1.82    'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oinverse__class_Odivide'( X ), hAPP( 
% 1.42/1.82    'c_Int_Onumber__class_Onumber__of'( X ), 'c_Int_OMin' ) ), Y ), hAPP( 
% 1.42/1.82    'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y
% 1.42/1.82     ) ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP( 
% 1.42/1.82    'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 
% 1.42/1.82    'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X )
% 1.42/1.82    , Y, X ) ) ],
% 1.42/1.82     [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), ~( =( hAPP( Y, 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.42/1.82     ) ), 'c_Series_Osums'( Y, Z, X ), ~( 'c_Series_Osums'( 'c_COMBB'( Y, 
% 1.42/1.82    'c_Suc', 'tc_nat', X, 'tc_nat' ), Z, X ) ) ],
% 1.42/1.82     [ 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', X, 'tc_Int_Oint' ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( 
% 1.42/1.82    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), X ), 'tc_nat' ) ) ],
% 1.42/1.82     [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 
% 1.42/1.82    hAPP( 'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), X ), 'tc_nat' ), 
% 1.42/1.82    ~( 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', X, 'tc_Int_Oint' ) ) ],
% 1.42/1.82     [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP( 
% 1.42/1.82    'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( 'c_Suc', Z ) ), T ) ), 
% 1.42/1.82    hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 
% 1.42/1.82    'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z ), T ) ) ), Y ) ), ~( 
% 1.42/1.82    'c_lessequals'( T, Z, 'tc_nat' ) ) ],
% 1.42/1.82     [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), 'c_Series_Osums'( 
% 1.42/1.82    Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( Y, 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), X ), ~( 'c_Series_Osums'( 
% 1.42/1.82    'c_COMBB'( Y, 'c_Suc', 'tc_nat', X, 'tc_nat' ), Z, X ) ) ],
% 1.42/1.82     [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 
% 1.42/1.82    'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), 
% 1.42/1.82    'c_Divides_Odiv__class_Omod'( Y, Z, 'tc_nat' ) ) ), T ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ), 'tc_nat' ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( T, X, 'tc_nat' ) ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 
% 1.42/1.82    'tc_nat' ) ) ],
% 1.42/1.82     [ ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), =( Y, 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( hBOOL( hAPP( Z, 
% 1.42/1.82    'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 
% 1.42/1.82    'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), T
% 1.42/1.82     ) ), X ), Y, 'tc_nat' ) ) ) ), hBOOL( hAPP( Z, X ) ) ],
% 1.42/1.82     [ ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), =( Y, 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( hBOOL( hAPP( Z, 
% 1.42/1.82    'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 
% 1.42/1.82    'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), T
% 1.42/1.82     ) ), X ), Y, 'tc_nat' ) ) ) ), hBOOL( hAPP( Z, T ) ) ],
% 1.42/1.82     [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( 
% 1.42/1.82    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), X ) ), hAPP( 
% 1.42/1.82    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), Y ) ), hAPP( 
% 1.42/1.82    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), X ), Y ) ) ), 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( Y, 'c_Int_OPls', 'tc_Int_Oint' ), 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( X, 'c_Int_OPls', 'tc_Int_Oint' ) ],
% 1.42/1.82     [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ), 
% 1.42/1.82    'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'( 
% 1.42/1.82    'tc_nat' ) ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.42/1.82     [ ~( 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'( 
% 1.42/1.82    'tc_nat' ) ), 'tc_nat' ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 
% 1.42/1.82    'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 
% 1.42/1.82    'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.42/1.82     [ =( X, hAPP( 'c_Suc', hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 
% 1.42/1.82    'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ) ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 
% 1.42/1.82    'tc_nat' ) ) ],
% 1.42/1.82     [ =( hAPP( 'c_Suc', hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' )
% 1.42/1.82    , X ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), X ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 
% 1.42/1.82    'tc_nat' ) ) ],
% 1.42/1.82     [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( 
% 1.42/1.82    'c_Finite__Set_Osetsum'( Y, 'tc_nat', X ), hAPP( 
% 1.42/1.82    'c_SetInterval_Oord__class_OatLeastLessThan'( Z, 'tc_nat' ), hAPP( 
% 1.42/1.82    'c_Suc', T ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( T, Z, 'tc_nat' ) ) ],
% 1.42/1.82     [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 
% 1.42/1.82    'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 
% 1.42/1.82    hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), Z ) ), T ), U
% 1.42/1.82    , 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), T ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ), U ), 'tc_nat' ) ), 
% 1.42/1.82    ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.42/1.82     [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 
% 1.42/1.82    'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y
% 1.42/1.82     ) ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), T ), Y ) ), U ), 'tc_nat' ), 
% 1.42/1.82    ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 
% 1.42/1.82    'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 
% 1.42/1.82    hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), T ) ), Y ) ), Z ), U
% 1.42/1.82    , 'tc_nat' ) ), ~( 'c_lessequals'( T, X, 'tc_nat' ) ) ],
% 1.42/1.82     [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 
% 1.42/1.82    'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 
% 1.42/1.82    hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), Z ) ), T ) ), U ), 
% 1.42/1.82    'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ), X ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), T ) ), U ), 'tc_nat' ) ), 
% 1.42/1.82    ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 1.42/1.82     [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 
% 1.42/1.82    'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y
% 1.42/1.82     ) ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), T ), Y ) ), U ), 'tc_nat' ), 
% 1.42/1.82    ~( 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 
% 1.42/1.82    'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 
% 1.42/1.82    hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), T ), X ) ), Y ) ), U ), 
% 1.42/1.82    'tc_nat' ) ), ~( 'c_lessequals'( X, T, 'tc_nat' ) ) ],
% 1.42/1.82     [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( 
% 1.42/1.82    'c_Finite__Set_Osetsum'( Y, 'tc_nat', X ), hAPP( 
% 1.42/1.82    'c_SetInterval_Oord__class_OatLeastLessThan'( Z, 'tc_nat' ), hAPP( 
% 1.42/1.82    'c_Suc', T ) ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 
% 1.42/1.82    'c_Finite__Set_Osetsum'( Y, 'tc_nat', X ), hAPP( 
% 1.42/1.82    'c_SetInterval_Oord__class_OatLeastLessThan'( Z, 'tc_nat' ), T ) ) ), 
% 1.42/1.82    hAPP( Y, T ) ) ), 'c_HOL_Oord__class_Oless'( T, Z, 'tc_nat' ) ],
% 1.42/1.82     [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( 
% 1.42/1.82    'c_Finite__Set_Osetsum'( Y, 'tc_nat', X ), hAPP( 
% 1.42/1.82    'c_SetInterval_Oord__class_OatLeastLessThan'( Z, 'tc_nat' ), T ) ), hAPP( 
% 1.42/1.82    hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( Y, Z ) ), hAPP( 
% 1.42/1.82    'c_Finite__Set_Osetsum'( Y, 'tc_nat', X ), hAPP( 
% 1.42/1.82    'c_SetInterval_Oord__class_OatLeastLessThan'( hAPP( 'c_Suc', Z ), 
% 1.42/1.82    'tc_nat' ), T ) ) ) ), ~( 'c_HOL_Oord__class_Oless'( Z, T, 'tc_nat' ) ) ]
% 1.42/1.82    ,
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP( 
% 1.42/1.82    hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.42/1.82    ,
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.42/1.82    , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.42/1.82    , ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.42/1.82    Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP( 
% 1.42/1.82    hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ]
% 1.42/1.82    ,
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.42/1.82    , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.42/1.82    , ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.42/1.82    , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.42/1.82    , ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.42/1.82    , ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.42/1.82    , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.42/1.82    , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) )
% 1.42/1.82    , ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.42/1.82    , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.42/1.82    , ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.42/1.82    , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.42/1.82    , ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.42/1.82    Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.42/1.82    , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X )
% 1.42/1.82    , ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.42/1.82    , ~( 'c_HOL_Oord__class_Oless'( T, Y, X ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.42/1.82    , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X )
% 1.42/1.82    , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) )
% 1.42/1.82    , ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.42/1.82    , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X )
% 1.42/1.82    , ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.42/1.82    , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X )
% 1.42/1.82    , ~( 'c_HOL_Oord__class_Oless'( T, Y, X ) ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.42/1.82    Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__comm__semiring__strict'( X ) ), 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.42/1.82    , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.42/1.82    , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) )
% 1.42/1.82    , ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.42/1.82    ,
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.42/1.82    ,
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), X ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ) ) ],
% 1.42/1.82     [ ~( 'class_Divides_Osemiring__div'( X ) ), =( 
% 1.42/1.82    'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.42/1.82     ), Y ), Z ), Y, X ), Z ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.82     [ ~( 'class_Divides_Osemiring__div'( X ) ), =( 
% 1.42/1.82    'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.42/1.82     ), Y ), Z ), Z, X ), Y ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.82     [ ~( 'class_Divides_Osemiring__div'( X ) ), =( 
% 1.42/1.82    'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.42/1.82     ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z )
% 1.42/1.82    , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), 
% 1.42/1.82    'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'( 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'( hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( 
% 1.42/1.82    X ), X ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), 
% 1.42/1.82    'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'( 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'( hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), 'c_HOL_Ozero__class_Ozero'( 
% 1.42/1.82    X ), X ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), 
% 1.42/1.82    'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'( 
% 1.42/1.82    Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( 
% 1.42/1.82    X ), X ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), 
% 1.42/1.82    'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'( 
% 1.42/1.82    Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), 'c_HOL_Ozero__class_Ozero'( 
% 1.42/1.82    X ), X ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.42/1.82    , Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.42/1.82    ,
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.42/1.82    , Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.42/1.82    ,
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.42/1.82    , Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 1.42/1.82    ,
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Omult__mono1'( X ) ), 'c_lessequals'( hAPP( 
% 1.42/1.82    hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~( 'c_lessequals'( 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Z, T, X ) )
% 1.42/1.82     ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ), 'c_lessequals'( hAPP( 
% 1.42/1.82    hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~( 'c_lessequals'( 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Z, T, X ) )
% 1.42/1.82     ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ), 'c_lessequals'( hAPP( 
% 1.42/1.82    hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ), ~( 'c_lessequals'( 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 1.42/1.82     ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'( 
% 1.42/1.82    hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~( 'c_lessequals'( Y, 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( T, Z, X ) ) ]
% 1.42/1.82    ,
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'( 
% 1.42/1.82    hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ), ~( 'c_lessequals'( Z, 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( T, Y, X ) ) ]
% 1.42/1.82    ,
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'( 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.42/1.82    X ), Y ), Z ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z
% 1.42/1.82    , X ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.42/1.82    ,
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'( 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.42/1.82    X ), Y ), Z ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.42/1.82    , X ) ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.42/1.82    ,
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'( 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.42/1.82    X ), Y ), Z ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.42/1.82    , X ) ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.42/1.82    ,
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), 
% 1.42/1.82    'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ), X ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), 
% 1.42/1.82    'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~( 'c_lessequals'( 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), 
% 1.42/1.82    'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~( 'c_lessequals'( Z, 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y, 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ), 
% 1.42/1.82    'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~( 'c_lessequals'( 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), 
% 1.42/1.82    'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'( 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'( 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.42/1.82    X ), Y ), Z ), X ) ) ],
% 1.42/1.82     [ ~( =( hAPP( 'c_Suc', X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ]
% 1.42/1.82    ,
% 1.42/1.82     [ ~( =( hAPP( 'c_Suc', X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ]
% 1.42/1.82    ,
% 1.42/1.82     [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Ozero__class_Ozero'( 
% 1.42/1.82    'tc_nat' ), 'tc_nat' ) ],
% 1.42/1.82     [ ~( 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.42/1.82     ), 'tc_nat' ) ) ],
% 1.42/1.82     [ ~( 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.42/1.82     ), 'tc_nat' ) ) ],
% 1.42/1.82     [ ~( =( 'c_Fact_Ofact__class_Ofact'( X, 'tc_nat' ), 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.42/1.82     [ =( hAPP( hAPP( X, Y ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Z ), 
% 1.42/1.82    ~( 'c_Groebner__Basis_Ogb__semiring'( T, U, X, W, Z, V0 ) ) ],
% 1.42/1.82     [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_lessequals'( X, 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 1.42/1.82     [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( 'c_Suc', X ) ) ) ]
% 1.42/1.82    ,
% 1.42/1.82     [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( 'c_Suc', X ) ) ) ]
% 1.42/1.82    ,
% 1.42/1.82     [ 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' )
% 1.42/1.82     ],
% 1.42/1.82     [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), 
% 1.42/1.82    'c_lessequals'( hAPP( 'c_HOL_Oabs__class_Oabs'( X ), hAPP( 
% 1.42/1.82    'c_Finite__Set_Osetsum'( Y, Z, X ), T ) ), hAPP( 'c_Finite__Set_Osetsum'( 
% 1.42/1.82    'c_COMBB'( 'c_HOL_Oabs__class_Oabs'( X ), Y, X, X, Z ), Z, X ), T ), X )
% 1.42/1.82     ],
% 1.42/1.82     [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP( 
% 1.42/1.82    'c_Power_Opower__class_Opower'( X ), hAPP( 
% 1.42/1.82    'c_Int_Onumber__class_Onumber__of'( X ), 'c_Int_OMin' ) ), Y ), hAPP( 
% 1.42/1.82    'c_Int_Onumber__class_Onumber__of'( X ), 'c_Int_OMin' ) ), 
% 1.42/1.82    'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( 
% 1.42/1.82    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.42/1.82    'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oinverse__class_Odivide'( X ), Y ), hAPP( 
% 1.42/1.82    'c_Int_Onumber__class_Onumber__of'( X ), 'c_Int_OMin' ) ), hAPP( 
% 1.42/1.82    'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.42/1.82     ), Y ), Z ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), T ), 
% 1.42/1.82    X ), ~( 'c_HOL_Oord__class_Oless'( Z, T, 'tc_nat' ) ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.42/1.82    hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), T ), Y ), hAPP( hAPP( 
% 1.42/1.82    'c_Power_Opower__class_Opower'( X ), T ), Z ), X ) ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), T, X ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.42/1.82     ), Y ), Z ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), T ), 
% 1.42/1.82    X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X )
% 1.42/1.82     ), ~( 'c_HOL_Oord__class_Oless'( Z, T, 'tc_nat' ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.42/1.82    hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), T ), Y ), hAPP( hAPP( 
% 1.42/1.82    'c_Power_Opower__class_Opower'( X ), T ), Z ), X ) ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), T, X ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =( hAPP( hAPP( 
% 1.42/1.82    'c_Power_Opower__class_Opower'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( 
% 1.42/1.82    X ), 'c_HOL_Oone__class_Oone'( X ) ) ), Y ), hAPP( 
% 1.42/1.82    'c_HOL_Ouminus__class_Ouminus'( X ), 'c_HOL_Oone__class_Oone'( X ) ) ), 
% 1.42/1.82    'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP( 
% 1.42/1.82    'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ), X ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'( 
% 1.42/1.82    hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP( 
% 1.42/1.82    'c_Power_Opower__class_Opower'( X ), Y ), T ), X ), ~( 'c_lessequals'( 
% 1.42/1.82    'c_HOL_Oone__class_Oone'( X ), Y, X ) ), ~( 'c_lessequals'( Z, T, 
% 1.42/1.82    'tc_nat' ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =( hAPP( hAPP( 
% 1.42/1.82    'c_Power_Opower__class_Opower'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( 
% 1.42/1.82    X ), 'c_HOL_Oone__class_Oone'( X ) ) ), Y ), 'c_HOL_Oone__class_Oone'( X
% 1.42/1.82     ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ) ],
% 1.42/1.82     [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 
% 1.42/1.82    hAPP( hAPP( 'c_Power_Opower__class_Opower'( 'tc_nat' ), X ), hAPP( 
% 1.42/1.82    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), Y ) ), 'tc_nat' ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 
% 1.42/1.82    'tc_nat' ) ) ],
% 1.42/1.82     [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 
% 1.42/1.82    'tc_nat' ), =( hAPP( 'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), Y )
% 1.42/1.82    , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( hAPP( 
% 1.42/1.82    'c_Power_Opower__class_Opower'( 'tc_nat' ), X ), hAPP( 
% 1.42/1.82    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), Y ) ), 'tc_nat' ) ) ]
% 1.42/1.82    ,
% 1.42/1.82     [ ~( =( hAPP( 'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), X ), 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Oord__class_Oless'( 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( hAPP( 
% 1.42/1.82    'c_Power_Opower__class_Opower'( 'tc_nat' ), Y ), hAPP( 
% 1.42/1.82    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), X ) ), 'tc_nat' ) ],
% 1.42/1.82     [ =( 'c_Int_OBit1'( 'c_Int_OMin' ), 'c_Int_OMin' ) ],
% 1.42/1.82     [ ~( =( 'c_Int_OBit1'( X ), 'c_Int_OMin' ) ), =( X, 'c_Int_OMin' ) ]
% 1.42/1.82    ,
% 1.42/1.82     [ ~( =( 'c_Int_OMin', 'c_Int_OBit1'( X ) ) ), =( 'c_Int_OMin', X ) ]
% 1.42/1.82    ,
% 1.42/1.82     [ 'c_lessequals'( 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ), 'tc_Int_Oint'
% 1.42/1.82     ), ~( 'c_lessequals'( X, Y, 'tc_Int_Oint' ) ) ],
% 1.42/1.82     [ 'c_lessequals'( X, Y, 'tc_Int_Oint' ), ~( 'c_lessequals'( 
% 1.42/1.82    'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ), 'tc_Int_Oint' ) ) ],
% 1.42/1.82     [ 'c_lessequals'( 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ), 'tc_Int_Oint'
% 1.42/1.82     ), ~( 'c_lessequals'( X, Y, 'tc_Int_Oint' ) ) ],
% 1.42/1.82     [ 'c_lessequals'( X, Y, 'tc_Int_Oint' ), ~( 'c_lessequals'( 
% 1.42/1.82    'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ), 'tc_Int_Oint' ) ) ],
% 1.42/1.82     [ 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ), 
% 1.42/1.82    'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ) ) ]
% 1.42/1.82    ,
% 1.42/1.82     [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ), 
% 1.42/1.82    'tc_Int_Oint' ) ) ],
% 1.42/1.82     [ 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ), 
% 1.42/1.82    'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ) ) ]
% 1.42/1.82    ,
% 1.42/1.82     [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ), 
% 1.42/1.82    'tc_Int_Oint' ) ) ],
% 1.42/1.82     [ =( 'c_Int_OMin', 'c_Int_OBit1'( 'c_Int_OMin' ) ) ],
% 1.42/1.82     [ 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', 'c_Int_OBit1'( X ), 
% 1.42/1.82    'tc_Int_Oint' ), ~( 'c_lessequals'( 'c_Int_OPls', X, 'tc_Int_Oint' ) ) ]
% 1.42/1.82    ,
% 1.42/1.82     [ 'c_lessequals'( 'c_Int_OPls', X, 'tc_Int_Oint' ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( 'c_Int_OPls', 'c_Int_OBit1'( X ), 
% 1.42/1.82    'tc_Int_Oint' ) ) ],
% 1.42/1.82     [ 'c_lessequals'( 'c_Int_OBit1'( X ), 'c_Int_OPls', 'tc_Int_Oint' ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( X, 'c_Int_OPls', 'tc_Int_Oint' ) ) ],
% 1.42/1.82     [ 'c_HOL_Oord__class_Oless'( X, 'c_Int_OPls', 'tc_Int_Oint' ), ~( 
% 1.42/1.82    'c_lessequals'( 'c_Int_OBit1'( X ), 'c_Int_OPls', 'tc_Int_Oint' ) ) ]
% 1.42/1.82    ,
% 1.42/1.82     [ ~( =( 'c_Int_OPls', 'c_Int_OMin' ) ) ],
% 1.42/1.82     [ ~( =( 'c_Int_OMin', 'c_Int_OPls' ) ) ],
% 1.42/1.82     [ ~( 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', 'c_Int_OPls', 
% 1.42/1.82    'tc_Int_Oint' ) ) ],
% 1.42/1.82     [ 'c_lessequals'( 'c_Int_OPls', 'c_Int_OPls', 'tc_Int_Oint' ) ],
% 1.42/1.82     [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), 
% 1.42/1.82    'c_Int_OPls' ), X ), X ) ],
% 1.42/1.82     [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), X ), 
% 1.42/1.82    'c_Int_OPls' ), X ) ],
% 1.42/1.82     [ 'c_lessequals'( 'c_Int_OBit1'( X ), 'c_Int_OBit0'( Y ), 'tc_Int_Oint'
% 1.42/1.82     ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ) ) ],
% 1.42/1.82     [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ), ~( 'c_lessequals'( 
% 1.42/1.82    'c_Int_OBit1'( X ), 'c_Int_OBit0'( Y ), 'tc_Int_Oint' ) ) ],
% 1.42/1.82     [ 'c_lessequals'( 'c_Int_OBit1'( X ), 'c_Int_OBit0'( Y ), 'tc_Int_Oint'
% 1.42/1.82     ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ) ) ],
% 1.42/1.82     [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ), ~( 'c_lessequals'( 
% 1.42/1.82    'c_Int_OBit1'( X ), 'c_Int_OBit0'( Y ), 'tc_Int_Oint' ) ) ],
% 1.42/1.82     [ 'c_HOL_Oord__class_Oless'( 'c_Int_OBit0'( X ), 'c_Int_OBit1'( Y ), 
% 1.42/1.82    'tc_Int_Oint' ), ~( 'c_lessequals'( X, Y, 'tc_Int_Oint' ) ) ],
% 1.42/1.82     [ 'c_lessequals'( X, Y, 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.42/1.82    'c_Int_OBit0'( X ), 'c_Int_OBit1'( Y ), 'tc_Int_Oint' ) ) ],
% 1.42/1.82     [ 'c_HOL_Oord__class_Oless'( 'c_Int_OBit0'( X ), 'c_Int_OBit1'( Y ), 
% 1.42/1.82    'tc_Int_Oint' ), ~( 'c_lessequals'( X, Y, 'tc_Int_Oint' ) ) ],
% 1.42/1.82     [ 'c_lessequals'( X, Y, 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.42/1.82    'c_Int_OBit0'( X ), 'c_Int_OBit1'( Y ), 'tc_Int_Oint' ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP( 
% 1.42/1.82    'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( 
% 1.42/1.82    X ), Y ), Z ) ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), hAPP( 
% 1.42/1.82    'c_HOL_Oabs__class_Oabs'( X ), Y ) ), Z ) ) ],
% 1.42/1.82     [ ~( =( 'c_Int_OMin', 'c_Int_OBit0'( X ) ) ) ],
% 1.42/1.82     [ ~( =( 'c_Int_OBit0'( X ), 'c_Int_OMin' ) ) ],
% 1.42/1.82     [ 'c_lessequals'( 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ), 'tc_Int_Oint'
% 1.42/1.82     ), ~( 'c_lessequals'( X, Y, 'tc_Int_Oint' ) ) ],
% 1.42/1.82     [ 'c_lessequals'( X, Y, 'tc_Int_Oint' ), ~( 'c_lessequals'( 
% 1.42/1.82    'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ), 'tc_Int_Oint' ) ) ],
% 1.42/1.82     [ 'c_lessequals'( 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ), 'tc_Int_Oint'
% 1.42/1.82     ), ~( 'c_lessequals'( X, Y, 'tc_Int_Oint' ) ) ],
% 1.42/1.82     [ 'c_lessequals'( X, Y, 'tc_Int_Oint' ), ~( 'c_lessequals'( 
% 1.42/1.82    'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ), 'tc_Int_Oint' ) ) ],
% 1.42/1.82     [ 'c_HOL_Oord__class_Oless'( 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ), 
% 1.42/1.82    'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ) ) ]
% 1.42/1.82    ,
% 1.42/1.82     [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ), 
% 1.42/1.82    'tc_Int_Oint' ) ) ],
% 1.42/1.82     [ 'c_HOL_Oord__class_Oless'( 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ), 
% 1.42/1.82    'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ) ) ]
% 1.42/1.82    ,
% 1.42/1.82     [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ), 
% 1.42/1.82    'tc_Int_Oint' ) ) ],
% 1.42/1.82     [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), 
% 1.42/1.82    'c_Int_OBit0'( X ) ), 'c_Int_OBit0'( Y ) ), 'c_Int_OBit0'( hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), X ), Y ) ) ) ],
% 1.42/1.82     [ =( 'c_Int_OBit0'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 
% 1.42/1.82    'tc_Int_Oint' ), X ), X ) ) ],
% 1.42/1.82     [ 'c_lessequals'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.42/1.82     ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), 
% 1.42/1.82    'tc_nat' ), ~( 'c_lessequals'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 
% 1.42/1.82    'tc_nat' ) ), Y, 'tc_nat' ) ), ~( 'c_lessequals'( hAPP( 'c_Suc', 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X, 'tc_nat' ) ) ],
% 1.42/1.82     [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.42/1.82    'tc_nat' ), Y ), X ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( hAPP( 
% 1.42/1.82    'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 
% 1.42/1.82    'tc_nat' ) ), X, 'tc_nat' ) ) ],
% 1.42/1.82     [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.42/1.82    'tc_nat' ), X ), Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( hAPP( 
% 1.42/1.82    'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 
% 1.42/1.82    'tc_nat' ) ), X, 'tc_nat' ) ) ],
% 1.42/1.82     [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), X, 'tc_nat' ), Y ), 
% 1.42/1.82    ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 
% 1.42/1.82    'tc_nat' ) ) ],
% 1.42/1.82     [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), Y, 'tc_nat' ), X ), 
% 1.42/1.82    ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 
% 1.42/1.82    'tc_nat' ) ) ],
% 1.42/1.82     [ 'c_lessequals'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.42/1.82     ), X, 'tc_nat' ), ~( 'c_lessequals'( hAPP( 'c_Suc', 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), 'tc_nat' ) ) ],
% 1.42/1.82     [ 'c_lessequals'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.42/1.82     ), X, 'tc_nat' ), ~( 'c_lessequals'( hAPP( 'c_Suc', 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ],
% 1.42/1.82     [ 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 
% 1.42/1.82    'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), 
% 1.42/1.82    Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X, 'tc_nat' ) ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 
% 1.42/1.82    'tc_nat' ) ), Y, 'tc_nat' ) ) ],
% 1.42/1.82     [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ), 'tc_nat' ), 
% 1.42/1.82    'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 
% 1.42/1.82    'tc_nat' ) ) ],
% 1.42/1.82     [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc', hAPP( 'c_Suc', 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), X ), 'tc_nat' ) ],
% 1.42/1.82     [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 
% 1.42/1.82    X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z )
% 1.42/1.82    , 'tc_nat' ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 
% 1.42/1.82    'tc_nat' ), X, 'tc_nat' ) ],
% 1.42/1.82     [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 
% 1.42/1.82    X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y )
% 1.42/1.82    , 'tc_nat' ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 
% 1.42/1.82    'tc_nat' ), Y, 'tc_nat' ) ],
% 1.42/1.82     [ ~( 'c_Parity_Oeven__odd__class_Oeven'( hAPP( 'c_Suc', hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc', hAPP( 'c_Suc', 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), X ) ), 'tc_nat' ) ) ],
% 1.42/1.82     [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 
% 1.42/1.82    X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z )
% 1.42/1.82    , 'tc_nat' ), ~( 'c_lessequals'( Y, Z, 'tc_nat' ) ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 
% 1.42/1.82    'tc_nat' ) ) ],
% 1.42/1.82     [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), X ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ), 'tc_nat' ) ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 
% 1.42/1.82    'tc_nat' ) ) ],
% 1.42/1.82     [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_nat' ) ), ~( 
% 1.42/1.82    'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z )
% 1.42/1.82    , X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ), 
% 1.42/1.82    'tc_nat' ) ) ],
% 1.42/1.82     [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_nat' ) ), ~( 
% 1.42/1.82    'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X )
% 1.42/1.82    , Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ), 
% 1.42/1.82    'tc_nat' ) ) ],
% 1.42/1.82     [ 'c_lessequals'( hAPP( 'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 
% 1.42/1.82    X ), hAPP( 'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), Y ), 'tc_nat'
% 1.42/1.82     ), ~( 'c_lessequals'( X, 'c_Int_OPls', 'tc_Int_Oint' ) ) ],
% 1.42/1.82     [ 'c_lessequals'( X, 'c_Int_OPls', 'tc_Int_Oint' ), 'c_lessequals'( X, Y
% 1.42/1.82    , 'tc_Int_Oint' ), ~( 'c_lessequals'( hAPP( 
% 1.42/1.82    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), X ), hAPP( 
% 1.42/1.82    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), Y ), 'tc_nat' ) ) ],
% 1.42/1.82     [ 'c_HOL_Oord__class_Oless'( hAPP( 'c_Int_Onumber__class_Onumber__of'( 
% 1.42/1.82    'tc_nat' ), X ), hAPP( 'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), Y
% 1.42/1.82     ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ) ), 
% 1.42/1.82    ~( 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', Y, 'tc_Int_Oint' ) ) ],
% 1.42/1.82     [ 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', X, 'tc_Int_Oint' ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( Y, X, 'tc_Int_Oint' ) ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( hAPP( 'c_Int_Onumber__class_Onumber__of'( 
% 1.42/1.82    'tc_nat' ), Y ), hAPP( 'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), X
% 1.42/1.82     ), 'tc_nat' ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP( hAPP( 
% 1.42/1.82    'c_Power_Opower__class_Opower'( X ), hAPP( 'c_HOL_Oabs__class_Oabs'( X )
% 1.42/1.82    , Y ) ), hAPP( 'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), Z ) ), 
% 1.42/1.82    hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 
% 1.42/1.82    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), Z ) ) ), ~( 
% 1.42/1.82    'c_Parity_Oeven__odd__class_Oeven'( hAPP( 
% 1.42/1.82    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), Z ), 'tc_nat' ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( 
% 1.42/1.82    'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oinverse__class_Odivide'( X ), hAPP( 
% 1.42/1.82    'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ), Z ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( 
% 1.42/1.82    'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( 
% 1.42/1.82    'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oinverse__class_Odivide'( X ), Y ), hAPP( 
% 1.42/1.82    'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( 
% 1.42/1.82    'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oinverse__class_Odivide'( X ), hAPP( 
% 1.42/1.82    'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ), hAPP( 
% 1.42/1.82    'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ) ],
% 1.42/1.82     [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =( hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oinverse__class_Odivide'( X ), hAPP( 
% 1.42/1.82    'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ), Z ), hAPP( 
% 1.42/1.82    'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.82    'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( 
% 1.42/1.82    'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oinverse__class_Odivide'( X ), hAPP( 'c_HOL_Oabs__class_Oabs'( X )
% 1.42/1.82    , Y ) ), hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Z ) ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oring__1'( X ) ), =( hAPP( 
% 1.42/1.82    'c_Nat_Osemiring__1__class_Oof__nat'( X ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Ominus__class_Ominus'( X ), hAPP( 
% 1.42/1.82    'c_Nat_Osemiring__1__class_Oof__nat'( X ), Y ) ), hAPP( 
% 1.42/1.82    'c_Nat_Osemiring__1__class_Oof__nat'( X ), Z ) ) ), ~( 'c_lessequals'( Z
% 1.42/1.82    , Y, 'tc_nat' ) ) ],
% 1.42/1.82     [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 
% 1.42/1.82    'tc_nat' ), X ), hAPP( 'c_Suc', Y ) ), X, 'tc_nat' ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 
% 1.42/1.82    'tc_nat' ) ) ],
% 1.42/1.82     [ =( hAPP( 'c_Suc', hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' )
% 1.42/1.82    , X ), hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), X ), 
% 1.42/1.82    ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 
% 1.42/1.82    'tc_nat' ) ) ],
% 1.42/1.82     [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( 
% 1.42/1.82    'c_Finite__Set_Osetsum'( Y, 'tc_nat', X ), 
% 1.42/1.82    'c_SetInterval_Oord__class_OlessThan'( hAPP( 'c_Suc', Z ), 'tc_nat' ) ), 
% 1.42/1.82    hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 
% 1.42/1.82    'c_Finite__Set_Osetsum'( Y, 'tc_nat', X ), 
% 1.42/1.82    'c_SetInterval_Oord__class_OlessThan'( Z, 'tc_nat' ) ) ), hAPP( Y, Z ) )
% 1.42/1.82     ) ],
% 1.42/1.82     [ 'c_HOL_Oord__class_Oless'( 'c_Divides_Odiv__class_Odiv'( X, Y, 
% 1.42/1.82    'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), Y, 
% 1.42/1.82    'tc_nat' ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), 
% 1.42/1.82    'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'( 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'( 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.42/1.82    X ), Z ), Y ), X ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), 
% 1.42/1.82    'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'( 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'( 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.42/1.82    X ), Y ), Z ), X ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), 
% 1.42/1.82    'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'( 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'( 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.42/1.82    X ), Z ), Y ), X ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ), 'c_lessequals'( 
% 1.42/1.82    hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X ), ~( 'c_lessequals'( 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( Z, U, X ) )
% 1.42/1.82    , ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ), 'c_lessequals'( 
% 1.42/1.82    hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X ), ~( 'c_lessequals'( 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Z, U, X ) )
% 1.42/1.82    , ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.42/1.82     [ ~( 'class_Divides_Osemiring__div'( X ) ), =( 
% 1.42/1.82    'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.42/1.82     ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X
% 1.42/1.82     ), 'c_Divides_Odiv__class_Odiv'( Z, T, X ) ), =( Y, 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.82     [ ~( 'class_Divides_Osemiring__div'( X ) ), =( 
% 1.42/1.82    'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.42/1.82     ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X
% 1.42/1.82     ), 'c_Divides_Odiv__class_Odiv'( Y, T, X ) ), =( Z, 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.42/1.82    , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.42/1.82     ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.42/1.82    , Z ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X )
% 1.42/1.82     ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.42/1.82    , Y ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), 
% 1.42/1.82    'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z, 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), 
% 1.42/1.82    'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y, 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ), 
% 1.42/1.82    'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z, 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ), 
% 1.42/1.82    'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y, 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ), 
% 1.42/1.82    'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z, 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ), 
% 1.42/1.82    'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y, 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ), 
% 1.42/1.82    'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y, 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.42/1.82     [ ~( 'class_Divides_Osemiring__div'( X ) ), =( 
% 1.42/1.82    'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.42/1.82     ), Y ), Z ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.82     [ ~( 'class_Divides_Osemiring__div'( X ) ), =( 
% 1.42/1.82    'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.42/1.82     ), Y ), Z ), Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.42/1.82    hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP( 
% 1.42/1.82    hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.42/1.82    hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP( 
% 1.42/1.82    hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ) ],
% 1.42/1.82     [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.42/1.82     ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.42/1.82    ,
% 1.42/1.82     [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.42/1.82     ), Y ) ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.82     [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( 
% 1.42/1.82    'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ), 'c_HOL_Ozero__class_Ozero'( X
% 1.42/1.82     ) ) ],
% 1.42/1.82     [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.42/1.82     ), Y ) ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.82     [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.42/1.82     ), Y ) ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.82     [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( 
% 1.42/1.82    'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 
% 1.42/1.82    =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ), 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.82     [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.42/1.82    , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y, 
% 1.42/1.82    hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ), ~( 
% 1.42/1.82    'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.42/1.82     [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.42/1.82    , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y, 
% 1.42/1.82    hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ), ~( 
% 1.42/1.82    'c_lessequals'( Y, Z, X ) ), ~( 'c_lessequals'( 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ],
% 1.42/1.82     [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( =( 
% 1.42/1.82    hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( 'c_lessequals'( 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Y, 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.82     [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( =( 
% 1.42/1.82    hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( 'c_lessequals'( 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Z, 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.42/1.82     ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.42/1.82    ,
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.42/1.82     ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.42/1.82     [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.42/1.82     ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.42/1.82     [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.42/1.82     ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.42/1.82    ,
% 1.42/1.82     [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_Power_Opower_Opower'( 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.42/1.82     ), Z ) ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( 
% 1.42/1.82    hAPP( 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ), 
% 1.42/1.82    'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), Z ) ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.42/1.82    , Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 1.42/1.82    ,
% 1.42/1.82     [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ) ) ],
% 1.42/1.82     [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.42/1.82    ,
% 1.42/1.82     [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), 
% 1.42/1.82    'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~( 'c_lessequals'( 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.42/1.82     [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP( 
% 1.42/1.82    'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ), 
% 1.42/1.82    'c_HOL_Oplus__class_Oplus'( X ), X ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), T ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_Power_Opower_Opower'( 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.42/1.82     ), T ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Z
% 1.42/1.82     ), T ) ) ) ],
% 1.42/1.82     [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), 
% 1.42/1.82    'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 
% 1.42/1.82    'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ) ) ],
% 1.42/1.82     [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), 
% 1.42/1.82    'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ), ~( 'c_lessequals'( 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.42/1.82     [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =( hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X
% 1.42/1.82     ) ) ), =( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Z ) ],
% 1.42/1.82     [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =( hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X
% 1.42/1.82     ) ) ), =( Y, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ],
% 1.42/1.82     [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP( 
% 1.42/1.82    'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ), 
% 1.42/1.82    'c_HOL_Oplus__class_Oplus'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ), 
% 1.42/1.82    Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.82     [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.42/1.82    ,
% 1.42/1.82     [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), 
% 1.42/1.82    'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 
% 1.42/1.82    'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.42/1.82     [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), 
% 1.42/1.82    'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y, 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.42/1.82     [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), 
% 1.42/1.82    'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z, 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y, 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.42/1.82     [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), 'c_Deriv_Oderiv'( 
% 1.42/1.82    'c_COMBB'( Y, Z, X, X, X ), T, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.42/1.82    X ), U ), W ), X ), ~( 'c_Deriv_Oderiv'( Z, T, W, X ) ), ~( 
% 1.42/1.82    'c_Deriv_Oderiv'( Y, hAPP( Z, T ), U, X ) ) ],
% 1.42/1.82     [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), 'c_Deriv_Oderiv'( 
% 1.42/1.82    'c_COMBB'( Y, Z, X, X, X ), T, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.42/1.82    X ), U ), W ), X ), ~( 'c_Deriv_Oderiv'( Y, hAPP( Z, T ), U, X ) ), ~( 
% 1.42/1.82    'c_Deriv_Oderiv'( Z, T, W, X ) ) ],
% 1.42/1.82     [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), 'c_Deriv_Oderiv'( 
% 1.42/1.82    'c_COMBB'( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z, X, X, X ), T
% 1.42/1.82    , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), U ), X ), ~( 
% 1.42/1.82    'c_Deriv_Oderiv'( Z, T, U, X ) ) ],
% 1.42/1.82     [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Ominus__class_Ominus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.42/1.82    , hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ) ],
% 1.42/1.82     [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), 
% 1.42/1.82    'c_lessequals'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 1.42/1.82    ,
% 1.42/1.82     [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), 
% 1.42/1.82    'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( 
% 1.42/1.82    X ), X ) ) ],
% 1.42/1.82     [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X )
% 1.42/1.82    , Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.42/1.82     [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP( 
% 1.42/1.82    hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.42/1.82     [ ~( 'class_Divides_Osemiring__div'( X ) ), =( 
% 1.42/1.82    'c_Divides_Odiv__class_Odiv'( Y, Y, X ), 'c_HOL_Oone__class_Oone'( X ) )
% 1.42/1.82    , =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'( 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ), X ) ]
% 1.42/1.82    ,
% 1.42/1.82     [ ~( 'class_Divides_Osemiring__div'( X ) ), =( 
% 1.42/1.82    'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( 
% 1.42/1.82    'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'( 
% 1.42/1.82    X ), X ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), 
% 1.42/1.82    'c_HOL_Oone__class_Oone'( X ), X ) ],
% 1.42/1.82     [ ~( 'class_Divides_Osemiring__div'( X ) ), =( 
% 1.42/1.82    'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.42/1.82    , Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), T, X )
% 1.42/1.82    , 'c_Divides_Odiv__class_Omod'( Y, T, X ) ) ],
% 1.42/1.82     [ ~( 'class_Divides_Osemiring__div'( X ) ), =( 
% 1.42/1.82    'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.42/1.82    , Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), Z, X )
% 1.42/1.82    , 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =( hAPP( 
% 1.42/1.82    'c_Nat_Osemiring__1__class_Oof__nat'( X ), 'c_HOL_Ozero__class_Ozero'( 
% 1.42/1.82    'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.82     [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( 
% 1.42/1.82    'c_Int_Onumber__class_Onumber__of'( X ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), Y ), Z ) ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_Int_Onumber__class_Onumber__of'( 
% 1.42/1.82    X ), Y ) ), hAPP( 'c_Int_Onumber__class_Onumber__of'( X ), Z ) ) ) ],
% 1.42/1.82     [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_Int_Onumber__class_Onumber__of'( 
% 1.42/1.82    X ), Y ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 
% 1.42/1.82    'c_Int_Onumber__class_Onumber__of'( X ), Z ) ), T ) ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_Int_Onumber__class_Onumber__of'( 
% 1.42/1.82    X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), Y ), Z ) )
% 1.42/1.82     ), T ) ) ],
% 1.42/1.82     [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_Int_Onumber__class_Onumber__of'( 
% 1.42/1.82    X ), Y ) ), hAPP( 'c_Int_Onumber__class_Onumber__of'( X ), Z ) ), hAPP( 
% 1.42/1.82    'c_Int_Onumber__class_Onumber__of'( X ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), Y ), Z ) ) ) ],
% 1.42/1.82     [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Ominus__class_Ominus'( X ), Y ), hAPP( 
% 1.42/1.82    'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) ],
% 1.42/1.82     [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( 
% 1.42/1.82    'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ) ],
% 1.42/1.82     [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( 
% 1.42/1.82    'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ) ],
% 1.42/1.82     [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( 
% 1.42/1.82    'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ) ],
% 1.42/1.82     [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( 
% 1.42/1.82    'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ) ],
% 1.42/1.82     [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), 'c_Deriv_Oderiv'( 
% 1.42/1.82    'c_COMBS'( 'c_COMBB'( 'c_HOL_Oplus__class_Oplus'( X ), Y, X, 'tc_fun'( X
% 1.42/1.82    , X ), X ), 'c_COMBB'( 'c_HOL_Ouminus__class_Ouminus'( X ), Z, X, X, X )
% 1.42/1.82    , X, X, X ), T, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), U ), hAPP( 
% 1.42/1.82    'c_HOL_Ouminus__class_Ouminus'( X ), W ) ), X ), ~( 'c_Deriv_Oderiv'( Z, 
% 1.42/1.82    T, W, X ) ), ~( 'c_Deriv_Oderiv'( Y, T, U, X ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Z, X ) ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.42/1.82     [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( 
% 1.42/1.82    'c_HOL_Ouminus__class_Ouminus'( X ), Y ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( 
% 1.42/1.82    X ), 'c_HOL_Oone__class_Oone'( X ) ) ), Y ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.82    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.42/1.82    'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Otimes__class_Otimes'( X ), Z ), hAPP( 
