TSTP Solution File: SWV586-1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWV586-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n006.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 16:26:55 EDT 2022
% Result : Timeout 300.02s 300.38s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWV586-1 : TPTP v8.1.0. Released v4.1.0.
% 0.03/0.13 % Command : bliksem %s
% 0.12/0.33 % Computer : n006.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % DateTime : Tue Jun 14 21:06:26 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.42/1.80 *** allocated 10000 integers for termspace/termends
% 1.42/1.80 *** allocated 10000 integers for clauses
% 1.42/1.80 *** allocated 10000 integers for justifications
% 1.42/1.80 *** allocated 15000 integers for termspace/termends
% 1.42/1.80 *** allocated 22500 integers for termspace/termends
% 1.42/1.80 *** allocated 33750 integers for termspace/termends
% 1.42/1.80 *** allocated 50625 integers for termspace/termends
% 1.42/1.80 *** allocated 75937 integers for termspace/termends
% 1.42/1.80 Bliksem 1.12
% 1.42/1.80
% 1.42/1.80
% 1.42/1.80 Automatic Strategy Selection
% 1.42/1.80
% 1.42/1.80 Clauses:
% 1.42/1.80 [
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.80 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ),
% 1.42/1.80 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X )
% 1.42/1.80 , X ), hAPP( 'c_HOL_Oinverse__class_Oinverse'( X ), Y ) ) ) ) ],
% 1.42/1.80 [ ~( 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.42/1.80 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.42/1.80 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.42/1.80 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.42/1.80 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.80 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.42/1.80 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_lessequals'(
% 1.42/1.80 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ), hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ), X
% 1.42/1.80 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.42/1.80 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( T,
% 1.42/1.80 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), X ), Y ) ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.80 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.42/1.80 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_lessequals'(
% 1.42/1.80 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.42/1.80 , X ), X ), X ), T ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.42/1.80 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ), hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ), X
% 1.42/1.80 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.42/1.80 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.80 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.42/1.80 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_lessequals'( Y, X ),
% 1.42/1.80 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ), X
% 1.42/1.80 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.42/1.80 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( Y, X ), 'c_HOL_Oinverse__class_Odivide'( T,
% 1.42/1.80 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ) ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.80 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.42/1.80 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_lessequals'( Y, X ),
% 1.42/1.80 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.42/1.80 , X ), X ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ),
% 1.42/1.80 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X ), X
% 1.42/1.80 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.42/1.80 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ) ],
% 1.42/1.80 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ), hAPP( hAPP(
% 1.42/1.80 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), U ), W ) ), hAPP( hAPP(
% 1.42/1.80 'c_Power_Opower_Opower'( X, Y, Z ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.42/1.80 X, Y, Z ), T ), U ) ), W ) ), ~( 'c_OrderedGroup_Omonoid__mult'( X, Y, Z
% 1.42/1.80 ) ) ],
% 1.42/1.80 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.42/1.80 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.42/1.80 , Y ), Z ), Y, X ), 'c_Divides_Odiv__class_Omod'( Z, Y, X ) ) ],
% 1.42/1.80 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.42/1.80 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.42/1.80 , Y ), Z ), Z, X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 1.42/1.80 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.42/1.80 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.42/1.80 ), Z ) ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP(
% 1.42/1.80 hAPP( 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), Z ) ) ) ],
% 1.42/1.80 [ =( hAPP( X, hAPP( hAPP( 'c_Power_Opower_Opower'( Y, Z, T ), U ), W ) )
% 1.42/1.80 , hAPP( hAPP( 'c_Power_Opower_Opower'( Y, Z, T ), hAPP( X, U ) ), W ) ),
% 1.42/1.80 ~( 'c_Ring__and__Field_Oordered__idom'( V0, V1, V2, V3, V4, V5, X, Y, Z,
% 1.42/1.80 V6, T ) ) ],
% 1.42/1.80 [ =( hAPP( X, hAPP( hAPP( 'c_Power_Opower_Opower'( Y, Z, T ), hAPP( U, W
% 1.42/1.80 ) ), V0 ) ), hAPP( X, hAPP( hAPP( 'c_Power_Opower_Opower'( Y, Z, T ), W
% 1.42/1.80 ), V0 ) ) ), ~( 'c_Ring__and__Field_Oordered__idom'( V1, U, V2, V3, V4,
% 1.42/1.80 V5, X, Y, Z, V6, T ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( Y, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.42/1.80 X ), Z ), T ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), T )
% 1.42/1.80 ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.80 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ) ],
% 1.42/1.80 [ =( 'c_Divides_Odiv__class_Omod'( X, hAPP( hAPP(
% 1.42/1.80 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ), 'tc_nat' ), hAPP(
% 1.42/1.80 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.42/1.80 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ),
% 1.42/1.80 'c_Divides_Odiv__class_Omod'( 'c_Divides_Odiv__class_Odiv'( X, Y,
% 1.42/1.80 'tc_nat' ), Z, 'tc_nat' ) ) ), 'c_Divides_Odiv__class_Omod'( X, Y,
% 1.42/1.80 'tc_nat' ) ) ) ],
% 1.42/1.80 [ ~( 'c_Ring__and__Field_Oordered__idom'( X, Y, Z, T, U, W, V0, V1, V2,
% 1.42/1.80 V3, V4 ) ), hBOOL( hAPP( hAPP( W, Z ), hAPP( hAPP(
% 1.42/1.80 'c_Power_Opower_Opower'( V1, V2, V4 ), hAPP( V0, V5 ) ),
% 1.42/1.80 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.42/1.80 =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Oinverse__class_Oinverse'( X ), Y
% 1.42/1.80 ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.42/1.80 ), Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.42/1.80 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ), ~( hBOOL(
% 1.42/1.80 hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), X ), Y )
% 1.42/1.80 ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.42/1.80 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP(
% 1.42/1.80 'c_HOL_Oinverse__class_Oinverse'( X ), 'c_HOL_Oinverse__class_Odivide'( Y
% 1.42/1.80 , Z, X ) ), 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ) ) ],
% 1.42/1.80 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.42/1.80 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.42/1.80 'c_Divides_Odiv__class_Omod'( Y, Z, 'tc_nat' ) ) ), T ), 'tc_nat' ), hAPP(
% 1.42/1.80 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), ~( hBOOL(
% 1.42/1.80 hAPP( 'c_HOL_Oord__class_Oless'( T, 'tc_nat' ), X ) ) ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.42/1.80 'tc_nat' ), Z ) ) ) ],
% 1.42/1.80 [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ),
% 1.42/1.80 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.42/1.80 'tc_nat' ), Y, 'tc_nat' ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X,
% 1.42/1.80 'tc_nat' ), Y ) ) ],
% 1.42/1.80 [ =( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ), hAPP( 'c_Suc',
% 1.42/1.80 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.42/1.80 'tc_nat' ), Y, 'tc_nat' ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y,
% 1.42/1.80 'tc_nat' ), X ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.80 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), Y ) ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~( =( hAPP( hAPP(
% 1.42/1.80 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), 'c_HOL_Oone__class_Oone'( X
% 1.42/1.80 ) ) ), =( hAPP( 'c_HOL_Oinverse__class_Oinverse'( X ), Y ), Z ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z )
% 1.42/1.80 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ),
% 1.42/1.80 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ), =( Z,
% 1.42/1.80 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.42/1.80 ), Y ), Z ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.42/1.80 , 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.42/1.80 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( Y, X ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.42/1.80 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T, X ), X ), Z ) ) ) ]
% 1.42/1.80 ,
% 1.42/1.80 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( Y, X ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.42/1.80 'c_Lattices_Oupper__semilattice__class_Osup'( T, Y, X ), X ), Z ) ) ) ]
% 1.42/1.80 ,
% 1.42/1.80 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( Y, X ), 'c_Lattices_Oupper__semilattice__class_Osup'( Z,
% 1.42/1.80 T, X ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ), Z ) ) ) ],
% 1.42/1.80 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( Y, X ), 'c_Lattices_Oupper__semilattice__class_Osup'( Z,
% 1.42/1.80 T, X ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ), T ) ) ) ],