% 1.42/1.82    'c_Int_Onumber__class_Onumber__of'( X ), T ) ), X ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( 
% 1.42/1.82    'c_Int_Onumber__class_Onumber__of'( X ), T ), X ) ), ~( 'c_lessequals'( 
% 1.42/1.82    hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), hAPP( 
% 1.42/1.82    'c_Int_Onumber__class_Onumber__of'( X ), T ) ), Z, X ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.82    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.42/1.82    'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oinverse__class_Odivide'( X ), Y ), hAPP( 
% 1.42/1.82    'c_Int_Onumber__class_Onumber__of'( X ), Z ) ), T, X ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( 
% 1.42/1.82    'c_Int_Onumber__class_Onumber__of'( X ), Z ), X ) ), ~( 'c_lessequals'( Y
% 1.42/1.82    , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), hAPP( 
% 1.42/1.82    'c_Int_Onumber__class_Onumber__of'( X ), Z ) ), X ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.82    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.42/1.82    'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( 
% 1.42/1.82    'c_Int_Onumber__class_Onumber__of'( X ), Z ) ), T, X ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( 
% 1.42/1.82    'c_Int_Onumber__class_Onumber__of'( X ), Z ), X ) ), ~( 'c_lessequals'( Y
% 1.42/1.82    , hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), T ), hAPP( 
% 1.42/1.82    'c_Int_Onumber__class_Onumber__of'( X ), Z ) ), X ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.82    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.42/1.82    'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oinverse__class_Odivide'( X ), Z ), hAPP( 
% 1.42/1.82    'c_Int_Onumber__class_Onumber__of'( X ), T ) ), X ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( 
% 1.42/1.82    'c_Int_Onumber__class_Onumber__of'( X ), T ), X ) ), ~( 'c_lessequals'( 
% 1.42/1.82    hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( 
% 1.42/1.82    'c_Int_Onumber__class_Onumber__of'( X ), T ) ), Z, X ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.82    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.42/1.82    'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), hAPP( 
% 1.42/1.82    'c_Int_Onumber__class_Onumber__of'( X ), T ), X ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 
% 1.42/1.82    'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 
% 1.42/1.82    'c_Int_Onumber__class_Onumber__of'( X ), T ) ), Z ), Y, X ) ), 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.82    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.42/1.82    'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Otimes__class_Otimes'( X ), hAPP( 
% 1.42/1.82    'c_Int_Onumber__class_Onumber__of'( X ), Y ) ), Z ), T, X ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 
% 1.42/1.82    'c_lessequals'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z
% 1.42/1.82     ), hAPP( 'c_Int_Onumber__class_Onumber__of'( X ), Y ), X ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.82    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.42/1.82    'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( 
% 1.42/1.82    'c_Int_Onumber__class_Onumber__of'( X ), Y ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 
% 1.42/1.82    'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 
% 1.42/1.82    'c_Int_Onumber__class_Onumber__of'( X ), Y ) ), T ), X ) ), ~( 
% 1.42/1.82    'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 
% 1.42/1.82    'c_Int_Onumber__class_Onumber__of'( X ), Y ) ), T ), Z, X ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.82    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.42/1.82    'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( 
% 1.42/1.82    'c_Int_Onumber__class_Onumber__of'( X ), Y ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 
% 1.42/1.82    'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 
% 1.42/1.82    'c_Int_Onumber__class_Onumber__of'( X ), Y ) ), T ), Z, X ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.82    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.42/1.82    'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Otimes__class_Otimes'( X ), hAPP( 
% 1.42/1.82    'c_Int_Onumber__class_Onumber__of'( X ), Y ) ), Z ), T, X ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 
% 1.42/1.82    'c_lessequals'( hAPP( 'c_Int_Onumber__class_Onumber__of'( X ), Y ), hAPP( 
% 1.42/1.82    hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ), X ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.82    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.42/1.82    'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( 
% 1.42/1.82    'c_Int_Onumber__class_Onumber__of'( X ), Y ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~( 'c_lessequals'( 
% 1.42/1.82    hAPP( 'c_Int_Onumber__class_Onumber__of'( X ), Y ), 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( T, 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Otimes__class_Otimes'( X ), hAPP( 
% 1.42/1.82    'c_Int_Onumber__class_Onumber__of'( X ), Y ) ), T ), Z, X ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.82    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.42/1.82    'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( 
% 1.42/1.82    'c_Int_Onumber__class_Onumber__of'( X ), Y ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~( 'c_lessequals'( 
% 1.42/1.82    hAPP( 'c_Int_Onumber__class_Onumber__of'( X ), Y ), 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Z, hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Otimes__class_Otimes'( X ), hAPP( 
% 1.42/1.82    'c_Int_Onumber__class_Onumber__of'( X ), Y ) ), T ), X ) ), 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.82    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.42/1.82    'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oinverse__class_Odivide'( X ), Y ), hAPP( 
% 1.42/1.82    'c_Int_Onumber__class_Onumber__of'( X ), Z ) ), T, X ), ~( 'c_lessequals'( 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 'c_HOL_Oord__class_Oless'( 
% 1.42/1.82    hAPP( 'c_Int_Onumber__class_Onumber__of'( X ), Z ), 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y, hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Otimes__class_Otimes'( X ), T ), hAPP( 
% 1.42/1.82    'c_Int_Onumber__class_Onumber__of'( X ), Z ) ), X ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.82    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.42/1.82    'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oinverse__class_Odivide'( X ), Z ), hAPP( 
% 1.42/1.82    'c_Int_Onumber__class_Onumber__of'( X ), T ) ), X ), ~( 'c_lessequals'( Y
% 1.42/1.82    , 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( hAPP( 
% 1.42/1.82    'c_Int_Onumber__class_Onumber__of'( X ), T ), 'c_HOL_Ozero__class_Ozero'( 
% 1.42/1.82    X ), X ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.42/1.82     ), Y ), hAPP( 'c_Int_Onumber__class_Onumber__of'( X ), T ) ), Z, X ) ) ]
% 1.42/1.82    ,
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.82    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.42/1.82    'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), hAPP( 
% 1.42/1.82    'c_Int_Onumber__class_Onumber__of'( X ), T ), X ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 
% 1.42/1.82    'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 
% 1.42/1.82    'c_Int_Onumber__class_Onumber__of'( X ), T ) ), Z ), X ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.82    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.42/1.82    'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Otimes__class_Otimes'( X ), hAPP( 
% 1.42/1.82    'c_Int_Onumber__class_Onumber__of'( X ), Z ) ), T ), X ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 
% 1.42/1.82    'c_lessequals'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T
% 1.42/1.82     ), hAPP( 'c_Int_Onumber__class_Onumber__of'( X ), Z ), X ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.82    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.42/1.82    'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oinverse__class_Odivide'( X ), Y ), hAPP( 
% 1.42/1.82    'c_Int_Onumber__class_Onumber__of'( X ), Z ) ), T, X ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( hAPP( 'c_Int_Onumber__class_Onumber__of'( X )
% 1.42/1.82    , Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( hAPP( 
% 1.42/1.82    hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), hAPP( 
% 1.42/1.82    'c_Int_Onumber__class_Onumber__of'( X ), Z ) ), Y, X ) ), ~( 
% 1.42/1.82    'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), 
% 1.42/1.82    hAPP( 'c_Int_Onumber__class_Onumber__of'( X ), Z ) ), X ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.82    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.42/1.82    'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oinverse__class_Odivide'( X ), Z ), hAPP( 
% 1.42/1.82    'c_Int_Onumber__class_Onumber__of'( X ), T ) ), X ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( hAPP( 'c_Int_Onumber__class_Onumber__of'( X )
% 1.42/1.82    , T ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Z, hAPP( 
% 1.42/1.82    hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( 
% 1.42/1.82    'c_Int_Onumber__class_Onumber__of'( X ), T ) ), X ) ), ~( 'c_lessequals'( 
% 1.42/1.82    hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( 
% 1.42/1.82    'c_Int_Onumber__class_Onumber__of'( X ), T ) ), Z, X ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.82    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.42/1.82    'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), hAPP( 
% 1.42/1.82    'c_Int_Onumber__class_Onumber__of'( X ), T ), X ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 
% 1.42/1.82    'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 
% 1.42/1.82    'c_Int_Onumber__class_Onumber__of'( X ), T ) ), Z ), Y, X ) ), ~( 
% 1.42/1.82    'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 
% 1.42/1.82    'c_Int_Onumber__class_Onumber__of'( X ), T ) ), Z ), X ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.82    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.42/1.82    'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( 
% 1.42/1.82    'c_Int_Onumber__class_Onumber__of'( X ), Z ) ), T, X ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( hAPP( 'c_Int_Onumber__class_Onumber__of'( X )
% 1.42/1.82    , Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), hAPP( 'c_Int_Onumber__class_Onumber__of'( 
% 1.42/1.82    X ), Z ), X ), ~( 'c_lessequals'( hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oinverse__class_Odivide'( X ), T ), hAPP( 
% 1.42/1.82    'c_Int_Onumber__class_Onumber__of'( X ), Z ) ), Y, X ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.82    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.42/1.82    'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oinverse__class_Odivide'( X ), Y ), hAPP( 
% 1.42/1.82    'c_Int_Onumber__class_Onumber__of'( X ), Z ) ), T, X ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( hAPP( 'c_Int_Onumber__class_Onumber__of'( X )
% 1.42/1.82    , Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( hAPP( 
% 1.42/1.82    hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), hAPP( 
% 1.42/1.82    'c_Int_Onumber__class_Onumber__of'( X ), Z ) ), Y, X ) ), 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( 
% 1.42/1.82    'c_Int_Onumber__class_Onumber__of'( X ), Z ), X ) ],
% 1.42/1.82     [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 
% 1.42/1.82    'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.42/1.82    , X ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) )
% 1.42/1.82     ],
% 1.42/1.82     [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 
% 1.42/1.82    'tc_nat' ), Z ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.42/1.82    , Z ), Y ), 'tc_nat' ) ) ],
% 1.42/1.82     [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 
% 1.42/1.82    'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.42/1.82    , Z ), Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) )
% 1.42/1.82     ],
% 1.42/1.82     [ ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 
% 1.42/1.82    'tc_nat' ), X ), Y ), X, 'tc_nat' ) ) ],
% 1.42/1.82     [ ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 
% 1.42/1.82    'tc_nat' ), X ), Y ), Y, 'tc_nat' ) ) ],
% 1.42/1.82     [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 
% 1.42/1.82    'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.42/1.82    , Z ), T ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, T, 'tc_nat' ) )
% 1.42/1.82    , ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 1.42/1.82     [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.42/1.82    , X ), Y ), 'tc_nat' ) ],
% 1.42/1.82     [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.42/1.82    , Y ), X ), 'tc_nat' ) ],
% 1.42/1.82     [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.42/1.82    , X ), Y ), 'tc_nat' ) ],
% 1.42/1.82     [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.42/1.82    , X ), Y ), 'tc_nat' ) ],
% 1.42/1.82     [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), hAPP( hAPP( Y, Z ), U ) )
% 1.42/1.82    , hAPP( hAPP( Y, Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.42/1.82    , T ), U ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, Y, V0, V1, V2
% 1.42/1.82     ) ) ],
% 1.42/1.82     [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 
% 1.42/1.82    hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ) ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( 
% 1.42/1.82    X, T, 'tc_nat' ) ],
% 1.42/1.82     [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( 
% 1.42/1.82    'c_Suc', Y ) ), hAPP( 'c_Suc', hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 
% 1.42/1.82    'tc_nat' ), X ), Y ) ) ) ],
% 1.42/1.82     [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( 'c_Suc', 
% 1.42/1.82    X ) ), Y ), hAPP( 'c_Suc', hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 
% 1.42/1.82    'tc_nat' ), X ), Y ) ) ) ],
% 1.42/1.82     [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X
% 1.42/1.82     ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ), 
% 1.42/1.82    'tc_nat' ), ~( 'c_lessequals'( Y, T, 'tc_nat' ) ), ~( 'c_lessequals'( X, 
% 1.42/1.82    Z, 'tc_nat' ) ) ],
% 1.42/1.82     [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( 'c_Suc', 
% 1.42/1.82    X ) ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( 
% 1.42/1.82    'c_Suc', Y ) ) ) ],
% 1.42/1.82     [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ), ~( 
% 1.42/1.82    'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), 
% 1.42/1.82    'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ],
% 1.42/1.82     [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ), 
% 1.42/1.82    'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), 
% 1.42/1.82    'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ) ],
% 1.42/1.82     [ ~( 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ) ), ~( 
% 1.42/1.82    'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), 
% 1.42/1.82    'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.42/1.82     [ ~( 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ) ), 
% 1.42/1.82    'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~( 
% 1.42/1.82    'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.42/1.82     [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ), ~( 
% 1.42/1.82    'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~( 
% 1.42/1.82    'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ],
% 1.42/1.82     [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ), ~( 
% 1.42/1.82    'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~( 
% 1.42/1.82    'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ) ) ],
% 1.42/1.82     [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ), 
% 1.42/1.82    'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), 
% 1.42/1.82    'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.42/1.82     [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ), ~( 
% 1.42/1.82    'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~( 
% 1.42/1.82    'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.42/1.82     [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ), 
% 1.42/1.82    'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~( 
% 1.42/1.82    'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ],
% 1.42/1.82     [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ), 
% 1.42/1.82    'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~( 
% 1.42/1.82    'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ) ) ],
% 1.42/1.82     [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ), ~( 
% 1.42/1.82    'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~( 
% 1.42/1.82    'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.42/1.82     [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ), 
% 1.42/1.82    'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), 
% 1.42/1.82    'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.42/1.82     [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X
% 1.42/1.82     ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ), 
% 1.42/1.82    'tc_nat' ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 1.42/1.82     [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), X ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ), 'tc_nat' ) ) ],
% 1.42/1.82     [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X
% 1.42/1.82     ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ), 
% 1.42/1.82    'tc_nat' ), ~( 'c_lessequals'( Y, Z, 'tc_nat' ) ) ],
% 1.42/1.82     [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 
% 1.42/1.82    'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 
% 1.42/1.82    'tc_nat' ) ) ],
% 1.42/1.82     [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 
% 1.42/1.82    'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 
% 1.42/1.82    'tc_nat' ) ) ],
% 1.42/1.82     [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 
% 1.42/1.82    'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ) ],
% 1.42/1.82     [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 
% 1.42/1.82    'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 
% 1.42/1.82    'tc_nat' ) ) ],
% 1.42/1.82     [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 
% 1.42/1.82    'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 
% 1.42/1.82    'tc_nat' ) ) ],
% 1.42/1.82     [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.42/1.82    , Y ), Z ), 'tc_nat' ), ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.42/1.82     [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.42/1.82    , Y ), Z ), 'tc_nat' ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 1.42/1.82     [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ) ],
% 1.42/1.82     [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), X ), Y, 'tc_nat' ) ) ],
% 1.42/1.82     [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.42/1.82    , Y ), Z ), 'tc_nat' ), ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.42/1.82     [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.42/1.82    , Y ), Z ), 'tc_nat' ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 1.42/1.82     [ =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ) ), Y, 'tc_nat'
% 1.42/1.82     ), 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', Z ), Y, 'tc_nat' ) ) ]
% 1.42/1.82    ,
% 1.42/1.82     [ =( 'c_Divides_Odiv__class_Omod'( X, hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ), 'tc_nat' ), hAPP( 
% 1.42/1.82    hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), 
% 1.42/1.82    'c_Divides_Odiv__class_Omod'( 'c_Divides_Odiv__class_Odiv'( X, Y, 
% 1.42/1.82    'tc_nat' ), Z, 'tc_nat' ) ) ), 'c_Divides_Odiv__class_Omod'( X, Y, 
% 1.42/1.82    'tc_nat' ) ) ) ],
% 1.42/1.82     [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), Z, 'tc_nat' ), hAPP( 
% 1.42/1.82    hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), 
% 1.42/1.82    'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ) ), 
% 1.42/1.82    'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.42/1.82    'tc_nat' ), X ), 'c_Divides_Odiv__class_Omod'( Y, Z, 'tc_nat' ) ), Z, 
% 1.42/1.82    'tc_nat' ) ) ) ],
% 1.42/1.82     [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ), 
% 1.42/1.82    'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~( 
% 1.42/1.82    'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ],
% 1.42/1.82     [ =( 'c_Divides_Odiv__class_Odiv'( X, hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ), 'tc_nat' ), 
% 1.42/1.82    'c_Divides_Odiv__class_Odiv'( 'c_Divides_Odiv__class_Odiv'( X, Y, 
% 1.42/1.82    'tc_nat' ), Z, 'tc_nat' ) ) ],
% 1.42/1.82     [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), 'tc_nat' ), ~( 
% 1.42/1.82    'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.42/1.82     [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), 'tc_nat' ), ~( 
% 1.42/1.82    'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ) ],
% 1.42/1.82     [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, Y ), 
% 1.42/1.82    hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ) ), ~( 
% 1.42/1.82    'c_Groebner__Basis_Ogb__semiring'( U, W, X, V0, V1, V2 ) ) ],
% 1.42/1.82     [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.42/1.82     ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), X ) )
% 1.42/1.82    , 'tc_nat' ) ],
% 1.42/1.82     [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 
% 1.42/1.82    X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T )
% 1.42/1.82    , 'tc_nat' ), ~( 'c_lessequals'( Y, T, 'tc_nat' ) ), ~( 'c_lessequals'( X
% 1.42/1.82    , Z, 'tc_nat' ) ) ],
% 1.42/1.82     [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 
% 1.42/1.82    'c_Suc', X ) ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' )
% 1.42/1.82    , hAPP( 'c_Suc', X ) ), Z ) ) ), =( Y, Z ) ],
% 1.42/1.82     [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 
% 1.42/1.82    X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y )
% 1.42/1.82    , 'tc_nat' ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 1.42/1.82     [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 
% 1.42/1.82    X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z )
% 1.42/1.82    , 'tc_nat' ), ~( 'c_lessequals'( Y, Z, 'tc_nat' ) ) ],
% 1.42/1.82     [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 
% 1.42/1.82    X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z )
% 1.42/1.82    , 'tc_nat' ), ~( 'c_lessequals'( Y, Z, 'tc_nat' ) ) ],
% 1.42/1.82     [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 
% 1.42/1.82    X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y )
% 1.42/1.82    , 'tc_nat' ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 1.42/1.82     [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.42/1.82    'tc_nat' ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.42/1.82     ), Z ), Y ), 'tc_nat' ) ) ],
% 1.42/1.82     [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.42/1.82    'tc_nat' ), X ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.42/1.82     ), Y ), Z ), 'tc_nat' ) ) ],
% 1.42/1.82     [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.42/1.82     ), X ), X ), 'tc_nat' ) ],
% 1.42/1.82     [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 
% 1.42/1.82    'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), Z ), 
% 1.42/1.82    'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.42/1.82    'tc_nat' ), X ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.42/1.82     ), Y ), Z ), 'tc_nat' ) ) ],
% 1.42/1.82     [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), 
% 1.42/1.82    'c_Divides_Odiv__class_Omod'( Y, Z, 'tc_nat' ) ), 
% 1.42/1.82    'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.42/1.82    'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.42/1.82     ), X ), Z ), 'tc_nat' ) ) ],
% 1.42/1.82     [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( 
% 1.42/1.82    'c_Finite__Set_Osetsum'( Y, 'tc_nat', X ), 
% 1.42/1.82    'c_SetInterval_Oord__class_OatLeastAtMost'( Z, hAPP( 'c_Suc', T ), 
% 1.42/1.82    'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( Y, Z ) )
% 1.42/1.82    , hAPP( 'c_Finite__Set_Osetsum'( 'c_COMBB'( Y, 'c_Suc', 'tc_nat', X, 
% 1.42/1.82    'tc_nat' ), 'tc_nat', X ), 'c_SetInterval_Oord__class_OatLeastAtMost'( Z
% 1.42/1.82    , T, 'tc_nat' ) ) ) ), 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', T ), Z, 
% 1.42/1.82    'tc_nat' ) ],
% 1.42/1.82     [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), hAPP( 
% 1.42/1.82    'c_Suc', hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), Z ) )
% 1.42/1.82     ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ), hAPP( 'c_Suc', Y ) )
% 1.42/1.82     ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 1.42/1.82     [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( 'c_Suc'
% 1.42/1.82    , hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ) ), Z )
% 1.42/1.82    , hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( 'c_Suc', X
% 1.42/1.82     ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ), 
% 1.42/1.82    ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.42/1.82     [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), 
% 1.42/1.82    'c_Divides_Odiv__class_Odiv'( Y, X, 'tc_nat' ) ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), 
% 1.42/1.82    'c_Divides_Odiv__class_Omod'( Y, X, 'tc_nat' ) ) ) ],
% 1.42/1.82     [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 
% 1.42/1.82    'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ) ), Y ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), 
% 1.42/1.82    'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ) ) ],
% 1.42/1.82     [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( X
% 1.42/1.82    , Y, 'tc_nat' ) ), Y ) ) ) ],
% 1.42/1.82     [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 
% 1.42/1.82    'tc_nat' ), X ), Y ), Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 
% 1.42/1.82    'tc_nat' ) ) ],
% 1.42/1.82     [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( 'c_Suc'
% 1.42/1.82    , X ) ), hAPP( 'c_Suc', Y ) ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 
% 1.42/1.82    'tc_nat' ), X ), Y ) ) ],
% 1.42/1.82     [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 
% 1.42/1.82    'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat'
% 1.42/1.82     ), X ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Z, X, 'tc_nat' )
% 1.42/1.82     ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ) ],
% 1.42/1.82     [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( 'c_Suc', X ) ), Y ) ), 
% 1.42/1.82    hAPP( 'c_Suc', Z ) ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat'
% 1.42/1.82     ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), Z )
% 1.42/1.82     ) ],
% 1.42/1.82     [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), hAPP( 
% 1.42/1.82    hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), Y ), ~( 
% 1.42/1.82    'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.42/1.82     [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Z ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), Z ), 'tc_nat' ) ), ~( 
% 1.42/1.82    'c_lessequals'( Z, Y, 'tc_nat' ) ), ~( 'c_lessequals'( Z, X, 'tc_nat' ) )
% 1.42/1.82     ],
% 1.42/1.82     [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), 
% 1.42/1.82    X ), Y ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z ), Y )
% 1.42/1.82    , 'tc_nat' ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y
% 1.42/1.82    , Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.42/1.82     [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), 
% 1.42/1.82    X ), Y ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z ), Y )
% 1.42/1.82    , 'tc_nat' ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 1.42/1.82     [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), 
% 1.42/1.82    X ), Y ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Z )
% 1.42/1.82    , 'tc_nat' ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 1.42/1.82     [ ~( =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ), 
% 1.42/1.82    hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z ), Y ) ) ), ~( 
% 1.42/1.82    'c_lessequals'( Y, Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) )
% 1.42/1.82    , =( X, Z ) ],
% 1.42/1.82     [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ), 'tc_nat' ), 
% 1.42/1.82    'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), 
% 1.42/1.82    'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.42/1.82     [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ), 'tc_nat' ), ~( 
% 1.42/1.82    'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~( 
% 1.42/1.82    'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.42/1.82     [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), 
% 1.42/1.82    X ), Y ), X, 'tc_nat' ) ],
% 1.42/1.82     [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z ), Y ) ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Z ) ), ~( 'c_lessequals'( 
% 1.42/1.82    Y, Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.42/1.82     [ =( hAPP( hAPP( X, Y ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), Y ), 
% 1.42/1.82    ~( 'c_Groebner__Basis_Ogb__semiring'( Z, T, X, U, W, V0 ) ) ],
% 1.42/1.82     [ ~( 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oone__class_Oone'( 
% 1.42/1.82    'tc_nat' ), 'tc_nat' ) ) ],
% 1.42/1.82     [ =( 'c_Fact_Ofact__class_Ofact'( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 
% 1.42/1.82    'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.42/1.82     [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( 
% 1.42/1.82    'c_Finite__Set_Osetsum'( Y, 'tc_nat', X ), 
% 1.42/1.82    'c_SetInterval_Oord__class_OatLeastAtMost'( hAPP( 'c_Suc', Z ), hAPP( 
% 1.42/1.82    'c_Suc', T ), 'tc_nat' ) ), hAPP( 'c_Finite__Set_Osetsum'( 'c_COMBB'( Y, 
% 1.42/1.82    'c_Suc', 'tc_nat', X, 'tc_nat' ), 'tc_nat', X ), 
% 1.42/1.82    'c_SetInterval_Oord__class_OatLeastAtMost'( Z, T, 'tc_nat' ) ) ) ],
% 1.42/1.82     [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_Complex_Ocomplex' ), 
% 1.42/1.82    'c_Complex_Oii' ), 'c_Complex_Oii' ), hAPP( 
% 1.42/1.82    'c_HOL_Ouminus__class_Ouminus'( 'tc_Complex_Ocomplex' ), 
% 1.42/1.82    'c_HOL_Oone__class_Oone'( 'tc_Complex_Ocomplex' ) ) ) ],
% 1.42/1.82     [ ~( =( 'c_FFT__Mirabelle_Oroot'( X ), 'c_HOL_Ozero__class_Ozero'( 
% 1.42/1.82    'tc_Complex_Ocomplex' ) ) ) ],
% 1.42/1.82     [ ~( =( 'c_Complex_Oii', 'c_HOL_Oone__class_Oone'( 'tc_Complex_Ocomplex'
% 1.42/1.82     ) ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.82    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y, 
% 1.42/1.82    hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 
% 1.42/1.82    'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T
% 1.42/1.82     ), X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T
% 1.42/1.82    , X ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.82    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y, 
% 1.42/1.82    hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 
% 1.42/1.82    'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y )
% 1.42/1.82    , T ), X ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.82    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP( 
% 1.42/1.82    hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), T, X ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 
% 1.42/1.82    'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), 
% 1.42/1.82    Y, X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, 
% 1.42/1.82    X ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.82    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP( 
% 1.42/1.82    hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), T, X ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 
% 1.42/1.82    'c_lessequals'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z
% 1.42/1.82     ), Y, X ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.82    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y, 
% 1.42/1.82    hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~( 
% 1.42/1.82    'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 
% 1.42/1.82    'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), 
% 1.42/1.82    Z, X ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.82    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y, 
% 1.42/1.82    hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~( 
% 1.42/1.82    'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 
% 1.42/1.82    'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T
% 1.42/1.82     ), X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T
% 1.42/1.82    , X ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.82    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP( 
% 1.42/1.82    hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), T, X ), ~( 
% 1.42/1.82    'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 
% 1.42/1.82    'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z
% 1.42/1.82     ), X ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.82    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP( 
% 1.42/1.82    hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), T, X ), ~( 
% 1.42/1.82    'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 
% 1.42/1.82    'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), 
% 1.42/1.82    Y, X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, 
% 1.42/1.82    X ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.82    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y, 
% 1.42/1.82    hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 
% 1.42/1.82    'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T
% 1.42/1.82     ), X ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.42/1.82     ), Y ), T ), Z, X ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.82    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP( 
% 1.42/1.82    hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), T, X ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 
% 1.42/1.82    'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), 
% 1.42/1.82    Y, X ) ), ~( 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.42/1.82    X ), T ), Z ), X ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'( Y
% 1.42/1.82    , hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~( 
% 1.42/1.82    'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), 
% 1.42/1.82    Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), 
% 1.42/1.82    T, X ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.82    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.42/1.82    'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Otimes__class_Otimes'( X ), Z ), hAPP( 
% 1.42/1.82    'c_Int_Onumber__class_Onumber__of'( X ), T ) ), X ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( hAPP( 'c_Int_Onumber__class_Onumber__of'( X )
% 1.42/1.82    , T ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), hAPP( 'c_Int_Onumber__class_Onumber__of'( 
% 1.42/1.82    X ), T ), X ), ~( 'c_lessequals'( Z, hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oinverse__class_Odivide'( X ), Y ), hAPP( 
% 1.42/1.82    'c_Int_Onumber__class_Onumber__of'( X ), T ) ), X ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.82    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.42/1.82    'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oinverse__class_Odivide'( X ), Z ), hAPP( 
% 1.42/1.82    'c_Int_Onumber__class_Onumber__of'( X ), T ) ), X ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( hAPP( 'c_Int_Onumber__class_Onumber__of'( X )
% 1.42/1.82    , T ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Z, hAPP( 
% 1.42/1.82    hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( 
% 1.42/1.82    'c_Int_Onumber__class_Onumber__of'( X ), T ) ), X ) ), 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( 
% 1.42/1.82    'c_Int_Onumber__class_Onumber__of'( X ), T ), X ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.82    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.42/1.82    'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( 
% 1.42/1.82    'c_Int_Onumber__class_Onumber__of'( X ), Y ), hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 
% 1.42/1.82    'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 
% 1.42/1.82    'c_Int_Onumber__class_Onumber__of'( X ), Y ) ), T ), X ) ), 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.82    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.42/1.82    'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Otimes__class_Otimes'( X ), hAPP( 
% 1.42/1.82    'c_Int_Onumber__class_Onumber__of'( X ), Z ) ), T ), X ), ~( 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 
% 1.42/1.82    'c_lessequals'( hAPP( 'c_Int_Onumber__class_Onumber__of'( X ), Z ), hAPP( 
% 1.42/1.82    hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ), X ) ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.82    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.42/1.82    'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oinverse__class_Odivide'( X ), Y ), hAPP( 
% 1.42/1.82    'c_Int_Onumber__class_Onumber__of'( X ), Z ) ), T, X ), ~( 'c_lessequals'( 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Otimes__class_Otimes'( X ), T ), hAPP( 
% 1.42/1.82    'c_Int_Onumber__class_Onumber__of'( X ), Z ) ), Y, X ) ), 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( 
% 1.42/1.82    'c_Int_Onumber__class_Onumber__of'( X ), Z ), X ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.82    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.42/1.82    'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oinverse__class_Odivide'( X ), Z ), hAPP( 
% 1.42/1.82    'c_Int_Onumber__class_Onumber__of'( X ), T ) ), X ), ~( 'c_lessequals'( Y
% 1.42/1.82    , 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Z, hAPP( 
% 1.42/1.82    hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( 
% 1.42/1.82    'c_Int_Onumber__class_Onumber__of'( X ), T ) ), X ) ), 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( 
% 1.42/1.82    'c_Int_Onumber__class_Onumber__of'( X ), T ), X ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.82    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.42/1.82    'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), hAPP( 
% 1.42/1.82    'c_Int_Onumber__class_Onumber__of'( X ), T ), X ), ~( 'c_lessequals'( 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), hAPP( 'c_Int_Onumber__class_Onumber__of'( 
% 1.42/1.82    X ), T ), X ) ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( 
% 1.42/1.82    X ), X ), ~( 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.42/1.82    X ), hAPP( 'c_Int_Onumber__class_Onumber__of'( X ), T ) ), Z ), X ) ) ]
% 1.42/1.82    ,
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.82    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.42/1.82    'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), hAPP( 
% 1.42/1.82    'c_Int_Onumber__class_Onumber__of'( X ), T ), X ), ~( 'c_lessequals'( 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), hAPP( 'c_Int_Onumber__class_Onumber__of'( 
% 1.42/1.82    X ), T ), X ) ), ~( 'c_lessequals'( hAPP( hAPP( 
% 1.42/1.82    'c_HOL_Otimes__class_Otimes'( X ), hAPP( 
% 1.42/1.82    'c_Int_Onumber__class_Onumber__of'( X ), T ) ), Z ), Y, X ) ), 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 
% 1.42/1.82    'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.42/1.82    , Y ), 'c_HOL_Oone__class_Oone'( X ) ), X ) ],
% 1.42/1.82     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y, 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ) ), 'c_lessequals'( Y, 
% 1.42/1.82    'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP( 
% 1.42/1.83    'c_Power_Opower__class_Opower'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( 
% 1.42/1.83    X ), X ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.42/1.83     ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'( 
% 1.42/1.83    hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP( 
% 1.42/1.83    'c_Power_Opower__class_Opower'( X ), T ), Z ), X ), ~( 'c_lessequals'( 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 1.42/1.83     ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~( 
% 1.42/1.83    'class_Power_Opower'( X ) ), =( hAPP( hAPP( 
% 1.42/1.83    'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), 
% 1.42/1.83    hAPP( 'c_Suc', Y ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'( 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 
% 1.42/1.83    'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~( 'c_lessequals'( 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'( 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 
% 1.42/1.83    'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~( 'c_lessequals'( 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 
% 1.42/1.83    'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.42/1.83    ,
% 1.42/1.83     [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), 'c_Series_Osums'( 
% 1.42/1.83    'c_COMBB'( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z, X, X, 
% 1.42/1.83    'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.42/1.83    , ~( 'c_Series_Osums'( Z, T, X ) ) ],
% 1.42/1.83     [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), 'c_Series_Osums'( 
% 1.42/1.83    'c_COMBB'( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z, X, X, 
% 1.42/1.83    'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.42/1.83    , ~( 'c_Series_Osums'( Z, T, X ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.83    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.42/1.83     ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.83    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.42/1.83     ), Z ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.83    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.42/1.83     ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.83    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.42/1.83     ), Z ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.83    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y, 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'( 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'( 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), X ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.83    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y, 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'( 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'( 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oinverse__class_Odivide'( X ), Z ), Y ), X ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.83    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y, 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'( 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'( 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), X ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.83    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y, 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'( 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'( 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oinverse__class_Odivide'( X ), Z ), Y ), X ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( 
% 1.42/1.83    'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oinverse__class_Odivide'( X ), Y ), hAPP( 
% 1.42/1.83    'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ), =( Z, 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.83    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP( 
% 1.42/1.83    hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z, 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.83    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP( 
% 1.42/1.83    hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y, 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.83    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), X ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.83    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oinverse__class_Odivide'( X ), Z ), Y ), X ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.83    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), X ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.83    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oinverse__class_Odivide'( X ), Z ), Y ), X ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.83    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP( 
% 1.42/1.83    hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ), X ), ~( 'c_lessequals'( 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 1.42/1.83     ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.83    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP( 
% 1.42/1.83    hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ), X ), ~( 'c_lessequals'( Z
% 1.42/1.83    , 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( T, Y, X ) )
% 1.42/1.83     ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.83    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.42/1.83     ), T ), Z ), Y, X ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.83    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.42/1.83     ), Y ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 'c_HOL_Oord__class_Oless'( Z, 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'( 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.83    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( 
% 1.42/1.83    X ), T ), Z ), X ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.83    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( 
% 1.42/1.83    X ), Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( T, 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'( 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), X ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.42/1.83    ,
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), X ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.42/1.83    ,
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.83    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), X ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.42/1.83    ,
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.83    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), X ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.42/1.83    ,
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oinverse__class_Odivide'( X ), hAPP( 
% 1.42/1.83    'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ), hAPP( 
% 1.42/1.83    'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), =( Z, 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.42/1.83     ), Y ), Z ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z )
% 1.42/1.83    , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, 
% 1.42/1.83    X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.42/1.83     ), Y ), Z ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z )
% 1.42/1.83    , X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), 
% 1.42/1.83    X ) ), ~( 'c_HOL_Oord__class_Oless'( T, Y, X ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), =( hAPP( 
% 1.42/1.83    'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oinverse__class_Odivide'( X ), hAPP( 'c_HOL_Oabs__class_Oabs'( X )
% 1.42/1.83    , Y ) ), hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Z ) ) ), =( Z, 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.83    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y, 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'( 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'( hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.83    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'( 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'( hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oinverse__class_Odivide'( X ), Z ), Y ), 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.83    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y, 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'( Z, 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.83    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'( Y, 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oinverse__class_Odivide'( X ), Z ), Y ), 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.83    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), X ), ~( 'c_lessequals'( 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.83    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), X ), ~( 'c_lessequals'( Z
% 1.42/1.83    , 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y, 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.42/1.83     ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.42/1.83    ,
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.42/1.83     ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.42/1.83    ,
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.83    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.42/1.83     ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.42/1.83    ,
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.83    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.42/1.83     ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.42/1.83    ,
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP( 
% 1.42/1.83    'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ), hAPP( 
% 1.42/1.83    hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP( 
% 1.42/1.83    'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.42/1.83     [ ~( 'class_Power_Opower'( X ) ), =( hAPP( hAPP( 
% 1.42/1.83    'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ), hAPP( 
% 1.42/1.83    hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP( 
% 1.42/1.83    'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.42/1.83     [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP( 
% 1.42/1.83    'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ), hAPP( 
% 1.42/1.83    hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 
% 1.42/1.83    'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), Y ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP( 
% 1.42/1.83    'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ), hAPP( 
% 1.42/1.83    hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP( 
% 1.42/1.83    'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP( 
% 1.42/1.83    'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP( 
% 1.42/1.83    'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 
% 1.42/1.83    'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), Y ), hAPP( hAPP( 
% 1.42/1.83    'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( 
% 1.42/1.83    'c_Parity_Oeven__odd__class_Oeven'( hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), Y ), 'tc_nat' ) ), =( 
% 1.42/1.83    hAPP( 'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), Y ), 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_lessequals'( hAPP( hAPP( 
% 1.42/1.83    'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), 
% 1.42/1.83    hAPP( 'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), Y ) ), 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'( 
% 1.42/1.83    hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), Z ) ), 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y, 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), X ) ), 
% 1.42/1.83    'c_Parity_Oeven__odd__class_Oeven'( hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), Z ), 'tc_nat' ), =( hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), Z ), 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 
% 1.42/1.83    'c_Parity_Oeven__odd__class_Oeven'( hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), Z ), 'tc_nat' ), =( hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), Z ), 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 
% 1.42/1.83    'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), Z ) ), X ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), Y ), 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 
% 1.42/1.83    'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), 
% 1.42/1.83    hAPP( 'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), Y ) ), X ) ), ~( 
% 1.42/1.83    'c_Parity_Oeven__odd__class_Oeven'( hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), Y ), 'tc_nat' ) ) ],
% 1.42/1.83     [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( 
% 1.42/1.83    'c_Finite__Set_Osetsum'( 'c_COMBB'( 'c_HOL_Ouminus__class_Ouminus'( X ), 
% 1.42/1.83    Y, X, X, Z ), Z, X ), T ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), 
% 1.42/1.83    hAPP( 'c_Finite__Set_Osetsum'( Y, Z, X ), T ) ) ) ],
% 1.42/1.83     [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =( hAPP( 
% 1.42/1.83    'c_HOL_Oabs__class_Oabs'( X ), hAPP( 'c_Finite__Set_Osetsum'( 'c_COMBB'( 
% 1.42/1.83    'c_HOL_Oabs__class_Oabs'( X ), Y, X, X, Z ), Z, X ), T ) ), hAPP( 
% 1.42/1.83    'c_Finite__Set_Osetsum'( 'c_COMBB'( 'c_HOL_Oabs__class_Oabs'( X ), Y, X, 
% 1.42/1.83    X, Z ), Z, X ), T ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( 
% 1.42/1.83    'class_Int_Onumber__ring'( X ) ), 'c_lessequals'( 'c_Int_OBit1'( 
% 1.42/1.83    'c_Int_OPls' ), Y, 'tc_Int_Oint' ), ~( 'c_lessequals'( 
% 1.42/1.83    'c_HOL_Oone__class_Oone'( X ), hAPP( 'c_Int_Onumber__class_Onumber__of'( 
% 1.42/1.83    X ), Y ), X ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( 
% 1.42/1.83    'class_Int_Onumber__ring'( X ) ), 'c_lessequals'( 
% 1.42/1.83    'c_HOL_Oone__class_Oone'( X ), hAPP( 'c_Int_Onumber__class_Onumber__of'( 
% 1.42/1.83    X ), Y ), X ), ~( 'c_lessequals'( 'c_Int_OBit1'( 'c_Int_OPls' ), Y, 
% 1.42/1.83    'tc_Int_Oint' ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( 
% 1.42/1.83    'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'( 
% 1.42/1.83    'c_Int_OBit1'( 'c_Int_OPls' ), Y, 'tc_Int_Oint' ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( X ), Y ), X ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( 
% 1.42/1.83    'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'( 
% 1.42/1.83    'c_HOL_Oone__class_Oone'( X ), hAPP( 'c_Int_Onumber__class_Onumber__of'( 
% 1.42/1.83    X ), Y ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( 'c_Int_OPls'
% 1.42/1.83     ), Y, 'tc_Int_Oint' ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( 
% 1.42/1.83    'class_Int_Onumber__ring'( X ) ), 'c_lessequals'( Y, 'c_Int_OBit1'( 
% 1.42/1.83    'c_Int_OPls' ), 'tc_Int_Oint' ), ~( 'c_lessequals'( hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( X ), Y ), 'c_HOL_Oone__class_Oone'( X
% 1.42/1.83     ), X ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( 
% 1.42/1.83    'class_Int_Onumber__ring'( X ) ), 'c_lessequals'( hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( X ), Y ), 'c_HOL_Oone__class_Oone'( X
% 1.42/1.83     ), X ), ~( 'c_lessequals'( Y, 'c_Int_OBit1'( 'c_Int_OPls' ), 
% 1.42/1.83    'tc_Int_Oint' ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( 
% 1.42/1.83    'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'( Y, 
% 1.42/1.83    'c_Int_OBit1'( 'c_Int_OPls' ), 'tc_Int_Oint' ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( hAPP( 'c_Int_Onumber__class_Onumber__of'( X )
% 1.42/1.83    , Y ), 'c_HOL_Oone__class_Oone'( X ), X ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( 
% 1.42/1.83    'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( X ), Y ), 'c_HOL_Oone__class_Oone'( X
% 1.42/1.83     ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_Int_OBit1'( 'c_Int_OPls' ), 
% 1.42/1.83    'tc_Int_Oint' ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'( 
% 1.42/1.83    'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( 
% 1.42/1.83    X ), Y ), Z ), X ), ~( 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), Y, 
% 1.42/1.83    X ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =( hAPP( hAPP( 
% 1.42/1.83    'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP( 
% 1.42/1.83    'c_Power_Opower__class_Opower'( X ), Y ), T ) ) ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ), =( Z
% 1.42/1.83    , T ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =( hAPP( 
% 1.42/1.83    'c_Nat_Osemiring__1__class_Oof__nat'( X ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oplus__class_Oplus'( X ), hAPP( 
% 1.42/1.83    'c_Nat_Osemiring__1__class_Oof__nat'( X ), Y ) ), hAPP( 
% 1.42/1.83    'c_Nat_Osemiring__1__class_Oof__nat'( X ), Z ) ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =( hAPP( 
% 1.42/1.83    'c_Nat_Osemiring__1__class_Oof__nat'( X ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( X ), hAPP( 
% 1.42/1.83    'c_Nat_Osemiring__1__class_Oof__nat'( X ), Y ) ), hAPP( 
% 1.42/1.83    'c_Nat_Osemiring__1__class_Oof__nat'( X ), Z ) ) ) ],
% 1.42/1.83     [ =( hAPP( 'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OMin'
% 1.42/1.83     ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.42/1.83     [ 'c_HOL_Oord__class_Oless'( X, 'c_Int_OPls', 'tc_Int_Oint' ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OPls', 
% 1.42/1.83    'tc_Int_Oint' ) ) ],
% 1.42/1.83     [ 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OPls', 
% 1.42/1.83    'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Int_OPls', 
% 1.42/1.83    'tc_Int_Oint' ) ) ],
% 1.42/1.83     [ 'c_lessequals'( 'c_Int_OPls', X, 'tc_Int_Oint' ), ~( 'c_lessequals'( 
% 1.42/1.83    'c_Int_OPls', 'c_Int_OBit1'( X ), 'tc_Int_Oint' ) ) ],
% 1.42/1.83     [ 'c_lessequals'( 'c_Int_OPls', 'c_Int_OBit1'( X ), 'tc_Int_Oint' ), ~( 
% 1.42/1.83    'c_lessequals'( 'c_Int_OPls', X, 'tc_Int_Oint' ) ) ],
% 1.42/1.83     [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OBit0'( Y ), 
% 1.42/1.83    'tc_Int_Oint' ) ) ],
% 1.42/1.83     [ 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OBit0'( Y ), 
% 1.42/1.83    'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ) ) ]
% 1.42/1.83    ,
% 1.42/1.83     [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OBit0'( Y ), 
% 1.42/1.83    'tc_Int_Oint' ) ) ],
% 1.42/1.83     [ 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OBit0'( Y ), 
% 1.42/1.83    'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ) ) ]
% 1.42/1.83    ,
% 1.42/1.83     [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), 
% 1.42/1.83    'c_Int_OBit0'( X ) ), 'c_Int_OBit1'( Y ) ), 'c_Int_OBit1'( hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), X ), Y ) ) ) ],
% 1.42/1.83     [ 'c_lessequals'( X, Y, 'tc_Int_Oint' ), ~( 'c_lessequals'( 
% 1.42/1.83    'c_Int_OBit0'( X ), 'c_Int_OBit1'( Y ), 'tc_Int_Oint' ) ) ],
% 1.42/1.83     [ 'c_lessequals'( 'c_Int_OBit0'( X ), 'c_Int_OBit1'( Y ), 'tc_Int_Oint'
% 1.42/1.83     ), ~( 'c_lessequals'( X, Y, 'tc_Int_Oint' ) ) ],
% 1.42/1.83     [ 'c_lessequals'( X, Y, 'tc_Int_Oint' ), ~( 'c_lessequals'( 
% 1.42/1.83    'c_Int_OBit0'( X ), 'c_Int_OBit1'( Y ), 'tc_Int_Oint' ) ) ],
% 1.42/1.83     [ 'c_lessequals'( 'c_Int_OBit0'( X ), 'c_Int_OBit1'( Y ), 'tc_Int_Oint'
% 1.42/1.83     ), ~( 'c_lessequals'( X, Y, 'tc_Int_Oint' ) ) ],
% 1.42/1.83     [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), 
% 1.42/1.83    'c_Int_OBit1'( X ) ), 'c_Int_OBit0'( Y ) ), 'c_Int_OBit1'( hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), X ), Y ) ) ) ],
% 1.42/1.83     [ 'c_lessequals'( 'c_Int_OPls', X, 'tc_Int_Oint' ), ~( 'c_lessequals'( 
% 1.42/1.83    'c_Int_OPls', 'c_Int_OBit0'( X ), 'tc_Int_Oint' ) ) ],
% 1.42/1.83     [ 'c_lessequals'( 'c_Int_OPls', 'c_Int_OBit0'( X ), 'tc_Int_Oint' ), ~( 
% 1.42/1.83    'c_lessequals'( 'c_Int_OPls', X, 'tc_Int_Oint' ) ) ],
% 1.42/1.83     [ 'c_HOL_Oord__class_Oless'( X, 'c_Int_OPls', 'tc_Int_Oint' ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( 'c_Int_OBit0'( X ), 'c_Int_OPls', 
% 1.42/1.83    'tc_Int_Oint' ) ) ],
% 1.42/1.83     [ 'c_HOL_Oord__class_Oless'( 'c_Int_OBit0'( X ), 'c_Int_OPls', 
% 1.42/1.83    'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Int_OPls', 
% 1.42/1.83    'tc_Int_Oint' ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'( 
% 1.42/1.83    hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), T, X ), ~( 
% 1.42/1.83    'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z
% 1.42/1.83     ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X )
% 1.42/1.83    , Z, X ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.83    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y, 
% 1.42/1.83    hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 
% 1.42/1.83    'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), 
% 1.42/1.83    Z, X ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.83    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP( 
% 1.42/1.83    hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), T, X ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 
% 1.42/1.83    'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), T )
% 1.42/1.83    , Z ), X ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.83    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP( 
% 1.42/1.83    hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), T, X ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 
% 1.42/1.83    'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z
% 1.42/1.83     ), X ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.83    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y, 
% 1.42/1.83    hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 
% 1.42/1.83    'c_lessequals'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T
% 1.42/1.83     ), Z, X ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.83    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP( 
% 1.42/1.83    hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ), X ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ), ~( 'c_lessequals'( Y
% 1.42/1.83    , 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Z, T, X ) )
% 1.42/1.83     ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'( 
% 1.42/1.83    hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ), X ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ), ~( 'c_lessequals'( 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( T, Z, X ) )
% 1.42/1.83     ],
% 1.42/1.83     [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), 
% 1.42/1.83    'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( 
% 1.42/1.83    'c_Finite__Set_Osetsum'( 'c_COMBB'( 'c_HOL_Oabs__class_Oabs'( X ), Y, X, 
% 1.42/1.83    X, Z ), Z, X ), T ), X ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( 
% 1.42/1.83    'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( 
% 1.42/1.83    X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_Int_OPls', 'tc_Int_Oint' )
% 1.42/1.83     ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( 
% 1.42/1.83    'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'( Y, 
% 1.42/1.83    'c_Int_OPls', 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( 
% 1.42/1.83    X ), X ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( 
% 1.42/1.83    'class_Int_Onumber__ring'( X ) ), 'c_lessequals'( hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( 
% 1.42/1.83    X ), X ), ~( 'c_lessequals'( Y, 'c_Int_OPls', 'tc_Int_Oint' ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( 
% 1.42/1.83    'class_Int_Onumber__ring'( X ) ), 'c_lessequals'( Y, 'c_Int_OPls', 
% 1.42/1.83    'tc_Int_Oint' ), ~( 'c_lessequals'( hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( 
% 1.42/1.83    X ), X ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( 
% 1.42/1.83    'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'( 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), hAPP( 'c_Int_Onumber__class_Onumber__of'( 
% 1.42/1.83    X ), Y ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', Y, 
% 1.42/1.83    'tc_Int_Oint' ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( 
% 1.42/1.83    'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'( 'c_Int_OPls'
% 1.42/1.83    , Y, 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), hAPP( 'c_Int_Onumber__class_Onumber__of'( 
% 1.42/1.83    X ), Y ), X ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( 
% 1.42/1.83    'class_Int_Onumber__ring'( X ) ), 'c_lessequals'( 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), hAPP( 'c_Int_Onumber__class_Onumber__of'( 
% 1.42/1.83    X ), Y ), X ), ~( 'c_lessequals'( 'c_Int_OPls', Y, 'tc_Int_Oint' ) ) ]
% 1.42/1.83    ,
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( 
% 1.42/1.83    'class_Int_Onumber__ring'( X ) ), 'c_lessequals'( 'c_Int_OPls', Y, 
% 1.42/1.83    'tc_Int_Oint' ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( X ), Y ), X ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.83    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.42/1.83    'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( 
% 1.42/1.83    X ), X ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), 
% 1.42/1.83    X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), 
% 1.42/1.83    ~( 'c_lessequals'( hAPP( 'c_Int_Onumber__class_Onumber__of'( X ), Y ), 
% 1.42/1.83    hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ), X ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.83    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.42/1.83    'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( X ), Y ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~( 'c_lessequals'( 
% 1.42/1.83    hAPP( 'c_Int_Onumber__class_Onumber__of'( X ), Y ), 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( T, 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'( 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.83    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.42/1.83    'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oinverse__class_Odivide'( X ), Z ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( X ), T ) ), X ), ~( 'c_lessequals'( Y
% 1.42/1.83    , 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( X ), T ), 'c_HOL_Ozero__class_Ozero'( 
% 1.42/1.83    X ), X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), 
% 1.42/1.83    hAPP( 'c_Int_Onumber__class_Onumber__of'( X ), T ), X ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.83    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.42/1.83    'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( 
% 1.42/1.83    X ), X ), 'c_HOL_Oord__class_Oless'( hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( X ), Z ), 'c_HOL_Ozero__class_Ozero'( 
% 1.42/1.83    X ), X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), 
% 1.42/1.83    hAPP( 'c_Int_Onumber__class_Onumber__of'( X ), Z ), X ), ~( 
% 1.42/1.83    'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), T )
% 1.42/1.83    , hAPP( 'c_Int_Onumber__class_Onumber__of'( X ), Z ) ), X ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.83    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.42/1.83    'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oinverse__class_Odivide'( X ), Y ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( X ), Z ) ), T, X ), ~( 'c_lessequals'( 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 'c_HOL_Oord__class_Oless'( 
% 1.42/1.83    hAPP( 'c_Int_Onumber__class_Onumber__of'( X ), Z ), 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'( 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), hAPP( 'c_Int_Onumber__class_Onumber__of'( 
% 1.42/1.83    X ), Z ), X ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.83    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.42/1.83    'class_Int_Onumber'( X ) ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X
% 1.42/1.83     ), Y, X ), 'c_HOL_Oord__class_Oless'( hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( X ), Z ), 'c_HOL_Ozero__class_Ozero'( 
% 1.42/1.83    X ), X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), 
% 1.42/1.83    hAPP( 'c_Int_Onumber__class_Onumber__of'( X ), Z ), X ), ~( 
% 1.42/1.83    'c_lessequals'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), T ), 
% 1.42/1.83    hAPP( 'c_Int_Onumber__class_Onumber__of'( X ), Z ) ), Y, X ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.83    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.42/1.83    'class_Int_Onumber'( X ) ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X
% 1.42/1.83     ), hAPP( 'c_Int_Onumber__class_Onumber__of'( X ), Y ), X ), 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 
% 1.42/1.83    'c_lessequals'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z
% 1.42/1.83     ), hAPP( 'c_Int_Onumber__class_Onumber__of'( X ), Y ), X ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.83    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.42/1.83    'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( X ), T ), X ), ~( 'c_lessequals'( 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), hAPP( 'c_Int_Onumber__class_Onumber__of'( 
% 1.42/1.83    X ), T ), X ) ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( 
% 1.42/1.83    X ), X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, 
% 1.42/1.83    X ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'( 
% 1.42/1.83    hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP( 
% 1.42/1.83    'c_Power_Opower__class_Opower'( X ), Y ), T ), X ), ~( 'c_lessequals'( Y
% 1.42/1.83    , 'c_HOL_Oone__class_Oone'( X ), X ) ), ~( 'c_lessequals'( 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( T, Z, 
% 1.42/1.83    'tc_nat' ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.42/1.83     ), Y ), Z ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), T ), 
% 1.42/1.83    X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X )
% 1.42/1.83     ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.42/1.83     ), ~( 'c_HOL_Oord__class_Oless'( T, Z, 'tc_nat' ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.42/1.83     ), Y ), hAPP( 'c_Suc', Z ) ), 'c_HOL_Oone__class_Oone'( X ), X ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.42/1.83    ,
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y, 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 
% 1.42/1.83    'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y
% 1.42/1.83     ), X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'( 
% 1.42/1.83    hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y, 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), X ) ), 
% 1.42/1.83    'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ), =( Z, 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 
% 1.42/1.83    'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ), =( Z, 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 
% 1.42/1.83    'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( 
% 1.42/1.83    'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), =( Y, 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_lessequals'( hAPP( hAPP( 
% 1.42/1.83    'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y
% 1.42/1.83     ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =( hAPP( hAPP( 
% 1.42/1.83    'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP( 
% 1.42/1.83    'c_Power_Opower__class_Opower'( X ), T ), Z ) ) ), =( Y, T ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 
% 1.42/1.83    'tc_nat' ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X )
% 1.42/1.83     ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 
% 1.42/1.83    X ), 'c_HOL_Oone__class_Oone'( X ) ), 'c_HOL_Oone__class_Oone'( X ) ) ), 
% 1.42/1.83    hAPP( 'c_Finite__Set_Osetsum'( 'c_Nat_Osemiring__1__class_Oof__nat'( X )
% 1.42/1.83    , 'tc_nat', X ), 'c_SetInterval_Oord__class_OatLeastAtMost'( 
% 1.42/1.83    'c_HOL_Oone__class_Oone'( 'tc_nat' ), Y, 'tc_nat' ) ) ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( X ), hAPP( 
% 1.42/1.83    'c_Nat_Osemiring__1__class_Oof__nat'( X ), Y ) ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oplus__class_Oplus'( X ), hAPP( 
% 1.42/1.83    'c_Nat_Osemiring__1__class_Oof__nat'( X ), Y ) ), 
% 1.42/1.83    'c_HOL_Oone__class_Oone'( X ) ) ) ) ],
% 1.42/1.83     [ ~( 'c_Parity_Oeven__odd__class_Oeven'( hAPP( 'c_Suc', hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.83    'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ), X ) ), 'tc_nat' ) ) ],
% 1.42/1.83     [ =( hAPP( hAPP( X, Y ), hAPP( 'c_Suc', hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.83    'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ), Z ) ) ), hAPP( hAPP( T, Y ), hAPP( 
% 1.42/1.83    hAPP( T, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, Y ), Z ) ) ) ), ~( 
% 1.42/1.83    'c_Groebner__Basis_Ogb__semiring'( U, T, X, W, V0, V1 ) ) ],
% 1.42/1.83     [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_Complex_Ocomplex' ), 
% 1.42/1.83    X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_Complex_Ocomplex' )
% 1.42/1.83    , X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( 'tc_Complex_Ocomplex' ), Y )
% 1.42/1.83     ) ) ],
% 1.42/1.83     [ ~( 'class_Divides_Osemiring__div'( X ) ), =( 
% 1.42/1.83    'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.42/1.83    , Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), Z, X )
% 1.42/1.83    , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), 
% 1.42/1.83    'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ) ), =( Z, 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.83     [ ~( 'class_Divides_Osemiring__div'( X ) ), =( 
% 1.42/1.83    'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.42/1.83    , Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), T, X )
% 1.42/1.83    , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), 
% 1.42/1.83    'c_Divides_Odiv__class_Odiv'( Y, T, X ) ) ), =( T, 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.42/1.83    X ), 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.42/1.83     ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), X
% 1.42/1.83     ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), 
% 1.42/1.83    'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ) ) ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ) ) ), 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.42/1.83     ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 
% 1.42/1.83    hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ), 'c_HOL_Ozero__class_Ozero'( 
% 1.42/1.83    X ), X ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), 
% 1.42/1.83    'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.42/1.83    X ), Y ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z )
% 1.42/1.83     ), X ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( Y, 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'( hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.42/1.83    X ), Z ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y )
% 1.42/1.83     ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( Y, 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'( hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.42/1.83    X ), Y ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z )
% 1.42/1.83     ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.42/1.83    X ), Y ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z )
% 1.42/1.83     ), X ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.42/1.83    X ), Y ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z )
% 1.42/1.83     ), X ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'( 
% 1.42/1.83    hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), Y, X ), ~( 
% 1.42/1.83    'c_lessequals'( Z, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~( 
% 1.42/1.83    'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 
% 1.42/1.83    'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'( 
% 1.42/1.83    hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), Z, X ), ~( 
% 1.42/1.83    'c_lessequals'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~( 
% 1.42/1.83    'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 
% 1.42/1.83    'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ), 
% 1.42/1.83    'c_HOL_Oone__class_Oone'( X ) ), X ) ],
% 1.42/1.83     [ ~( 'class_Divides_Osemiring__div'( X ) ), =( 
% 1.42/1.83    'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.42/1.83    , Y ), Z ), Z, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 
% 1.42/1.83    'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ), 'c_HOL_Oone__class_Oone'( X )
% 1.42/1.83     ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.83     [ ~( 'class_Divides_Osemiring__div'( X ) ), =( 
% 1.42/1.83    'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.42/1.83    , Y ), Z ), Y, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 
% 1.42/1.83    'c_Divides_Odiv__class_Odiv'( Z, Y, X ) ), 'c_HOL_Oone__class_Oone'( X )
% 1.42/1.83     ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.83     [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP( 
% 1.42/1.83    'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ), 
% 1.42/1.83    'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), 'c_HOL_Ozero__class_Ozero'( 
% 1.42/1.83    'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 
% 1.42/1.83    hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( 
% 1.42/1.83    hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), W ), X ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( T, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.42/1.83    , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Ominus__class_Ominus'( X ), U ), Y ) ), Z ) ), W ), X ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.42/1.83    , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Ominus__class_Ominus'( X ), Z ), T ) ), U ) ), W ), X ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 
% 1.42/1.83    hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), Y ), hAPP( 
% 1.42/1.83    hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ), W ), X ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 
% 1.42/1.83    hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( 
% 1.42/1.83    hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), W ), X ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 
% 1.42/1.83    hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Ominus__class_Ominus'( X ), Y ), U ) ), Z ) ), T ), W, X ) ) ]
% 1.42/1.83    ,
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 
% 1.42/1.83    hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ), T ) ), U ), W, X ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 
% 1.42/1.83    hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), U ), hAPP( 
% 1.42/1.83    hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), W ), X ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'( 
% 1.42/1.83    hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.42/1.83    X ), U ), Z ) ), W ), X ), ~( 'c_lessequals'( T, hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.42/1.83    X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), U ), Y ) ), Z ) ), W
% 1.42/1.83     ), X ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'( Y
% 1.42/1.83    , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Ominus__class_Ominus'( X ), Z ), T ) ), U ) ), W ), X ), ~( 
% 1.42/1.83    'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), Y ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.42/1.83    X ), Z ), U ) ), W ), X ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'( 
% 1.42/1.83    hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.42/1.83    X ), U ), Z ) ), W ), X ), ~( 'c_lessequals'( hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.42/1.83    X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), U ) ), Z ) ), T
% 1.42/1.83     ), W, X ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'( 
% 1.42/1.83    hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ), T ) ), U ), W, X ), ~( 
% 1.42/1.83    'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), U ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.42/1.83    X ), Z ), T ) ), W ), X ) ) ],
% 1.42/1.83     [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_Int_Onumber__class_Onumber__of'( 
% 1.42/1.83    X ), Y ) ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( X ), Z ) ), T ) ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Ominus__class_Ominus'( X ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( X ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), Y ), Z ) ) ), T ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.42/1.83     ), Y ), Z ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T )
% 1.42/1.83    , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), 
% 1.42/1.83    hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.42/1.83     ), Y ), Z ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T )
% 1.42/1.83    , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), 
% 1.42/1.83    hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.83    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( 
% 1.42/1.83    X ), Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( T, 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( hAPP( 
% 1.42/1.83    hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), Z, X ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.83    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( 
% 1.42/1.83    X ), Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, 
% 1.42/1.83    hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ), 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.83    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( 
% 1.42/1.83    X ), Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( T, 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, 
% 1.42/1.83    hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ), 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.83    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.42/1.83     ), Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( T, 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'( Z
% 1.42/1.83    , hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ), X ) ) ]
% 1.42/1.83    ,
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.83    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.42/1.83     ), Y ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 'c_HOL_Oord__class_Oless'( Z, 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, 
% 1.42/1.83    hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.83    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.42/1.83     ), Y ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.42/1.83    hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), Y, X ) ), 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.83    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.42/1.83     ), Y ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'( Z, 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.42/1.83    hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), Y, X ) ), 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.83    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.42/1.83    , Y ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'( Z, 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.42/1.83    hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ), Y, X ) ) ]
% 1.42/1.83    ,
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.83    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( 
% 1.42/1.83    X ), Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, 
% 1.42/1.83    hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.42/1.83    , Y ), T ), Z, X ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.83    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( 
% 1.42/1.83    X ), Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( T, 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, 
% 1.42/1.83    hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.42/1.83    , Y ), T ), Z, X ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.83    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.42/1.83     ), Y ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.42/1.83    hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), Y, X ) ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.42/1.83     ), T ), Z ), X ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.83    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.42/1.83     ), Y ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'( Z, 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.42/1.83    hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), Y, X ) ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.42/1.83     ), T ), Z ), X ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( 
% 1.42/1.83    X ), Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), Z, X ) ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ]
% 1.42/1.83    ,
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.42/1.83     ), Y ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 1.42/1.83    ,
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.83    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( 
% 1.42/1.83    X ), Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.42/1.83    hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), Z, X ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.83    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.42/1.83    , Y ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.42/1.83    Y, hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ), X ) ) ]
% 1.42/1.83    ,
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.83    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.42/1.83     ), Y ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.42/1.83    Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.83    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.42/1.83     ), Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.42/1.83    hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ), Z, X ) ) ]
% 1.42/1.83    ,
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.83    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y, 
% 1.42/1.83    hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~( 
% 1.42/1.83    'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 
% 1.42/1.83    'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T
% 1.42/1.83     ), X ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.42/1.83     ), Y ), T ), Z, X ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.83    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP( 
% 1.42/1.83    hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), T, X ), ~( 
% 1.42/1.83    'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 
% 1.42/1.83    'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), 
% 1.42/1.83    Y, X ) ), ~( 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.42/1.83    X ), T ), Z ), X ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.83    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.42/1.83    'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( X ), Y ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( hAPP( 'c_Int_Onumber__class_Onumber__of'( X )
% 1.42/1.83    , Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( 
% 1.42/1.83    T, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'( 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.83    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.42/1.83    'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( 
% 1.42/1.83    X ), X ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), 
% 1.42/1.83    X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), 
% 1.42/1.83    ~( 'c_HOL_Oord__class_Oless'( hAPP( 'c_Int_Onumber__class_Onumber__of'( X
% 1.42/1.83     ), Y ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ), X )
% 1.42/1.83     ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.83    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.42/1.83    'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( X ), T ), X ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( X ), T ), X ) ), 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.83    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.42/1.83    'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), hAPP( 'c_Int_Onumber__class_Onumber__of'( 
% 1.42/1.83    X ), Y ), X ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( 
% 1.42/1.83    X ), X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, 
% 1.42/1.83    X ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( X ), Y ), X ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.83    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.42/1.83    'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oinverse__class_Odivide'( X ), Z ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( X ), T ) ), X ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( hAPP( 'c_Int_Onumber__class_Onumber__of'( X )
% 1.42/1.83    , T ), 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'( 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), hAPP( 'c_Int_Onumber__class_Onumber__of'( 
% 1.42/1.83    X ), T ), X ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.83    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.42/1.83    'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'( hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( X ), Z ), 'c_HOL_Ozero__class_Ozero'( 
% 1.42/1.83    X ), X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), 
% 1.42/1.83    hAPP( 'c_Int_Onumber__class_Onumber__of'( X ), Z ), X ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( 
% 1.42/1.83    X ), T ), hAPP( 'c_Int_Onumber__class_Onumber__of'( X ), Z ) ), X ) ) ]
% 1.42/1.83    ,
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.83    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.42/1.83    'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oinverse__class_Odivide'( X ), Y ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( X ), Z ) ), T, X ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( hAPP( 'c_Int_Onumber__class_Onumber__of'( X )
% 1.42/1.83    , Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'( 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), hAPP( 'c_Int_Onumber__class_Onumber__of'( 
% 1.42/1.83    X ), Z ), X ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.83    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.42/1.83    'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Oord__class_Oless'( hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( X ), Z ), 'c_HOL_Ozero__class_Ozero'( 
% 1.42/1.83    X ), X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), 
% 1.42/1.83    hAPP( 'c_Int_Onumber__class_Onumber__of'( X ), Z ), X ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.42/1.83     ), T ), hAPP( 'c_Int_Onumber__class_Onumber__of'( X ), Z ) ), Y, X ) ) ]
% 1.42/1.83    ,
% 1.42/1.83     [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), 'c_Deriv_Oderiv'( 
% 1.42/1.83    'c_COMBS'( 'c_COMBB'( 'c_HOL_Oplus__class_Oplus'( X ), Y, X, 'tc_fun'( X
% 1.42/1.83    , X ), X ), Z, X, X, X ), T, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.42/1.83    , U ), W ), X ), ~( 'c_Deriv_Oderiv'( Z, T, W, X ) ), ~( 'c_Deriv_Oderiv'( 
% 1.42/1.83    Y, T, U, X ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( 'c_lessequals'( 
% 1.42/1.83    hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.42/1.83    , X ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 
% 1.42/1.83    'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( 
% 1.42/1.83    'tc_nat' ) ), X ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y, 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 
% 1.42/1.83    'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y
% 1.42/1.83     ), X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.42/1.83     [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP( 
% 1.42/1.83    'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ), 
% 1.42/1.83    'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_Power_Opower_Opower'( 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.42/1.83     ), Z ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.42/1.83     ), T ) ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.83    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y
% 1.42/1.83     ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y
% 1.42/1.83    , X ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.83    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y
% 1.42/1.83     ), X ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.83    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.42/1.83     ), 'c_HOL_Oone__class_Oone'( X ) ), Y ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.42/1.83    , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), 
% 1.42/1.83    X ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.83    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.42/1.83     ), 'c_HOL_Oone__class_Oone'( X ) ), Y ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.42/1.83    , X ) ) ],
% 1.42/1.83     [ 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', X, 'tc_Int_Oint' ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( 'c_Int_OPls', 'c_Int_OBit0'( X ), 
% 1.42/1.83    'tc_Int_Oint' ) ) ],
% 1.42/1.83     [ 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', 'c_Int_OBit0'( X ), 
% 1.42/1.83    'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', X, 
% 1.42/1.83    'tc_Int_Oint' ) ) ],
% 1.42/1.83     [ 'c_lessequals'( X, 'c_Int_OPls', 'tc_Int_Oint' ), ~( 'c_lessequals'( 
% 1.42/1.83    'c_Int_OBit0'( X ), 'c_Int_OPls', 'tc_Int_Oint' ) ) ],
% 1.42/1.83     [ 'c_lessequals'( 'c_Int_OBit0'( X ), 'c_Int_OPls', 'tc_Int_Oint' ), ~( 
% 1.42/1.83    'c_lessequals'( X, 'c_Int_OPls', 'tc_Int_Oint' ) ) ],
% 1.42/1.83     [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 
% 1.42/1.83    hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, hAPP( 
% 1.42/1.83    'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y, 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.42/1.83     [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 
% 1.42/1.83    hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X, 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, hAPP( 'c_Suc', 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.42/1.83     [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 
% 1.42/1.83    'tc_nat' ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 
% 1.42/1.83    'tc_nat' ), Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ],
% 1.42/1.83     [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( 'c_Suc', 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( 
% 1.42/1.83    'tc_nat' ) ), hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ]
% 1.42/1.83    ,
% 1.42/1.83     [ =( 'c_Fact_Ofact__class_Ofact'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 
% 1.42/1.83    'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), 'tc_nat' ), 
% 1.42/1.83    'c_Fact_Ofact__class_Ofact'( X, 'tc_nat' ) ) ],
% 1.42/1.83     [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 
% 1.42/1.83    hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X, 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y, 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.42/1.83     [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 
% 1.42/1.83    hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, hAPP( 
% 1.42/1.83    'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, hAPP( 'c_Suc'
% 1.42/1.83    , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.42/1.83     [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 
% 1.42/1.83    hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' )
% 1.42/1.83    , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y
% 1.42/1.83    , 'tc_nat' ) ) ],
% 1.42/1.83     [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 
% 1.42/1.83    hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' )
% 1.42/1.83    , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X
% 1.42/1.83    , 'tc_nat' ) ) ],
% 1.42/1.83     [ ~( =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( 
% 1.42/1.83    hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( Y, hAPP( 
% 1.42/1.83    'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y, 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.42/1.83     [ ~( =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( 
% 1.42/1.83    hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( X, 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, hAPP( 'c_Suc', 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.42/1.83     [ =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 
% 1.42/1.83    'tc_nat' ) ), hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) )
% 1.42/1.83     ],
% 1.42/1.83     [ ~( =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( 
% 1.42/1.83    hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( X, 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y, 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.42/1.83     [ ~( =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( 
% 1.42/1.83    hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( Y, hAPP( 
% 1.42/1.83    'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, hAPP( 'c_Suc'
% 1.42/1.83    , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.42/1.83     [ =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( 'c_Suc', 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( 
% 1.42/1.83    'tc_nat' ) ) ) ],
% 1.42/1.83     [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( 'c_Suc', 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), hAPP( 'c_Suc', 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.42/1.83     [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), 'c_Deriv_Oderiv'( 
% 1.42/1.83    'c_COMBC'( 'c_COMBB'( 'c_Power_Opower__class_Opower'( X ), Y, X, 'tc_fun'( 
% 1.42/1.83    'tc_nat', X ), X ), hAPP( 'c_Suc', Z ), X, 'tc_nat', X ), T, hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 
% 1.42/1.83    X ), 'c_HOL_Oone__class_Oone'( X ) ), hAPP( 
% 1.42/1.83    'c_Nat_Osemiring__1__class_Oof__nat'( X ), Z ) ) ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( X ), U ), hAPP( hAPP( 
% 1.42/1.83    'c_Power_Opower__class_Opower'( X ), hAPP( Y, T ) ), Z ) ) ), X ), ~( 
% 1.42/1.83    'c_Deriv_Oderiv'( Y, T, U, X ) ) ],
% 1.42/1.83     [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_Divides_Odiv__class_Omod'( X, 
% 1.42/1.83    hAPP( 'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.83    'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ), 'tc_nat' ), 'tc_nat'
% 1.42/1.83     ), ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.42/1.83     [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ), ~( 
% 1.42/1.83    'c_Parity_Oeven__odd__class_Oeven'( 'c_Divides_Odiv__class_Omod'( X, hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.83    'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ), 'tc_nat' ), 'tc_nat'
% 1.42/1.83     ) ) ],
% 1.42/1.83     [ =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', hAPP( 'c_Suc', X ) ), 
% 1.42/1.83    hAPP( 'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.83    'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' ), 
% 1.42/1.83    'c_Divides_Odiv__class_Omod'( X, hAPP( 'c_Int_Onumber__class_Onumber__of'( 
% 1.42/1.83    'tc_nat' ), 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' )
% 1.42/1.83     ) ],
% 1.42/1.83     [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( 'c_Suc', hAPP( 'c_Suc', X ) ), 
% 1.42/1.83    hAPP( 'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.83    'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' ), hAPP( 'c_Suc', 
% 1.42/1.83    'c_Divides_Odiv__class_Odiv'( X, hAPP( 'c_Int_Onumber__class_Onumber__of'( 
% 1.42/1.83    'tc_nat' ), 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' )
% 1.42/1.83     ) ) ],
% 1.42/1.83     [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.42/1.83    'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.42/1.83     ), Z ), Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' )
% 1.42/1.83     ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.42/1.83    , Y, 'tc_nat' ) ) ],
% 1.42/1.83     [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.42/1.83    'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.42/1.83     ), X ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' )
% 1.42/1.83     ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.42/1.83    , X, 'tc_nat' ) ) ],
% 1.42/1.83     [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.42/1.83    'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.42/1.83     ), X ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 1.42/1.83     [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.42/1.83    'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.42/1.83     ), Z ), Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 1.42/1.83     [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.42/1.83    'tc_nat' ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.42/1.83     ), Z ), Y ), 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_nat' ) ) ],
% 1.42/1.83     [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.42/1.83    'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.42/1.83     ), X ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' )
% 1.42/1.83     ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.42/1.83    , X, 'tc_nat' ) ) ],
% 1.42/1.83     [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 
% 1.42/1.83    'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 
% 1.42/1.83    'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X
% 1.42/1.83     ), 'tc_nat' ) ) ],
% 1.42/1.83     [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 
% 1.42/1.83    'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 
% 1.42/1.83    'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y
% 1.42/1.83     ), 'tc_nat' ) ) ],
% 1.42/1.83     [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 
% 1.42/1.83    'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), X ), 'tc_nat' ) ) ],
% 1.42/1.83     [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 
% 1.42/1.83    'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ), 'tc_nat' ) ) ],
% 1.42/1.83     [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), 
% 1.42/1.83    hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 
% 1.42/1.83    'tc_nat' ) ), =( Y, Z ) ],
% 1.42/1.83     [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), 
% 1.42/1.83    hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, hAPP( 
% 1.42/1.83    'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.42/1.83     [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), 
% 1.42/1.83    hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X, hAPP( 
% 1.42/1.83    'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.42/1.83     [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 
% 1.42/1.83    hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), 'tc_nat'
% 1.42/1.83     ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.42/1.83    , Y, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.42/1.83     [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 
% 1.42/1.83    'tc_nat' ) ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y ), 'tc_nat' ), 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.42/1.83     [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ), 'tc_nat' ), 
% 1.42/1.83    'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ), =( X, 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.42/1.83     [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc'
% 1.42/1.83    , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), hAPP( 'c_Suc', 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), hAPP( 'c_Suc', 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.42/1.83     [ =( 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), X, 'tc_nat' ), 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.42/1.83     [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP( 
% 1.42/1.83    'c_Suc', X ) ) ), Y, 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit1'( 
% 1.42/1.83    'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ), X ), Y, 'tc_nat' ) ) ],
% 1.42/1.83     [ =( 'c_Divides_Odiv__class_Odiv'( X, hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP( 
% 1.42/1.83    'c_Suc', Y ) ) ), 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( X, hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit1'( 
% 1.42/1.83    'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ), Y ), 'tc_nat' ) ) ],
% 1.42/1.83     [ =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP( 
% 1.42/1.83    'c_Suc', X ) ) ), Y, 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit1'( 
% 1.42/1.83    'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ), X ), Y, 'tc_nat' ) ) ],
% 1.42/1.83     [ =( 'c_Divides_Odiv__class_Omod'( X, hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP( 
% 1.42/1.83    'c_Suc', Y ) ) ), 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X, hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit1'( 
% 1.42/1.83    'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ), Y ), 'tc_nat' ) ) ],
% 1.42/1.83     [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP( 
% 1.42/1.83    'c_Suc', X ) ) ), hAPP( 'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), Y
% 1.42/1.83     ), 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit1'( 
% 1.42/1.83    'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ), X ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), Y ), 'tc_nat' ) ) ],
% 1.42/1.83     [ =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP( 
% 1.42/1.83    'c_Suc', X ) ) ), hAPP( 'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), Y
% 1.42/1.83     ), 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit1'( 
% 1.42/1.83    'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ), X ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), Y ), 'tc_nat' ) ) ],
% 1.42/1.83     [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 
% 1.42/1.83    hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ), 'tc_nat'
% 1.42/1.83     ), ~( 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ) ],
% 1.42/1.83     [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( 
% 1.42/1.83    hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ]
% 1.42/1.83    ,
% 1.42/1.83     [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ), 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_lessequals'( X, Y, 
% 1.42/1.83    'tc_nat' ) ) ],
% 1.42/1.83     [ ~( =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ), 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_lessequals'( X, Y, 
% 1.42/1.83    'tc_nat' ) ],
% 1.42/1.83     [ hBOOL( hAPP( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ), ~( hBOOL( hAPP( X, hAPP( 
% 1.42/1.83    hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), Z ) ) ) ) ],
% 1.42/1.83     [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 
% 1.42/1.83    'tc_nat' ), X ), Y ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 
% 1.42/1.83    'tc_nat' ) ) ],
% 1.42/1.83     [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( 'c_Suc'
% 1.42/1.83    , X ) ), Y ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), 
% 1.42/1.83    hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit1'( 
% 1.42/1.83    'c_Int_OPls' ) ) ) ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OPls' ), Y, 
% 1.42/1.83    'tc_nat' ) ) ],
% 1.42/1.83     [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'( 
% 1.42/1.83    'tc_nat' ) ), hAPP( 'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 
% 1.42/1.83    'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' ), hAPP( 
% 1.42/1.83    'c_Suc', 'c_Divides_Odiv__class_Odiv'( X, hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.83    'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' ) ) ), 
% 1.42/1.83    'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =( hAPP( 
% 1.42/1.83    'c_Nat_Osemiring__1__class_Oof__nat'( X ), 'c_HOL_Oone__class_Oone'( 
% 1.42/1.83    'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.42/1.83     [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), 'c_Deriv_Oderiv'( 
% 1.42/1.83    'c_COMBC'( 'c_COMBB'( 'c_Power_Opower__class_Opower'( X ), Y, X, 'tc_fun'( 
% 1.42/1.83    'tc_nat', X ), X ), Z, X, 'tc_nat', X ), T, hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( X ), hAPP( 
% 1.42/1.83    'c_Nat_Osemiring__1__class_Oof__nat'( X ), Z ) ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( X ), U ), hAPP( hAPP( 
% 1.42/1.83    'c_Power_Opower__class_Opower'( X ), hAPP( Y, T ) ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z ), hAPP( 'c_Suc', 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ) ), X ), ~( 
% 1.42/1.83    'c_Deriv_Oderiv'( Y, T, U, X ) ) ],
% 1.42/1.83     [ ~( =( 'c_Divides_Odiv__class_Omod'( X, hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.83    'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ), 'tc_nat' ), 
% 1.42/1.83    'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), 
% 1.42/1.83    'c_Parity_Oeven__odd__class_Oeven'( 'c_Divides_Odiv__class_Odiv'( hAPP( 
% 1.42/1.83    hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), 
% 1.42/1.83    'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.83    'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' ), 'tc_nat' ) ],
% 1.42/1.83     [ ~( =( 'c_Divides_Odiv__class_Omod'( X, hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.83    'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ), 'tc_nat' ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit1'( 
% 1.42/1.83    'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ) ), ~( 
% 1.42/1.83    'c_Parity_Oeven__odd__class_Oeven'( 'c_Divides_Odiv__class_Odiv'( hAPP( 
% 1.42/1.83    hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), 
% 1.42/1.83    'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.83    'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' ), 'tc_nat' ) ) ],
% 1.42/1.83     [ =( 'c_Fact_Ofact__class_Ofact'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.42/1.83    , 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.42/1.83     [ =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( 'tc_nat' ), X ), 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( 
% 1.42/1.83    'tc_nat' ) ) ],
% 1.42/1.83     [ =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), hAPP( 'c_Suc', 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.42/1.83     [ =( hAPP( 'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), X ), hAPP( 
% 1.42/1.83    'c_Suc', hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), X ) ), 
% 1.42/1.83    'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ) ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), X ), 'tc_nat' ) ) ],
% 1.42/1.83     [ =( 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ), Y, 'tc_nat' )
% 1.42/1.83    , 'c_Divides_Odiv__class_Omod'( Z, Y, 'tc_nat' ) ) ],
% 1.42/1.83     [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc'
% 1.42/1.83    , X ) ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), 
% 1.42/1.83    hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.42/1.83     [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), hAPP( 
% 1.42/1.83    'c_Suc', Y ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), 
% 1.42/1.83    hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.42/1.83     [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( 
% 1.42/1.83    hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), T ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), U ) ) ) ), =( 
% 1.42/1.83    'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), 
% 1.42/1.83    'c_Divides_Odiv__class_Omod'( T, Y, 'tc_nat' ) ) ],
% 1.42/1.83     [ =( hAPP( 'c_SetInterval_Oord__class_OatLeastLessThan'( 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), X ), 
% 1.42/1.83    'c_SetInterval_Oord__class_OlessThan'( X, 'tc_nat' ) ) ],
% 1.42/1.83     [ =( 'c_Fact_Ofact__class_Ofact'( X, 'tc_nat' ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), 
% 1.42/1.83    'c_Fact_Ofact__class_Ofact'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 
% 1.42/1.83    'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), 'tc_nat' ) ) ), 
% 1.42/1.83    ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 
% 1.42/1.83    'tc_nat' ) ) ],
% 1.42/1.83     [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( 
% 1.42/1.83    'c_Finite__Set_Osetsum'( Y, 'tc_nat', X ), 
% 1.42/1.83    'c_SetInterval_Oord__class_OatLeastAtMost'( Z, hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), T ), U ), 'tc_nat' ) ), hAPP( 
% 1.42/1.83    hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_Finite__Set_Osetsum'( Y, 
% 1.42/1.83    'tc_nat', X ), 'c_SetInterval_Oord__class_OatLeastAtMost'( Z, T, 'tc_nat'
% 1.42/1.83     ) ) ), hAPP( 'c_Finite__Set_Osetsum'( Y, 'tc_nat', X ), 
% 1.42/1.83    'c_SetInterval_Oord__class_OatLeastAtMost'( hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), T ), 'c_HOL_Oone__class_Oone'( 
% 1.42/1.83    'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), T ), U
% 1.42/1.83     ), 'tc_nat' ) ) ) ), ~( 'c_lessequals'( Z, hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), T ), 'c_HOL_Oone__class_Oone'( 
% 1.42/1.83    'tc_nat' ) ), 'tc_nat' ) ) ],
% 1.42/1.83     [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat'
% 1.42/1.83     ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ) ), Z ), 
% 1.42/1.83    'tc_nat' ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 1.42/1.83     [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat'
% 1.42/1.83     ), Y ), Z ), 'tc_nat' ), ~( 'c_lessequals'( hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ), ~( 
% 1.42/1.83    'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 1.42/1.83     [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X
% 1.42/1.83     ), Y ), Z, 'tc_nat' ), ~( 'c_lessequals'( X, hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z ), Y ), 'tc_nat' ) ), ~( 
% 1.42/1.83    'c_lessequals'( Y, Z, 'tc_nat' ) ) ],
% 1.42/1.83     [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Z ) ), Y ) ), ~( 
% 1.42/1.83    'c_lessequals'( Z, X, 'tc_nat' ) ) ],
% 1.42/1.83     [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), Z ) ) ), ~( 'c_lessequals'( 
% 1.42/1.83    Z, Y, 'tc_nat' ) ) ],
% 1.42/1.83     [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), 
% 1.42/1.83    X ), Y ), Z, 'tc_nat' ), ~( 'c_lessequals'( X, hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ), 'tc_nat' ) ) ],
% 1.42/1.83     [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.42/1.83    , Y ), Z ), 'tc_nat' ), ~( 'c_lessequals'( hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ) ]
% 1.42/1.83    ,
% 1.42/1.83     [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), hAPP( 
% 1.42/1.83    hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ), Y ) ), ~( 
% 1.42/1.83    'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 1.42/1.83     [ ~( 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat'
% 1.42/1.83     ), Y ), X ), 'tc_nat' ) ), =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 
% 1.42/1.83    'tc_nat' ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X )
% 1.42/1.83     ), X ), Y ) ],
% 1.42/1.83     [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), Y ), X ), ~( 
% 1.42/1.83    'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.42/1.83     [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), X ) ), Y ), ~( 
% 1.42/1.83    'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.42/1.83     [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), =( Y, hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), X ) ), X ) ) ],
% 1.42/1.83     [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ), Y ) ), ~( 
% 1.42/1.83    'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.42/1.83     [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), Z ) ), ~( 
% 1.42/1.83    'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 1.42/1.83     [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 
% 1.42/1.83    'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( hAPP( 
% 1.42/1.83    hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ) ]
% 1.42/1.83    ,
% 1.42/1.83     [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 
% 1.42/1.83    'tc_nat' ), X ), Y ), Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, 
% 1.42/1.83    hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z ), Y ), 'tc_nat'
% 1.42/1.83     ) ) ],
% 1.42/1.83     [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), X ) ), Y ), 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ],
% 1.42/1.83     [ =( hAPP( 'c_Suc', X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 
% 1.42/1.83    'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ) ],
% 1.42/1.83     [ =( hAPP( 'c_Suc', X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 
% 1.42/1.83    'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), X ) ) ],
% 1.42/1.83     [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( 'c_Suc'
% 1.42/1.83    , X ) ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), X ) ],
% 1.42/1.83     [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), hAPP( 
% 1.42/1.83    'c_Suc', Y ) ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), 
% 1.42/1.83    hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), 
% 1.42/1.83    'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), Y ) ) ],
% 1.42/1.83     [ 'c_Fun_Oinj__on'( 'c_COMBC'( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X
% 1.42/1.83    , 'tc_nat', 'tc_nat', 'tc_nat' ), Y, 'tc_nat', 'tc_nat' ) ],
% 1.42/1.83     [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 
% 1.42/1.83    'v_m', 'tc_nat' ) ],
% 1.42/1.83     [ 'c_lessequals'( 'v_m', 'v_i', 'tc_nat' ) ],
% 1.42/1.83     [ =( X, hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X
% 1.42/1.83    , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.42/1.83    X, hAPP( 'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.83    'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' ) ) ],
% 1.42/1.83     [ =( hAPP( 'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit1'( 
% 1.42/1.83    'c_Int_OBit1'( 'c_Int_OPls' ) ) ), hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP( 
% 1.42/1.83    'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ) ],
% 1.42/1.83     [ =( hAPP( 'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit1'( 
% 1.42/1.83    'c_Int_OPls' ) ), hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 1.42/1.83     ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP( 
% 1.42/1.83    'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP( 
% 1.42/1.83    'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP( 
% 1.42/1.83    'c_Power_Opower__class_Opower'( X ), Y ), T ) ) ), ~( 'c_lessequals'( T, 
% 1.42/1.83    Z, 'tc_nat' ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.83    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP( 
% 1.42/1.83    hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Oone__class_Oone'( X )
% 1.42/1.83     ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y, 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.83    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y, 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y
% 1.42/1.83     ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.83    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y
% 1.42/1.83     ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.42/1.83    ,
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.83    'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'( 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y
% 1.42/1.83     ), X ) ) ],
% 1.42/1.83     [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP( 
% 1.42/1.83    'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ), 
% 1.42/1.83    'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP( 
% 1.42/1.83    'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ), 
% 1.42/1.83    'c_HOL_Oplus__class_Oplus'( X ), X ), hAPP( hAPP( 'c_Power_Opower_Opower'( 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.42/1.83     ), Z ) ), T ) ) ],
% 1.42/1.83     [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), 'c_Deriv_Oderiv'( 
% 1.42/1.83    'c_COMBS'( 'c_COMBB'( 'c_HOL_Ominus__class_Ominus'( X ), Y, X, 'tc_fun'( 
% 1.42/1.83    X, X ), X ), Z, X, X, X ), T, hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X
% 1.42/1.83     ), U ), W ), X ), ~( 'c_Deriv_Oderiv'( Z, T, W, X ) ), ~( 
% 1.42/1.83    'c_Deriv_Oderiv'( Y, T, U, X ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oring__1'( X ) ), =( hAPP( hAPP( 
% 1.42/1.83    'c_Power_Opower__class_Opower'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( 
% 1.42/1.83    X ), Y ) ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 
% 1.42/1.83    hAPP( 'c_Power_Opower__class_Opower'( X ), hAPP( 
% 1.42/1.83    'c_HOL_Ouminus__class_Ouminus'( X ), 'c_HOL_Oone__class_Oone'( X ) ) ), Z
% 1.42/1.83     ) ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ]
% 1.42/1.83    ,
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.42/1.83     ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( 
% 1.42/1.83    hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), X ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP( 
% 1.42/1.83    'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), X ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.42/1.83     [ ~( 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'( X )
% 1.42/1.83    , 'c_Power_Opower_Opower'( 'c_HOL_Oone__class_Oone'( X ), 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( X ), X ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( 
% 1.42/1.83    X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ), 
% 1.42/1.83    'c_HOL_Oone__class_Oone'( X ) ) ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, 
% 1.42/1.83    Z, X ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.42/1.83     ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ), 
% 1.42/1.83    'c_HOL_Oone__class_Oone'( X ) ) ), Z, X ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.42/1.83    Y, Z, X ) ) ],
% 1.42/1.83     [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), 'c_Deriv_Oderiv'( 
% 1.42/1.83    'c_COMBC'( 'c_COMBB'( 'c_HOL_Oinverse__class_Odivide'( X ), Y, X, 
% 1.42/1.83    'tc_fun'( X, X ), X ), Z, X, X, X ), T, hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oinverse__class_Odivide'( X ), U ), Z ), X ), ~( 'c_Deriv_Oderiv'( 
% 1.42/1.83    Y, T, U, X ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y, 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ) ), 'c_lessequals'( Y, 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP( 
% 1.42/1.83    'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), Z ) ), 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.42/1.83     ), Y ), hAPP( 'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), Z ) ), 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.42/1.83     [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP( 
% 1.42/1.83    'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ), 
% 1.42/1.83    'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), 'c_HOL_Oone__class_Oone'( 
% 1.42/1.83    'tc_nat' ) ), Y ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.42/1.83    hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.83    'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ), hAPP( hAPP( 
% 1.42/1.83    'c_Power_Opower__class_Opower'( X ), Z ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.83    'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ), X ) ) ],
% 1.42/1.83     [ ~( =( hAPP( 'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), X ), 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_lessequals'( X, 
% 1.42/1.83    'c_Int_OPls', 'tc_Int_Oint' ) ],
% 1.42/1.83     [ =( hAPP( 'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), X ), 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_lessequals'( X, 
% 1.42/1.83    'c_Int_OPls', 'tc_Int_Oint' ) ) ],
% 1.42/1.83     [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), X ) ) ), 'c_lessequals'( 
% 1.42/1.83    X, 'c_Int_OPls', 'tc_Int_Oint' ) ],
% 1.42/1.83     [ =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), X ) ), ~( 'c_lessequals'( 
% 1.42/1.83    X, 'c_Int_OPls', 'tc_Int_Oint' ) ) ],
% 1.42/1.83     [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), 'c_Series_Osums'( 
% 1.42/1.83    'c_COMBS'( 'c_COMBB'( 'c_HOL_Oplus__class_Oplus'( X ), Y, X, 'tc_fun'( X
% 1.42/1.83    , X ), 'tc_nat' ), Z, 'tc_nat', X, X ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~( 'c_Series_Osums'( Z, U
% 1.42/1.83    , X ) ), ~( 'c_Series_Osums'( Y, T, X ) ) ],
% 1.42/1.83     [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), 'c_Series_Osums'( 
% 1.42/1.83    'c_COMBC'( 'c_COMBB'( 'c_HOL_Otimes__class_Otimes'( X ), Y, X, 'tc_fun'( 
% 1.42/1.83    X, X ), 'tc_nat' ), Z, 'tc_nat', X, X ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ), ~( 'c_Series_Osums'( Y
% 1.42/1.83    , T, X ) ) ],
% 1.42/1.83     [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), 'c_Series_Osums'( 
% 1.42/1.83    'c_COMBC'( 'c_COMBB'( 'c_HOL_Otimes__class_Otimes'( X ), Y, X, 'tc_fun'( 
% 1.42/1.83    X, X ), 'tc_nat' ), Z, 'tc_nat', X, X ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ), ~( 'c_Series_Osums'( Y
% 1.42/1.83    , T, X ) ) ],
% 1.42/1.83     [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), 'c_Series_Osums'( 
% 1.42/1.83    'c_COMBS'( 'c_COMBB'( 'c_HOL_Ominus__class_Ominus'( X ), Y, X, 'tc_fun'( 
% 1.42/1.83    X, X ), 'tc_nat' ), Z, 'tc_nat', X, X ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Ominus__class_Ominus'( X ), T ), U ), X ), ~( 'c_Series_Osums'( Z
% 1.42/1.83    , U, X ) ), ~( 'c_Series_Osums'( Y, T, X ) ) ],
% 1.42/1.83     [ =( 'c_Divides_Odiv__class_Omod'( X, hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.83    'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 
% 1.42/1.83    'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 
% 1.42/1.83    'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X, hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.83    'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' ), 'tc_nat' ) ) ],
% 1.42/1.83     [ ~( =( 'c_Divides_Odiv__class_Omod'( X, hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.83    'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 
% 1.42/1.83    'tc_nat' ) ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 
% 1.42/1.83    'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X, hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.83    'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' ), 'tc_nat' ) ],
% 1.42/1.83     [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 
% 1.42/1.83    'c_Divides_Odiv__class_Odiv'( X, hAPP( 'c_Int_Onumber__class_Onumber__of'( 
% 1.42/1.83    'tc_nat' ), 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' )
% 1.42/1.83    , 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( 
% 1.42/1.83    'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.42/1.83     [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), X ) ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), Y ) ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), X ) ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( Y, 'c_Int_OPls', 'tc_Int_Oint' ) ), 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( X, 'c_Int_OPls', 'tc_Int_Oint' ) ],
% 1.42/1.83     [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), X ) ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), Y ) ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), Y ) ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( X, 'c_Int_OPls', 'tc_Int_Oint' ) ) ],
% 1.42/1.83     [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'( 
% 1.42/1.83    'tc_nat' ) ), hAPP( 'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 
% 1.42/1.83    'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' ), 
% 1.42/1.83    'c_Divides_Odiv__class_Odiv'( X, hAPP( 'c_Int_Onumber__class_Onumber__of'( 
% 1.42/1.83    'tc_nat' ), 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' )
% 1.42/1.83     ), ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.42/1.83     [ =( hAPP( 'c_Finite__Set_Osetsum'( hAPP( 'c_Power_Opower__class_Opower'( 
% 1.42/1.83    'tc_Complex_Ocomplex' ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( 
% 1.42/1.83    'tc_Complex_Ocomplex' ), 'c_FFT__Mirabelle_Oroot'( X ) ), Y ) ), 'tc_nat'
% 1.42/1.83    , 'tc_Complex_Ocomplex' ), hAPP( 
% 1.42/1.83    'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'( 
% 1.42/1.83    'tc_nat' ), 'tc_nat' ), X ) ), 'c_HOL_Ozero__class_Ozero'( 
% 1.42/1.83    'tc_Complex_Ocomplex' ) ), ~( 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' )
% 1.42/1.83     ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.42/1.83    , Y, 'tc_nat' ) ) ],
% 1.42/1.83     [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), 'c_Series_Osums'( 
% 1.42/1.83    'c_COMBC'( 'c_COMBB'( 'c_HOL_Oinverse__class_Odivide'( X ), Y, X, 
% 1.42/1.83    'tc_fun'( X, X ), 'tc_nat' ), Z, 'tc_nat', X, X ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ), X ), ~( 'c_Series_Osums'( 
% 1.42/1.83    Y, T, X ) ) ],
% 1.42/1.83     [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), 'c_Series_Osums'( 
% 1.42/1.83    'c_COMBC'( 'c_COMBB'( 'c_HOL_Oinverse__class_Odivide'( X ), Y, X, 
% 1.42/1.83    'tc_fun'( X, X ), 'tc_nat' ), Z, 'tc_nat', X, X ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ), X ), ~( 'c_Series_Osums'( 
% 1.42/1.83    Y, T, X ) ) ],
% 1.42/1.83     [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), X ) ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), Y ) ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), X ) ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( Y, 'c_Int_OPls', 'tc_Int_Oint' ) ) ],
% 1.42/1.83     [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( 
% 1.42/1.83    'c_Fact_Ofact__class_Ofact'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 
% 1.42/1.83    'tc_nat' ), X ), Y ), 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) )
% 1.42/1.83     ],
% 1.42/1.83     [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 
% 1.42/1.83    hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ), 
% 1.42/1.83    hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), T ), Y ) ), U ), 'tc_nat' ), 
% 1.42/1.83    ~( 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.42/1.83    , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), T ), X ) ), Y ) ), U ), 
% 1.42/1.83    'tc_nat' ) ), ~( 'c_lessequals'( X, T, 'tc_nat' ) ) ],
% 1.42/1.83     [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.42/1.83    , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), Z ) ), T ) ), U ), 
% 1.42/1.83    'tc_nat' ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 
% 1.42/1.83    'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T
% 1.42/1.83     ) ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), T ) ), U ), 'tc_nat' ) ), 
% 1.42/1.83    ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 1.42/1.83     [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 
% 1.42/1.83    hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ), 
% 1.42/1.83    hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), T ), Y ) ), U ), 'tc_nat' ), 
% 1.42/1.83    ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 
% 1.42/1.83    hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), T ) ), Y ) ), Z ), U, 
% 1.42/1.83    'tc_nat' ) ), ~( 'c_lessequals'( T, X, 'tc_nat' ) ) ],
% 1.42/1.83     [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 
% 1.42/1.83    hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), Z ) ), T ), U, 
% 1.42/1.83    'tc_nat' ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 
% 1.42/1.83    'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z
% 1.42/1.83     ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ), U ), 'tc_nat' ) ), 
% 1.42/1.83    ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.42/1.83     [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), =( hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), X ) ), Z ) ), T ) ), hAPP( 
% 1.42/1.83    hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ), T ) ) ],
% 1.42/1.83     [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ) ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), T ), Y ) ), U ) ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), T ), X ) ), Y ) ), U ) ) ), ~( 
% 1.42/1.83    'c_lessequals'( X, T, 'tc_nat' ) ) ],
% 1.42/1.83     [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ) ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), T ), Y ) ), U ) ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), T ) ), Y ) ), Z ) ), U ) )
% 1.42/1.83    , ~( 'c_lessequals'( T, X, 'tc_nat' ) ) ],
% 1.42/1.83     [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), T ), Y ) ), U ) ) ), ~( 
% 1.42/1.83    'c_lessequals'( X, T, 'tc_nat' ) ), =( Z, hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), T ), X ) ), Y ) ), U ) ) ],
% 1.42/1.83     [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), T ), Y ) ), U ) ) ), ~( 
% 1.42/1.83    'c_lessequals'( T, X, 'tc_nat' ) ), =( hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), T ) ), Y ) ), Z ), U ) ]
% 1.42/1.83    ,
% 1.42/1.83     [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), =( hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ), T ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), X ) ), Z ) ), T ) ) ) ]
% 1.42/1.83    ,
% 1.42/1.83     [ =( 'c_Fact_Ofact__class_Ofact'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 
% 1.42/1.83    'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), 'tc_nat' ), hAPP( 
% 1.42/1.83    hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'( 
% 1.42/1.83    'tc_nat' ) ) ), 'c_Fact_Ofact__class_Ofact'( X, 'tc_nat' ) ) ) ],
% 1.42/1.83     [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_Finite__Set_Osetsum'( Y, 
% 1.42/1.83    'tc_nat', X ), hAPP( 'c_SetInterval_Oord__class_OatLeastLessThan'( Z, 
% 1.42/1.83    'tc_nat' ), T ) ) ), hAPP( 'c_Finite__Set_Osetsum'( Y, 'tc_nat', X ), 
% 1.42/1.83    hAPP( 'c_SetInterval_Oord__class_OatLeastLessThan'( T, 'tc_nat' ), U ) )
% 1.42/1.83     ), hAPP( 'c_Finite__Set_Osetsum'( Y, 'tc_nat', X ), hAPP( 
% 1.42/1.83    'c_SetInterval_Oord__class_OatLeastLessThan'( Z, 'tc_nat' ), U ) ) ), ~( 
% 1.42/1.83    'c_lessequals'( T, U, 'tc_nat' ) ), ~( 'c_lessequals'( Z, T, 'tc_nat' ) )
% 1.42/1.83     ],
% 1.42/1.83     [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Ominus__class_Ominus'( X ), hAPP( 'c_Finite__Set_Osetsum'( Y, 
% 1.42/1.83    'tc_nat', X ), hAPP( 'c_SetInterval_Oord__class_OatLeastLessThan'( Z, 
% 1.42/1.83    'tc_nat' ), T ) ) ), hAPP( 'c_Finite__Set_Osetsum'( Y, 'tc_nat', X ), 
% 1.42/1.83    hAPP( 'c_SetInterval_Oord__class_OatLeastLessThan'( Z, 'tc_nat' ), U ) )
% 1.42/1.83     ), hAPP( 'c_Finite__Set_Osetsum'( Y, 'tc_nat', X ), hAPP( 
% 1.42/1.83    'c_SetInterval_Oord__class_OatLeastLessThan'( U, 'tc_nat' ), T ) ) ), ~( 
% 1.42/1.83    'c_lessequals'( U, T, 'tc_nat' ) ), ~( 'c_lessequals'( Z, U, 'tc_nat' ) )
% 1.42/1.83     ],
% 1.42/1.83     [ 'c_Fun_Oinj__on'( 'c_COMBB'( 'c_Suc', hAPP( 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.83    'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ), 'tc_nat', 'tc_nat', 'tc_nat' ), X, 
% 1.42/1.83    'tc_nat', 'tc_nat' ) ],
% 1.42/1.83     [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( 
% 1.42/1.83    'c_Finite__Set_Osetsum'( Y, 'tc_nat', X ), hAPP( 
% 1.42/1.83    'c_SetInterval_Oord__class_OatLeastLessThan'( hAPP( 'c_Suc', Z ), 
% 1.42/1.83    'tc_nat' ), hAPP( 'c_Suc', T ) ) ), hAPP( 'c_Finite__Set_Osetsum'( 
% 1.42/1.83    'c_COMBB'( Y, 'c_Suc', 'tc_nat', X, 'tc_nat' ), 'tc_nat', X ), hAPP( 
% 1.42/1.83    'c_SetInterval_Oord__class_OatLeastLessThan'( Z, 'tc_nat' ), T ) ) ) ]
% 1.42/1.83    ,
% 1.42/1.83     [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP( 
% 1.42/1.83    'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ), 
% 1.42/1.83    'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), hAPP( 'c_Suc', hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.83    'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ), Z ) ) ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP( 'c_Power_Opower_Opower'( 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), 
% 1.42/1.83    hAPP( hAPP( 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ), 
% 1.42/1.83    'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), Z ) ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.83    'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ) ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.42/1.83     ), Y ), hAPP( 'c_Suc', hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.42/1.83    'tc_nat' ), hAPP( 'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 
% 1.42/1.83    'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ), Z ) ) ), 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'( 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'( 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 
% 1.42/1.83    'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.83    'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ), Z ) ) ), X ) ) ],
% 1.42/1.83     [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP( 
% 1.42/1.83    'c_Power_Opower__class_Opower'( X ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( X ), 'c_Int_OMin' ) ), hAPP( 'c_Suc'
% 1.42/1.83    , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.83    'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ), Y ) ) ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( X ), 'c_Int_OMin' ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =( hAPP( hAPP( 
% 1.42/1.83    'c_Power_Opower__class_Opower'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( 
% 1.42/1.83    X ), 'c_HOL_Oone__class_Oone'( X ) ) ), hAPP( 'c_Suc', hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.83    'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ), Y ) ) ), hAPP( 
% 1.42/1.83    'c_HOL_Ouminus__class_Ouminus'( X ), 'c_HOL_Oone__class_Oone'( X ) ) ) ]
% 1.42/1.83    ,
% 1.42/1.83     [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 
% 1.42/1.83    'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 
% 1.42/1.83    'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.83    'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' ), 'tc_nat' ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 
% 1.42/1.83    'tc_nat' ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.83    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.42/1.83    'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oinverse__class_Odivide'( X ), Z ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( X ), T ) ), X ), ~( 'c_lessequals'( Y
% 1.42/1.83    , 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Z, hAPP( 
% 1.42/1.83    hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( X ), T ) ), X ) ), ~( 'c_lessequals'( 
% 1.42/1.83    hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( X ), T ) ), Z, X ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.83    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.42/1.83    'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oinverse__class_Odivide'( X ), Y ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( X ), Z ) ), T, X ), ~( 'c_lessequals'( 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( X ), T ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( X ), Z ) ), Y, X ) ), ~( 
% 1.42/1.83    'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), 
% 1.42/1.83    hAPP( 'c_Int_Onumber__class_Onumber__of'( X ), Z ) ), X ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.83    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.42/1.83    'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( X ), Y ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~( 'c_lessequals'( 
% 1.42/1.83    hAPP( 'c_Int_Onumber__class_Onumber__of'( X ), Y ), 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Z, hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( X ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( X ), Y ) ), T ), X ) ), ~( 
% 1.42/1.83    'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( X ), Y ) ), T ), Z, X ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.83    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.42/1.83    'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( X ), Y ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.42/1.83     ), hAPP( 'c_Int_Onumber__class_Onumber__of'( X ), Y ) ), T ), X ) ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.42/1.83    , hAPP( 'c_Int_Onumber__class_Onumber__of'( X ), Y ) ), T ), Z, X ) ) ]
% 1.42/1.83    ,
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.83    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.42/1.83    'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( X ), Y ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.42/1.83     ), hAPP( 'c_Int_Onumber__class_Onumber__of'( X ), Y ) ), T ), X ) ), 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.83    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.42/1.83    'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( X ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( X ), Z ) ), T ), X ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( hAPP( 'c_Int_Onumber__class_Onumber__of'( X )
% 1.42/1.83    , Z ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ), X ) )
% 1.42/1.83     ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.83    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.42/1.83    'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( X ), Y ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( hAPP( 'c_Int_Onumber__class_Onumber__of'( X )
% 1.42/1.83    , Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.42/1.83     ), hAPP( 'c_Int_Onumber__class_Onumber__of'( X ), Y ) ), T ), X ) ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.42/1.83    , hAPP( 'c_Int_Onumber__class_Onumber__of'( X ), Y ) ), T ), Z, X ) ) ]
% 1.42/1.83    ,
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.83    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.42/1.83    'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( X ), Y ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( hAPP( 'c_Int_Onumber__class_Onumber__of'( X )
% 1.42/1.83    , Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( 
% 1.42/1.83    T, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.42/1.83    hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( X ), Y ) ), T ), Z, X ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.83    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.42/1.83    'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( X ), Y ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( hAPP( 'c_Int_Onumber__class_Onumber__of'( X )
% 1.42/1.83    , Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.42/1.83     ), hAPP( 'c_Int_Onumber__class_Onumber__of'( X ), Y ) ), T ), X ) ), 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.83    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.42/1.83    'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( X ), T ), X ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( X ), T ), X ) ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.42/1.83    , hAPP( 'c_Int_Onumber__class_Onumber__of'( X ), T ) ), Z ), Y, X ) ), 
% 1.42/1.83    ~( 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.42/1.83    X ), hAPP( 'c_Int_Onumber__class_Onumber__of'( X ), T ) ), Z ), X ) ) ]
% 1.42/1.83    ,
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.83    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.42/1.83    'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oinverse__class_Odivide'( X ), Z ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( X ), T ) ), X ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.42/1.83     ), Y ), hAPP( 'c_Int_Onumber__class_Onumber__of'( X ), T ) ), X ) ), 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( X ), T ), X ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.83    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.42/1.83    'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oinverse__class_Odivide'( X ), Y ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( X ), Z ) ), T, X ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.42/1.83    , T ), hAPP( 'c_Int_Onumber__class_Onumber__of'( X ), Z ) ), Y, X ) ), 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( X ), Z ), X ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.83    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.42/1.83    'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( X ), T ), X ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( X ), T ), X ) ), 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.42/1.83     ), hAPP( 'c_Int_Onumber__class_Onumber__of'( X ), T ) ), Z ), X ) ) ]
% 1.42/1.83    ,
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.83    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.42/1.83    'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( X ), T ), X ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( X ), T ), X ) ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.42/1.83    , hAPP( 'c_Int_Onumber__class_Onumber__of'( X ), T ) ), Z ), Y, X ) ), 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.83    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.42/1.83    'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oinverse__class_Odivide'( X ), Z ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( X ), T ) ), X ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( hAPP( 'c_Int_Onumber__class_Onumber__of'( X )
% 1.42/1.83    , T ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.42/1.83     ), Y ), hAPP( 'c_Int_Onumber__class_Onumber__of'( X ), T ) ), X ) ), 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( X ), T ), X ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.83    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.42/1.83    'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( X ), Z ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( X ), T ) ), X ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( hAPP( 'c_Int_Onumber__class_Onumber__of'( X )
% 1.42/1.83    , T ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), hAPP( 'c_Int_Onumber__class_Onumber__of'( 
% 1.42/1.83    X ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oinverse__class_Odivide'( X ), Y ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( X ), T ) ), X ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.83    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.42/1.83    'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oinverse__class_Odivide'( X ), Y ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( X ), Z ) ), T, X ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( hAPP( 'c_Int_Onumber__class_Onumber__of'( X )
% 1.42/1.83    , Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.42/1.83    , T ), hAPP( 'c_Int_Onumber__class_Onumber__of'( X ), Z ) ), Y, X ) ), 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( X ), Z ), X ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.83    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.42/1.83    'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( X ), Z ) ), T, X ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( hAPP( 'c_Int_Onumber__class_Onumber__of'( X )
% 1.42/1.83    , Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), hAPP( 'c_Int_Onumber__class_Onumber__of'( 
% 1.42/1.83    X ), Z ), X ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oinverse__class_Odivide'( X ), T ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( X ), Z ) ), Y, X ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.83    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.42/1.83    'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( X ), T ), X ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.42/1.83     ), hAPP( 'c_Int_Onumber__class_Onumber__of'( X ), T ) ), Z ), X ) ) ]
% 1.42/1.83    ,
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.83    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.42/1.83    'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( X ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( X ), Z ) ), T ), X ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.42/1.83     ), Y ), T ), hAPP( 'c_Int_Onumber__class_Onumber__of'( X ), Z ), X ) ) ]
% 1.42/1.83    ,
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.83    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.42/1.83    'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( X ), Y ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.42/1.83    , hAPP( 'c_Int_Onumber__class_Onumber__of'( X ), Y ) ), T ), Z, X ) ) ]
% 1.42/1.83    ,
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.83    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.42/1.83    'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( X ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( X ), Y ) ), Z ), T, X ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( hAPP( 'c_Int_Onumber__class_Onumber__of'( X )
% 1.42/1.83    , Y ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ), X ) )
% 1.42/1.83     ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.83    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.42/1.83    'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( X ), T ), X ), ~( 'c_lessequals'( 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), hAPP( 'c_Int_Onumber__class_Onumber__of'( 
% 1.42/1.83    X ), T ), X ) ), ~( 'c_lessequals'( hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( X ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( X ), T ) ), Z ), Y, X ) ), ~( 
% 1.42/1.83    'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( X ), T ) ), Z ), X ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.83    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.42/1.83    'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( X ), T ), X ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.42/1.83    , hAPP( 'c_Int_Onumber__class_Onumber__of'( X ), T ) ), Z ), Y, X ) ), 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.83    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.42/1.83    'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( X ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( X ), Y ) ), Z ), T, X ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.42/1.83     ), T ), Z ), hAPP( 'c_Int_Onumber__class_Onumber__of'( X ), Y ), X ) ) ]
% 1.42/1.83    ,
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.83    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.42/1.83    'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oinverse__class_Odivide'( X ), Z ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( X ), T ) ), X ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.42/1.83     ), Y ), hAPP( 'c_Int_Onumber__class_Onumber__of'( X ), T ) ), X ) ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.42/1.83    , Y ), hAPP( 'c_Int_Onumber__class_Onumber__of'( X ), T ) ), Z, X ) ) ]
% 1.42/1.83    ,
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.83    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.42/1.83    'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oinverse__class_Odivide'( X ), Y ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( X ), Z ) ), T, X ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.42/1.83    , T ), hAPP( 'c_Int_Onumber__class_Onumber__of'( X ), Z ) ), Y, X ) ), 
% 1.42/1.83    ~( 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.42/1.83    X ), T ), hAPP( 'c_Int_Onumber__class_Onumber__of'( X ), Z ) ), X ) ) ]
% 1.42/1.83    ,
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.83    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.42/1.83    'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( X ), T ), X ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.42/1.83    , hAPP( 'c_Int_Onumber__class_Onumber__of'( X ), T ) ), Z ), Y, X ) ), 
% 1.42/1.83    ~( 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.42/1.83    X ), hAPP( 'c_Int_Onumber__class_Onumber__of'( X ), T ) ), Z ), X ) ) ]
% 1.42/1.83    ,
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.83    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.42/1.83    'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oinverse__class_Odivide'( X ), Z ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( X ), T ) ), X ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( hAPP( 'c_Int_Onumber__class_Onumber__of'( X )
% 1.42/1.83    , T ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.42/1.83    hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( X ), T ) ), Z, X ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.83    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.42/1.83    'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oinverse__class_Odivide'( X ), Y ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( X ), Z ) ), T, X ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( hAPP( 'c_Int_Onumber__class_Onumber__of'( X )
% 1.42/1.83    , Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.42/1.83    Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( X ), Z ) ), X ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.83    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.42/1.83    'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oinverse__class_Odivide'( X ), Z ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( X ), T ) ), X ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( hAPP( 'c_Int_Onumber__class_Onumber__of'( X )
% 1.42/1.83    , T ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.42/1.83     ), Y ), hAPP( 'c_Int_Onumber__class_Onumber__of'( X ), T ) ), X ) ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.42/1.83    , Y ), hAPP( 'c_Int_Onumber__class_Onumber__of'( X ), T ) ), Z, X ) ) ]
% 1.42/1.83    ,
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.83    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.42/1.83    'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oinverse__class_Odivide'( X ), Y ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( X ), Z ) ), T, X ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( hAPP( 'c_Int_Onumber__class_Onumber__of'( X )
% 1.42/1.83    , Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.42/1.83    , T ), hAPP( 'c_Int_Onumber__class_Onumber__of'( X ), Z ) ), Y, X ) ), 
% 1.42/1.83    ~( 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.42/1.83    X ), T ), hAPP( 'c_Int_Onumber__class_Onumber__of'( X ), Z ) ), X ) ) ]
% 1.42/1.83    ,
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.83    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.42/1.83    'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oinverse__class_Odivide'( X ), Z ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( X ), T ) ), X ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( X ), T ), X ) ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.42/1.83    , Y ), hAPP( 'c_Int_Onumber__class_Onumber__of'( X ), T ) ), Z, X ) ) ]
% 1.42/1.83    ,
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.83    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.42/1.83    'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( X ), Z ) ), T, X ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( X ), Z ), X ) ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( 
% 1.42/1.83    X ), T ), hAPP( 'c_Int_Onumber__class_Onumber__of'( X ), Z ) ), X ) ) ]
% 1.42/1.83    ,
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.83    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.42/1.83    'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oinverse__class_Odivide'( X ), Y ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( X ), Z ) ), T, X ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( X ), Z ), X ) ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.42/1.83     ), T ), hAPP( 'c_Int_Onumber__class_Onumber__of'( X ), Z ) ), X ) ) ]
% 1.42/1.83    ,
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.83    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.42/1.83    'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( X ), Z ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( X ), T ) ), X ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( X ), T ), X ) ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.42/1.83     ), Y ), hAPP( 'c_Int_Onumber__class_Onumber__of'( X ), T ) ), Z, X ) ) ]
% 1.42/1.83    ,
% 1.42/1.83     [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), 'c_Deriv_Oderiv'( 
% 1.42/1.83    'c_COMBS'( 'c_COMBB'( 'c_HOL_Otimes__class_Otimes'( X ), Y, X, 'tc_fun'( 
% 1.42/1.83    X, X ), X ), Z, X, X, X ), T, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.42/1.83    , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), U ), hAPP( Z, T ) ) ), 
% 1.42/1.83    hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), W ), hAPP( Y, T ) ) ), X )
% 1.42/1.83    , ~( 'c_Deriv_Oderiv'( Z, T, W, X ) ), ~( 'c_Deriv_Oderiv'( Y, T, U, X )
% 1.42/1.83     ) ],
% 1.42/1.83     [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), 'c_Deriv_Oderiv'( 
% 1.42/1.83    'c_COMBS'( 'c_COMBB'( 'c_HOL_Otimes__class_Otimes'( X ), Y, X, 'tc_fun'( 
% 1.42/1.83    X, X ), X ), Z, X, X, X ), T, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.42/1.83    , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( Y, T ) ), U ) ), 
% 1.42/1.83    hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), W ), hAPP( Z, T ) ) ), X )
% 1.42/1.83    , ~( 'c_Deriv_Oderiv'( Z, T, U, X ) ), ~( 'c_Deriv_Oderiv'( Y, T, W, X )
% 1.42/1.83     ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.42/1.83    , Y ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( 
% 1.42/1.83    hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.42/1.83    ,
% 1.42/1.83     [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), 'c_Deriv_Oderiv'( 
% 1.42/1.83    'c_COMBS'( 'c_COMBB'( 'c_HOL_Oinverse__class_Odivide'( X ), Y, X, 
% 1.42/1.83    'tc_fun'( X, X ), X ), Z, X, X, X ), T, hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( X ), U ), hAPP( Z, T ) ) ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( X ), W ), hAPP( Y, T ) ) ) ), hAPP( hAPP( 
% 1.42/1.83    'c_Power_Opower__class_Opower'( X ), hAPP( Z, T ) ), hAPP( 'c_Suc', hAPP( 
% 1.42/1.83    'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ), X ), =( hAPP( Z
% 1.42/1.83    , T ), 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_Deriv_Oderiv'( Z, T, W, X
% 1.42/1.83     ) ), ~( 'c_Deriv_Oderiv'( Y, T, U, X ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), Y ), 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 
% 1.42/1.83    'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), 
% 1.42/1.83    hAPP( 'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), Y ) ), X ) ), 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =( hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), Y ), 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Oord__class_Oless'( 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 
% 1.42/1.83    'c_Power_Opower__class_Opower'( X ), Z ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), Y ) ), X ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =( hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), Y ), 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( 'c_lessequals'( hAPP( hAPP( 
% 1.42/1.83    'c_Power_Opower__class_Opower'( X ), Z ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), Y ) ), 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.42/1.83     [ =( hAPP( hAPP( X, Y ), Y ), hAPP( hAPP( Z, Y ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.83    'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ) ), ~( 
% 1.42/1.83    'c_Groebner__Basis_Ogb__semiring'( T, X, Z, U, W, V0 ) ) ],
% 1.42/1.83     [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), X ) ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), Y ) ), Z ) ), 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X
% 1.42/1.83    , 'c_Int_OPls', 'tc_Int_Oint' ) ) ],
% 1.42/1.83     [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), X ) ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), Y ) ), 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X
% 1.42/1.83    , 'c_Int_OPls', 'tc_Int_Oint' ) ) ],
% 1.42/1.83     [ =( hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP( 'c_Suc', X ) ) ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit1'( 
% 1.42/1.83    'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ), X ) ) ],
% 1.42/1.83     [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), ~( =( hAPP( Y, 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.42/1.83     ) ), =( hAPP( 'c_Finite__Set_Osetsum'( Y, 'tc_nat', X ), hAPP( 
% 1.42/1.83    'c_SetInterval_Oord__class_OatLeastLessThan'( hAPP( 'c_Suc', 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ), Z ) ), hAPP( 
% 1.42/1.83    'c_Finite__Set_Osetsum'( Y, 'tc_nat', X ), hAPP( 
% 1.42/1.83    'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'( 
% 1.42/1.83    'tc_nat' ), 'tc_nat' ), Z ) ) ) ],
% 1.42/1.83     [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 
% 1.42/1.83    'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), X ) ), 
% 1.42/1.83    'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X, 
% 1.42/1.83    'c_Int_OPls', 'tc_Int_Oint' ) ) ],
% 1.42/1.83     [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), X ) ), 
% 1.42/1.83    'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( 
% 1.42/1.83    'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Int_OPls', 
% 1.42/1.83    'tc_Int_Oint' ) ) ],
% 1.42/1.83     [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), hAPP( 
% 1.42/1.83    'c_Suc', hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'( 
% 1.42/1.83    'tc_nat' ) ) ), Y ) ) ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ]
% 1.42/1.83    ,
% 1.42/1.83     [ =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( 'tc_nat' ), X ), Y ), 
% 1.42/1.83    hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), hAPP( hAPP( 
% 1.42/1.83    'c_Power_Opower__class_Opower'( 'tc_nat' ), X ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), 'c_HOL_Oone__class_Oone'( 
% 1.42/1.83    'tc_nat' ) ) ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.42/1.83     [ =( 'c_Fact_Ofact__class_Ofact'( X, 'tc_nat' ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), 
% 1.42/1.83    'c_Fact_Ofact__class_Ofact'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 
% 1.42/1.83    'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), 'tc_nat' ) ) ), 
% 1.42/1.83    =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.42/1.83     [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( 
% 1.42/1.83    'c_Finite__Set_Osetsum'( 'c_COMBS'( 'c_COMBB'( 
% 1.42/1.83    'c_HOL_Ominus__class_Ominus'( X ), Y, X, 'tc_fun'( X, X ), 'tc_nat' ), 
% 1.42/1.83    'c_COMBB'( Y, 'c_COMBC'( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 
% 1.42/1.83    'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat', 'tc_nat', 'tc_nat' ), 
% 1.42/1.83    'tc_nat', X, 'tc_nat' ), 'tc_nat', X, X ), 'tc_nat', X ), 
% 1.42/1.83    'c_SetInterval_Oord__class_OatLeastAtMost'( Z, T, 'tc_nat' ) ), hAPP( 
% 1.42/1.83    hAPP( 'c_HOL_Ominus__class_Ominus'( X ), hAPP( Y, Z ) ), hAPP( Y, hAPP( 
% 1.42/1.83    hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), T ), 
% 1.42/1.83    'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ) ) ), ~( 'c_lessequals'( Z, T, 
% 1.42/1.83    'tc_nat' ) ) ],
% 1.42/1.83     [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( 
% 1.42/1.83    'c_Finite__Set_Osetsum'( Y, 'tc_nat', X ), 
% 1.42/1.83    'c_SetInterval_Oord__class_OatLeastAtMost'( hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), U ), T ), 'tc_nat' ) ), hAPP( 
% 1.42/1.83    'c_Finite__Set_Osetsum'( 'c_COMBB'( Y, 'c_COMBC'( 
% 1.42/1.83    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), T, 'tc_nat', 'tc_nat', 'tc_nat' )
% 1.42/1.83    , 'tc_nat', X, 'tc_nat' ), 'tc_nat', X ), 
% 1.42/1.83    'c_SetInterval_Oord__class_OatLeastAtMost'( Z, U, 'tc_nat' ) ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP( 
% 1.42/1.83    'c_Power_Opower__class_Opower'( X ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), T ) ), hAPP( hAPP( 
% 1.42/1.83    'c_Power_Opower__class_Opower'( X ), Y ), T ) ) ), Z ) ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( X ), hAPP( 
% 1.42/1.83    'c_Nat_Osemiring__1__class_Oof__nat'( X ), T ) ), hAPP( hAPP( 
% 1.42/1.83    'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), T ), hAPP( 'c_Suc', 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ) ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( X ), Z ), hAPP( 'c_Finite__Set_Osetsum'( 
% 1.42/1.83    'c_COMBB'( 'c_Finite__Set_Osetsum'( 'c_COMBS'( 'c_COMBB'( 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_Power_Opower__class_Opower'( 
% 1.42/1.83    X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), X, 'tc_fun'( 
% 1.42/1.83    X, X ), 'tc_nat' ), 'c_COMBB'( hAPP( 'c_Power_Opower__class_Opower'( X )
% 1.42/1.83    , Y ), hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), T ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.83    'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ) ), 'tc_nat', X, 'tc_nat' ), 'tc_nat'
% 1.42/1.83    , X, X ), 'tc_nat', X ), 'c_COMBB'( 
% 1.42/1.83    'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'( 
% 1.42/1.83    'tc_nat' ), 'tc_nat' ), hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), 
% 1.42/1.83    hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), T ), hAPP( 'c_Suc'
% 1.42/1.83    , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), 'tc_nat', 'tc_fun'( 
% 1.42/1.83    'tc_nat', 'tc_bool' ), 'tc_nat' ), 'tc_fun'( 'tc_nat', 'tc_bool' ), X, 
% 1.42/1.83    'tc_nat' ), 'tc_nat', X ), hAPP( 
% 1.42/1.83    'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'( 
% 1.42/1.83    'tc_nat' ), 'tc_nat' ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 
% 1.42/1.83    'tc_nat' ), T ), hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 1.42/1.83     ) ) ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.83     [ =( hAPP( 'c_Finite__Set_Osetsum'( hAPP( 'c_Power_Opower__class_Opower'( 
% 1.42/1.83    'tc_Complex_Ocomplex' ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( 
% 1.42/1.83    'tc_Complex_Ocomplex' ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( 
% 1.42/1.83    'tc_Complex_Ocomplex' ), 'c_HOL_Oone__class_Oone'( 'tc_Complex_Ocomplex'
% 1.42/1.83     ) ), 'c_FFT__Mirabelle_Oroot'( X ) ) ), Y ) ), 'tc_nat', 
% 1.42/1.83    'tc_Complex_Ocomplex' ), hAPP( 
% 1.42/1.83    'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'( 
% 1.42/1.83    'tc_nat' ), 'tc_nat' ), X ) ), 'c_HOL_Ozero__class_Ozero'( 
% 1.42/1.83    'tc_Complex_Ocomplex' ) ), ~( 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' )
% 1.42/1.83     ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.42/1.83    , Y, 'tc_nat' ) ) ],
% 1.42/1.83     [ =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( 'tc_Complex_Ocomplex' )
% 1.42/1.83    , 'c_FFT__Mirabelle_Oroot'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.42/1.83    'tc_nat' ), X ), Y ) ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.42/1.83    'tc_nat' ), X ), Z ) ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( 
% 1.42/1.83    'tc_Complex_Ocomplex' ), 'c_FFT__Mirabelle_Oroot'( Y ) ), Z ) ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 
% 1.42/1.83    'tc_nat' ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 
% 1.42/1.83    X ), 'c_HOL_Oone__class_Oone'( X ) ), 'c_HOL_Oone__class_Oone'( X ) ) ), 
% 1.42/1.83    hAPP( 'c_Finite__Set_Osetsum'( 'c_COMBB'( hAPP( 
% 1.42/1.83    'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_COMBC'( 'c_COMBB'( 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( X ), 'c_Nat_Osemiring__1__class_Oof__nat'( 
% 1.42/1.83    X ), X, 'tc_fun'( X, X ), 'tc_nat' ), Z, 'tc_nat', X, X ), X, X, 'tc_nat'
% 1.42/1.83     ), 'tc_nat', X ), 'c_SetInterval_Oord__class_OlessThan'( T, 'tc_nat' ) )
% 1.42/1.83     ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 
% 1.42/1.83    'c_Nat_Osemiring__1__class_Oof__nat'( X ), T ) ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( X ), hAPP( 
% 1.42/1.83    'c_Nat_Osemiring__1__class_Oof__nat'( X ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), T ), 'c_HOL_Oone__class_Oone'( 
% 1.42/1.83    'tc_nat' ) ) ) ), Z ) ) ) ) ) ],
% 1.42/1.83     [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( 
% 1.42/1.83    'c_Finite__Set_Osetsum'( 'c_COMBS'( 'c_COMBB'( 
% 1.42/1.83    'c_HOL_Ominus__class_Ominus'( X ), Y, X, 'tc_fun'( X, X ), 'tc_nat' ), 
% 1.42/1.83    'c_COMBB'( Y, 'c_COMBC'( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 
% 1.42/1.83    'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat', 'tc_nat', 'tc_nat' ), 
% 1.42/1.83    'tc_nat', X, 'tc_nat' ), 'tc_nat', X, X ), 'tc_nat', X ), 
% 1.42/1.83    'c_SetInterval_Oord__class_OatLeastAtMost'( Z, T, 'tc_nat' ) ), 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ) ), 'c_lessequals'( Z, T, 'tc_nat' ) ]
% 1.42/1.83    ,
% 1.42/1.83     [ ~( 'class_Int_Onumber__ring'( X ) ), 'c_Int_Onumber__ring__axioms'( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( X ), 'c_HOL_Oone__class_Oone'( X ), 
% 1.42/1.83    'c_HOL_Ominus__class_Ominus'( X ), 'c_HOL_Ozero__class_Ozero'( X ), 
% 1.42/1.83    'c_HOL_Oplus__class_Oplus'( X ), X ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), 
% 1.42/1.83    'c_Groebner__Basis_Ogb__semiring'( 'c_HOL_Oplus__class_Oplus'( X ), 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( X ), 'c_Power_Opower__class_Opower'( X ), 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ), X ) ]
% 1.42/1.83    ,
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'( 
% 1.42/1.83    X ) ), 'c_Groebner__Basis_Osemiringb'( 'c_HOL_Oplus__class_Oplus'( X ), 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( X ), 'c_Power_Opower__class_Opower'( X ), 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ), X ) ]
% 1.42/1.83    ,
% 1.42/1.83     [ =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( 'tc_Complex_Ocomplex' )
% 1.42/1.83    , 'c_FFT__Mirabelle_Oroot'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.42/1.83    'tc_nat' ), hAPP( 'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 
% 1.42/1.83    'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ), X ) ) ), X ), hAPP( 
% 1.42/1.83    'c_HOL_Ouminus__class_Ouminus'( 'tc_Complex_Ocomplex' ), 
% 1.42/1.83    'c_HOL_Oone__class_Oone'( 'tc_Complex_Ocomplex' ) ) ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 
% 1.42/1.83    'tc_nat' ) ) ],
% 1.42/1.83     [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( X ), Y ) ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( X ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), 'c_Int_OBit1'( 'c_Int_OPls'
% 1.42/1.83     ) ), Y ) ) ) ],
% 1.42/1.83     [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_Int_Onumber__class_Onumber__of'( 
% 1.42/1.83    X ), Y ) ), 'c_HOL_Oone__class_Oone'( X ) ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( X ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), Y ), 'c_Int_OBit1'( 
% 1.42/1.83    'c_Int_OPls' ) ) ) ) ],
% 1.42/1.83     [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP( 
% 1.42/1.83    'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ), 
% 1.42/1.83    'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit1'( 
% 1.42/1.83    'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 
% 1.42/1.83    X ), Y ), Y ) ), Y ) ) ],
% 1.42/1.83     [ =( hAPP( 'c_Suc', hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.42/1.83     ) ) ), hAPP( 'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 
% 1.42/1.83    'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ) ],
% 1.42/1.83     [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 
% 1.42/1.83    hAPP( 'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.83    'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' ) ],
% 1.42/1.83     [ =( hAPP( 'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.83    'c_Int_OBit1'( 'c_Int_OPls' ) ) ), hAPP( 'c_Suc', hAPP( 'c_Suc', 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP( 
% 1.42/1.83    'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( 
% 1.42/1.83    X ), Y ), hAPP( 'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 
% 1.42/1.83    'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ) ), hAPP( hAPP( 
% 1.42/1.83    'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.83    'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =( hAPP( hAPP( 
% 1.42/1.83    'c_Power_Opower__class_Opower'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( 
% 1.42/1.83    X ), Y ) ), hAPP( 'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 
% 1.42/1.83    'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ), hAPP( hAPP( 
% 1.42/1.83    'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.83    'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP( hAPP( 
% 1.42/1.83    'c_Power_Opower__class_Opower'( X ), hAPP( 'c_HOL_Oabs__class_Oabs'( X )
% 1.42/1.83    , Y ) ), hAPP( 'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 
% 1.42/1.83    'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ), hAPP( hAPP( 
% 1.42/1.83    'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.83    'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ) ) ],
% 1.42/1.83     [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.83    'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ), hAPP( 'c_Suc', hAPP( 'c_Suc', X ) )
% 1.42/1.83     ) ],
% 1.42/1.83     [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.83    'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ), X ), hAPP( 'c_Suc', hAPP( 'c_Suc', X
% 1.42/1.83     ) ) ) ],
% 1.42/1.83     [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), X ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.83    'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' ), X ) ],
% 1.42/1.83     [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.83    'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ), X ), 'tc_nat' ) ],
% 1.42/1.83     [ 'c_Fun_Oinj__on'( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.83    'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ), X, 'tc_nat', 'tc_nat' ) ],
% 1.42/1.83     [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.42/1.83    'tc_nat' ), hAPP( 'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 
% 1.42/1.83    'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ), Z ) ), hAPP( hAPP( T
% 1.42/1.83    , hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, Y ), Z ) ) ), ~( 
% 1.42/1.83    'c_Groebner__Basis_Ogb__semiring'( U, T, X, W, V0, V1 ) ) ],
% 1.42/1.83     [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), X ) ), 
% 1.42/1.83    'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( 
% 1.42/1.83    'tc_nat' ) ), ~( 'c_lessequals'( X, 'c_Int_OPls', 'tc_Int_Oint' ) ) ]
% 1.42/1.83    ,
% 1.42/1.83     [ =( 'c_Fact_Ofact__class_Ofact'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 
% 1.42/1.83    'tc_nat' ), X ), Y ), 'tc_nat' ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), 
% 1.42/1.83    'c_Fact_Ofact__class_Ofact'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 
% 1.42/1.83    'tc_nat' ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), 
% 1.42/1.83    'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), Y ), 'tc_nat' ) ) ), =( X, 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.42/1.83     [ =( 'c_Fact_Ofact__class_Ofact'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 
% 1.42/1.83    'tc_nat' ), X ), Y ), 'tc_nat' ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), 
% 1.42/1.83    'c_Fact_Ofact__class_Ofact'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 
% 1.42/1.83    'tc_nat' ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y )
% 1.42/1.83     ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), 'tc_nat' ) ) ), =( hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.42/1.83     [ =( 'c_FFT__Mirabelle_Oroot'( hAPP( 'c_Int_Onumber__class_Onumber__of'( 
% 1.42/1.83    'tc_nat' ), 'c_Int_OBit0'( 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) )
% 1.42/1.83     ) ) ), 'c_Complex_Oii' ) ],
% 1.42/1.83     [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), 'c_Deriv_Oderiv'( 
% 1.42/1.83    'c_COMBS'( 'c_COMBB'( 'c_HOL_Oinverse__class_Odivide'( X ), Y, X, 
% 1.42/1.83    'tc_fun'( X, X ), X ), Z, X, X, X ), T, hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( X ), U ), hAPP( Z, T ) ) ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( X ), hAPP( Y, T ) ), W ) ) ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( X ), hAPP( Z, T ) ), hAPP( Z, T ) ) ), X )
% 1.42/1.83    , =( hAPP( Z, T ), 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_Deriv_Oderiv'( 
% 1.42/1.83    Z, T, W, X ) ), ~( 'c_Deriv_Oderiv'( Y, T, U, X ) ) ],
% 1.42/1.83     [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP( 
% 1.42/1.83    'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ), 
% 1.42/1.83    'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.83    'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.83    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.42/1.83    'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'( 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oinverse__class_Odivide'( X ), Y ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( X ), 'c_Int_OBit0'( 'c_Int_OBit1'( 
% 1.42/1.83    'c_Int_OPls' ) ) ) ), X ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.83    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.42/1.83    'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'( 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oinverse__class_Odivide'( X ), Y ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( X ), 'c_Int_OBit0'( 'c_Int_OBit1'( 
% 1.42/1.83    'c_Int_OPls' ) ) ) ), X ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.42/1.83     [ ~( 'class_RealVector_Oreal__normed__algebra__1'( X ) ), =( 
% 1.42/1.83    'c_Series_Osuminf'( 'c_COMBS'( 'c_COMBB'( 'c_HOL_Otimes__class_Otimes'( X
% 1.42/1.83     ), Y, X, 'tc_fun'( X, X ), 'tc_nat' ), hAPP( 
% 1.42/1.83    'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), 
% 1.42/1.83    'tc_nat', X, X ), X ), hAPP( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 1.42/1.83     ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 
% 1.42/1.83    'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.83    'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ), X ), =( Y, 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =( hAPP( hAPP( 
% 1.42/1.83    'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.83    'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ), hAPP( hAPP( 
% 1.42/1.83    'c_Power_Opower__class_Opower'( X ), Z ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.83    'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ) ) ), =( Y, Z ), ~( 'c_lessequals'( 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'( 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 
% 1.42/1.83    'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.83    'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ), X ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'( 
% 1.42/1.83    Y, Z, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), 
% 1.42/1.83    ~( 'c_lessequals'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), 
% 1.42/1.83    hAPP( 'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.83    'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ), hAPP( hAPP( 
% 1.42/1.83    'c_Power_Opower__class_Opower'( X ), Z ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.83    'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ), X ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 
% 1.42/1.83    'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), 
% 1.42/1.83    hAPP( 'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.83    'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ), X ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.42/1.83     ), Y ), hAPP( 'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 
% 1.42/1.83    'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ), 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.42/1.83     [ =( 'c_FFT__Mirabelle_ODFT'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.42/1.83    'tc_nat' ), hAPP( 'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 
% 1.42/1.83    'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ), X ), Y, Z ), hAPP( 
% 1.42/1.83    hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_Complex_Ocomplex' ), 
% 1.42/1.83    'c_FFT__Mirabelle_ODFT'( X, 'c_COMBB'( Y, hAPP( 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.83    'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ), 'tc_nat', 'tc_Complex_Ocomplex', 
% 1.42/1.83    'tc_nat' ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z ), X
% 1.42/1.83     ) ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_Complex_Ocomplex' )
% 1.42/1.83    , hAPP( hAPP( 'c_Power_Opower__class_Opower'( 'tc_Complex_Ocomplex' ), 
% 1.42/1.83    'c_FFT__Mirabelle_Oroot'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.42/1.83    'tc_nat' ), hAPP( 'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 
% 1.42/1.83    'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ), X ) ) ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z ), X ) ) ), 
% 1.42/1.83    'c_FFT__Mirabelle_ODFT'( X, 'c_COMBB'( Y, 'c_COMBC'( 'c_COMBB'( 
% 1.42/1.83    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.83    'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ), 'tc_nat', 'tc_fun'( 'tc_nat', 
% 1.42/1.83    'tc_nat' ), 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat', 
% 1.42/1.83    'tc_nat', 'tc_nat' ), 'tc_nat', 'tc_Complex_Ocomplex', 'tc_nat' ), hAPP( 
% 1.42/1.83    hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z ), X ) ) ) ) ), ~( 
% 1.42/1.83    'c_lessequals'( X, Z, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =( hAPP( hAPP( 
% 1.42/1.83    'c_Power_Opower__class_Opower'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( 
% 1.42/1.83    X ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.83    'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ), Z ) ), hAPP( hAPP( 
% 1.42/1.83    'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.83    'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ), Z ) ) ) ],
% 1.42/1.83     [ =( 'c_Divides_Odiv__class_Omod'( X, hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.83    'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ), 'tc_nat' ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit1'( 
% 1.42/1.83    'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ), =( 'c_Divides_Odiv__class_Omod'( X, 
% 1.42/1.83    hAPP( 'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.83    'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ), 'tc_nat' ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.83    'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ), =( 'c_Divides_Odiv__class_Omod'( X, 
% 1.42/1.83    hAPP( 'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.83    'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ), 'tc_nat' ), 
% 1.42/1.83    'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), =( 'c_Divides_Odiv__class_Omod'( 
% 1.42/1.83    X, hAPP( 'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.83    'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ), 'tc_nat' ), 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~( 
% 1.42/1.83    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.42/1.83    'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'( 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Oone__class_Oone'( X ) ), 
% 1.42/1.83    hAPP( 'c_Int_Onumber__class_Onumber__of'( X ), 'c_Int_OBit0'( 
% 1.42/1.83    'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ), X ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 
% 1.42/1.83    hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.83    'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ) ), hAPP( hAPP( 
% 1.42/1.83    'c_Power_Opower__class_Opower'( X ), Z ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.83    'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ) ), 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.42/1.83     ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'( 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 
% 1.42/1.83    X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.83    'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ) ), hAPP( hAPP( 
% 1.42/1.83    'c_Power_Opower__class_Opower'( X ), Z ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.83    'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ) ), X ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 
% 1.42/1.83    'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.83    'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ) ), hAPP( hAPP( 
% 1.42/1.83    'c_Power_Opower__class_Opower'( X ), Z ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.83    'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ) ), X ), =( Y, 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 
% 1.42/1.83    'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.83    'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ) ), hAPP( hAPP( 
% 1.42/1.83    'c_Power_Opower__class_Opower'( X ), Z ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.83    'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ) ), X ), =( Z, 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( 
% 1.42/1.83    'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 
% 1.42/1.83    'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), 
% 1.42/1.83    hAPP( 'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.83    'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ) ), hAPP( hAPP( 
% 1.42/1.83    'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), 
% 1.42/1.83    hAPP( 'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.83    'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ) ), X ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'( 
% 1.42/1.83    hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 
% 1.42/1.83    'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), 
% 1.42/1.83    hAPP( 'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.83    'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ) ), hAPP( hAPP( 
% 1.42/1.83    'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), 
% 1.42/1.83    hAPP( 'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.83    'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ) ), 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.42/1.83     ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y, 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'( hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 
% 1.42/1.83    'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.83    'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ) ), hAPP( hAPP( 
% 1.42/1.83    'c_Power_Opower__class_Opower'( X ), Z ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.83    'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ) ), 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.42/1.83     ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y, 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'( hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 
% 1.42/1.83    'c_Power_Opower__class_Opower'( X ), Z ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.83    'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ) ), hAPP( hAPP( 
% 1.42/1.83    'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.83    'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ) ), 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.42/1.83     ) ) ],
% 1.42/1.83     [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP( 
% 1.42/1.83    'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ), 
% 1.42/1.83    'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.83    'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ), Z ) ), hAPP( hAPP( 
% 1.42/1.83    'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ), 
% 1.42/1.83    'c_HOL_Oplus__class_Oplus'( X ), X ), hAPP( hAPP( 'c_Power_Opower_Opower'( 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.42/1.83     ), Z ) ), hAPP( 'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 
% 1.42/1.83    'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y, 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'( hAPP( hAPP( 
% 1.42/1.83    'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.83    'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ), Z ) ), 'c_HOL_Ozero__class_Ozero'( X
% 1.42/1.83     ), X ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'( 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 
% 1.42/1.83    'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.83    'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ), Z ) ), X ) ],
% 1.42/1.83     [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP( 
% 1.42/1.83    'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.83    'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ), Z ) ) ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP( 
% 1.42/1.83    'c_Power_Opower__class_Opower'( X ), hAPP( hAPP( 
% 1.42/1.83    'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.83    'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ) ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP( 
% 1.42/1.83    'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.83    'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ), Z ) ) ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 
% 1.42/1.83    'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP( 
% 1.42/1.83    'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =( hAPP( hAPP( 
% 1.42/1.83    'c_Power_Opower__class_Opower'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( 
% 1.42/1.83    X ), 'c_HOL_Oone__class_Oone'( X ) ) ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.83    'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ), Y ) ), 'c_HOL_Oone__class_Oone'( X )
% 1.42/1.83     ) ],
% 1.42/1.83     [ =( hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.83    'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ) ), X ) ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.83    'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ) ) ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.83    'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ) ), X ) ), =( X, 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.42/1.83     [ =( hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.83    'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ), X ) ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.83    'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ) ) ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.83    'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ), X ) ), =( X, 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Oring__1'( X ) ), =( hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Ominus__class_Ominus'( X ), hAPP( 'c_Finite__Set_Osetsum'( Y, 
% 1.42/1.83    'tc_nat', X ), hAPP( 'c_SetInterval_Oord__class_OatLeastLessThan'( 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), Z ) ) ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( X ), hAPP( 
% 1.42/1.83    'c_Nat_Osemiring__1__class_Oof__nat'( X ), Z ) ), T ) ), hAPP( 
% 1.42/1.83    'c_Finite__Set_Osetsum'( 'c_COMBC'( 'c_COMBB'( 
% 1.42/1.83    'c_HOL_Ominus__class_Ominus'( X ), Y, X, 'tc_fun'( X, X ), 'tc_nat' ), T
% 1.42/1.83    , 'tc_nat', X, X ), 'tc_nat', X ), hAPP( 
% 1.42/1.83    'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'( 
% 1.42/1.83    'tc_nat' ), 'tc_nat' ), Z ) ) ) ],
% 1.42/1.83     [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), 'c_Series_Osums'( 
% 1.42/1.83    'c_COMBB'( Y, 'c_COMBC'( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z, 
% 1.42/1.83    'tc_nat', 'tc_nat', 'tc_nat' ), 'tc_nat', X, 'tc_nat' ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Ominus__class_Ominus'( X ), T ), hAPP( 'c_Finite__Set_Osetsum'( Y
% 1.42/1.83    , 'tc_nat', X ), hAPP( 'c_SetInterval_Oord__class_OatLeastLessThan'( 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), Z ) ) ), X ), ~( 
% 1.42/1.83    'c_Series_Osums'( Y, T, X ) ) ],
% 1.42/1.83     [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP( 
% 1.42/1.83    'c_Power_Opower__class_Opower'( X ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( X ), 'c_Int_OMin' ) ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.83    'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ), Y ) ), 'c_HOL_Oone__class_Oone'( X )
% 1.42/1.83     ) ],
% 1.42/1.83     [ =( hAPP( 'c_Suc', hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' )
% 1.42/1.83    , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 
% 1.42/1.83    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.83    'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ), X ) ), 'c_HOL_Oone__class_Oone'( 
% 1.42/1.83    'tc_nat' ) ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 
% 1.42/1.83    hAPP( 'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.83    'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ), X ) ), =( X, 
% 1.42/1.83    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ), ~( 
% 1.42/1.83    'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( 
% 1.42/1.83    'c_Finite__Set_Osetsum'( 'c_COMBS'( 'c_COMBB'( 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_Power_Opower__class_Opower'( 
% 1.42/1.83    X ), Y ), X, 'tc_fun'( X, X ), 'tc_nat' ), 'c_COMBB'( hAPP( 
% 1.42/1.83    'c_Power_Opower__class_Opower'( X ), Z ), hAPP( 
% 1.42/1.83    'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( 'c_Suc', T ) ), 'tc_nat'
% 1.42/1.83    , X, 'tc_nat' ), 'tc_nat', X, X ), 'tc_nat', X ), hAPP( 
% 1.42/1.83    'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'( 
% 1.42/1.83    'tc_nat' ), 'tc_nat' ), hAPP( 'c_Suc', T ) ) ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( X ), Z ), hAPP( 'c_Finite__Set_Osetsum'( 
% 1.42/1.83    'c_COMBS'( 'c_COMBB'( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 
% 1.42/1.83    'c_Power_Opower__class_Opower'( X ), Y ), X, 'tc_fun'( X, X ), 'tc_nat' )
% 1.42/1.83    , 'c_COMBB'( hAPP( 'c_Power_Opower__class_Opower'( X ), Z ), hAPP( 
% 1.42/1.83    'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), T ), 'tc_nat', X, 'tc_nat' ), 
% 1.42/1.83    'tc_nat', X, X ), 'tc_nat', X ), hAPP( 
% 1.42/1.83    'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'( 
% 1.42/1.83    'tc_nat' ), 'tc_nat' ), hAPP( 'c_Suc', T ) ) ) ) ) ],
% 1.42/1.83     [ ~( 'class_Power_Opower'( X ) ), ~( 
% 1.42/1.83    'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( 
% 1.42/1.83    'c_Finite__Set_Osetsum'( 'c_COMBS'( 'c_COMBB'( 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_Power_Opower__class_Opower'( 
% 1.42/1.83    X ), Y ), X, 'tc_fun'( X, X ), 'tc_nat' ), 'c_COMBB'( hAPP( 
% 1.42/1.83    'c_Power_Opower__class_Opower'( X ), Z ), hAPP( 
% 1.42/1.83    'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), T ), 'tc_nat', X, 'tc_nat' ), 
% 1.42/1.83    'tc_nat', X, X ), 'tc_nat', X ), hAPP( 
% 1.42/1.83    'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'( 
% 1.42/1.83    'tc_nat' ), 'tc_nat' ), hAPP( 'c_Suc', T ) ) ), hAPP( 
% 1.42/1.83    'c_Finite__Set_Osetsum'( 'c_COMBS'( 'c_COMBB'( 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( X ), 'c_COMBB'( hAPP( 
% 1.42/1.83    'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 
% 1.42/1.83    'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), T ), 'tc_nat', X, 'tc_nat' ), X
% 1.42/1.83    , 'tc_fun'( X, X ), 'tc_nat' ), hAPP( 'c_Power_Opower__class_Opower'( X )
% 1.42/1.83    , Z ), 'tc_nat', X, X ), 'tc_nat', X ), hAPP( 
% 1.42/1.83    'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'( 
% 1.42/1.83    'tc_nat' ), 'tc_nat' ), hAPP( 'c_Suc', T ) ) ) ) ],
% 1.42/1.83     [ ~( 'class_Ring__and__Field_Ocomm__ring'( X ) ), ~( 
% 1.42/1.83    'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP( 
% 1.42/1.83    'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ) ), hAPP( 
% 1.42/1.83    hAPP( 'c_Power_Opower__class_Opower'( X ), T ), hAPP( 'c_Suc', Z ) ) ), 
% 1.42/1.83    hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 
% 1.42/1.83    'c_HOL_Ominus__class_Ominus'( X ), Y ), T ) ), hAPP( 
% 1.42/1.83    'c_Finite__Set_Osetsum'( 'c_COMBS'( 'c_COMBB'( 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_Power_Opower__class_Opower'( 
% 1.42/1.83    X ), Y ), X, 'tc_fun'( X, X ), 'tc_nat' ), 'c_COMBB'( hAPP( 
% 1.42/1.83    'c_Power_Opower__class_Opower'( X ), T ), hAPP( 
% 1.42/1.83    'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z ), 'tc_nat', X, 'tc_nat' ), 
% 1.42/1.83    'tc_nat', X, X ), 'tc_nat', X ), hAPP( 
% 1.42/1.83    'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'( 
% 1.42/1.83    'tc_nat' ), 'tc_nat' ), hAPP( 'c_Suc', Z ) ) ) ) ) ],
% 1.42/1.83     [ =( 'c_FFT__Mirabelle_ODFT'( X, Y, 'v_i' ), hAPP( 
% 1.42/1.83    'c_Finite__Set_Osetsum'( 'c_COMBS'( 'c_COMBB'( 
% 1.42/1.83    'c_HOL_Otimes__class_Otimes'( 'tc_Complex_Ocomplex' ), 'c_COMBB'( hAPP( 
% 1.42/1.83    'c_Power_Opower__class_Opower'( 'tc_Complex_Ocomplex' ), 
% 1.42/1.83    'c_FFT__Mirabelle_Oroot'( X ) ), hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.42/1.83    'tc_nat' ), 'v_i' ), 'tc_nat', 'tc_Complex_Ocomplex', 'tc_nat' ), 
% 1.42/1.83    'tc_Complex_Ocomplex', 'tc_fun'( 'tc_Complex_Ocomplex', 
% 1.42/1.83    'tc_Complex_Ocomplex' ), 'tc_nat' ), Y, 'tc_nat', 'tc_Complex_Ocomplex', 
% 1.42/1.83    'tc_Complex_Ocomplex' ), 'tc_nat', 'tc_Complex_Ocomplex' ), hAPP( 
% 1.42/1.83    'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'( 
% 1.42/1.83    'tc_nat' ), 'tc_nat' ), X ) ) ) ],
% 1.42/1.83     [ =( 'c_FFT__Mirabelle_OIDFT'( X, Y, 'v_i' ), hAPP( 
% 1.42/1.83    'c_Finite__Set_Osetsum'( 'c_COMBS'( 'c_COMBB'( 
% 1.42/1.83    'c_HOL_Oinverse__class_Odivide'( 'tc_Complex_Ocomplex' ), Y, 
% 1.42/1.83    'tc_Complex_Ocomplex', 'tc_fun'( 'tc_Complex_Ocomplex', 
% 1.42/1.83    'tc_Complex_Ocomplex' ), 'tc_nat' ), 'c_COMBB'( hAPP( 
% 1.42/1.83    'c_Power_Opower__class_Opower'( 'tc_Complex_Ocomplex' ), 
% 1.42/1.83    'c_FFT__Mirabelle_Oroot'( X ) ), hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.42/1.83    'tc_nat' ), 'v_i' ), 'tc_nat', 'tc_Complex_Ocomplex', 'tc_nat' ), 
% 1.42/1.83    'tc_nat', 'tc_Complex_Ocomplex', 'tc_Complex_Ocomplex' ), 'tc_nat', 
% 1.42/1.83    'tc_Complex_Ocomplex' ), hAPP( 
% 1.42/1.83    'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'( 
% 1.42/1.83    'tc_nat' ), 'tc_nat' ), X ) ) ) ],
% 1.42/1.83     [ =( 'c_FFT__Mirabelle_ODFT'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.42/1.83    'tc_nat' ), hAPP( 'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 
% 1.42/1.84    'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ), X ), Y, Z ), hAPP( 
% 1.42/1.84    hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_Complex_Ocomplex' ), 
% 1.42/1.84    'c_FFT__Mirabelle_ODFT'( X, 'c_COMBB'( Y, hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 
% 1.42/1.84    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.84    'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ), 'tc_nat', 'tc_Complex_Ocomplex', 
% 1.42/1.84    'tc_nat' ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.42/1.84    'tc_Complex_Ocomplex' ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( 
% 1.42/1.84    'tc_Complex_Ocomplex' ), 'c_FFT__Mirabelle_Oroot'( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 
% 1.42/1.84    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.84    'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ), X ) ) ), Z ) ), 
% 1.42/1.84    'c_FFT__Mirabelle_ODFT'( X, 'c_COMBB'( Y, 'c_COMBC'( 'c_COMBB'( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 
% 1.42/1.84    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.84    'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ), 'tc_nat', 'tc_fun'( 'tc_nat', 
% 1.42/1.84    'tc_nat' ), 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat', 
% 1.42/1.84    'tc_nat', 'tc_nat' ), 'tc_nat', 'tc_Complex_Ocomplex', 'tc_nat' ), Z ) )
% 1.42/1.84     ) ) ],
% 1.42/1.84     [ =( 'c_FFT__Mirabelle_OIDFT'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.42/1.84    'tc_nat' ), hAPP( 'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 
% 1.42/1.84    'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ), X ), Y, Z ), hAPP( 
% 1.42/1.84    hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_Complex_Ocomplex' ), 
% 1.42/1.84    'c_FFT__Mirabelle_OIDFT'( X, 'c_COMBB'( Y, hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 
% 1.42/1.84    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.84    'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ), 'tc_nat', 'tc_Complex_Ocomplex', 
% 1.42/1.84    'tc_nat' ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.42/1.84    'tc_Complex_Ocomplex' ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( 
% 1.42/1.84    'tc_Complex_Ocomplex' ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( 
% 1.42/1.84    'tc_Complex_Ocomplex' ), 'c_HOL_Oone__class_Oone'( 'tc_Complex_Ocomplex'
% 1.42/1.84     ) ), 'c_FFT__Mirabelle_Oroot'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.42/1.84    'tc_nat' ), hAPP( 'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 
% 1.42/1.84    'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ), X ) ) ) ), Z ) ), 
% 1.42/1.84    'c_FFT__Mirabelle_OIDFT'( X, 'c_COMBB'( Y, 'c_COMBC'( 'c_COMBB'( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 
% 1.42/1.84    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.84    'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ), 'tc_nat', 'tc_fun'( 'tc_nat', 
% 1.42/1.84    'tc_nat' ), 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat', 
% 1.42/1.84    'tc_nat', 'tc_nat' ), 'tc_nat', 'tc_Complex_Ocomplex', 'tc_nat' ), Z ) )
% 1.42/1.84     ) ) ],
% 1.42/1.84     [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ), 
% 1.42/1.84    'c_HOL_Oone__class_Oone'( X ) ), hAPP( 'c_Int_Onumber__class_Onumber__of'( 
% 1.42/1.84    X ), 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( 
% 1.42/1.84    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.42/1.84    'class_Int_Onumber'( X ) ), ~( =( hAPP( 
% 1.42/1.84    'c_Int_Onumber__class_Onumber__of'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( 
% 1.42/1.84    X ) ) ), =( hAPP( 'c_Int_Onumber__class_Onumber__of'( X ), Y ), hAPP( 
% 1.42/1.84    hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), hAPP( 
% 1.42/1.84    'c_Int_Onumber__class_Onumber__of'( X ), Y ) ), Z ) ), Z ) ) ],
% 1.42/1.84     [ ~( =( 'c_Int_OBit1'( X ), 'c_Int_OBit0'( Y ) ) ) ],
% 1.42/1.84     [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( 
% 1.42/1.84    'c_Int_Onumber__class_Onumber__of'( X ), 'c_Int_OBit1'( Y ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 
% 1.42/1.84    X ), 'c_HOL_Oone__class_Oone'( X ) ), hAPP( 
% 1.42/1.84    'c_Int_Onumber__class_Onumber__of'( X ), Y ) ) ), hAPP( 
% 1.42/1.84    'c_Int_Onumber__class_Onumber__of'( X ), Y ) ) ) ],
% 1.42/1.84     [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( 
% 1.42/1.84    'c_Int_Onumber__class_Onumber__of'( X ), 'c_Int_OBit1'( 'c_Int_OPls' ) )
% 1.42/1.84    , 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.42/1.84     [ =( hAPP( 'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit1'( 
% 1.42/1.84    'c_Int_OPls' ) ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.42/1.84     [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_Power_Opower__class_Opower'( X ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ), hAPP( 
% 1.42/1.84    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.84    'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 
% 1.42/1.84    X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 
% 1.42/1.84    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.84    'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ) ), hAPP( hAPP( 
% 1.42/1.84    'c_Power_Opower__class_Opower'( X ), Z ), hAPP( 
% 1.42/1.84    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.84    'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ) ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), hAPP( 
% 1.42/1.84    'c_Int_Onumber__class_Onumber__of'( X ), 'c_Int_OBit0'( 'c_Int_OBit1'( 
% 1.42/1.84    'c_Int_OPls' ) ) ) ), Y ) ), Z ) ) ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( 
% 1.42/1.84    'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), T ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ), Z ) ), =( Z, 
% 1.42/1.84    'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( 
% 1.42/1.84    'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ), T ) ), =( T, 
% 1.42/1.84    'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 
% 1.42/1.84    X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) )
% 1.42/1.84    , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) ) ) ],
% 1.42/1.84     [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( 
% 1.42/1.84    'c_Finite__Set_Osetsum'( 'c_COMBB'( Y, 'c_COMBC'( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z, 'tc_nat', 'tc_nat', 'tc_nat' )
% 1.42/1.84    , 'tc_nat', X, 'tc_nat' ), 'tc_nat', X ), hAPP( 
% 1.42/1.84    'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'( 
% 1.42/1.84    'tc_nat' ), 'tc_nat' ), T ) ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 
% 1.42/1.84    X ), hAPP( 'c_Finite__Set_Osetsum'( Y, 'tc_nat', X ), hAPP( 
% 1.42/1.84    'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'( 
% 1.42/1.84    'tc_nat' ), 'tc_nat' ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat'
% 1.42/1.84     ), T ), Z ) ) ) ), hAPP( 'c_Finite__Set_Osetsum'( Y, 'tc_nat', X ), hAPP( 
% 1.42/1.84    'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'( 
% 1.42/1.84    'tc_nat' ), 'tc_nat' ), Z ) ) ) ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oinverse__class_Odivide'( X ), Y ), 'c_HOL_Oone__class_Oone'( X )
% 1.42/1.84     ), Y ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( 
% 1.42/1.84    'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), 
% 1.42/1.84    'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.42/1.84    ,
% 1.42/1.84     [ =( 'c_FFT__Mirabelle_Oroot'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 1.42/1.84    , 'c_HOL_Oone__class_Oone'( 'tc_Complex_Ocomplex' ) ) ],
% 1.42/1.84     [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 
% 1.42/1.84    hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ) ) ), =( X, Z
% 1.42/1.84     ) ],
% 1.42/1.84     [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 
% 1.42/1.84    hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ), =( Y, Z
% 1.42/1.84     ) ],
% 1.42/1.84     [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 
% 1.42/1.84    hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ), =( Y, Z
% 1.42/1.84     ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'( 
% 1.42/1.84    X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( 
% 1.42/1.84    hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 1.42/1.84     [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 
% 1.42/1.84    'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( 
% 1.42/1.84    'tc_nat' ) ), hAPP( 'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 
% 1.42/1.84    'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ) ],
% 1.42/1.84     [ =( 'c_Int_OPls', 'c_Int_OBit0'( 'c_Int_OPls' ) ) ],
% 1.42/1.84     [ =( 'c_FFT__Mirabelle_Oroot'( 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), 
% 1.42/1.84    'c_HOL_Oone__class_Oone'( 'tc_Complex_Ocomplex' ) ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oinverse__class_Odivide'( X ), T ), U ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), Y ), U ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ) ), =( U, 
% 1.42/1.84    'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.42/1.84     ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.42/1.84    X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.42/1.84     ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ) ],
% 1.42/1.84     [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_Power_Opower__class_Opower'( X ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( 
% 1.42/1.84    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.84    'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 
% 1.42/1.84    X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 
% 1.42/1.84    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.84    'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ) ), hAPP( hAPP( 
% 1.42/1.84    'c_Power_Opower__class_Opower'( X ), Z ), hAPP( 
% 1.42/1.84    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.84    'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ) ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), hAPP( 
% 1.42/1.84    'c_Int_Onumber__class_Onumber__of'( X ), 'c_Int_OBit0'( 'c_Int_OBit1'( 
% 1.42/1.84    'c_Int_OPls' ) ) ) ), Y ) ), Z ) ) ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( 
% 1.42/1.84    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.42/1.84    'class_Int_Onumber'( X ) ), ~( =( hAPP( 
% 1.42/1.84    'c_Int_Onumber__class_Onumber__of'( X ), Y ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), hAPP( 
% 1.42/1.84    'c_Int_Onumber__class_Onumber__of'( X ), Y ) ), T ), Z ), =( T, 
% 1.42/1.84    'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Ocomm__semiring'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 
% 1.42/1.84    X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 
% 1.42/1.84    hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.42/1.84    X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.42/1.84     ) ) ],
% 1.42/1.84     [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ) ) ],
% 1.42/1.84     [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), hAPP( 
% 1.42/1.84    hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ) ],
% 1.42/1.84     [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 
% 1.42/1.84    X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 
% 1.42/1.84    hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.42/1.84     [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 
% 1.42/1.84    X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 
% 1.42/1.84    hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.42/1.84     [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.42/1.84    X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.42/1.84     ) ) ],
% 1.42/1.84     [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.42/1.84    X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.42/1.84     ) ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 
% 1.42/1.84    X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 
% 1.42/1.84    hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ) ) ],
% 1.42/1.84     [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ) ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), Z ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ) ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), Z ) ) ],
% 1.42/1.84     [ ~( 'class_OrderedGroup_Oab__semigroup__mult'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.42/1.84     [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oone__class_Oone'( X )
% 1.42/1.84    , hAPP( 'c_Int_Onumber__class_Onumber__of'( X ), 'c_Int_OBit1'( 
% 1.42/1.84    'c_Int_OPls' ) ) ) ],
% 1.42/1.84     [ =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), hAPP( 
% 1.42/1.84    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit1'( 
% 1.42/1.84    'c_Int_OPls' ) ) ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), 'c_HOL_Oone__class_Oone'( 
% 1.42/1.84    X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, Z ) ],
% 1.42/1.84     [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 
% 1.42/1.84    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.84    'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ) ],
% 1.42/1.84     [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_Power_Opower__class_Opower'( X ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 
% 1.42/1.84    'c_Power_Opower__class_Opower'( X ), Y ), T ) ), hAPP( hAPP( 
% 1.42/1.84    'c_Power_Opower__class_Opower'( X ), Z ), T ) ) ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_Power_Opower__class_Opower'( X ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 
% 1.42/1.84    'c_Power_Opower__class_Opower'( X ), Y ), T ) ), hAPP( hAPP( 
% 1.42/1.84    'c_Power_Opower__class_Opower'( X ), Z ), T ) ) ) ],
% 1.42/1.84     [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_Int_Onumber__class_Onumber__of'( 
% 1.42/1.84    X ), 'c_Int_OPls' ) ), Y ), Y ) ],
% 1.42/1.84     [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( 
% 1.42/1.84    'c_Int_Onumber__class_Onumber__of'( X ), 'c_Int_OPls' ) ), Y ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_Finite__Set_Osetsum'( Y, Z, X
% 1.42/1.84     ), T ) ), U ), hAPP( 'c_Finite__Set_Osetsum'( 'c_COMBC'( 'c_COMBB'( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), Y, X, 'tc_fun'( X, X ), Z ), U, Z, X, 
% 1.42/1.84    X ), Z, X ), T ) ) ],
% 1.42/1.84     [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_Finite__Set_Osetsum'( Y, Z, X
% 1.42/1.84     ), T ) ), U ), hAPP( 'c_Finite__Set_Osetsum'( 'c_COMBC'( 'c_COMBB'( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), Y, X, 'tc_fun'( X, X ), Z ), U, Z, X, 
% 1.42/1.84    X ), Z, X ), T ) ) ],
% 1.42/1.84     [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =( hAPP( 
% 1.42/1.84    hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ), Y ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~( 
% 1.42/1.84    'class_Power_Opower'( X ) ), ~( =( hAPP( 
% 1.42/1.84    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), Y ), 
% 1.42/1.84    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), 
% 1.42/1.84    hAPP( 'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), Y ) ), 
% 1.42/1.84    'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =( hAPP( 
% 1.42/1.84    hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ), 'c_HOL_Ozero__class_Ozero'( 
% 1.42/1.84    X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =( hAPP( 
% 1.42/1.84    hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ), 'c_HOL_Ozero__class_Ozero'( 
% 1.42/1.84    X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'( 
% 1.42/1.84    X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ) ) ), =( T, U ), =( Z, 
% 1.42/1.84    'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.84     [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( 
% 1.42/1.84    hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), T ) ) ) ), =( Z, T ), =( Y
% 1.42/1.84    , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.42/1.84     [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 
% 1.42/1.84    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 
% 1.42/1.84    'tc_nat' ) ), Y ) ) ],
% 1.42/1.84     [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), 
% 1.42/1.84    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), 'c_HOL_Ozero__class_Ozero'( 
% 1.42/1.84    'tc_nat' ) ) ) ],
% 1.42/1.84     [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( 
% 1.42/1.84    'c_Finite__Set_Osetsum'( Y, 'tc_nat', X ), hAPP( 
% 1.42/1.84    'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'( 
% 1.42/1.84    'tc_nat' ), 'tc_nat' ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat'
% 1.42/1.84     ), Z ), T ) ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 
% 1.42/1.84    'c_Finite__Set_Osetsum'( 'c_COMBB'( Y, 'c_COMBC'( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), T, 'tc_nat', 'tc_nat', 'tc_nat' )
% 1.42/1.84    , 'tc_nat', X, 'tc_nat' ), 'tc_nat', X ), hAPP( 
% 1.42/1.84    'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'( 
% 1.42/1.84    'tc_nat' ), 'tc_nat' ), Z ) ) ), hAPP( 'c_Finite__Set_Osetsum'( Y, 
% 1.42/1.84    'tc_nat', X ), hAPP( 'c_SetInterval_Oord__class_OatLeastLessThan'( 
% 1.42/1.84    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), T ) ) ) ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 
% 1.42/1.84    'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 
% 1.42/1.84    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.84    'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ) ), hAPP( hAPP( 
% 1.42/1.84    'c_Power_Opower__class_Opower'( X ), Z ), hAPP( 
% 1.42/1.84    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.84    'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.42/1.84     ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 
% 1.42/1.84    'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 
% 1.42/1.84    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.84    'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ) ), hAPP( hAPP( 
% 1.42/1.84    'c_Power_Opower__class_Opower'( X ), Z ), hAPP( 
% 1.42/1.84    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.84    'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.42/1.84     ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~( 
% 1.42/1.84    'class_Power_Opower'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y
% 1.42/1.84     ), 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 
% 1.42/1.84    'tc_nat' ) ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( 
% 1.42/1.84    'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( 
% 1.42/1.84    'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.42/1.84     ), =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), 
% 1.42/1.84    'c_HOL_Ozero__class_Ozero'( X ) ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.42/1.84    , =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( 
% 1.42/1.84    'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.42/1.84     [ ~( 'class_Power_Opower'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( 
% 1.42/1.84    'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( 
% 1.42/1.84    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.42/1.84    'class_Int_Onumber'( X ) ), =( Y, hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( 
% 1.42/1.84    'c_Int_Onumber__class_Onumber__of'( X ), Z ) ) ), hAPP( 
% 1.42/1.84    'c_Int_Onumber__class_Onumber__of'( X ), Z ) ) ), =( hAPP( 
% 1.42/1.84    'c_Int_Onumber__class_Onumber__of'( X ), Z ), 'c_HOL_Ozero__class_Ozero'( 
% 1.42/1.84    X ) ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( 
% 1.42/1.84    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.42/1.84    'class_Int_Onumber'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( 
% 1.42/1.84    'c_Int_Onumber__class_Onumber__of'( X ), Z ) ) ), hAPP( 
% 1.42/1.84    'c_Int_Onumber__class_Onumber__of'( X ), Z ) ), Y ), =( hAPP( 
% 1.42/1.84    'c_Int_Onumber__class_Onumber__of'( X ), Z ), 'c_HOL_Ozero__class_Ozero'( 
% 1.42/1.84    X ) ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Oring__1__no__zero__divisors'( X ) ), ~( 
% 1.42/1.84    =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), 
% 1.42/1.84    'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.42/1.84     ) ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( 
% 1.42/1.84    'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( 
% 1.42/1.84    'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.42/1.84     ), ~( =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), 
% 1.42/1.84    'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.42/1.84     ) ) ],
% 1.42/1.84     [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =( hAPP( 
% 1.42/1.84    hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( 
% 1.42/1.84    'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oinverse__class_Odivide'( X ), T ), U ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ) ) ],
% 1.42/1.84     [ ~( =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ), 
% 1.42/1.84    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), X ), 
% 1.42/1.84    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y, X ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( 
% 1.42/1.84    'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_Power_Opower__class_Opower'( X ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), T ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP( 
% 1.42/1.84    'c_Power_Opower__class_Opower'( X ), Y ), T ) ), hAPP( hAPP( 
% 1.42/1.84    'c_Power_Opower__class_Opower'( X ), Z ), T ) ) ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y, 
% 1.42/1.84    'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ), Y ) ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y, 
% 1.42/1.84    'c_HOL_Ozero__class_Ozero'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ), Y ), Z ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( 
% 1.42/1.84    'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( Y, hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), Z ) ), =( Z, 
% 1.42/1.84    'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( 
% 1.42/1.84    'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), Z ), Y ), =( Z, 
% 1.42/1.84    'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.84     [ =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( 'tc_Complex_Ocomplex' )
% 1.42/1.84    , 'c_FFT__Mirabelle_Oroot'( X ) ), X ), 'c_HOL_Oone__class_Oone'( 
% 1.42/1.84    'tc_Complex_Ocomplex' ) ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( 
% 1.42/1.84    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.42/1.84    'class_Int_Onumber'( X ) ), ~( =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oinverse__class_Odivide'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X
% 1.42/1.84     ) ), hAPP( 'c_Int_Onumber__class_Onumber__of'( X ), Z ) ) ), =( hAPP( 
% 1.42/1.84    'c_Int_Onumber__class_Onumber__of'( X ), Z ), 'c_HOL_Ozero__class_Ozero'( 
% 1.42/1.84    X ) ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( 
% 1.42/1.84    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.42/1.84    'class_Int_Onumber'( X ) ), ~( =( hAPP( 
% 1.42/1.84    'c_Int_Onumber__class_Onumber__of'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( 
% 1.42/1.84    X ) ) ), =( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Z ), 
% 1.42/1.84    'c_HOL_Ozero__class_Ozero'( X ) ), hAPP( 
% 1.42/1.84    'c_Int_Onumber__class_Onumber__of'( X ), Y ) ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), T ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), U ) ) ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), Z ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) ) ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ) ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =( 
% 1.42/1.84    'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( 
% 1.42/1.84    'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( 
% 1.42/1.84    'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.42/1.84     ), ~( =( hAPP( 'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), Y ), 
% 1.42/1.84    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( =( hAPP( hAPP( 
% 1.42/1.84    'c_Power_Opower__class_Opower'( X ), Z ), hAPP( 
% 1.42/1.84    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), Y ) ), 
% 1.42/1.84    'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( 
% 1.42/1.84    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.42/1.84    'class_Int_Onumber'( X ) ), =( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( 
% 1.42/1.84    hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), 
% 1.42/1.84    hAPP( 'c_Int_Onumber__class_Onumber__of'( X ), Y ) ) ), hAPP( 
% 1.42/1.84    'c_Int_Onumber__class_Onumber__of'( X ), Y ) ) ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), ~( =( 
% 1.42/1.84    hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), 
% 1.42/1.84    'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 1.42/1.84     ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =( hAPP( 
% 1.42/1.84    hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), 
% 1.42/1.84    'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 1.42/1.84     ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =( hAPP( 
% 1.42/1.84    hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), 
% 1.42/1.84    'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.42/1.84     ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.84     [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), 
% 1.42/1.84    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y, 
% 1.42/1.84    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, 
% 1.42/1.84    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oone__class_Oone'( X ) ), 
% 1.42/1.84    hAPP( 'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.84    'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ), 'c_HOL_Oone__class_Oone'( X ) ) ]
% 1.42/1.84    ,
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ), T ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ) ) ],
% 1.42/1.84     [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ), T ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ) ) ],
% 1.42/1.84     [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 
% 1.42/1.84    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 
% 1.42/1.84    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.42/1.84     [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 
% 1.42/1.84    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y, 
% 1.42/1.84    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.42/1.84     [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), ~( =( hAPP( 
% 1.42/1.84    hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), 
% 1.42/1.84    'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.42/1.84     ) ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( 
% 1.42/1.84    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.42/1.84    'class_Int_Onumber'( X ) ), ~( =( hAPP( 
% 1.42/1.84    'c_Int_Onumber__class_Onumber__of'( X ), Y ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oinverse__class_Odivide'( X ), Z ), 'c_HOL_Ozero__class_Ozero'( X
% 1.42/1.84     ) ) ) ), =( hAPP( 'c_Int_Onumber__class_Onumber__of'( X ), Y ), 
% 1.42/1.84    'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( 
% 1.42/1.84    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.42/1.84    'class_Int_Onumber'( X ) ), ~( =( hAPP( 
% 1.42/1.84    'c_Int_Onumber__class_Onumber__of'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( 
% 1.42/1.84    X ) ) ), =( hAPP( 'c_Int_Onumber__class_Onumber__of'( X ), Y ), hAPP( 
% 1.42/1.84    hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Z ), 
% 1.42/1.84    'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( 
% 1.42/1.84    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.42/1.84    'class_Int_Onumber'( X ) ), ~( =( hAPP( 
% 1.42/1.84    'c_Int_Onumber__class_Onumber__of'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( 
% 1.42/1.84    X ) ) ), =( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oinverse__class_Odivide'( X ), Z ), hAPP( 
% 1.42/1.84    'c_Int_Onumber__class_Onumber__of'( X ), Y ) ) ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 
% 1.42/1.84    'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP( 
% 1.42/1.84    'c_Power_Opower__class_Opower'( X ), Y ), T ) ), hAPP( hAPP( 
% 1.42/1.84    'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ) ) ],
% 1.42/1.84     [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Ominus__class_Ominus'( X ), Y ), Y ), 'c_HOL_Ozero__class_Ozero'( 
% 1.42/1.84    X ) ) ],
% 1.42/1.84     [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Ominus__class_Ominus'( X ), Y ), Y ), 'c_HOL_Ozero__class_Ozero'( 
% 1.42/1.84    X ) ) ],
% 1.42/1.84     [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Ominus__class_Ominus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.42/1.84    , Y ) ],
% 1.42/1.84     [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Ominus__class_Ominus'( X ), Y ), Y ), 'c_HOL_Ozero__class_Ozero'( 
% 1.42/1.84    X ) ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'( 
% 1.42/1.84    X ) ), =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Y ), 
% 1.42/1.84    'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.84     [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), X ), 
% 1.42/1.84    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.42/1.84     [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), 
% 1.42/1.84    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'( 
% 1.42/1.84    X ) ), ~( =( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) )
% 1.42/1.84    , =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.84     [ ~( =( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y )
% 1.42/1.84     ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.42/1.84     [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), X
% 1.42/1.84     ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.42/1.84     [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), hAPP( 
% 1.42/1.84    'c_Int_Onumber__class_Onumber__of'( X ), 'c_Int_OBit1'( 'c_Int_OPls' ) )
% 1.42/1.84     ), Y ), Y ) ],
% 1.42/1.84     [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( 
% 1.42/1.84    'c_Int_Onumber__class_Onumber__of'( X ), 'c_Int_OBit1'( 'c_Int_OPls' ) )
% 1.42/1.84     ), Y ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( 'class_Int_Onumber'( X )
% 1.42/1.84     ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 
% 1.42/1.84    'c_Int_Onumber__class_Onumber__of'( X ), Y ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Ominus__class_Ominus'( X ), Z ), T ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), hAPP( 
% 1.42/1.84    'c_Int_Onumber__class_Onumber__of'( X ), Y ) ), Z ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), hAPP( 
% 1.42/1.84    'c_Int_Onumber__class_Onumber__of'( X ), Y ) ), T ) ) ) ],
% 1.42/1.84     [ =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 
% 1.42/1.84    'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ) ],
% 1.42/1.84     [ ~( =( 'c_Int_OPls', 'c_Int_OBit0'( X ) ) ), =( 'c_Int_OPls', X ) ]
% 1.42/1.84    ,
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.42/1.84    X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Ominus__class_Ominus'( X ), T ), Y ) ), Z ) ), U ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.42/1.84    X ), T ), Z ) ), U ) ) ],
% 1.42/1.84     [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 
% 1.42/1.84    X ), 'c_HOL_Oone__class_Oone'( X ) ), 'c_HOL_Oone__class_Oone'( X ) ) ), 
% 1.42/1.84    hAPP( 'c_Int_Onumber__class_Onumber__of'( X ), Y ) ), hAPP( 
% 1.42/1.84    'c_Int_Onumber__class_Onumber__of'( X ), 'c_Int_OBit0'( Y ) ) ) ],
% 1.42/1.84     [ ~( 'class_OrderedGroup_Ocancel__ab__semigroup__add'( X ) ), ~( =( hAPP( 
% 1.42/1.84    hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 1.42/1.84     [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =( hAPP( 
% 1.42/1.84    hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 1.42/1.84     [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =( hAPP( 
% 1.42/1.84    hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ), =( Y, T ) ],
% 1.42/1.84     [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 
% 1.42/1.84    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.84    'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ), Z ) ), hAPP( hAPP( 
% 1.42/1.84    'c_Power_Opower__class_Opower'( X ), hAPP( hAPP( 
% 1.42/1.84    'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( 
% 1.42/1.84    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.84    'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ) ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( 
% 1.42/1.84    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.42/1.84    'class_Int_Onumber'( X ) ), ~( =( hAPP( 
% 1.42/1.84    'c_Int_Onumber__class_Onumber__of'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( 
% 1.42/1.84    X ) ) ), =( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), hAPP( 
% 1.42/1.84    'c_Int_Onumber__class_Onumber__of'( X ), Y ) ), Z ) ), Z ), hAPP( 
% 1.42/1.84    'c_Int_Onumber__class_Onumber__of'( X ), Y ) ) ],
% 1.42/1.84     [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Z ) ) ],
% 1.42/1.84     [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), Z ) ) ],
% 1.42/1.84     [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( 'c_Finite__Set_Osetsum'( Z
% 1.42/1.84    , T, X ), U ) ), hAPP( 'c_Finite__Set_Osetsum'( 'c_COMBB'( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), Y ), Z, X, X, T ), T, X ), U ) ) ]
% 1.42/1.84    ,
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( 'c_Finite__Set_Osetsum'( Z
% 1.42/1.84    , T, X ), U ) ), hAPP( 'c_Finite__Set_Osetsum'( 'c_COMBB'( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), Y ), Z, X, X, T ), T, X ), U ) ) ]
% 1.42/1.84    ,
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =( 
% 1.42/1.84    'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ) ) ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( 
% 1.42/1.84    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.42/1.84    'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oinverse__class_Odivide'( X ), Y ), hAPP( 
% 1.42/1.84    'c_Int_Onumber__class_Onumber__of'( X ), 'c_Int_OPls' ) ), 
% 1.42/1.84    'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.84     [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y )
% 1.42/1.84    , 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.42/1.84     [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), U ) ],
% 1.42/1.84     [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), 
% 1.42/1.84    hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'( 
% 1.42/1.84    'tc_nat' ) ) ), Y ) ) ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ]
% 1.42/1.84    ,
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( 
% 1.42/1.84    'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oinverse__class_Odivide'( X ), Y ), hAPP( 
% 1.42/1.84    'c_Int_Onumber__class_Onumber__of'( X ), 'c_Int_OBit1'( 'c_Int_OPls' ) )
% 1.42/1.84     ), Y ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( 
% 1.42/1.84    'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oinverse__class_Odivide'( X ), Y ), hAPP( 
% 1.42/1.84    'c_Int_Onumber__class_Onumber__of'( X ), 'c_Int_OBit1'( 'c_Int_OPls' ) )
% 1.42/1.84     ), Y ) ],
% 1.42/1.84     [ ~( =( 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ) ) ), =( X, Y ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Ocomm__ring'( X ) ), ~( 
% 1.42/1.84    'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( 
% 1.42/1.84    'c_Finite__Set_Osetsum'( 'c_COMBC'( 'c_COMBB'( 
% 1.42/1.84    'c_HOL_Ominus__class_Ominus'( X ), 'c_COMBS'( 'c_COMBB'( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), 'c_COMBB'( hAPP( 
% 1.42/1.84    'c_Power_Opower__class_Opower'( X ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( 
% 1.42/1.84    'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), T ), 'tc_nat', X, 'tc_nat' ), X
% 1.42/1.84    , 'tc_fun'( X, X ), 'tc_nat' ), hAPP( 'c_Power_Opower__class_Opower'( X )
% 1.42/1.84    , Y ), 'tc_nat', X, X ), X, 'tc_fun'( X, X ), 'tc_nat' ), hAPP( hAPP( 
% 1.42/1.84    'c_Power_Opower__class_Opower'( X ), Y ), T ), 'tc_nat', X, X ), 'tc_nat'
% 1.42/1.84    , X ), hAPP( 'c_SetInterval_Oord__class_OatLeastLessThan'( 
% 1.42/1.84    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), T ) ), hAPP( 
% 1.42/1.84    'c_Finite__Set_Osetsum'( 'c_COMBS'( 'c_COMBB'( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_Power_Opower__class_Opower'( 
% 1.42/1.84    X ), Y ), X, 'tc_fun'( X, X ), 'tc_nat' ), 'c_COMBS'( 'c_COMBB'( 
% 1.42/1.84    'c_HOL_Ominus__class_Ominus'( X ), 'c_COMBB'( hAPP( 
% 1.42/1.84    'c_Power_Opower__class_Opower'( X ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( 
% 1.42/1.84    'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), T ), 'tc_nat', X, 'tc_nat' ), X
% 1.42/1.84    , 'tc_fun'( X, X ), 'tc_nat' ), 'c_COMBB'( hAPP( 
% 1.42/1.84    'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 
% 1.42/1.84    'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), T ), 'tc_nat', X, 'tc_nat' ), 
% 1.42/1.84    'tc_nat', X, X ), 'tc_nat', X, X ), 'tc_nat', X ), hAPP( 
% 1.42/1.84    'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'( 
% 1.42/1.84    'tc_nat' ), 'tc_nat' ), T ) ) ) ],
% 1.42/1.84     [ ~( hBOOL( hAPP( X, hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat'
% 1.42/1.84     ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ), Y ) )
% 1.42/1.84     ) ), hBOOL( hAPP( X, Z ) ) ],
% 1.42/1.84     [ ~( hBOOL( hAPP( X, hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat'
% 1.42/1.84     ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ), Y ) )
% 1.42/1.84     ) ), hBOOL( hAPP( X, Z ) ) ],
% 1.42/1.84     [ ~( =( 'c_Int_OBit0'( X ), 'c_Int_OPls' ) ), =( X, 'c_Int_OPls' ) ]
% 1.42/1.84    ,
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~( 
% 1.42/1.84    'class_Power_Opower'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), 
% 1.42/1.84    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( X ) )
% 1.42/1.84     ],
% 1.42/1.84     [ ~( =( 'c_Int_OBit1'( X ), 'c_Int_OPls' ) ) ],
% 1.42/1.84     [ ~( 'class_RealVector_Oreal__field'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) ), W ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.42/1.84    X ), Y ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Ominus__class_Ominus'( X ), Z ), U ) ), W ) ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Ominus__class_Ominus'( X ), Y ), T ) ), W ) ), U ) ) ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( 'class_Int_Onumber'( X )
% 1.42/1.84     ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ), hAPP( 
% 1.42/1.84    'c_Int_Onumber__class_Onumber__of'( X ), T ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( 
% 1.42/1.84    'c_Int_Onumber__class_Onumber__of'( X ), T ) ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), Z ), hAPP( 
% 1.42/1.84    'c_Int_Onumber__class_Onumber__of'( X ), T ) ) ) ) ],
% 1.42/1.84     [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( 
% 1.42/1.84    'c_Finite__Set_Osetsum'( 'c_COMBS'( 'c_COMBB'( 
% 1.42/1.84    'c_HOL_Ominus__class_Ominus'( X ), Y, X, 'tc_fun'( X, X ), Z ), T, Z, X, 
% 1.42/1.84    X ), Z, X ), U ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), hAPP( 
% 1.42/1.84    'c_Finite__Set_Osetsum'( Y, Z, X ), U ) ), hAPP( 'c_Finite__Set_Osetsum'( 
% 1.42/1.84    T, Z, X ), U ) ) ) ],
% 1.42/1.84     [ =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( 'tc_Complex_Ocomplex' )
% 1.42/1.84    , 'c_FFT__Mirabelle_Oroot'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.42/1.84    'tc_nat' ), hAPP( 'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 
% 1.42/1.84    'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ), X ) ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 
% 1.42/1.84    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.84    'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ), Z ) ) ), hAPP( hAPP( 
% 1.42/1.84    'c_Power_Opower__class_Opower'( 'tc_Complex_Ocomplex' ), 
% 1.42/1.84    'c_FFT__Mirabelle_Oroot'( X ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.42/1.84    'tc_nat' ), Y ), Z ) ) ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.42/1.84    X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 
% 1.42/1.84    hAPP( 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.42/1.84    X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), U ) ), Z ) ), T
% 1.42/1.84     ) ) ) ],
% 1.42/1.84     [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), ~( 'class_Int_Onumber'( 
% 1.42/1.84    X ) ), =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), hAPP( 
% 1.42/1.84    'c_Int_Onumber__class_Onumber__of'( X ), Y ) ), hAPP( 
% 1.42/1.84    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.84    'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), hAPP( 
% 1.42/1.84    'c_Int_Onumber__class_Onumber__of'( X ), Y ) ), hAPP( 
% 1.42/1.84    'c_Int_Onumber__class_Onumber__of'( X ), Y ) ) ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.42/1.84    X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 
% 1.42/1.84    hAPP( 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), W ) ) ), =( hAPP( 
% 1.42/1.84    hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Ominus__class_Ominus'( X ), Y ), U ) ), Z ) ), T ), W ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.42/1.84    X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 
% 1.42/1.84    hAPP( 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), W ) ) ), =( T, hAPP( 
% 1.42/1.84    hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Ominus__class_Ominus'( X ), U ), Y ) ), Z ) ), W ) ) ],
% 1.42/1.84     [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oinverse__class_Odivide'( X ), hAPP( 'c_Finite__Set_Osetsum'( Y, Z
% 1.42/1.84    , X ), T ) ), U ), hAPP( 'c_Finite__Set_Osetsum'( 'c_COMBC'( 'c_COMBB'( 
% 1.42/1.84    'c_HOL_Oinverse__class_Odivide'( X ), Y, X, 'tc_fun'( X, X ), Z ), U, Z, 
% 1.42/1.84    X, X ), Z, X ), T ) ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oinverse__class_Odivide'( X ), hAPP( 'c_Finite__Set_Osetsum'( Y, Z
% 1.42/1.84    , X ), T ) ), U ), hAPP( 'c_Finite__Set_Osetsum'( 'c_COMBC'( 'c_COMBB'( 
% 1.42/1.84    'c_HOL_Oinverse__class_Odivide'( X ), Y, X, 'tc_fun'( X, X ), Z ), U, Z, 
% 1.42/1.84    X, X ), Z, X ), T ) ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 1.42/1.84     [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), hAPP( 
% 1.42/1.84    hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ) ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 1.42/1.84     [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 1.42/1.84     [ ~( =( 'c_Int_OPls', 'c_Int_OBit1'( X ) ) ) ],
% 1.42/1.84     [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 
% 1.42/1.84    'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), Y ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP( 
% 1.42/1.84    'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.42/1.84     [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), 
% 1.42/1.84    hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ), =( Y
% 1.42/1.84    , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, Z ) ],
% 1.42/1.84     [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), 
% 1.42/1.84    hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), =( X
% 1.42/1.84    , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y, Z ) ],
% 1.42/1.84     [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), 
% 1.42/1.84    hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), =( Y
% 1.42/1.84    , Z ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( 
% 1.42/1.84    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.42/1.84    'class_Int_Onumber'( X ) ), =( hAPP( 'c_Int_Onumber__class_Onumber__of'( 
% 1.42/1.84    X ), Y ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), hAPP( 
% 1.42/1.84    'c_Int_Onumber__class_Onumber__of'( X ), Y ) ), Z ) ), Z ) ), =( Z, 
% 1.42/1.84    'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 
% 1.42/1.84    X ), 'c_HOL_Oone__class_Oone'( X ) ), 'c_HOL_Oone__class_Oone'( X ) ) ), 
% 1.42/1.84    Y ) ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Oone__class_Oone'( 
% 1.42/1.84    'tc_nat' ) ), Y ) ],
% 1.42/1.84     [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Oone__class_Oone'( 
% 1.42/1.84    'tc_nat' ) ), Y ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( 
% 1.42/1.84    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.42/1.84    'class_Int_Onumber'( X ) ), =( Y, hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oinverse__class_Odivide'( X ), Y ), hAPP( 
% 1.42/1.84    'c_Int_Onumber__class_Onumber__of'( X ), Z ) ) ), hAPP( 
% 1.42/1.84    'c_Int_Onumber__class_Onumber__of'( X ), Z ) ) ), =( hAPP( 
% 1.42/1.84    'c_Int_Onumber__class_Onumber__of'( X ), Z ), 'c_HOL_Ozero__class_Ozero'( 
% 1.42/1.84    X ) ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( 
% 1.42/1.84    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.42/1.84    'class_Int_Onumber'( X ) ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.42/1.84    X ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), hAPP( 
% 1.42/1.84    'c_Int_Onumber__class_Onumber__of'( X ), Z ) ) ), hAPP( 
% 1.42/1.84    'c_Int_Onumber__class_Onumber__of'( X ), Z ) ), Y ), =( hAPP( 
% 1.42/1.84    'c_Int_Onumber__class_Onumber__of'( X ), Z ), 'c_HOL_Ozero__class_Ozero'( 
% 1.42/1.84    X ) ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( 
% 1.42/1.84    'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( 
% 1.42/1.84    'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.42/1.84     ), Y ) ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~( 
% 1.42/1.84    'class_Power_Opower'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), 
% 1.42/1.84    hAPP( 'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), Y ) ), 
% 1.42/1.84    'c_HOL_Ozero__class_Ozero'( X ) ), =( hAPP( 
% 1.42/1.84    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), Y ), 
% 1.42/1.84    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( 
% 1.42/1.84    'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( 
% 1.42/1.84    'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.42/1.84     ), =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), 
% 1.42/1.84    'c_HOL_Ozero__class_Ozero'( X ) ), hAPP( 
% 1.42/1.84    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), Y ) ), 
% 1.42/1.84    'c_HOL_Ozero__class_Ozero'( X ) ), =( hAPP( 
% 1.42/1.84    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), Y ), 
% 1.42/1.84    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.42/1.84     [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( 
% 1.42/1.84    'c_Finite__Set_Osetsum'( Y, 'tc_nat', X ), hAPP( 
% 1.42/1.84    'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'( 
% 1.42/1.84    'tc_nat' ), 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.42/1.84    'tc_nat' ), hAPP( 'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 
% 1.42/1.84    'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ), Z ) ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_Finite__Set_Osetsum'( 'c_COMBB'( 
% 1.42/1.84    Y, hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 
% 1.42/1.84    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.84    'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ), 'tc_nat', X, 'tc_nat' ), 'tc_nat', X
% 1.42/1.84     ), hAPP( 'c_SetInterval_Oord__class_OatLeastLessThan'( 
% 1.42/1.84    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), Z ) ) ), hAPP( 
% 1.42/1.84    'c_Finite__Set_Osetsum'( 'c_COMBB'( Y, 'c_COMBC'( 'c_COMBB'( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 
% 1.42/1.84    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.84    'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ), 'tc_nat', 'tc_fun'( 'tc_nat', 
% 1.42/1.84    'tc_nat' ), 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat', 
% 1.42/1.84    'tc_nat', 'tc_nat' ), 'tc_nat', X, 'tc_nat' ), 'tc_nat', X ), hAPP( 
% 1.42/1.84    'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'( 
% 1.42/1.84    'tc_nat' ), 'tc_nat' ), Z ) ) ) ) ],
% 1.42/1.84     [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), T ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ) ), =( Y, T ), =( X
% 1.42/1.84    , Z ) ],
% 1.42/1.84     [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), T ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ) ), =( Y, T ), =( X
% 1.42/1.84    , Z ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'( 
% 1.42/1.84    X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.42/1.84    X ), Y ), U ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.42/1.84     ) ) ), =( Z, U ), =( Y, T ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'( 
% 1.42/1.84    X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.42/1.84    X ), Y ), U ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.42/1.84     ) ) ), =( Z, U ), =( Y, T ) ],
% 1.42/1.84     [ ~( =( X, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y
% 1.42/1.84     ) ) ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y, 
% 1.42/1.84    'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( 
% 1.42/1.84    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.42/1.84    'class_Int_Onumber'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), hAPP( 
% 1.42/1.84    'c_Int_Onumber__class_Onumber__of'( X ), Y ) ), Z ) ), Z ), hAPP( 
% 1.42/1.84    'c_Int_Onumber__class_Onumber__of'( X ), Y ) ), =( Z, 
% 1.42/1.84    'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oinverse__class_Odivide'( X ), T ), U ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.42/1.84    X ), Y ), U ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.42/1.84     ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ) ), =( U, 
% 1.42/1.84    'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.42/1.84     ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( 
% 1.42/1.84    'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( Y, hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), Z ) ), =( Z, 
% 1.42/1.84    'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( 
% 1.42/1.84    'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), Z ), Y ), =( Z, 
% 1.42/1.84    'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.42/1.84    , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.42/1.84    , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.84     [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.42/1.84    , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.84     [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.42/1.84    , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.84     [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), 
% 1.42/1.84    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( 
% 1.42/1.84    'tc_nat' ) ) ],
% 1.42/1.84     [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 
% 1.42/1.84    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), 'c_HOL_Ozero__class_Ozero'( 
% 1.42/1.84    'tc_nat' ) ) ],
% 1.42/1.84     [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.42/1.84    , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.84     [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.42/1.84    , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.42/1.84    , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.42/1.84    , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.42/1.84    , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =( hAPP( 
% 1.42/1.84    hAPP( 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.42/1.84     ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =( hAPP( 
% 1.42/1.84    hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( 
% 1.42/1.84    X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.42/1.84    X ), Y ), Z ) ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 
% 1.42/1.84    hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Oone__class_Oone'( X )
% 1.42/1.84     ) ), Z ) ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 
% 1.42/1.84    X ), Z ), 'c_HOL_Oone__class_Oone'( X ) ) ), Y ) ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), ~( 'class_Int_Onumber'( 
% 1.42/1.84    X ) ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( 
% 1.42/1.84    'c_Int_Onumber__class_Onumber__of'( X ), T ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.42/1.84    X ), Y ), hAPP( 'c_Int_Onumber__class_Onumber__of'( X ), T ) ) ), hAPP( 
% 1.42/1.84    hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), hAPP( 
% 1.42/1.84    'c_Int_Onumber__class_Onumber__of'( X ), T ) ) ) ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =( hAPP( hAPP( 
% 1.42/1.84    'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 
% 1.42/1.84    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.84    'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.42/1.84    , =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.84     [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( 
% 1.42/1.84    'c_Int_Onumber__class_Onumber__of'( X ), 'c_Int_OPls' ), 
% 1.42/1.84    'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.84     [ =( hAPP( 'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OPls'
% 1.42/1.84     ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( 
% 1.42/1.84    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.42/1.84    'class_Int_Onumber'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), 
% 1.42/1.84    hAPP( 'c_Int_Onumber__class_Onumber__of'( X ), Y ) ) ), hAPP( 
% 1.42/1.84    'c_Int_Onumber__class_Onumber__of'( X ), Y ) ), 
% 1.42/1.84    'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.84     [ =( 'c_Int_OBit0'( 'c_Int_OPls' ), 'c_Int_OPls' ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( 
% 1.42/1.84    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.42/1.84    'class_Int_Onumber'( X ) ), ~( =( hAPP( 
% 1.42/1.84    'c_Int_Onumber__class_Onumber__of'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( 
% 1.42/1.84    X ) ) ), =( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Z ), hAPP( 
% 1.42/1.84    'c_Int_Onumber__class_Onumber__of'( X ), Y ) ), 
% 1.42/1.84    'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( 
% 1.42/1.84    'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( 
% 1.42/1.84    'class_Int_Onumber'( X ) ), ~( =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), hAPP( 
% 1.42/1.84    'c_Int_Onumber__class_Onumber__of'( X ), T ) ) ), =( Y, hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), hAPP( 
% 1.42/1.84    'c_Int_Onumber__class_Onumber__of'( X ), T ) ), Z ) ), =( Z, 
% 1.42/1.84    'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), 
% 1.42/1.84    hAPP( 'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.84    'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.42/1.84    ,
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), 
% 1.42/1.84    hAPP( 'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.84    'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.42/1.84    ,
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_Power_Opower__class_Opower'( X ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), T ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP( 
% 1.42/1.84    'c_Power_Opower__class_Opower'( X ), Y ), T ) ), hAPP( hAPP( 
% 1.42/1.84    'c_Power_Opower__class_Opower'( X ), Z ), T ) ) ), =( Z, 
% 1.42/1.84    'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( hAPP( 
% 1.42/1.84    hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), 
% 1.42/1.84    'c_HOL_Ozero__class_Ozero'( X ) ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), 
% 1.42/1.84    'c_HOL_Ozero__class_Ozero'( X ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.42/1.84    ,
% 1.42/1.84     [ =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( 
% 1.42/1.84    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OPls' ) ) ],
% 1.42/1.84     [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Ozero__class_Ozero'( X
% 1.42/1.84     ), hAPP( 'c_Int_Onumber__class_Onumber__of'( X ), 'c_Int_OPls' ) ) ]
% 1.42/1.84    ,
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( 
% 1.42/1.84    'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( 
% 1.42/1.84    'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oinverse__class_Odivide'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X
% 1.42/1.84     ) ) ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 
% 1.42/1.84    'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), 
% 1.42/1.84    hAPP( 'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.84    'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ) ), hAPP( hAPP( 
% 1.42/1.84    'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), 
% 1.42/1.84    hAPP( 'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.84    'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.42/1.84     ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ), hAPP( hAPP( 
% 1.42/1.84    'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 
% 1.42/1.84    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.84    'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ) ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oinverse__class_Odivide'( X ), T ), U ) ) ), =( U, 
% 1.42/1.84    'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.42/1.84     ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), U ), hAPP( 
% 1.42/1.84    hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) ), =( Z, 
% 1.42/1.84    'c_HOL_Ozero__class_Ozero'( X ) ), =( U, 'c_HOL_Ozero__class_Ozero'( X )
% 1.42/1.84     ), =( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), U ), hAPP( 
% 1.42/1.84    hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ) ) ],
% 1.42/1.84     [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP( 
% 1.42/1.84    'c_Power_Opower__class_Opower'( X ), hAPP( hAPP( 
% 1.42/1.84    'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), T ) ) ],
% 1.42/1.84     [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( 
% 1.42/1.84    'c_Finite__Set_Osetsum'( Y, 'tc_nat', X ), hAPP( 
% 1.42/1.84    'c_SetInterval_Oord__class_OatLeastLessThan'( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ), 'tc_nat' ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), U ), T ) ) ), hAPP( 
% 1.42/1.84    'c_Finite__Set_Osetsum'( 'c_COMBB'( Y, 'c_COMBC'( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), T, 'tc_nat', 'tc_nat', 'tc_nat' )
% 1.42/1.84    , 'tc_nat', X, 'tc_nat' ), 'tc_nat', X ), hAPP( 
% 1.42/1.84    'c_SetInterval_Oord__class_OatLeastLessThan'( Z, 'tc_nat' ), U ) ) ) ]
% 1.42/1.84    ,
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( 
% 1.42/1.84    'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.42/1.84     ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.84     [ ~( =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ), =( Y, 
% 1.42/1.84    'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.42/1.84     [ ~( =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ), =( X, 
% 1.42/1.84    'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.42/1.84     [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Oone__class_Oone'( X ) ), 
% 1.42/1.84    Y ) ],
% 1.42/1.84     [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ), 
% 1.42/1.84    Y ) ],
% 1.42/1.84     [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ), 
% 1.42/1.84    Y ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ), 
% 1.42/1.84    Y ) ],
% 1.42/1.84     [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 
% 1.42/1.84    'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), X ), X ) ],
% 1.42/1.84     [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), 
% 1.42/1.84    'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), X ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Oone__class_Oone'( X ) ), 
% 1.42/1.84    Y ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ), 
% 1.42/1.84    Y ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( 
% 1.42/1.84    'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Oone__class_Oone'( X ) ), 
% 1.42/1.84    hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP( 
% 1.42/1.84    'c_Power_Opower__class_Opower'( X ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y
% 1.42/1.84     ) ), Z ) ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'( 
% 1.42/1.84    X ) ), =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.42/1.84    X ), Y ), T ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z )
% 1.42/1.84     ) ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'( 
% 1.42/1.84    X ) ), =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.42/1.84    X ), Y ), T ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z )
% 1.42/1.84     ) ) ],
% 1.42/1.84     [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.42/1.84     [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.42/1.84     [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 
% 1.42/1.84    X ), Y ), Z ) ), Z ), Y ) ],
% 1.42/1.84     [ ~( =( 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ) ) ), =( X, Y ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_Power_Opower__class_Opower'( X ), hAPP( hAPP( 
% 1.42/1.84    'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), T ), hAPP( hAPP( 
% 1.42/1.84    'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ) ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ) ],
% 1.42/1.84     [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 
% 1.42/1.84    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( 
% 1.42/1.84    'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.42/1.84     [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =( hAPP( 
% 1.42/1.84    hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.42/1.84    , 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.42/1.84    ,
% 1.42/1.84     [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), 
% 1.42/1.84    hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X ) ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ) ],
% 1.42/1.84     [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 1.42/1.84     [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 
% 1.42/1.84    X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), 
% 1.42/1.84    hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 
% 1.42/1.84    X ), Y ), Z ) ), T ) ) ],
% 1.42/1.84     [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 1.42/1.84     [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ) ],
% 1.42/1.84     [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ) ],
% 1.42/1.84     [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 
% 1.42/1.84    X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), 
% 1.42/1.84    hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 
% 1.42/1.84    X ), Y ), Z ) ), T ) ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 
% 1.42/1.84    X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 
% 1.42/1.84    hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 
% 1.42/1.84    X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), 
% 1.42/1.84    hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 1.42/1.84     [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 
% 1.42/1.84    'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP( 
% 1.42/1.84    'c_Power_Opower__class_Opower'( X ), Y ), T ) ) ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( 
% 1.42/1.84    'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( 
% 1.42/1.84    'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.42/1.84     ), ~( =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), 
% 1.42/1.84    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.42/1.84     ) ) ],
% 1.42/1.84     [ =( hAPP( 'c_COMBB'( X, Y, Z, T, U ), W ), hAPP( X, hAPP( Y, W ) ) ) ]
% 1.42/1.84    ,
% 1.42/1.84     [ =( hAPP( 'c_COMBC'( X, Y, Z, T, U ), W ), hAPP( hAPP( X, W ), Y ) ) ]
% 1.42/1.84    ,
% 1.42/1.84     [ =( hAPP( 'c_COMBS'( X, Y, Z, T, U ), W ), hAPP( hAPP( X, W ), hAPP( Y
% 1.42/1.84    , W ) ) ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y, 
% 1.42/1.84    'c_HOL_Ozero__class_Ozero'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oinverse__class_Odivide'( X ), Y ), Y ), 'c_HOL_Oone__class_Oone'( 
% 1.42/1.84    X ) ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oinverse__class_Odivide'( X ), Y ), Y ), 'c_HOL_Oone__class_Oone'( 
% 1.42/1.84    X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( 
% 1.42/1.84    'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oinverse__class_Odivide'( X ), Y ), Y ), 'c_HOL_Oone__class_Oone'( 
% 1.42/1.84    X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.84     [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), 
% 1.42/1.84    'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), =( X, 'c_HOL_Oone__class_Oone'( 
% 1.42/1.84    'tc_nat' ) ) ],
% 1.42/1.84     [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), 
% 1.42/1.84    'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), =( Y, 'c_HOL_Oone__class_Oone'( 
% 1.42/1.84    'tc_nat' ) ) ],
% 1.42/1.84     [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), hAPP( 
% 1.42/1.84    hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), 
% 1.42/1.84    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.42/1.84     [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ) ],
% 1.42/1.84     [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Ominus__class_Ominus'( X ), Y ), Y ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Ominus__class_Ominus'( X ), Z ), T ) ) ), =( Z, T ) ],
% 1.42/1.84     [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Ominus__class_Ominus'( X ), T ), T ) ) ), =( Y, Z ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), ~( 'class_Int_Onumber'( 
% 1.42/1.84    X ) ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 
% 1.42/1.84    'c_Int_Onumber__class_Onumber__of'( X ), Y ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.42/1.84    X ), hAPP( 'c_Int_Onumber__class_Onumber__of'( X ), Y ) ), Z ) ), hAPP( 
% 1.42/1.84    hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 
% 1.42/1.84    'c_Int_Onumber__class_Onumber__of'( X ), Y ) ), T ) ) ) ],
% 1.42/1.84     [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 
% 1.42/1.84    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit1'( 
% 1.42/1.84    'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), Y ) ) ],
% 1.42/1.84     [ ~( 'class_Int_Oring__char__0'( X ) ), ~( 'class_Int_Onumber__ring'( X
% 1.42/1.84     ) ), ~( =( hAPP( 'c_Int_Onumber__class_Onumber__of'( X ), Y ), hAPP( 
% 1.42/1.84    'c_Int_Onumber__class_Onumber__of'( X ), Z ) ) ), =( Y, Z ) ],
% 1.42/1.84     [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), 
% 1.42/1.84    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), 'c_HOL_Ozero__class_Ozero'( 
% 1.42/1.84    'tc_nat' ) ) ],
% 1.42/1.84     [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 
% 1.42/1.84    X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Ominus__class_Ominus'( X ), Y ), T ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Ominus__class_Ominus'( X ), Z ), U ) ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Ominus__class_Ominus'( X ), Y ), T ) ), U ) ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), T ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Ominus__class_Ominus'( X ), Z ), U ) ) ) ) ],
% 1.42/1.84     [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( 
% 1.42/1.84    'c_Finite__Set_Osetsum'( 'c_COMBS'( 'c_COMBB'( 'c_HOL_Oplus__class_Oplus'( 
% 1.42/1.84    X ), Y, X, 'tc_fun'( X, X ), Z ), T, Z, X, X ), Z, X ), U ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_Finite__Set_Osetsum'( Y, Z, X )
% 1.42/1.84    , U ) ), hAPP( 'c_Finite__Set_Osetsum'( T, Z, X ), U ) ) ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.42/1.84    X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ), U ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.42/1.84    X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ), U )
% 1.42/1.84     ) ],
% 1.42/1.84     [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ), T ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ), Y ) ), T ) ) ],
% 1.42/1.84     [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( 
% 1.42/1.84    'c_Int_Onumber__class_Onumber__of'( X ), 'c_Int_OBit0'( Y ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 
% 1.42/1.84    X ), 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP( 
% 1.42/1.84    'c_Int_Onumber__class_Onumber__of'( X ), Y ) ) ), hAPP( 
% 1.42/1.84    'c_Int_Onumber__class_Onumber__of'( X ), Y ) ) ) ],
% 1.42/1.84     [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( 
% 1.42/1.84    X ) ) ), =( Y, Z ) ],
% 1.42/1.84     [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( 
% 1.42/1.84    X ) ) ), =( Y, Z ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'( 
% 1.42/1.84    X ) ), ~( =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), 
% 1.42/1.84    'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, Z ) ],
% 1.42/1.84     [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Ominus__class_Ominus'( X ), Z ), T ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ],
% 1.42/1.84     [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Ominus__class_Ominus'( X ), Z ), T ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ],
% 1.42/1.84     [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ) ) ],
% 1.42/1.84     [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), hAPP( 
% 1.42/1.84    hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ) ],
% 1.42/1.84     [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ), T ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.42/1.84     [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ), T ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.42/1.84     [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 
% 1.42/1.84    X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) )
% 1.42/1.84    , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Ominus__class_Ominus'( X ), Y ), T ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Ominus__class_Ominus'( X ), Z ), U ) ) ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), 
% 1.42/1.84    Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( 
% 1.42/1.84    'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oinverse__class_Odivide'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X
% 1.42/1.84     ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( 
% 1.42/1.84    'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oinverse__class_Odivide'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X
% 1.42/1.84     ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.84     [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), 
% 1.42/1.84    Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.84     [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Z ) ), Y ) ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 
% 1.42/1.84    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.84    'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ), Z ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 
% 1.42/1.84    'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP( 
% 1.42/1.84    'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.42/1.84     [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( 
% 1.42/1.84    'c_Finite__Set_Osetsum'( Y, 'tc_nat', X ), hAPP( 
% 1.42/1.84    'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'( 
% 1.42/1.84    'tc_nat' ), 'tc_nat' ), hAPP( 'c_Int_Onumber__class_Onumber__of'( 
% 1.42/1.84    'tc_nat' ), 'c_Int_OBit0'( 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) )
% 1.42/1.84     ) ) ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 
% 1.42/1.84    X ), hAPP( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), hAPP( Y, 
% 1.42/1.84    'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ) ), hAPP( Y, hAPP( 
% 1.42/1.84    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.84    'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ) ) ), hAPP( Y, hAPP( 
% 1.42/1.84    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit1'( 
% 1.42/1.84    'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ) ) ) ],
% 1.42/1.84     [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), hAPP( 
% 1.42/1.84    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.84    'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), X ) ) ],
% 1.42/1.84     [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), hAPP( 
% 1.42/1.84    'c_Int_Onumber__class_Onumber__of'( X ), 'c_Int_OBit0'( 'c_Int_OBit1'( 
% 1.42/1.84    'c_Int_OPls' ) ) ) ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.42/1.84     ), Y ) ) ],
% 1.42/1.84     [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( 
% 1.42/1.84    'c_Int_Onumber__class_Onumber__of'( X ), 'c_Int_OBit0'( 'c_Int_OBit1'( 
% 1.42/1.84    'c_Int_OPls' ) ) ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y
% 1.42/1.84     ) ) ],
% 1.42/1.84     [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 
% 1.42/1.84    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.84    'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ), X ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), X ) ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( 
% 1.42/1.84    'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ) ), =( Z, 
% 1.42/1.84    'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( 
% 1.42/1.84    'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ), =( Y, 
% 1.42/1.84    'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.84     [ ~( =( 'c_Int_OBit0'( X ), 'c_Int_OBit1'( Y ) ) ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( 
% 1.42/1.84    'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), T ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), Z ) ) ],
% 1.42/1.84     [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 
% 1.42/1.84    'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( 
% 1.42/1.84    'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( 
% 1.42/1.84    'c_Finite__Set_Osetsum'( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), 
% 1.42/1.84    'tc_nat', X ), hAPP( 'c_SetInterval_Oord__class_OatLeastLessThan'( 
% 1.42/1.84    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), Z ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP( 
% 1.42/1.84    'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), 'c_HOL_Oone__class_Oone'( 
% 1.42/1.84    X ) ) ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), 
% 1.42/1.84    'c_HOL_Oone__class_Oone'( X ) ) ) ), =( Y, 'c_HOL_Oone__class_Oone'( X )
% 1.42/1.84     ) ],
% 1.42/1.84     [ =( hAPP( 'c_Finite__Set_Osetsum'( 'c_COMBS'( 'c_COMBB'( 
% 1.42/1.84    'c_HOL_Oinverse__class_Odivide'( 'tc_Complex_Ocomplex' ), 'v_a', 
% 1.42/1.84    'tc_Complex_Ocomplex', 'tc_fun'( 'tc_Complex_Ocomplex', 
% 1.42/1.84    'tc_Complex_Ocomplex' ), 'tc_nat' ), 'c_COMBB'( hAPP( 
% 1.42/1.84    'c_Power_Opower__class_Opower'( 'tc_Complex_Ocomplex' ), 
% 1.42/1.84    'c_FFT__Mirabelle_Oroot'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.42/1.84    'tc_nat' ), hAPP( 'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 
% 1.42/1.84    'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ), 'v_m' ) ) ), hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'v_i' ), 'tc_nat', 
% 1.42/1.84    'tc_Complex_Ocomplex', 'tc_nat' ), 'tc_nat', 'tc_Complex_Ocomplex', 
% 1.42/1.84    'tc_Complex_Ocomplex' ), 'tc_nat', 'tc_Complex_Ocomplex' ), hAPP( 
% 1.42/1.84    'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'( 
% 1.42/1.84    'tc_nat' ), 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.42/1.84    'tc_nat' ), hAPP( 'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 
% 1.42/1.84    'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ), 'v_m' ) ) ), hAPP( 
% 1.42/1.84    hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_Complex_Ocomplex' ), hAPP( 
% 1.42/1.84    'c_Finite__Set_Osetsum'( 'c_COMBS'( 'c_COMBB'( 
% 1.42/1.84    'c_HOL_Oinverse__class_Odivide'( 'tc_Complex_Ocomplex' ), 'c_COMBB'( 
% 1.42/1.84    'v_a', hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 
% 1.42/1.84    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.84    'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ), 'tc_nat', 'tc_Complex_Ocomplex', 
% 1.42/1.84    'tc_nat' ), 'tc_Complex_Ocomplex', 'tc_fun'( 'tc_Complex_Ocomplex', 
% 1.42/1.84    'tc_Complex_Ocomplex' ), 'tc_nat' ), 'c_COMBB'( hAPP( 
% 1.42/1.84    'c_Power_Opower__class_Opower'( 'tc_Complex_Ocomplex' ), 
% 1.42/1.84    'c_FFT__Mirabelle_Oroot'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.42/1.84    'tc_nat' ), hAPP( 'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 
% 1.42/1.84    'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ), 'v_m' ) ) ), 
% 1.42/1.84    'c_COMBB'( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'v_i' ), hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 
% 1.42/1.84    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.84    'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ), 'tc_nat', 'tc_nat', 'tc_nat' ), 
% 1.42/1.84    'tc_nat', 'tc_Complex_Ocomplex', 'tc_nat' ), 'tc_nat', 
% 1.42/1.84    'tc_Complex_Ocomplex', 'tc_Complex_Ocomplex' ), 'tc_nat', 
% 1.42/1.84    'tc_Complex_Ocomplex' ), hAPP( 
% 1.42/1.84    'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'( 
% 1.42/1.84    'tc_nat' ), 'tc_nat' ), 'v_m' ) ) ), hAPP( 'c_Finite__Set_Osetsum'( 
% 1.42/1.84    'c_COMBS'( 'c_COMBB'( 'c_HOL_Oinverse__class_Odivide'( 
% 1.42/1.84    'tc_Complex_Ocomplex' ), 'c_COMBB'( 'v_a', 'c_COMBC'( 'c_COMBB'( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 
% 1.42/1.84    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.84    'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ), 'tc_nat', 'tc_fun'( 'tc_nat', 
% 1.42/1.84    'tc_nat' ), 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat', 
% 1.42/1.84    'tc_nat', 'tc_nat' ), 'tc_nat', 'tc_Complex_Ocomplex', 'tc_nat' ), 
% 1.42/1.84    'tc_Complex_Ocomplex', 'tc_fun'( 'tc_Complex_Ocomplex', 
% 1.42/1.84    'tc_Complex_Ocomplex' ), 'tc_nat' ), 'c_COMBB'( hAPP( 
% 1.42/1.84    'c_Power_Opower__class_Opower'( 'tc_Complex_Ocomplex' ), 
% 1.42/1.84    'c_FFT__Mirabelle_Oroot'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.42/1.84    'tc_nat' ), hAPP( 'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 
% 1.42/1.84    'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ), 'v_m' ) ) ), 
% 1.42/1.84    'c_COMBB'( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'v_i' ), 
% 1.42/1.84    'c_COMBC'( 'c_COMBB'( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 
% 1.42/1.84    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.84    'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ), 'tc_nat', 'tc_fun'( 'tc_nat', 
% 1.42/1.84    'tc_nat' ), 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat', 
% 1.42/1.84    'tc_nat', 'tc_nat' ), 'tc_nat', 'tc_nat', 'tc_nat' ), 'tc_nat', 
% 1.42/1.84    'tc_Complex_Ocomplex', 'tc_nat' ), 'tc_nat', 'tc_Complex_Ocomplex', 
% 1.42/1.84    'tc_Complex_Ocomplex' ), 'tc_nat', 'tc_Complex_Ocomplex' ), hAPP( 
% 1.42/1.84    'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'( 
% 1.42/1.84    'tc_nat' ), 'tc_nat' ), 'v_m' ) ) ) ) ],
% 1.42/1.84     [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ), 
% 1.42/1.84    Y ) ],
% 1.42/1.84     [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ), 
% 1.42/1.84    Y ) ],
% 1.42/1.84     [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ), 
% 1.42/1.84    Y ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'( 
% 1.42/1.84    X ) ), =( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), 
% 1.42/1.84    'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ), 
% 1.42/1.84    Y ) ],
% 1.42/1.84     [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ), 
% 1.42/1.84    Y ) ],
% 1.42/1.84     [ =( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), 
% 1.42/1.84    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.42/1.84     [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), 
% 1.42/1.84    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ],
% 1.42/1.84     [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 
% 1.42/1.84    'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), X ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ), 
% 1.42/1.84    Y ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ), 
% 1.42/1.84    Y ) ],
% 1.42/1.84     [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 
% 1.42/1.84    X ), Y ), Z ) ), Z ), Y ) ],
% 1.42/1.84     [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), X ), Y ) ],
% 1.42/1.84     [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), Y ), X ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( 
% 1.42/1.84    'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( 
% 1.42/1.84    'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.42/1.84     ), ~( =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 
% 1.42/1.84    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), Z ) ), 
% 1.42/1.84    'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.42/1.84     ) ) ],
% 1.42/1.84     [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), T ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ) ) ],
% 1.42/1.84     [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =( hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), T ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ) ) ],
% 1.42/1.84     [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_Complex_Ocomplex' )
% 1.42/1.84    , hAPP( 'c_Finite__Set_Osetsum'( 'c_COMBS'( 'c_COMBB'( 
% 1.42/1.84    'c_HOL_Oinverse__class_Odivide'( 'tc_Complex_Ocomplex' ), 'c_COMBB'( 
% 1.42/1.84    'v_a', hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 
% 1.42/1.84    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.84    'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ), 'tc_nat', 'tc_Complex_Ocomplex', 
% 1.42/1.84    'tc_nat' ), 'tc_Complex_Ocomplex', 'tc_fun'( 'tc_Complex_Ocomplex', 
% 1.42/1.84    'tc_Complex_Ocomplex' ), 'tc_nat' ), 'c_COMBB'( hAPP( 
% 1.42/1.84    'c_Power_Opower__class_Opower'( 'tc_Complex_Ocomplex' ), 
% 1.42/1.84    'c_FFT__Mirabelle_Oroot'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.42/1.84    'tc_nat' ), hAPP( 'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 
% 1.42/1.84    'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ), 'v_m' ) ) ), 
% 1.42/1.84    'c_COMBB'( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'v_i' ), hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 
% 1.42/1.84    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.84    'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ), 'tc_nat', 'tc_nat', 'tc_nat' ), 
% 1.42/1.84    'tc_nat', 'tc_Complex_Ocomplex', 'tc_nat' ), 'tc_nat', 
% 1.42/1.84    'tc_Complex_Ocomplex', 'tc_Complex_Ocomplex' ), 'tc_nat', 
% 1.42/1.84    'tc_Complex_Ocomplex' ), hAPP( 
% 1.42/1.84    'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'( 
% 1.42/1.84    'tc_nat' ), 'tc_nat' ), 'v_m' ) ) ), hAPP( 'c_Finite__Set_Osetsum'( 
% 1.42/1.84    'c_COMBS'( 'c_COMBB'( 'c_HOL_Oinverse__class_Odivide'( 
% 1.42/1.84    'tc_Complex_Ocomplex' ), 'c_COMBB'( 'v_a', 'c_COMBC'( 'c_COMBB'( 
% 1.42/1.84    'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 
% 1.42/1.84    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.84    'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ), 'tc_nat', 'tc_fun'( 'tc_nat', 
% 1.42/1.84    'tc_nat' ), 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat', 
% 1.42/1.84    'tc_nat', 'tc_nat' ), 'tc_nat', 'tc_Complex_Ocomplex', 'tc_nat' ), 
% 1.42/1.84    'tc_Complex_Ocomplex', 'tc_fun'( 'tc_Complex_Ocomplex', 
% 1.42/1.84    'tc_Complex_Ocomplex' ), 'tc_nat' ), 'c_COMBB'( hAPP( 
% 1.42/1.84    'c_Power_Opower__class_Opower'( 'tc_Complex_Ocomplex' ), 
% 1.42/1.84    'c_FFT__Mirabelle_Oroot'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.42/1.84    'tc_nat' ), hAPP( 'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 
% 1.42/1.84    'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ), 'v_m' ) ) ), 
% 1.42/1.84    'c_COMBB'( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'v_i' ), 
% 1.42/1.84    'c_COMBC'( 'c_COMBB'( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 
% 1.42/1.84    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.84    'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ), 'tc_nat', 'tc_fun'( 'tc_nat', 
% 1.42/1.84    'tc_nat' ), 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat', 
% 1.42/1.84    'tc_nat', 'tc_nat' ), 'tc_nat', 'tc_nat', 'tc_nat' ), 'tc_nat', 
% 1.42/1.84    'tc_Complex_Ocomplex', 'tc_nat' ), 'tc_nat', 'tc_Complex_Ocomplex', 
% 1.42/1.84    'tc_Complex_Ocomplex' ), 'tc_nat', 'tc_Complex_Ocomplex' ), hAPP( 
% 1.42/1.84    'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'( 
% 1.42/1.84    'tc_nat' ), 'tc_nat' ), 'v_m' ) ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Ominus__class_Ominus'( 'tc_Complex_Ocomplex' ), hAPP( 
% 1.42/1.84    'c_Finite__Set_Osetsum'( 'c_COMBS'( 'c_COMBB'( 
% 1.42/1.84    'c_HOL_Oinverse__class_Odivide'( 'tc_Complex_Ocomplex' ), 'c_COMBB'( 
% 1.42/1.84    'v_a', hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 
% 1.42/1.84    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.84    'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ), 'tc_nat', 'tc_Complex_Ocomplex', 
% 1.42/1.84    'tc_nat' ), 'tc_Complex_Ocomplex', 'tc_fun'( 'tc_Complex_Ocomplex', 
% 1.42/1.84    'tc_Complex_Ocomplex' ), 'tc_nat' ), 'c_COMBB'( hAPP( 
% 1.42/1.84    'c_Power_Opower__class_Opower'( 'tc_Complex_Ocomplex' ), 
% 1.42/1.84    'c_FFT__Mirabelle_Oroot'( 'v_m' ) ), hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.42/1.84    'tc_nat' ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), 'v_i' )
% 1.42/1.84    , 'v_m' ) ), 'tc_nat', 'tc_Complex_Ocomplex', 'tc_nat' ), 'tc_nat', 
% 1.42/1.84    'tc_Complex_Ocomplex', 'tc_Complex_Ocomplex' ), 'tc_nat', 
% 1.42/1.84    'tc_Complex_Ocomplex' ), hAPP( 
% 1.42/1.84    'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'( 
% 1.42/1.84    'tc_nat' ), 'tc_nat' ), 'v_m' ) ) ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( 'tc_Complex_Ocomplex' ), hAPP( hAPP( 
% 1.42/1.84    'c_Power_Opower__class_Opower'( 'tc_Complex_Ocomplex' ), hAPP( hAPP( 
% 1.42/1.84    'c_HOL_Oinverse__class_Odivide'( 'tc_Complex_Ocomplex' ), 
% 1.42/1.84    'c_HOL_Oone__class_Oone'( 'tc_Complex_Ocomplex' ) ), 
% 1.42/1.84    'c_FFT__Mirabelle_Oroot'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.42/1.84    'tc_nat' ), hAPP( 'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 
% 1.42/1.84    'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ), 'v_m' ) ) ) ), hAPP( 
% 1.42/1.84    hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), 'v_i' ), 'v_m' ) ) ), 
% 1.42/1.84    hAPP( 'c_Finite__Set_Osetsum'( 'c_COMBS'( 'c_COMBB'( 
% 1.42/1.84    'c_HOL_Oinverse__class_Odivide'( 'tc_Complex_Ocomplex' ), 'c_COMBB'( 
% 1.42/1.84    'v_a', 'c_COMBC'( 'c_COMBB'( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( 
% 1.42/1.84    'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 
% 1.42/1.84    'c_Int_Onumber__class_Onumber__of'( 'tc_nat' ), 'c_Int_OBit0'( 
% 1.42/1.84    'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ), 'tc_nat', 'tc_fun'( 'tc_nat', 
% 1.42/1.84    'tc_nat' ), 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat', 
% 1.42/1.84    'tc_nat', 'tc_nat' ), 'tc_nat', 'tc_Complex_Ocomplex', 'tc_nat' ), 
% 1.42/1.84    'tc_Complex_Ocomplex', 'tc_fun'( 'tc_Complex_Ocomplex', 
% 1.42/1.84    'tc_Complex_Ocomplex' ), 'tc_nat' ), 'c_COMBB'( hAPP( 
% 1.42/1.84    'c_Power_Opower__class_Opower'( 'tc_Complex_Ocomplex' ), 
% 1.42/1.84    'c_FFT__Mirabelle_Oroot'( 'v_m' ) ), hAPP( 'c_HOL_Otimes__class_Otimes'( 
% 1.42/1.84    'tc_nat' ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), 'v_i' )
% 1.42/1.84    , 'v_m' ) ), 'tc_nat', 'tc_Complex_Ocomplex', 'tc_nat' ), 'tc_nat', 
% 1.42/1.84    'tc_Complex_Ocomplex', 'tc_Complex_Ocomplex' ), 'tc_nat', 
% 1.42/1.84    'tc_Complex_Ocomplex' ), hAPP( 
% 1.42/1.84    'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'( 
% 1.42/1.84    'tc_nat' ), 'tc_nat' ), 'v_m' ) ) ) ) ) ) ],
% 1.42/1.84     [ 'class_Lattices_Oboolean__algebra'( 'tc_fun'( X, Y ) ), ~( 
% 1.42/1.84    'class_Lattices_Oboolean__algebra'( Y ) ) ],
% 1.42/1.84     [ 'class_Orderings_Opreorder'( 'tc_fun'( X, Y ) ), ~( 
% 1.42/1.84    'class_Orderings_Opreorder'( Y ) ) ],
% 1.42/1.84     [ 'class_Orderings_Oorder'( 'tc_fun'( X, Y ) ), ~( 
% 1.42/1.84    'class_Orderings_Oorder'( Y ) ) ],
% 1.42/1.84     [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( 'tc_nat' )
% 1.42/1.84     ],
% 1.42/1.84     [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( 'tc_nat'
% 1.42/1.84     ) ],
% 1.42/1.84     [ 'class_Ring__and__Field_Oordered__comm__semiring__strict'( 'tc_nat' )
% 1.42/1.84     ],
% 1.42/1.84     [ 'class_Ring__and__Field_Opordered__cancel__semiring'( 'tc_nat' ) ]
% 1.42/1.84    ,
% 1.42/1.84     [ 'class_Ring__and__Field_Oordered__semiring__strict'( 'tc_nat' ) ],
% 1.42/1.84     [ 'class_OrderedGroup_Opordered__ab__semigroup__add'( 'tc_nat' ) ],
% 1.42/1.84     [ 'class_OrderedGroup_Opordered__comm__monoid__add'( 'tc_nat' ) ],
% 1.42/1.84     [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'( 'tc_nat' ) ],
% 1.42/1.84     [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_nat' ) ],
% 1.42/1.84     [ 'class_Ring__and__Field_Opordered__semiring'( 'tc_nat' ) ],
% 1.42/1.84     [ 'class_Ring__and__Field_Oordered__semiring'( 'tc_nat' ) ],
% 1.42/1.84     [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_nat' ) ],
% 1.42/1.84     [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_nat' ) ],
% 1.42/1.84     [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_nat' ) ],
% 1.42/1.84     [ 'class_Ring__and__Field_Ocomm__semiring__0'( 'tc_nat' ) ],
% 1.42/1.84     [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_nat' ) ],
% 1.42/1.84     [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_nat' ) ],
% 1.42/1.84     [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_nat' ) ],
% 1.42/1.84     [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_nat' ) ],
% 1.42/1.84     [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_nat' ) ],
% 1.42/1.84     [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_nat' ) ],
% 1.42/1.84     [ 'class_Ring__and__Field_Osemiring__1'( 'tc_nat' ) ],
% 1.42/1.84     [ 'class_Ring__and__Field_Osemiring__0'( 'tc_nat' ) ],
% 1.42/1.84     [ 'class_Ring__and__Field_Omult__mono1'( 'tc_nat' ) ],
% 1.42/1.84     [ 'class_Ring__and__Field_Omult__zero'( 'tc_nat' ) ],
% 1.42/1.84     [ 'class_Ring__and__Field_Omult__mono'( 'tc_nat' ) ],
% 1.42/1.84     [ 'class_OrderedGroup_Omonoid__mult'( 'tc_nat' ) ],
% 1.42/1.84     [ 'class_Ring__and__Field_Osemiring'( 'tc_nat' ) ],
% 1.42/1.84     [ 'class_OrderedGroup_Omonoid__add'( 'tc_nat' ) ],
% 1.42/1.84     [ 'class_Divides_Osemiring__div'( 'tc_nat' ) ],
% 1.42/1.84     [ 'class_Nat_Osemiring__char__0'( 'tc_nat' ) ],
% 1.42/1.84     [ 'class_Orderings_Opreorder'( 'tc_nat' ) ],
% 1.42/1.84     [ 'class_Orderings_Olinorder'( 'tc_nat' ) ],
% 1.42/1.84     [ 'class_Orderings_Oorder'( 'tc_nat' ) ],
% 1.42/1.84     [ 'class_Power_Opower'( 'tc_nat' ) ],
% 1.42/1.84     [ 'class_Int_Onumber'( 'tc_nat' ) ],
% 1.42/1.84     [ 'class_Lattices_Oboolean__algebra'( 'tc_bool' ) ],
% 1.42/1.84     [ 'class_Orderings_Opreorder'( 'tc_bool' ) ],
% 1.42/1.84     [ 'class_Orderings_Oorder'( 'tc_bool' ) ],
% 1.42/1.84     [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( 
% 1.42/1.85    'tc_Int_Oint' ) ],
% 1.42/1.85     [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( 
% 1.42/1.85    'tc_Int_Oint' ) ],
% 1.42/1.85     [ 'class_Ring__and__Field_Oordered__comm__semiring__strict'( 
% 1.42/1.85    'tc_Int_Oint' ) ],
% 1.42/1.85     [ 'class_Ring__and__Field_Opordered__cancel__semiring'( 'tc_Int_Oint' )
% 1.42/1.85     ],
% 1.42/1.85     [ 'class_Ring__and__Field_Oring__1__no__zero__divisors'( 'tc_Int_Oint' )
% 1.42/1.85     ],
% 1.42/1.85     [ 'class_Ring__and__Field_Oordered__semiring__strict'( 'tc_Int_Oint' ) ]
% 1.42/1.85    ,
% 1.42/1.85     [ 'class_OrderedGroup_Opordered__ab__semigroup__add'( 'tc_Int_Oint' ) ]
% 1.42/1.85    ,
% 1.42/1.85     [ 'class_OrderedGroup_Opordered__ab__group__add__abs'( 'tc_Int_Oint' ) ]
% 1.42/1.85    ,
% 1.42/1.85     [ 'class_OrderedGroup_Olordered__ab__group__add__abs'( 'tc_Int_Oint' ) ]
% 1.42/1.85    ,
% 1.42/1.85     [ 'class_OrderedGroup_Opordered__comm__monoid__add'( 'tc_Int_Oint' ) ]
% 1.42/1.85    ,
% 1.42/1.85     [ 'class_Ring__and__Field_Oring__no__zero__divisors'( 'tc_Int_Oint' ) ]
% 1.42/1.85    ,
% 1.42/1.85     [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'( 'tc_Int_Oint' ) ]
% 1.42/1.85    ,
% 1.42/1.85     [ 'class_Ring__and__Field_Oordered__ring__strict'( 'tc_Int_Oint' ) ]
% 1.42/1.85    ,
% 1.42/1.85     [ 'class_OrderedGroup_Opordered__ab__group__add'( 'tc_Int_Oint' ) ],
% 1.42/1.85     [ 'class_OrderedGroup_Olordered__ab__group__add'( 'tc_Int_Oint' ) ],
% 1.42/1.85     [ 'class_OrderedGroup_Oordered__ab__group__add'( 'tc_Int_Oint' ) ],
% 1.42/1.85     [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_Int_Oint' ) ],
% 1.42/1.85     [ 'class_Ring__and__Field_Opordered__semiring'( 'tc_Int_Oint' ) ],
% 1.42/1.85     [ 'class_Ring__and__Field_Opordered__ring__abs'( 'tc_Int_Oint' ) ],
% 1.42/1.85     [ 'class_Ring__and__Field_Oordered__semiring'( 'tc_Int_Oint' ) ],
% 1.42/1.85     [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_Int_Oint' ) ],
% 1.42/1.85     [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_Int_Oint' ) ],
% 1.42/1.85     [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_Int_Oint' ) ],
% 1.42/1.85     [ 'class_Ring__and__Field_Ocomm__semiring__0'( 'tc_Int_Oint' ) ],
% 1.42/1.85     [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_Int_Oint' ) ],
% 1.42/1.85     [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_Int_Oint' ) ],
% 1.42/1.85     [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_Int_Oint' ) ],
% 1.42/1.85     [ 'class_Ring__and__Field_Opordered__ring'( 'tc_Int_Oint' ) ],
% 1.42/1.85     [ 'class_Ring__and__Field_Olordered__ring'( 'tc_Int_Oint' ) ],
% 1.42/1.85     [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_Int_Oint' ) ],
% 1.42/1.85     [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_Int_Oint' ) ],
% 1.42/1.85     [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_Int_Oint' ) ],
% 1.42/1.85     [ 'class_Ring__and__Field_Oordered__idom'( 'tc_Int_Oint' ) ],
% 1.42/1.85     [ 'class_Ring__and__Field_Ocomm__ring__1'( 'tc_Int_Oint' ) ],
% 1.42/1.85     [ 'class_Ring__and__Field_Osemiring__1'( 'tc_Int_Oint' ) ],
% 1.42/1.85     [ 'class_Ring__and__Field_Osemiring__0'( 'tc_Int_Oint' ) ],
% 1.42/1.85     [ 'class_Ring__and__Field_Omult__mono1'( 'tc_Int_Oint' ) ],
% 1.42/1.85     [ 'class_OrderedGroup_Oab__group__add'( 'tc_Int_Oint' ) ],
% 1.42/1.85     [ 'class_Ring__and__Field_Omult__zero'( 'tc_Int_Oint' ) ],
% 1.42/1.85     [ 'class_Ring__and__Field_Omult__mono'( 'tc_Int_Oint' ) ],
% 1.42/1.85     [ 'class_Ring__and__Field_Ocomm__ring'( 'tc_Int_Oint' ) ],
% 1.42/1.85     [ 'class_OrderedGroup_Omonoid__mult'( 'tc_Int_Oint' ) ],
% 1.42/1.85     [ 'class_Ring__and__Field_Osemiring'( 'tc_Int_Oint' ) ],
% 1.42/1.85     [ 'class_OrderedGroup_Omonoid__add'( 'tc_Int_Oint' ) ],
% 1.42/1.85     [ 'class_OrderedGroup_Ogroup__add'( 'tc_Int_Oint' ) ],
% 1.42/1.85     [ 'class_Ring__and__Field_Oring__1'( 'tc_Int_Oint' ) ],
% 1.42/1.85     [ 'class_Ring__and__Field_Oabs__if'( 'tc_Int_Oint' ) ],
% 1.42/1.85     [ 'class_Divides_Osemiring__div'( 'tc_Int_Oint' ) ],
% 1.42/1.85     [ 'class_Ring__and__Field_Oring'( 'tc_Int_Oint' ) ],
% 1.42/1.85     [ 'class_Ring__and__Field_Oidom'( 'tc_Int_Oint' ) ],
% 1.42/1.85     [ 'class_Nat_Osemiring__char__0'( 'tc_Int_Oint' ) ],
% 1.42/1.85     [ 'class_Orderings_Opreorder'( 'tc_Int_Oint' ) ],
% 1.42/1.85     [ 'class_Orderings_Olinorder'( 'tc_Int_Oint' ) ],
% 1.42/1.85     [ 'class_Divides_Oring__div'( 'tc_Int_Oint' ) ],
% 1.42/1.85     [ 'class_Orderings_Oorder'( 'tc_Int_Oint' ) ],
% 1.42/1.85     [ 'class_Int_Oring__char__0'( 'tc_Int_Oint' ) ],
% 1.42/1.85     [ 'class_Int_Onumber__ring'( 'tc_Int_Oint' ) ],
% 1.42/1.85     [ 'class_Power_Opower'( 'tc_Int_Oint' ) ],
% 1.42/1.85     [ 'class_Int_Onumber'( 'tc_Int_Oint' ) ],
% 1.42/1.85     [ 'class_Ring__and__Field_Oring__1__no__zero__divisors'( 
% 1.42/1.85    'tc_Complex_Ocomplex' ) ],
% 1.42/1.85     [ 'class_Ring__and__Field_Oring__no__zero__divisors'( 
% 1.42/1.85    'tc_Complex_Ocomplex' ) ],
% 1.42/1.85     [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'( 
% 1.42/1.85    'tc_Complex_Ocomplex' ) ],
% 1.42/1.85     [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_Complex_Ocomplex' )
% 1.42/1.85     ],
% 1.42/1.85     [ 'class_RealVector_Oreal__normed__algebra__1'( 'tc_Complex_Ocomplex' )
% 1.42/1.85     ],
% 1.42/1.85     [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_Complex_Ocomplex' )
% 1.42/1.85     ],
% 1.42/1.85     [ 'class_Ring__and__Field_Odivision__by__zero'( 'tc_Complex_Ocomplex' )
% 1.42/1.85     ],
% 1.42/1.85     [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_Complex_Ocomplex' ) ]
% 1.42/1.85    ,
% 1.42/1.85     [ 'class_Ring__and__Field_Ocomm__semiring__0'( 'tc_Complex_Ocomplex' ) ]
% 1.42/1.85    ,
% 1.42/1.85     [ 'class_RealVector_Oreal__normed__algebra'( 'tc_Complex_Ocomplex' ) ]
% 1.42/1.85    ,
% 1.42/1.85     [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_Complex_Ocomplex' ) ]
% 1.42/1.85    ,
% 1.42/1.85     [ 'class_RealVector_Oreal__normed__vector'( 'tc_Complex_Ocomplex' ) ]
% 1.42/1.85    ,
% 1.42/1.85     [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_Complex_Ocomplex' ) ]
% 1.42/1.85    ,
% 1.42/1.85     [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_Complex_Ocomplex' ) ]
% 1.42/1.85    ,
% 1.42/1.85     [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_Complex_Ocomplex' ) ]
% 1.42/1.85    ,
% 1.42/1.85     [ 'class_RealVector_Oreal__normed__field'( 'tc_Complex_Ocomplex' ) ]
% 1.42/1.85    ,
% 1.42/1.85     [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_Complex_Ocomplex' ) ]
% 1.42/1.85    ,
% 1.42/1.85     [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_Complex_Ocomplex' ) ]
% 1.42/1.85    ,
% 1.42/1.85     [ 'class_Ring__and__Field_Ocomm__ring__1'( 'tc_Complex_Ocomplex' ) ]
% 1.42/1.85    ,
% 1.42/1.85     [ 'class_Ring__and__Field_Osemiring__1'( 'tc_Complex_Ocomplex' ) ],
% 1.42/1.85     [ 'class_Ring__and__Field_Osemiring__0'( 'tc_Complex_Ocomplex' ) ],
% 1.42/1.85     [ 'class_OrderedGroup_Oab__group__add'( 'tc_Complex_Ocomplex' ) ],
% 1.42/1.85     [ 'class_Ring__and__Field_Omult__zero'( 'tc_Complex_Ocomplex' ) ],
% 1.42/1.85     [ 'class_Ring__and__Field_Ocomm__ring'( 'tc_Complex_Ocomplex' ) ],
% 1.42/1.85     [ 'class_OrderedGroup_Omonoid__mult'( 'tc_Complex_Ocomplex' ) ],
% 1.42/1.85     [ 'class_Ring__and__Field_Osemiring'( 'tc_Complex_Ocomplex' ) ],
% 1.42/1.85     [ 'class_OrderedGroup_Omonoid__add'( 'tc_Complex_Ocomplex' ) ],
% 1.42/1.85     [ 'class_OrderedGroup_Ogroup__add'( 'tc_Complex_Ocomplex' ) ],
% 1.42/1.85     [ 'class_Ring__and__Field_Oring__1'( 'tc_Complex_Ocomplex' ) ],
% 1.42/1.85     [ 'class_RealVector_Oreal__field'( 'tc_Complex_Ocomplex' ) ],
% 1.42/1.85     [ 'class_Ring__and__Field_Ofield'( 'tc_Complex_Ocomplex' ) ],
% 1.42/1.85     [ 'class_Ring__and__Field_Oring'( 'tc_Complex_Ocomplex' ) ],
% 1.42/1.85     [ 'class_Ring__and__Field_Oidom'( 'tc_Complex_Ocomplex' ) ],
% 1.42/1.85     [ 'class_Nat_Osemiring__char__0'( 'tc_Complex_Ocomplex' ) ],
% 1.42/1.85     [ 'class_Int_Oring__char__0'( 'tc_Complex_Ocomplex' ) ],
% 1.42/1.85     [ 'class_Int_Onumber__ring'( 'tc_Complex_Ocomplex' ) ],
% 1.42/1.85     [ 'class_Power_Opower'( 'tc_Complex_Ocomplex' ) ],
% 1.42/1.85     [ 'class_Int_Onumber'( 'tc_Complex_Ocomplex' ) ],
% 1.42/1.85     [ =( hAPP( 'c_COMBS'( X, Y, Z, T, U ), W ), hAPP( hAPP( X, W ), hAPP( Y
% 1.42/1.85    , W ) ) ) ],
% 1.42/1.85     [ =( hAPP( 'c_COMBC'( X, Y, Z, T, U ), W ), hAPP( hAPP( X, W ), Y ) ) ]
% 1.42/1.85    ,
% 1.42/1.85     [ =( hAPP( 'c_COMBB'( X, Y, Z, T, U ), W ), hAPP( X, hAPP( Y, W ) ) ) ]
% 1.42/1.85    ,
% 1.42/1.85     [ 'c_fequal'( X, X, Y ) ],
% 1.42/1.85     [ =( X, Y ), ~( 'c_fequal'( X, Y, Z ) ) ]
% 1.42/1.85  ] .
% 1.42/1.85  
% 1.42/1.85  
% 1.42/1.85  percentage equality = 0.241413, percentage horn = 0.865625
% 1.42/1.85  This is a problem with some equality
% 1.42/1.85  
% 1.42/1.85  
% 1.42/1.85  
% 1.42/1.85  Options Used:
% 1.42/1.85  
% 1.42/1.85  useres =            1
% 1.42/1.85  useparamod =        1
% 1.42/1.85  useeqrefl =         1
% 1.42/1.85  useeqfact =         1
% 1.42/1.85  usefactor =         1
% 1.42/1.85  usesimpsplitting =  0
% 1.42/1.85  usesimpdemod =      5
% 1.42/1.85  usesimpres =        3
% 1.42/1.85  
% 1.42/1.85  resimpinuse      =  1000
% 1.42/1.85  resimpclauses =     20000
% 1.42/1.85  substype =          eqrewr
% 1.42/1.85  backwardsubs =      1
% 1.42/1.85  selectoldest =      5
% 1.42/1.85  
% 1.42/1.85  litorderings [0] =  split
% 1.42/1.85  litorderings [1] =  extend the termordering, first sorting on arguments
% 1.42/1.85  
% 1.42/1.85  termordering =      kbo
% 1.42/1.85  
% 1.42/1.85  litapriori =        0
% 1.42/1.85  termapriori =       1
% 1.42/1.85  litaposteriori =    0
% 1.42/1.85  termaposteriori =   0
% 1.42/1.85  demodaposteriori =  0
% 1.42/1.85  ordereqreflfact =   0
% 1.42/1.85  
% 1.42/1.85  litselect =         negord
% 1.42/1.85  
% 1.42/1.85  maxweight =         15
% 1.42/1.85  maxdepth =          30000
% 1.42/1.85  maxlength =         115
% 1.42/1.85  maxnrvars =         195
% 1.42/1.85  excuselevel =       1
% 1.42/1.85  increasemaxweight = 1
% 1.42/1.85  
% 1.42/1.85  maxselected =       10000000
% 1.42/1.85  maxnrclauses =      10000000
% 1.42/1.85  
% 1.42/1.85  showgenerated =    0
% 1.42/1.85  showkept =         0
% 1.42/1.85  showselected =     0
% 1.42/1.85  showdeleted =      0
% 1.42/1.85  showresimp =       1
% 1.42/1.85  showstatus =       2000
% 1.42/1.85  
% 1.42/1.85  prologoutput =     1
% 1.42/1.85  nrgoals =          5000000
% 1.42/1.85  totalproof =       1
% 1.42/1.85  
% 1.42/1.85  Symbols occurring in the translation:
% 1.42/1.85  
% 1.42/1.85  {}  [0, 0]      (w:1, o:2, a:1, s:1, b:0), 
% 1.42/1.85  .  [1, 2]      (w:1, o:177, a:1, s:1, b:0), 
% 1.42/1.85  !  [4, 1]      (w:0, o:88, a:1, s:1, b:0), 
% 1.42/1.85  =  [13, 2]      (w:1, o:0, a:0, s:1, b:0), 
% 1.42/1.85  ==>  [14, 2]      (w:1, o:0, a:0, s:1, b:0), 
% 1.42/1.85  'tc_nat'  [41, 0]      (w:1, o:17, a:1, s:1, b:0), 
% 1.42/1.85  'c_HOL_Oord__class_Oless'  [42, 3]      (w:1, o:209, a:1, s:1, b:0), 
% 1.42/1.85  'tc_Int_Oint'  [45, 0]      (w:1, o:29, a:1, s:1, b:0), 
% 1.42/1.85  'c_lessequals'  [46, 3]      (w:1, o:210, a:1, s:1, b:0), 
% 1.42/1.85  'class_Orderings_Oorder'  [48, 1]      (w:1, o:94, a:1, s:1, b:0), 
% 1.42/1.85  'class_Orderings_Olinorder'  [51, 1]      (w:1, o:95, a:1, s:1, b:0), 
% 1.42/1.85  'class_Ring__and__Field_Oordered__idom'  [52, 1]      (w:1, o:98, a:1, s:1
% 1.42/1.85    , b:0), 
% 1.42/1.85  'class_OrderedGroup_Opordered__ab__group__add__abs'  [53, 1]      (w:1, o:
% 1.42/1.85    100, a:1, s:1, b:0), 
% 1.42/1.85  'c_HOL_Oabs__class_Oabs'  [54, 1]      (w:1, o:101, a:1, s:1, b:0), 
% 1.42/1.85  hAPP  [56, 2]      (w:1, o:202, a:1, s:1, b:0), 
% 1.42/1.85  'c_HOL_Ozero__class_Ozero'  [57, 1]      (w:1, o:102, a:1, s:1, b:0), 
% 1.42/1.85  'c_Power_Opower__class_Opower'  [58, 1]      (w:1, o:103, a:1, s:1, b:0), 
% 1.42/1.85  'c_Parity_Oeven__odd__class_Oeven'  [59, 2]      (w:1, o:203, a:1, s:1, b:0
% 1.42/1.85    ), 
% 1.42/1.85  'c_Suc'  [60, 0]      (w:1, o:34, a:1, s:1, b:0), 
% 1.42/1.85  'c_HOL_Oplus__class_Oplus'  [64, 1]      (w:1, o:105, a:1, s:1, b:0), 
% 1.42/1.85  'c_Groebner__Basis_Ogb__semiring'  [71, 6]      (w:1, o:225, a:1, s:1, b:0)
% 1.42/1.85    , 
% 1.42/1.85  'class_RealVector_Oreal__normed__field'  [72, 1]      (w:1, o:106, a:1, s:1
% 1.42/1.85    , b:0), 
% 1.42/1.85  'c_Deriv_Oderiv'  [76, 4]      (w:1, o:220, a:1, s:1, b:0), 
% 1.42/1.85  hBOOL  [78, 1]      (w:1, o:107, a:1, s:1, b:0), 
% 1.42/1.85  'class_Lattices_Oboolean__algebra'  [79, 1]      (w:1, o:108, a:1, s:1, b:0
% 1.42/1.85    ), 
% 1.42/1.85  'c_HOL_Ouminus__class_Ouminus'  [80, 1]      (w:1, o:110, a:1, s:1, b:0), 
% 1.42/1.85  'class_OrderedGroup_Ogroup__add'  [81, 1]      (w:1, o:111, a:1, s:1, b:0)
% 1.42/1.85    , 
% 1.42/1.85  'class_OrderedGroup_Olordered__ab__group__add__abs'  [83, 1]      (w:1, o:
% 1.42/1.85    112, a:1, s:1, b:0), 
% 1.42/1.85  'c_Divides_Odiv__class_Omod'  [85, 3]      (w:1, o:211, a:1, s:1, b:0), 
% 1.42/1.85  'c_Int_Onumber__class_Onumber__of'  [86, 1]      (w:1, o:115, a:1, s:1, b:0
% 1.42/1.85    ), 
% 1.42/1.85  'class_Int_Onumber__ring'  [89, 1]      (w:1, o:116, a:1, s:1, b:0), 
% 1.42/1.85  'c_Fact_Ofact__class_Ofact'  [90, 2]      (w:1, o:204, a:1, s:1, b:0), 
% 1.42/1.85  'class_OrderedGroup_Opordered__ab__group__add'  [91, 1]      (w:1, o:117
% 1.42/1.85    , a:1, s:1, b:0), 
% 1.42/1.85  'c_HOL_Ominus__class_Ominus'  [92, 1]      (w:1, o:113, a:1, s:1, b:0), 
% 1.42/1.85  'c_Divides_Odiv__class_Odiv'  [93, 3]      (w:1, o:212, a:1, s:1, b:0), 
% 1.42/1.85  'tc_Complex_Ocomplex'  [94, 0]      (w:1, o:59, a:1, s:1, b:0), 
% 1.42/1.85  'c_HOL_Otimes__class_Otimes'  [95, 1]      (w:1, o:109, a:1, s:1, b:0), 
% 1.42/1.85  'c_Complex_Oii'  [96, 0]      (w:1, o:60, a:1, s:1, b:0), 
% 1.42/1.85  'class_Ring__and__Field_Oabs__if'  [97, 1]      (w:1, o:118, a:1, s:1, b:0)
% 1.42/1.85    , 
% 1.42/1.85  'class_Nat_Osemiring__char__0'  [98, 1]      (w:1, o:93, a:1, s:1, b:0), 
% 1.42/1.85  'c_Nat_Osemiring__1__class_Oof__nat'  [99, 1]      (w:1, o:119, a:1, s:1
% 1.42/1.85    , b:0), 
% 1.42/1.85  'class_OrderedGroup_Ocomm__monoid__add'  [100, 1]      (w:1, o:120, a:1, s:
% 1.42/1.85    1, b:0), 
% 1.42/1.85  'c_Finite__Set_Osetsum'  [101, 3]      (w:1, o:213, a:1, s:1, b:0), 
% 1.42/1.85  'c_SetInterval_Oord__class_OatLeastAtMost'  [102, 3]      (w:1, o:214, a:1
% 1.42/1.85    , s:1, b:0), 
% 1.42/1.85  'c_Fun_Oinj__on'  [104, 4]      (w:1, o:221, a:1, s:1, b:0), 
% 1.42/1.85  'c_Int_OMin'  [105, 0]      (w:1, o:62, a:1, s:1, b:0), 
% 1.42/1.85  'c_Int_OBit0'  [106, 1]      (w:1, o:121, a:1, s:1, b:0), 
% 1.42/1.85  'c_Int_OBit1'  [107, 1]      (w:1, o:122, a:1, s:1, b:0), 
% 1.42/1.85  'class_Ring__and__Field_Olordered__ring'  [108, 1]      (w:1, o:123, a:1
% 1.42/1.85    , s:1, b:0), 
% 1.42/1.85  'class_Ring__and__Field_Oordered__semidom'  [109, 1]      (w:1, o:125, a:1
% 1.42/1.85    , s:1, b:0), 
% 1.42/1.85  'class_Orderings_Opreorder'  [111, 1]      (w:1, o:126, a:1, s:1, b:0), 
% 1.42/1.85  'c_Groebner__Basis_Osemiringb'  [116, 6]      (w:1, o:226, a:1, s:1, b:0), 
% 1.42/1.85    
% 1.42/1.85  'c_SetInterval_Oord__class_OlessThan'  [117, 2]      (w:1, o:205, a:1, s:1
% 1.42/1.85    , b:0), 
% 1.42/1.85  'c_Int_OPls'  [118, 0]      (w:1, o:68, a:1, s:1, b:0), 
% 1.42/1.85  'c_HOL_Oone__class_Oone'  [119, 1]      (w:1, o:104, a:1, s:1, b:0), 
% 1.42/1.85  'class_Divides_Oring__div'  [120, 1]      (w:1, o:127, a:1, s:1, b:0), 
% 1.42/1.85  'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'  [125, 1]      
% 1.42/1.85    (w:1, o:128, a:1, s:1, b:0), 
% 1.42/1.85  'class_OrderedGroup_Oordered__ab__group__add'  [128, 1]      (w:1, o:99, a:
% 1.42/1.85    1, s:1, b:0), 
% 1.42/1.85  'class_Divides_Osemiring__div'  [129, 1]      (w:1, o:129, a:1, s:1, b:0), 
% 4.48/4.89    
% 4.48/4.89  'class_Ring__and__Field_Oordered__semiring__strict'  [130, 1]      (w:1, o:
% 4.48/4.89    130, a:1, s:1, b:0), 
% 4.48/4.89  'class_Ring__and__Field_Opordered__ring__abs'  [131, 1]      (w:1, o:134
% 4.48/4.89    , a:1, s:1, b:0), 
% 4.48/4.89  'class_Ring__and__Field_Oordered__semiring'  [132, 1]      (w:1, o:131, a:1
% 4.48/4.89    , s:1, b:0), 
% 4.48/4.89  'class_Ring__and__Field_Oordered__ring__strict'  [133, 1]      (w:1, o:124
% 4.48/4.89    , a:1, s:1, b:0), 
% 4.48/4.89  'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'  [134, 1]      
% 4.48/4.89    (w:1, o:135, a:1, s:1, b:0), 
% 4.48/4.89  'class_OrderedGroup_Opordered__comm__monoid__add'  [135, 1]      (w:1, o:
% 4.48/4.89    136, a:1, s:1, b:0), 
% 4.48/4.89  'class_OrderedGroup_Olordered__ab__group__add'  [136, 1]      (w:1, o:137
% 4.48/4.89    , a:1, s:1, b:0), 
% 4.48/4.89  'c_Power_Opower_Opower'  [137, 3]      (w:1, o:215, a:1, s:1, b:0), 
% 4.48/4.89  'class_Ring__and__Field_Oring'  [138, 1]      (w:1, o:138, a:1, s:1, b:0), 
% 4.48/4.89    
% 4.48/4.89  'class_Ring__and__Field_Oidom'  [141, 1]      (w:1, o:139, a:1, s:1, b:0), 
% 4.48/4.89    
% 4.48/4.89  'class_RealVector_Oreal__normed__algebra'  [142, 1]      (w:1, o:140, a:1
% 4.48/4.89    , s:1, b:0), 
% 4.48/4.89  'class_Ring__and__Field_Osemiring__1'  [144, 1]      (w:1, o:145, a:1, s:1
% 4.48/4.89    , b:0), 
% 4.48/4.89  'class_Ring__and__Field_Ocomm__ring__1'  [145, 1]      (w:1, o:146, a:1, s:
% 4.48/4.89    1, b:0), 
% 4.48/4.89  'c_COMBB'  [150, 5]      (w:1, o:222, a:1, s:1, b:0), 
% 4.48/4.89  'class_RealVector_Oreal__normed__vector'  [151, 1]      (w:1, o:147, a:1
% 4.48/4.89    , s:1, b:0), 
% 4.48/4.89  'c_Series_Osuminf'  [153, 2]      (w:1, o:206, a:1, s:1, b:0), 
% 4.48/4.89  'c_Series_Osums'  [154, 3]      (w:1, o:216, a:1, s:1, b:0), 
% 4.48/4.89  'class_Int_Onumber'  [155, 1]      (w:1, o:148, a:1, s:1, b:0), 
% 4.48/4.89  'class_OrderedGroup_Oab__group__add'  [157, 1]      (w:1, o:149, a:1, s:1
% 4.48/4.89    , b:0), 
% 4.48/4.89  'class_OrderedGroup_Opordered__ab__semigroup__add'  [158, 1]      (w:1, o:
% 4.48/4.89    150, a:1, s:1, b:0), 
% 4.48/4.89  'class_OrderedGroup_Omonoid__mult'  [159, 1]      (w:1, o:151, a:1, s:1, b:
% 4.48/4.89    0), 
% 4.48/4.89  'class_Ring__and__Field_Oordered__field'  [162, 1]      (w:1, o:132, a:1
% 4.48/4.89    , s:1, b:0), 
% 4.48/4.89  'c_HOL_Oinverse__class_Odivide'  [163, 1]      (w:1, o:114, a:1, s:1, b:0)
% 4.48/4.89    , 
% 4.48/4.89  'class_Ring__and__Field_Odivision__by__zero'  [164, 1]      (w:1, o:156, a:
% 4.48/4.89    1, s:1, b:0), 
% 4.48/4.89  'c_SetInterval_Oord__class_OatLeastLessThan'  [166, 2]      (w:1, o:207, a:
% 4.48/4.89    1, s:1, b:0), 
% 4.48/4.89  'class_Ring__and__Field_Ofield'  [168, 1]      (w:1, o:157, a:1, s:1, b:0)
% 4.48/4.89    , 
% 4.48/4.89  'class_Ring__and__Field_Oordered__comm__semiring__strict'  [170, 1]      
% 4.48/4.89    (w:1, o:133, a:1, s:1, b:0), 
% 4.48/4.89  'class_Ring__and__Field_Omult__mono1'  [171, 1]      (w:1, o:158, a:1, s:1
% 4.48/4.89    , b:0), 
% 4.48/4.89  'class_Ring__and__Field_Omult__mono'  [172, 1]      (w:1, o:159, a:1, s:1
% 4.48/4.89    , b:0), 
% 4.48/4.89  'class_Ring__and__Field_Opordered__ring'  [173, 1]      (w:1, o:160, a:1
% 4.48/4.89    , s:1, b:0), 
% 4.48/4.89  'class_Ring__and__Field_Opordered__cancel__semiring'  [174, 1]      (w:1
% 4.48/4.89    , o:161, a:1, s:1, b:0), 
% 4.48/4.89  'class_Ring__and__Field_Oring__1'  [179, 1]      (w:1, o:141, a:1, s:1, b:0
% 4.48/4.89    ), 
% 4.48/4.89  'class_Ring__and__Field_Opordered__semiring'  [180, 1]      (w:1, o:162, a:
% 4.48/4.89    1, s:1, b:0), 
% 4.48/4.89  'tc_fun'  [184, 2]      (w:1, o:208, a:1, s:1, b:0), 
% 4.48/4.89  'c_COMBS'  [185, 5]      (w:1, o:223, a:1, s:1, b:0), 
% 4.48/4.89  'c_FFT__Mirabelle_Oroot'  [186, 1]      (w:1, o:163, a:1, s:1, b:0), 
% 4.48/4.89  'class_Ring__and__Field_Osemiring__0'  [187, 1]      (w:1, o:144, a:1, s:1
% 4.48/4.89    , b:0), 
% 4.48/4.89  'class_Power_Opower'  [188, 1]      (w:1, o:171, a:1, s:1, b:0), 
% 4.48/4.89  'class_Ring__and__Field_Ocomm__semiring__1'  [189, 1]      (w:1, o:154, a:1
% 4.48/4.89    , s:1, b:0), 
% 4.48/4.89  'c_COMBC'  [191, 5]      (w:1, o:224, a:1, s:1, b:0), 
% 4.48/4.89  'v_m'  [193, 0]      (w:1, o:78, a:1, s:1, b:0), 
% 4.48/4.89  'v_i'  [194, 0]      (w:1, o:79, a:1, s:1, b:0), 
% 4.48/4.89  'tc_bool'  [197, 0]      (w:1, o:81, a:1, s:1, b:0), 
% 4.48/4.89  'c_Int_Onumber__ring__axioms'  [198, 6]      (w:1, o:227, a:1, s:1, b:0), 
% 4.48/4.89  'class_RealVector_Oreal__normed__algebra__1'  [199, 1]      (w:1, o:172, a:
% 4.48/4.89    1, s:1, b:0), 
% 4.48/4.89  'c_FFT__Mirabelle_ODFT'  [200, 3]      (w:1, o:217, a:1, s:1, b:0), 
% 4.48/4.89  'class_Ring__and__Field_Ocomm__semiring__0'  [201, 1]      (w:1, o:153, a:1
% 4.48/4.89    , s:1, b:0), 
% 4.48/4.89  'class_Ring__and__Field_Ocomm__ring'  [202, 1]      (w:1, o:152, a:1, s:1
% 4.48/4.89    , b:0), 
% 4.48/4.89  'c_FFT__Mirabelle_OIDFT'  [203, 3]      (w:1, o:218, a:1, s:1, b:0), 
% 4.48/4.89  'class_Ring__and__Field_Ocomm__semiring'  [204, 1]      (w:1, o:155, a:1
% 4.48/4.89    , s:1, b:0), 
% 4.48/4.89  'class_OrderedGroup_Oab__semigroup__mult'  [206, 1]      (w:1, o:164, a:1
% 21.16/21.52    , s:1, b:0), 
% 21.16/21.52  'class_OrderedGroup_Ocomm__monoid__mult'  [207, 1]      (w:1, o:165, a:1
% 21.16/21.52    , s:1, b:0), 
% 21.16/21.52  'class_OrderedGroup_Oab__semigroup__idem__mult'  [208, 1]      (w:1, o:166
% 21.16/21.52    , a:1, s:1, b:0), 
% 21.16/21.52  'class_Ring__and__Field_Ozero__neq__one'  [209, 1]      (w:1, o:173, a:1
% 21.16/21.52    , s:1, b:0), 
% 21.16/21.52  'class_Ring__and__Field_Ono__zero__divisors'  [210, 1]      (w:1, o:97, a:1
% 21.16/21.52    , s:1, b:0), 
% 21.16/21.52  'class_Ring__and__Field_Omult__zero'  [211, 1]      (w:1, o:96, a:1, s:1
% 21.16/21.52    , b:0), 
% 21.16/21.52  'class_Ring__and__Field_Oring__1__no__zero__divisors'  [212, 1]      (w:1
% 21.16/21.52    , o:142, a:1, s:1, b:0), 
% 21.16/21.52  'class_Ring__and__Field_Oring__no__zero__divisors'  [213, 1]      (w:1, o:
% 21.16/21.52    143, a:1, s:1, b:0), 
% 21.16/21.52  'class_OrderedGroup_Ocancel__ab__semigroup__add'  [214, 1]      (w:1, o:167
% 21.16/21.52    , a:1, s:1, b:0), 
% 21.16/21.52  'class_OrderedGroup_Ocancel__semigroup__add'  [215, 1]      (w:1, o:168, a:
% 21.16/21.52    1, s:1, b:0), 
% 21.16/21.52  'class_RealVector_Oreal__field'  [216, 1]      (w:1, o:174, a:1, s:1, b:0)
% 21.16/21.52    , 
% 21.16/21.52  'class_Ring__and__Field_Osemiring'  [217, 1]      (w:1, o:175, a:1, s:1, b:
% 21.16/21.52    0), 
% 21.16/21.52  'class_OrderedGroup_Oab__semigroup__add'  [218, 1]      (w:1, o:169, a:1
% 21.16/21.52    , s:1, b:0), 
% 21.16/21.52  'class_Int_Oring__char__0'  [222, 1]      (w:1, o:176, a:1, s:1, b:0), 
% 21.16/21.52  'v_a'  [223, 0]      (w:1, o:85, a:1, s:1, b:0), 
% 21.16/21.52  'class_OrderedGroup_Omonoid__add'  [224, 1]      (w:1, o:170, a:1, s:1, b:0
% 21.16/21.52    ), 
% 21.16/21.52  'c_fequal'  [227, 3]      (w:1, o:219, a:1, s:1, b:0).
% 21.16/21.52  
% 21.16/21.52  
% 21.16/21.52  Starting Search:
% 21.16/21.52  
% 21.16/21.52  Resimplifying inuse:
% 21.16/21.52  Done
% 21.16/21.52  
% 21.16/21.52  
% 21.16/21.52  Intermediate Status:
% 21.16/21.52  Generated:    3575
% 21.16/21.52  Kept:         2005
% 21.16/21.52  Inuse:        44
% 21.16/21.52  Deleted:      0
% 21.16/21.52  Deletedinuse: 0
% 21.16/21.52  
% 21.16/21.52  Resimplifying inuse:
% 21.16/21.52  Done
% 21.16/21.52  
% 21.16/21.52  Resimplifying inuse:
% 21.16/21.52  Done
% 21.16/21.52  
% 21.16/21.52  
% 21.16/21.52  Intermediate Status:
% 21.16/21.52  Generated:    10248
% 21.16/21.52  Kept:         4065
% 21.16/21.52  Inuse:        145
% 21.16/21.52  Deleted:      1
% 21.16/21.52  Deletedinuse: 0
% 21.16/21.52  
% 21.16/21.52  Resimplifying inuse:
% 21.16/21.52  Done
% 21.16/21.52  
% 21.16/21.52  
% 21.16/21.52  Intermediate Status:
% 21.16/21.52  Generated:    17200
% 21.16/21.52  Kept:         6083
% 21.16/21.52  Inuse:        202
% 21.16/21.52  Deleted:      3
% 21.16/21.52  Deletedinuse: 0
% 21.16/21.52  
% 21.16/21.52  Resimplifying inuse:
% 21.16/21.52  Done
% 21.16/21.52  
% 21.16/21.52  Resimplifying inuse:
% 21.16/21.52  Done
% 21.16/21.52  
% 21.16/21.52  
% 21.16/21.52  Intermediate Status:
% 21.16/21.52  Generated:    26637
% 21.16/21.52  Kept:         8120
% 21.16/21.52  Inuse:        318
% 21.16/21.52  Deleted:      8
% 21.16/21.52  Deletedinuse: 0
% 21.16/21.52  
% 21.16/21.52  Resimplifying inuse:
% 21.16/21.52  Done
% 21.16/21.52  
% 21.16/21.52  Resimplifying inuse:
% 21.16/21.52  Done
% 21.16/21.52  
% 21.16/21.52  
% 21.16/21.52  Intermediate Status:
% 21.16/21.52  Generated:    41454
% 21.16/21.52  Kept:         10807
% 21.16/21.52  Inuse:        386
% 21.16/21.52  Deleted:      10
% 21.16/21.52  Deletedinuse: 0
% 21.16/21.52  
% 21.16/21.52  Resimplifying inuse:
% 21.16/21.52  Done
% 21.16/21.52  
% 21.16/21.52  Resimplifying inuse:
% 21.16/21.52  Done
% 21.16/21.52  
% 21.16/21.52  
% 21.16/21.52  Intermediate Status:
% 21.16/21.52  Generated:    56337
% 21.16/21.52  Kept:         13405
% 21.16/21.52  Inuse:        405
% 21.16/21.52  Deleted:      11
% 21.16/21.52  Deletedinuse: 0
% 21.16/21.52  
% 21.16/21.52  Resimplifying inuse:
% 21.16/21.52  Done
% 21.16/21.52  
% 21.16/21.52  Resimplifying inuse:
% 21.16/21.52  Done
% 21.16/21.52  
% 21.16/21.52  
% 21.16/21.52  Intermediate Status:
% 21.16/21.52  Generated:    67233
% 21.16/21.52  Kept:         16673
% 21.16/21.52  Inuse:        441
% 21.16/21.52  Deleted:      12
% 21.16/21.52  Deletedinuse: 0
% 21.16/21.52  
% 21.16/21.52  Resimplifying inuse:
% 21.16/21.52  Done
% 21.16/21.52  
% 21.16/21.52  Resimplifying inuse:
% 21.16/21.52  Done
% 21.16/21.52  
% 21.16/21.52  
% 21.16/21.52  Intermediate Status:
% 21.16/21.52  Generated:    75711
% 21.16/21.52  Kept:         18716
% 21.16/21.52  Inuse:        516
% 21.16/21.52  Deleted:      15
% 21.16/21.52  Deletedinuse: 0
% 21.16/21.52  
% 21.16/21.52  Resimplifying inuse:
% 21.16/21.52  Done
% 21.16/21.52  
% 21.16/21.52  Resimplifying inuse:
% 21.16/21.52  Done
% 21.16/21.52  
% 21.16/21.52  Resimplifying clauses:
% 21.16/21.52  Done
% 21.16/21.52  
% 21.16/21.52  
% 21.16/21.52  Intermediate Status:
% 21.16/21.52  Generated:    85175
% 21.16/21.52  Kept:         21865
% 21.16/21.52  Inuse:        551
% 21.16/21.52  Deleted:      297
% 21.16/21.52  Deletedinuse: 0
% 21.16/21.52  
% 21.16/21.52  Resimplifying inuse:
% 21.16/21.52  Done
% 21.16/21.52  
% 21.16/21.52  Resimplifying inuse:
% 21.16/21.52  Done
% 21.16/21.52  
% 21.16/21.52  
% 21.16/21.52  Intermediate Status:
% 21.16/21.52  Generated:    92580
% 21.16/21.52  Kept:         25641
% 21.16/21.52  Inuse:        561
% 21.16/21.52  Deleted:      297
% 21.16/21.52  Deletedinuse: 0
% 21.16/21.52  
% 21.16/21.52  Resimplifying inuse:
% 21.16/21.52  Done
% 21.16/21.52  
% 21.16/21.52  Resimplifying inuse:
% 21.16/21.52  Done
% 21.16/21.52  
% 21.16/21.52  
% 21.16/21.52  Intermediate Status:
% 21.16/21.52  Generated:    97814
% 21.16/21.52  Kept:         27822
% 21.16/21.52  Inuse:        576
% 21.16/21.52  Deleted:      297
% 21.16/21.52  Deletedinuse: 0
% 21.16/21.52  
% 21.16/21.52  Resimplifying inuse:
% 21.16/21.52  Done
% 21.16/21.52  
% 21.16/21.52  
% 21.16/21.52  Intermediate Status:
% 21.16/21.52  Generated:    107296
% 21.16/21.52  Kept:         30491
% 21.16/21.52  Inuse:        596
% 21.16/21.52  Deleted:      297
% 21.16/21.52  Deletedinuse: 0
% 21.16/21.52  
% 21.16/21.52  Resimplifying inuse:
% 21.16/21.52  Done
% 21.16/21.52  
% 21.16/21.52  Resimplifying inuse:
% 21.16/21.52  Done
% 21.16/21.52  
% 21.16/21.52  
% 21.16/21.52  Intermediate Status:
% 21.16/21.52  Generated:    114154
% 21.16/21.52  Kept:         32496
% 21.16/21.52  Inuse:        621
% 21.16/21.52  Deleted:      297
% 21.16/21.52  Deletedinuse: 0
% 21.16/21.52  
% 21.16/21.52  Resimplifying inuse:
% 21.16/21.52  Done
% 21.16/21.52  
% 21.16/21.52  Resimplifying inuse:
% 21.16/21.52  Done
% 21.16/21.52  
% 21.16/21.52  
% 21.16/21.52  Intermediate Status:
% 21.16/21.52  Generated:    121473
% 21.16/21.52  Kept:         34658
% 21.16/21.52  Inuse:        666
% 21.16/21.52  Deleted:      297
% 21.16/21.52  Deletedinuse: 0
% 21.16/21.52  
% 21.16/21.52  Resimplifying inuse:
% 21.16/21.52  Done
% 21.16/21.52  
% 21.16/21.52  Resimplifying inuse:
% 21.16/21.52  Done
% 21.16/21.52  
% 21.16/21.52  
% 21.16/21.52  Intermediate Status:
% 21.16/21.52  Generated:    128220
% 21.16/21.52  Kept:         36811
% 21.16/21.52  Inuse:        691
% 21.16/21.52  Deleted:      297
% 21.16/21.52  Deletedinuse: 0
% 21.16/21.52  
% 21.16/21.52  Resimplifying inuse:
% 21.16/21.52  Done
% 21.16/21.52  
% 21.16/21.52  Resimplifying inuse:
% 21.16/21.52  Done
% 21.16/21.52  
% 21.16/21.52  
% 21.16/21.52  Intermediate Status:
% 21.16/21.52  Generated:    136222
% 21.16/21.52  Kept:         38916
% 21.16/21.52  Inuse:        726
% 21.16/21.52  Deleted:      297
% 21.16/21.52  Deletedinuse: 0
% 21.16/21.52  
% 21.16/21.52  Resimplifying inuse:
% 59.84/60.28  Done
% 59.84/60.28  
% 59.84/60.28  Resimplifying inuse:
% 59.84/60.28  Done
% 59.84/60.28  
% 59.84/60.28  Resimplifying clauses:
% 59.84/60.28  Done
% 59.84/60.28  
% 59.84/60.28  
% 59.84/60.28  Intermediate Status:
% 59.84/60.28  Generated:    146001
% 59.84/60.28  Kept:         41137
% 59.84/60.28  Inuse:        756
% 59.84/60.28  Deleted:      476
% 59.84/60.28  Deletedinuse: 0
% 59.84/60.28  
% 59.84/60.28  Resimplifying inuse:
% 59.84/60.28  Done
% 59.84/60.28  
% 59.84/60.28  Resimplifying inuse:
% 59.84/60.28  Done
% 59.84/60.28  
% 59.84/60.28  
% 59.84/60.28  Intermediate Status:
% 59.84/60.28  Generated:    152950
% 59.84/60.28  Kept:         43145
% 59.84/60.28  Inuse:        788
% 59.84/60.28  Deleted:      476
% 59.84/60.28  Deletedinuse: 0
% 59.84/60.28  
% 59.84/60.28  Resimplifying inuse:
% 59.84/60.28  Done
% 59.84/60.28  
% 59.84/60.28  Resimplifying inuse:
% 59.84/60.28  Done
% 59.84/60.28  
% 59.84/60.28  
% 59.84/60.28  Intermediate Status:
% 59.84/60.28  Generated:    161806
% 59.84/60.28  Kept:         45195
% 59.84/60.28  Inuse:        825
% 59.84/60.28  Deleted:      476
% 59.84/60.28  Deletedinuse: 0
% 59.84/60.28  
% 59.84/60.28  Resimplifying inuse:
% 59.84/60.28  Done
% 59.84/60.28  
% 59.84/60.28  Resimplifying inuse:
% 59.84/60.28  Done
% 59.84/60.28  
% 59.84/60.28  
% 59.84/60.28  Intermediate Status:
% 59.84/60.28  Generated:    170086
% 59.84/60.28  Kept:         47222
% 59.84/60.28  Inuse:        854
% 59.84/60.28  Deleted:      476
% 59.84/60.28  Deletedinuse: 0
% 59.84/60.28  
% 59.84/60.28  Resimplifying inuse:
% 59.84/60.28  Done
% 59.84/60.28  
% 59.84/60.28  
% 59.84/60.28  Intermediate Status:
% 59.84/60.28  Generated:    177475
% 59.84/60.28  Kept:         49291
% 59.84/60.28  Inuse:        876
% 59.84/60.28  Deleted:      476
% 59.84/60.28  Deletedinuse: 0
% 59.84/60.28  
% 59.84/60.28  Resimplifying inuse:
% 59.84/60.28  Done
% 59.84/60.28  
% 59.84/60.28  Resimplifying inuse:
% 59.84/60.28  Done
% 59.84/60.28  
% 59.84/60.28  
% 59.84/60.28  Intermediate Status:
% 59.84/60.28  Generated:    186954
% 59.84/60.28  Kept:         51740
% 59.84/60.28  Inuse:        901
% 59.84/60.28  Deleted:      476
% 59.84/60.28  Deletedinuse: 0
% 59.84/60.28  
% 59.84/60.28  Resimplifying inuse:
% 59.84/60.28  Done
% 59.84/60.28  
% 59.84/60.28  
% 59.84/60.28  Intermediate Status:
% 59.84/60.28  Generated:    195858
% 59.84/60.28  Kept:         54278
% 59.84/60.28  Inuse:        926
% 59.84/60.28  Deleted:      476
% 59.84/60.28  Deletedinuse: 0
% 59.84/60.28  
% 59.84/60.28  Resimplifying inuse:
% 59.84/60.28  Done
% 59.84/60.28  
% 59.84/60.28  Resimplifying inuse:
% 59.84/60.28  Done
% 59.84/60.28  
% 59.84/60.28  
% 59.84/60.28  Intermediate Status:
% 59.84/60.28  Generated:    203876
% 59.84/60.28  Kept:         56331
% 59.84/60.28  Inuse:        951
% 59.84/60.28  Deleted:      476
% 59.84/60.28  Deletedinuse: 0
% 59.84/60.28  
% 59.84/60.28  Resimplifying inuse:
% 59.84/60.28  Done
% 59.84/60.28  
% 59.84/60.28  
% 59.84/60.28  Intermediate Status:
% 59.84/60.28  Generated:    210243
% 59.84/60.28  Kept:         58660
% 59.84/60.28  Inuse:        959
% 59.84/60.28  Deleted:      476
% 59.84/60.28  Deletedinuse: 0
% 59.84/60.28  
% 59.84/60.28  Resimplifying inuse:
% 59.84/60.28  Done
% 59.84/60.28  
% 59.84/60.28  Resimplifying inuse:
% 59.84/60.28  Done
% 59.84/60.28  
% 59.84/60.28  Resimplifying clauses:
% 59.84/60.28  Done
% 59.84/60.28  
% 59.84/60.28  
% 59.84/60.28  Intermediate Status:
% 59.84/60.28  Generated:    219672
% 59.84/60.28  Kept:         60977
% 59.84/60.28  Inuse:        976
% 59.84/60.28  Deleted:      933
% 59.84/60.28  Deletedinuse: 0
% 59.84/60.28  
% 59.84/60.28  Resimplifying inuse:
% 59.84/60.28  Done
% 59.84/60.28  
% 59.84/60.28  Resimplifying inuse:
% 59.84/60.28  Done
% 59.84/60.28  
% 59.84/60.28  
% 59.84/60.28  Intermediate Status:
% 59.84/60.28  Generated:    228778
% 59.84/60.28  Kept:         63294
% 59.84/60.28  Inuse:        996
% 59.84/60.28  Deleted:      933
% 59.84/60.28  Deletedinuse: 0
% 59.84/60.28  
% 59.84/60.28  Resimplifying inuse:
% 59.84/60.28  Done
% 59.84/60.28  
% 59.84/60.28  Resimplifying inuse:
% 59.84/60.28  Done
% 59.84/60.28  
% 59.84/60.28  
% 59.84/60.28  Intermediate Status:
% 59.84/60.28  Generated:    237368
% 59.84/60.28  Kept:         65664
% 59.84/60.28  Inuse:        1016
% 59.84/60.28  Deleted:      933
% 59.84/60.28  Deletedinuse: 0
% 59.84/60.28  
% 59.84/60.28  Resimplifying inuse:
% 59.84/60.28  Done
% 59.84/60.28  
% 59.84/60.28  Resimplifying inuse:
% 59.84/60.28  Done
% 59.84/60.28  
% 59.84/60.28  
% 59.84/60.28  Intermediate Status:
% 59.84/60.28  Generated:    243352
% 59.84/60.28  Kept:         67701
% 59.84/60.28  Inuse:        1035
% 59.84/60.28  Deleted:      933
% 59.84/60.28  Deletedinuse: 0
% 59.84/60.28  
% 59.84/60.28  Resimplifying inuse:
% 59.84/60.28  Done
% 59.84/60.28  
% 59.84/60.28  Resimplifying inuse:
% 59.84/60.28  Done
% 59.84/60.28  
% 59.84/60.28  
% 59.84/60.28  Intermediate Status:
% 59.84/60.28  Generated:    249362
% 59.84/60.28  Kept:         69751
% 59.84/60.28  Inuse:        1052
% 59.84/60.28  Deleted:      933
% 59.84/60.28  Deletedinuse: 0
% 59.84/60.28  
% 59.84/60.28  Resimplifying inuse:
% 59.84/60.28  Done
% 59.84/60.28  
% 59.84/60.28  Resimplifying inuse:
% 59.84/60.28  Done
% 59.84/60.28  
% 59.84/60.28  
% 59.84/60.28  Intermediate Status:
% 59.84/60.28  Generated:    255205
% 59.84/60.28  Kept:         71759
% 59.84/60.28  Inuse:        1071
% 59.84/60.28  Deleted:      933
% 59.84/60.28  Deletedinuse: 0
% 59.84/60.28  
% 59.84/60.28  Resimplifying inuse:
% 59.84/60.28  Done
% 59.84/60.28  
% 59.84/60.28  Resimplifying inuse:
% 59.84/60.28  Done
% 59.84/60.28  
% 59.84/60.28  
% 59.84/60.28  Intermediate Status:
% 59.84/60.28  Generated:    261801
% 59.84/60.28  Kept:         73801
% 59.84/60.28  Inuse:        1091
% 59.84/60.28  Deleted:      933
% 59.84/60.28  Deletedinuse: 0
% 59.84/60.28  
% 59.84/60.28  Resimplifying inuse:
% 59.84/60.28  Done
% 59.84/60.28  
% 59.84/60.28  Resimplifying inuse:
% 59.84/60.28  Done
% 59.84/60.28  
% 59.84/60.28  
% 59.84/60.28  Intermediate Status:
% 59.84/60.28  Generated:    269034
% 59.84/60.28  Kept:         75846
% 59.84/60.28  Inuse:        1114
% 59.84/60.28  Deleted:      933
% 59.84/60.28  Deletedinuse: 0
% 59.84/60.28  
% 59.84/60.28  Resimplifying inuse:
% 59.84/60.28  Done
% 59.84/60.28  
% 59.84/60.28  Resimplifying inuse:
% 59.84/60.28  Done
% 59.84/60.28  
% 59.84/60.28  
% 59.84/60.28  Intermediate Status:
% 59.84/60.28  Generated:    279086
% 59.84/60.28  Kept:         78110
% 59.84/60.28  Inuse:        1136
% 59.84/60.28  Deleted:      933
% 59.84/60.28  Deletedinuse: 0
% 59.84/60.28  
% 59.84/60.28  Resimplifying inuse:
% 59.84/60.28  Done
% 59.84/60.28  
% 59.84/60.28  
% 59.84/60.28  Intermediate Status:
% 59.84/60.28  Generated:    305578
% 59.84/60.28  Kept:         82440
% 59.84/60.28  Inuse:        1156
% 59.84/60.28  Deleted:      933
% 59.84/60.28  Deletedinuse: 0
% 59.84/60.28  
% 59.84/60.28  Resimplifying inuse:
% 59.84/60.28  Done
% 59.84/60.28  
% 59.84/60.28  Resimplifying clauses:
% 59.84/60.28  Done
% 59.84/60.28  
% 59.84/60.28  Resimplifying inuse:
% 59.84/60.28  Done
% 59.84/60.28  
% 59.84/60.28  
% 59.84/60.28  Intermediate Status:
% 59.84/60.28  Generated:    315081
% 59.84/60.28  Kept:         84446
% 59.84/60.28  Inuse:        1187
% 59.84/60.28  Deleted:      1394
% 59.84/60.28  Deletedinuse: 0
% 59.84/60.28  
% 59.84/60.28  Resimplifying inuse:
% 59.84/60.28  Done
% 59.84/60.28  
% 59.84/60.28  Resimplifying inuse:
% 59.84/60.28  Done
% 59.84/60.28  
% 59.84/60.28  
% 59.84/60.28  Intermediate Status:
% 59.84/60.28  Generated:    325320
% 59.84/60.28  Kept:         86452
% 59.84/60.28  Inuse:        1217
% 59.84/60.28  Deleted:      1394
% 59.84/60.28  Deletedinuse: 0
% 59.84/60.28  
% 59.84/60.28  Resimplifying inuse:
% 59.84/60.28  Done
% 59.84/60.28  
% 59.84/60.28  Resimplifying inuse:
% 59.84/60.28  Done
% 59.84/60.28  
% 59.84/60.28  
% 59.84/60.28  Intermediate Status:
% 59.84/60.28  Generated:    334971
% 59.84/60.28  Kept:         88525
% 59.84/60.28  Inuse:        1251
% 59.84/60.28  Deleted:      1394
% 59.84/60.28  Deletedinuse: 0
% 59.84/60.28  
% 59.84/60.28  Resimplifying inuse:
% 59.84/60.28  Done
% 59.84/60.28  
% 59.84/60.28  
% 59.84/60.28  Intermediate Status:
% 59.84/60.28  Generated:    347222
% 59.84/60.28  Kept:         91202
% 59.84/60.28  Inuse:        1271
% 59.84/60.28  Deleted:      1394
% 59.84/60.28  Deletedinuse: 0
% 59.84/60.28  
% 59.84/60.28  Resimplifying inuse:
% 59.84/60.28  Done
% 59.84/60.28  
% 59.84/60.28  Resimplifying inuse:
% 59.84/60.28  Done
% 59.84/60.28  
% 59.84/60.28  
% 59.84/60.28  Intermediate Status:
% 59.84/60.28  Generated:    355669
% 59.84/60.28  Kept:         93235
% 59.84/60.28  Inuse:        1285
% 59.84/60.28  Deleted:      1395
% 59.84/60.28  Deletedinuse: 0
% 59.84/60.28  
% 59.84/60.28  Resimplifying inuse:
% 59.84/60.28  Done
% 59.84/60.28  
% 59.84/60.28  Resimplifying inuse:
% 59.84/60.28  Done
% 59.84/60.28  
% 59.84/60.28  
% 59.84/60.28  Intermediate Status:
% 126.39/126.77  Generated:    367018
% 126.39/126.77  Kept:         95563
% 126.39/126.77  Inuse:        1315
% 126.39/126.77  Deleted:      1395
% 126.39/126.77  Deletedinuse: 0
% 126.39/126.77  
% 126.39/126.77  Resimplifying inuse:
% 126.39/126.77  Done
% 126.39/126.77  
% 126.39/126.77  
% 126.39/126.77  Intermediate Status:
% 126.39/126.77  Generated:    385807
% 126.39/126.77  Kept:         99819
% 126.39/126.77  Inuse:        1335
% 126.39/126.77  Deleted:      1395
% 126.39/126.77  Deletedinuse: 0
% 126.39/126.77  
% 126.39/126.77  Resimplifying inuse:
% 126.39/126.77  Done
% 126.39/126.77  
% 126.39/126.77  Resimplifying inuse:
% 126.39/126.77  Done
% 126.39/126.77  
% 126.39/126.77  
% 126.39/126.77  Intermediate Status:
% 126.39/126.77  Generated:    404843
% 126.39/126.77  Kept:         104627
% 126.39/126.77  Inuse:        1365
% 126.39/126.77  Deleted:      1395
% 126.39/126.77  Deletedinuse: 0
% 126.39/126.77  
% 126.39/126.77  Resimplifying inuse:
% 126.39/126.77  Done
% 126.39/126.77  
% 126.39/126.77  Resimplifying clauses:
% 126.39/126.77  Done
% 126.39/126.77  
% 126.39/126.77  Resimplifying inuse:
% 126.39/126.77  Done
% 126.39/126.77  
% 126.39/126.77  
% 126.39/126.77  Intermediate Status:
% 126.39/126.77  Generated:    417297
% 126.39/126.77  Kept:         106886
% 126.39/126.77  Inuse:        1405
% 126.39/126.77  Deleted:      1746
% 126.39/126.77  Deletedinuse: 1
% 126.39/126.77  
% 126.39/126.77  Resimplifying inuse:
% 126.39/126.77  Done
% 126.39/126.77  
% 126.39/126.77  Resimplifying inuse:
% 126.39/126.77  Done
% 126.39/126.77  
% 126.39/126.77  
% 126.39/126.77  Intermediate Status:
% 126.39/126.77  Generated:    428954
% 126.39/126.77  Kept:         111031
% 126.39/126.77  Inuse:        1420
% 126.39/126.77  Deleted:      1746
% 126.39/126.77  Deletedinuse: 1
% 126.39/126.77  
% 126.39/126.77  Resimplifying inuse:
% 126.39/126.77  Done
% 126.39/126.77  
% 126.39/126.77  Resimplifying inuse:
% 126.39/126.77  Done
% 126.39/126.77  
% 126.39/126.77  
% 126.39/126.77  Intermediate Status:
% 126.39/126.77  Generated:    437835
% 126.39/126.77  Kept:         113057
% 126.39/126.77  Inuse:        1445
% 126.39/126.77  Deleted:      1746
% 126.39/126.77  Deletedinuse: 1
% 126.39/126.77  
% 126.39/126.77  Resimplifying inuse:
% 126.39/126.77  Done
% 126.39/126.77  
% 126.39/126.77  Resimplifying inuse:
% 126.39/126.77  Done
% 126.39/126.77  
% 126.39/126.77  
% 126.39/126.77  Intermediate Status:
% 126.39/126.77  Generated:    448386
% 126.39/126.77  Kept:         115136
% 126.39/126.77  Inuse:        1470
% 126.39/126.77  Deleted:      1746
% 126.39/126.77  Deletedinuse: 1
% 126.39/126.77  
% 126.39/126.77  Resimplifying inuse:
% 126.39/126.77  Done
% 126.39/126.77  
% 126.39/126.77  Resimplifying inuse:
% 126.39/126.77  Done
% 126.39/126.77  
% 126.39/126.77  
% 126.39/126.77  Intermediate Status:
% 126.39/126.77  Generated:    459662
% 126.39/126.77  Kept:         117146
% 126.39/126.77  Inuse:        1504
% 126.39/126.77  Deleted:      1746
% 126.39/126.77  Deletedinuse: 1
% 126.39/126.77  
% 126.39/126.77  Resimplifying inuse:
% 126.39/126.77  Done
% 126.39/126.77  
% 126.39/126.77  
% 126.39/126.77  Intermediate Status:
% 126.39/126.77  Generated:    468616
% 126.39/126.77  Kept:         120639
% 126.39/126.77  Inuse:        1512
% 126.39/126.77  Deleted:      1746
% 126.39/126.77  Deletedinuse: 1
% 126.39/126.77  
% 126.39/126.77  Resimplifying inuse:
% 126.39/126.77  Done
% 126.39/126.77  
% 126.39/126.77  Resimplifying inuse:
% 126.39/126.77  Done
% 126.39/126.77  
% 126.39/126.77  
% 126.39/126.77  Intermediate Status:
% 126.39/126.77  Generated:    474970
% 126.39/126.77  Kept:         122684
% 126.39/126.77  Inuse:        1528
% 126.39/126.77  Deleted:      1747
% 126.39/126.77  Deletedinuse: 1
% 126.39/126.77  
% 126.39/126.77  Resimplifying inuse:
% 126.39/126.77  Done
% 126.39/126.77  
% 126.39/126.77  Resimplifying inuse:
% 126.39/126.77  Done
% 126.39/126.77  
% 126.39/126.77  Resimplifying clauses:
% 126.39/126.77  Done
% 126.39/126.77  
% 126.39/126.77  
% 126.39/126.77  Intermediate Status:
% 126.39/126.77  Generated:    481661
% 126.39/126.77  Kept:         124965
% 126.39/126.77  Inuse:        1544
% 126.39/126.77  Deleted:      2208
% 126.39/126.77  Deletedinuse: 1
% 126.39/126.77  
% 126.39/126.77  Resimplifying inuse:
% 126.39/126.77  Done
% 126.39/126.77  
% 126.39/126.77  Resimplifying inuse:
% 126.39/126.77  Done
% 126.39/126.77  
% 126.39/126.77  
% 126.39/126.77  Intermediate Status:
% 126.39/126.77  Generated:    488157
% 126.39/126.77  Kept:         127000
% 126.39/126.77  Inuse:        1560
% 126.39/126.77  Deleted:      2208
% 126.39/126.77  Deletedinuse: 1
% 126.39/126.77  
% 126.39/126.77  Resimplifying inuse:
% 126.39/126.77  Done
% 126.39/126.77  
% 126.39/126.77  
% 126.39/126.77  Intermediate Status:
% 126.39/126.77  Generated:    496750
% 126.39/126.77  Kept:         129067
% 126.39/126.77  Inuse:        1574
% 126.39/126.77  Deleted:      2208
% 126.39/126.77  Deletedinuse: 1
% 126.39/126.77  
% 126.39/126.77  Resimplifying inuse:
% 126.39/126.77  Done
% 126.39/126.77  
% 126.39/126.77  Resimplifying inuse:
% 126.39/126.77  Done
% 126.39/126.77  
% 126.39/126.77  
% 126.39/126.77  Intermediate Status:
% 126.39/126.77  Generated:    505014
% 126.39/126.77  Kept:         131466
% 126.39/126.77  Inuse:        1594
% 126.39/126.77  Deleted:      2208
% 126.39/126.77  Deletedinuse: 1
% 126.39/126.77  
% 126.39/126.77  Resimplifying inuse:
% 126.39/126.77  Done
% 126.39/126.77  
% 126.39/126.77  Resimplifying inuse:
% 126.39/126.77  Done
% 126.39/126.77  
% 126.39/126.77  
% 126.39/126.77  Intermediate Status:
% 126.39/126.77  Generated:    511923
% 126.39/126.77  Kept:         133699
% 126.39/126.77  Inuse:        1614
% 126.39/126.77  Deleted:      2208
% 126.39/126.77  Deletedinuse: 1
% 126.39/126.77  
% 126.39/126.77  Resimplifying inuse:
% 126.39/126.77  Done
% 126.39/126.77  
% 126.39/126.77  Resimplifying inuse:
% 126.39/126.77  Done
% 126.39/126.77  
% 126.39/126.77  
% 126.39/126.77  Intermediate Status:
% 126.39/126.77  Generated:    517998
% 126.39/126.77  Kept:         135703
% 126.39/126.77  Inuse:        1631
% 126.39/126.77  Deleted:      2208
% 126.39/126.77  Deletedinuse: 1
% 126.39/126.77  
% 126.39/126.77  
% 126.39/126.77  Intermediate Status:
% 126.39/126.77  Generated:    527344
% 126.39/126.77  Kept:         138339
% 126.39/126.77  Inuse:        1639
% 126.39/126.77  Deleted:      2208
% 126.39/126.77  Deletedinuse: 1
% 126.39/126.77  
% 126.39/126.77  Resimplifying inuse:
% 126.39/126.77  Done
% 126.39/126.77  
% 126.39/126.77  Resimplifying inuse:
% 126.39/126.77  Done
% 126.39/126.77  
% 126.39/126.77  
% 126.39/126.77  Intermediate Status:
% 126.39/126.77  Generated:    533453
% 126.39/126.77  Kept:         140342
% 126.39/126.77  Inuse:        1654
% 126.39/126.77  Deleted:      2208
% 126.39/126.77  Deletedinuse: 1
% 126.39/126.77  
% 126.39/126.77  Resimplifying inuse:
% 126.39/126.77  Done
% 126.39/126.77  
% 126.39/126.77  
% 126.39/126.77  Intermediate Status:
% 126.39/126.77  Generated:    539054
% 126.39/126.77  Kept:         142501
% 126.39/126.77  Inuse:        1664
% 126.39/126.77  Deleted:      2208
% 126.39/126.77  Deletedinuse: 1
% 126.39/126.77  
% 126.39/126.77  Resimplifying inuse:
% 126.39/126.77  Done
% 126.39/126.77  
% 126.39/126.77  Resimplifying inuse:
% 126.39/126.77  Done
% 126.39/126.77  
% 126.39/126.77  
% 126.39/126.77  Intermediate Status:
% 126.39/126.77  Generated:    545483
% 126.39/126.77  Kept:         144732
% 126.39/126.77  Inuse:        1679
% 126.39/126.77  Deleted:      2208
% 126.39/126.77  Deletedinuse: 1
% 126.39/126.77  
% 126.39/126.77  Resimplifying inuse:
% 126.39/126.77  Done
% 126.39/126.77  
% 126.39/126.77  Resimplifying clauses:
% 126.39/126.77  Done
% 126.39/126.77  
% 126.39/126.77  Resimplifying inuse:
% 126.39/126.77  Done
% 126.39/126.77  
% 126.39/126.77  
% 126.39/126.77  Intermediate Status:
% 126.39/126.77  Generated:    551299
% 126.39/126.77  Kept:         146759
% 126.39/126.77  Inuse:        1694
% 126.39/126.77  Deleted:      2303
% 126.39/126.77  Deletedinuse: 1
% 126.39/126.77  
% 126.39/126.77  Resimplifying inuse:
% 126.39/126.77  Done
% 126.39/126.77  
% 126.39/126.77  
% 126.39/126.77  Intermediate Status:
% 126.39/126.77  Generated:    559347
% 126.39/126.77  Kept:         148866
% 126.39/126.77  Inuse:        1699
% 126.39/126.77  Deleted:      2303
% 126.39/126.77  Deletedinuse: 1
% 126.39/126.77  
% 126.39/126.77  Resimplifying inuse:
% 126.39/126.77  Done
% 126.39/126.77  
% 126.39/126.77  
% 126.39/126.77  Intermediate Status:
% 126.39/126.77  Generated:    577860
% 126.39/126.77  Kept:         150930
% 126.39/126.77  Inuse:        1704
% 126.39/126.77  Deleted:      2303
% 126.39/126.77  Deletedinuse: 1
% 126.39/126.77  
% 126.39/126.77  Resimplifying inuse:
% 126.39/126.77  Done
% 126.39/126.77  
% 126.39/126.77  
% 126.39/126.77  Intermediate Status:
% 126.39/126.77  Generated:    588173
% 126.39/126.77  Kept:         153491
% 126.39/126.77  Inuse:        1714
% 126.39/126.77  Deleted:      2303
% 126.39/126.77  Deletedinuse: 1
% 126.39/126.77  
% 126.39/126.77  Resimplifying inuse:
% 126.39/126.77  Done
% 126.39/126.77  
% 126.39/126.77  Resimplifying inuse:
% 126.39/126.77  Done
% 126.39/126.77  
% 126.39/126.77  
% 126.39/126.77  Intermediate Status:
% 126.39/126.77  Generated:    596330
% 126.39/126.77  Kept:         155640
% 126.39/126.77  Inuse:        1734
% 126.39/126.77  Deleted:      2303
% 126.39/126.77  Deletedinuse: 1
% 216.06/216.44  
% 216.06/216.44  Resimplifying inuse:
% 216.06/216.44  Done
% 216.06/216.44  
% 216.06/216.44  Resimplifying inuse:
% 216.06/216.44  Done
% 216.06/216.44  
% 216.06/216.44  
% 216.06/216.44  Intermediate Status:
% 216.06/216.44  Generated:    609397
% 216.06/216.44  Kept:         157975
% 216.06/216.44  Inuse:        1759
% 216.06/216.44  Deleted:      2303
% 216.06/216.44  Deletedinuse: 1
% 216.06/216.44  
% 216.06/216.44  Resimplifying inuse:
% 216.06/216.44  Done
% 216.06/216.44  
% 216.06/216.44  Resimplifying inuse:
% 216.06/216.44  Done
% 216.06/216.44  
% 216.06/216.44  
% 216.06/216.44  Intermediate Status:
% 216.06/216.44  Generated:    621701
% 216.06/216.44  Kept:         160596
% 216.06/216.44  Inuse:        1779
% 216.06/216.44  Deleted:      2303
% 216.06/216.44  Deletedinuse: 1
% 216.06/216.44  
% 216.06/216.44  Resimplifying inuse:
% 216.06/216.44  Done
% 216.06/216.44  
% 216.06/216.44  Resimplifying inuse:
% 216.06/216.44  Done
% 216.06/216.44  
% 216.06/216.44  
% 216.06/216.44  Intermediate Status:
% 216.06/216.44  Generated:    632136
% 216.06/216.44  Kept:         162949
% 216.06/216.44  Inuse:        1799
% 216.06/216.44  Deleted:      2303
% 216.06/216.44  Deletedinuse: 1
% 216.06/216.44  
% 216.06/216.44  Resimplifying inuse:
% 216.06/216.44  Done
% 216.06/216.44  
% 216.06/216.44  Resimplifying inuse:
% 216.06/216.44  Done
% 216.06/216.44  
% 216.06/216.44  Resimplifying clauses:
% 216.06/216.44  Done
% 216.06/216.44  
% 216.06/216.44  
% 216.06/216.44  Intermediate Status:
% 216.06/216.44  Generated:    642360
% 216.06/216.44  Kept:         164974
% 216.06/216.44  Inuse:        1817
% 216.06/216.44  Deleted:      2516
% 216.06/216.44  Deletedinuse: 1
% 216.06/216.44  
% 216.06/216.44  Resimplifying inuse:
% 216.06/216.44  Done
% 216.06/216.44  
% 216.06/216.44  Resimplifying inuse:
% 216.06/216.44  Done
% 216.06/216.44  
% 216.06/216.44  
% 216.06/216.44  Intermediate Status:
% 216.06/216.44  Generated:    652810
% 216.06/216.44  Kept:         167339
% 216.06/216.44  Inuse:        1834
% 216.06/216.44  Deleted:      2516
% 216.06/216.44  Deletedinuse: 1
% 216.06/216.44  
% 216.06/216.44  Resimplifying inuse:
% 216.06/216.44  Done
% 216.06/216.44  
% 216.06/216.44  Resimplifying inuse:
% 216.06/216.44  Done
% 216.06/216.44  
% 216.06/216.44  
% 216.06/216.44  Intermediate Status:
% 216.06/216.44  Generated:    662648
% 216.06/216.44  Kept:         169357
% 216.06/216.44  Inuse:        1857
% 216.06/216.44  Deleted:      2516
% 216.06/216.44  Deletedinuse: 1
% 216.06/216.44  
% 216.06/216.44  Resimplifying inuse:
% 216.06/216.44  Done
% 216.06/216.44  
% 216.06/216.44  
% 216.06/216.44  Intermediate Status:
% 216.06/216.44  Generated:    674133
% 216.06/216.44  Kept:         174669
% 216.06/216.44  Inuse:        1869
% 216.06/216.44  Deleted:      2516
% 216.06/216.44  Deletedinuse: 1
% 216.06/216.44  
% 216.06/216.44  Resimplifying inuse:
% 216.06/216.44  Done
% 216.06/216.44  
% 216.06/216.44  Resimplifying inuse:
% 216.06/216.44  Done
% 216.06/216.44  
% 216.06/216.44  
% 216.06/216.44  Intermediate Status:
% 216.06/216.44  Generated:    683789
% 216.06/216.44  Kept:         176725
% 216.06/216.44  Inuse:        1894
% 216.06/216.44  Deleted:      2516
% 216.06/216.44  Deletedinuse: 1
% 216.06/216.44  
% 216.06/216.44  Resimplifying inuse:
% 216.06/216.44  Done
% 216.06/216.44  
% 216.06/216.44  
% 216.06/216.44  Intermediate Status:
% 216.06/216.44  Generated:    702442
% 216.06/216.44  Kept:         181100
% 216.06/216.44  Inuse:        1904
% 216.06/216.44  Deleted:      2516
% 216.06/216.44  Deletedinuse: 1
% 216.06/216.44  
% 216.06/216.44  Resimplifying inuse:
% 216.06/216.44  Done
% 216.06/216.44  
% 216.06/216.44  Resimplifying inuse:
% 216.06/216.44  Done
% 216.06/216.44  
% 216.06/216.44  
% 216.06/216.44  Intermediate Status:
% 216.06/216.44  Generated:    713106
% 216.06/216.44  Kept:         183322
% 216.06/216.44  Inuse:        1929
% 216.06/216.44  Deleted:      2516
% 216.06/216.44  Deletedinuse: 1
% 216.06/216.44  
% 216.06/216.44  Resimplifying inuse:
% 216.06/216.44  Done
% 216.06/216.44  
% 216.06/216.44  Resimplifying inuse:
% 216.06/216.44  Done
% 216.06/216.44  
% 216.06/216.44  Resimplifying clauses:
% 216.06/216.44  Done
% 216.06/216.44  
% 216.06/216.44  
% 216.06/216.44  Intermediate Status:
% 216.06/216.44  Generated:    722412
% 216.06/216.44  Kept:         185559
% 216.06/216.44  Inuse:        1954
% 216.06/216.44  Deleted:      3355
% 216.06/216.44  Deletedinuse: 1
% 216.06/216.44  
% 216.06/216.44  Resimplifying inuse:
% 216.06/216.44  Done
% 216.06/216.44  
% 216.06/216.44  Resimplifying inuse:
% 216.06/216.44  Done
% 216.06/216.44  
% 216.06/216.44  
% 216.06/216.44  Intermediate Status:
% 216.06/216.44  Generated:    736784
% 216.06/216.44  Kept:         187968
% 216.06/216.44  Inuse:        1993
% 216.06/216.44  Deleted:      3361
% 216.06/216.44  Deletedinuse: 6
% 216.06/216.44  
% 216.06/216.44  Resimplifying inuse:
% 216.06/216.44  Done
% 216.06/216.44  
% 216.06/216.44  Resimplifying inuse:
% 216.06/216.44  Done
% 216.06/216.44  
% 216.06/216.44  
% 216.06/216.44  Intermediate Status:
% 216.06/216.44  Generated:    745742
% 216.06/216.44  Kept:         190065
% 216.06/216.44  Inuse:        2013
% 216.06/216.44  Deleted:      3361
% 216.06/216.44  Deletedinuse: 6
% 216.06/216.44  
% 216.06/216.44  Resimplifying inuse:
% 216.06/216.44  Done
% 216.06/216.44  
% 216.06/216.44  Resimplifying inuse:
% 216.06/216.44  Done
% 216.06/216.44  
% 216.06/216.44  
% 216.06/216.44  Intermediate Status:
% 216.06/216.44  Generated:    763527
% 216.06/216.44  Kept:         194026
% 216.06/216.44  Inuse:        2028
% 216.06/216.44  Deleted:      3363
% 216.06/216.44  Deletedinuse: 8
% 216.06/216.44  
% 216.06/216.44  Resimplifying inuse:
% 216.06/216.44  Done
% 216.06/216.44  
% 216.06/216.44  
% 216.06/216.44  Intermediate Status:
% 216.06/216.44  Generated:    774875
% 216.06/216.44  Kept:         196518
% 216.06/216.44  Inuse:        2033
% 216.06/216.44  Deleted:      3364
% 216.06/216.44  Deletedinuse: 9
% 216.06/216.44  
% 216.06/216.44  Resimplifying inuse:
% 216.06/216.44  Done
% 216.06/216.44  
% 216.06/216.44  Resimplifying inuse:
% 216.06/216.44  Done
% 216.06/216.44  
% 216.06/216.44  
% 216.06/216.44  Intermediate Status:
% 216.06/216.44  Generated:    786151
% 216.06/216.44  Kept:         198623
% 216.06/216.44  Inuse:        2053
% 216.06/216.44  Deleted:      3365
% 216.06/216.44  Deletedinuse: 10
% 216.06/216.44  
% 216.06/216.44  Resimplifying inuse:
% 216.06/216.44  Done
% 216.06/216.44  
% 216.06/216.44  Resimplifying inuse:
% 216.06/216.44  Done
% 216.06/216.44  
% 216.06/216.44  
% 216.06/216.44  Intermediate Status:
% 216.06/216.44  Generated:    797406
% 216.06/216.44  Kept:         201695
% 216.06/216.44  Inuse:        2068
% 216.06/216.44  Deleted:      3365
% 216.06/216.44  Deletedinuse: 10
% 216.06/216.44  
% 216.06/216.44  Resimplifying inuse:
% 216.06/216.44  Done
% 216.06/216.44  
% 216.06/216.44  Resimplifying inuse:
% 216.06/216.44  Done
% 216.06/216.44  
% 216.06/216.44  
% 216.06/216.44  Intermediate Status:
% 216.06/216.44  Generated:    807359
% 216.06/216.44  Kept:         204679
% 216.06/216.44  Inuse:        2078
% 216.06/216.44  Deleted:      3365
% 216.06/216.44  Deletedinuse: 10
% 216.06/216.44  
% 216.06/216.44  Resimplifying inuse:
% 216.06/216.44  Done
% 216.06/216.44  
% 216.06/216.44  Resimplifying clauses:
% 216.06/216.44  Done
% 216.06/216.44  
% 216.06/216.44  Resimplifying inuse:
% 216.06/216.44  Done
% 216.06/216.44  
% 216.06/216.44  
% 216.06/216.44  Intermediate Status:
% 216.06/216.44  Generated:    817914
% 216.06/216.44  Kept:         206695
% 216.06/216.44  Inuse:        2095
% 216.06/216.44  Deleted:      6884
% 216.06/216.44  Deletedinuse: 11
% 216.06/216.44  
% 216.06/216.44  Resimplifying inuse:
% 216.06/216.44  Done
% 216.06/216.44  
% 216.06/216.44  Resimplifying inuse:
% 216.06/216.44  Done
% 216.06/216.44  
% 216.06/216.44  
% 216.06/216.44  Intermediate Status:
% 216.06/216.44  Generated:    824852
% 216.06/216.44  Kept:         208714
% 216.06/216.44  Inuse:        2106
% 216.06/216.44  Deleted:      6884
% 216.06/216.44  Deletedinuse: 11
% 216.06/216.44  
% 216.06/216.44  Resimplifying inuse:
% 216.06/216.44  Done
% 216.06/216.44  
% 216.06/216.44  
% 216.06/216.44  Intermediate Status:
% 216.06/216.44  Generated:    833233
% 216.06/216.44  Kept:         211032
% 216.06/216.44  Inuse:        2118
% 216.06/216.44  Deleted:      6884
% 216.06/216.44  Deletedinuse: 11
% 216.06/216.44  
% 216.06/216.44  Resimplifying inuse:
% 216.06/216.44  Done
% 216.06/216.44  
% 216.06/216.44  Resimplifying inuse:
% 216.06/216.44  Done
% 216.06/216.44  
% 216.06/216.44  
% 216.06/216.44  Intermediate Status:
% 216.06/216.44  Generated:    842614
% 216.06/216.44  Kept:         213465
% 216.06/216.44  Inuse:        2133
% 216.06/216.44  Deleted:      6884
% 216.06/216.44  Deletedinuse: 11
% 216.06/216.44  
% 216.06/216.44  Resimplifying inuse:
% 216.06/216.44  Done
% 216.06/216.44  
% 216.06/216.44  Resimplifying inuse:
% 216.06/216.44  Done
% 216.06/216.44  
% 216.06/216.44  
% 216.06/216.44  Intermediate Status:
% 216.06/216.44  Generated:    850683
% 216.06/216.44  Kept:         215502
% 216.06/216.44  Inuse:        2148
% 216.06/216.44  Deleted:      6884
% 216.06/216.44  Deletedinuse: 11
% 216.06/216.44  
% 216.06/216.44  Resimplifying inuse:
% 216.06/216.44  Done
% 216.06/216.44  
% 216.06/216.44  
% 216.06/216.44  Intermediate Status:
% 216.06/216.44  Generated:    864313
% 216.06/216.44  Kept:         218743
% 216.06/216.44  Inuse:        2158
% 216.06/216.44  Deleted: Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------