% 1.42/1.80 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( Y, X ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.42/1.80 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T, X ), X ), Z ) ) ) ]
% 1.42/1.80 ,
% 1.42/1.80 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( Y, X ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.42/1.80 'c_Lattices_Oupper__semilattice__class_Osup'( T, Y, X ), X ), Z ) ) ) ]
% 1.42/1.80 ,
% 1.42/1.80 [ hBOOL( hAPP( 'c_lessequals'( 'c_Int_OMin', 'tc_Int_Oint' ),
% 1.42/1.80 'c_Int_OMin' ) ) ],
% 1.42/1.80 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ), hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), U ), W ) ), hAPP( hAPP( Y, hAPP(
% 1.42/1.80 hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ), U ) ), hAPP( hAPP(
% 1.42/1.80 'c_Power_Opower_Opower'( X, Y, Z ), T ), W ) ) ), ~(
% 1.42/1.80 'c_OrderedGroup_Omonoid__mult'( X, Y, Z ) ) ],
% 1.42/1.80 [ ~( 'class_Orderings_Oorder'( X ) ), ~( =(
% 1.42/1.80 'c_SetInterval_Oord__class_OatLeastAtMost'( Y, Z, X ),
% 1.42/1.80 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ) ), ~( hBOOL(
% 1.42/1.80 hAPP( 'c_lessequals'( Y, X ), Z ) ) ) ],
% 1.42/1.80 [ ~( 'class_Orderings_Oorder'( X ) ), =(
% 1.42/1.80 'c_SetInterval_Oord__class_OatLeastAtMost'( Y, Z, X ),
% 1.42/1.80 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ), hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( Y, X ), Z ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.80 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.42/1.80 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.42/1.80 X ), Y ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.80 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oinverse__class_Odivide'( Y
% 1.42/1.80 , Z, X ) ) ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.80 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.42/1.80 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.42/1.80 X ), Z ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.80 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oinverse__class_Odivide'( Z
% 1.42/1.80 , Y, X ) ) ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.80 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.42/1.80 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.42/1.80 X ), Z ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.80 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oinverse__class_Odivide'( Y
% 1.42/1.80 , Z, X ) ) ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.80 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.42/1.80 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.42/1.80 X ), Y ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.80 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oinverse__class_Odivide'( Z
% 1.42/1.80 , Y, X ) ) ) ) ],
% 1.42/1.80 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.42/1.80 'c_Finite__Set_Osetsum'( Y, 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.42/1.80 Z, hAPP( 'c_Suc', T ), 'tc_nat' ), 'tc_nat', X ), hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( X ), 'c_Finite__Set_Osetsum'( Y,
% 1.42/1.80 'c_SetInterval_Oord__class_OatLeastLessThan'( Z, T, 'tc_nat' ), 'tc_nat'
% 1.42/1.80 , X ) ), hAPP( Y, T ) ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( T,
% 1.42/1.80 'tc_nat' ), Z ) ) ],
% 1.42/1.80 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( X ), 'c_Finite__Set_Osetsum'( Y,
% 1.42/1.80 'c_SetInterval_Oord__class_OatLeastLessThan'( Z, T, 'tc_nat' ), 'tc_nat'
% 1.42/1.80 , X ) ), 'c_Finite__Set_Osetsum'( Y,
% 1.42/1.80 'c_SetInterval_Oord__class_OatLeastLessThan'( T, U, 'tc_nat' ), 'tc_nat'
% 1.42/1.80 , X ) ), 'c_Finite__Set_Osetsum'( Y,
% 1.42/1.80 'c_SetInterval_Oord__class_OatLeastLessThan'( Z, U, 'tc_nat' ), 'tc_nat'
% 1.42/1.80 , X ) ), ~( hBOOL( hAPP( 'c_lessequals'( T, 'tc_nat' ), U ) ) ), ~( hBOOL(
% 1.42/1.80 hAPP( 'c_lessequals'( Z, 'tc_nat' ), T ) ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.80 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.42/1.80 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_lessequals'(
% 1.42/1.80 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.42/1.80 Y, X ) ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ),
% 1.42/1.80 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ),
% 1.42/1.80 ~( hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X
% 1.42/1.80 ), X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.80 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.42/1.80 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_lessequals'(
% 1.42/1.80 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ),
% 1.42/1.80 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.42/1.80 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ) ), hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.42/1.80 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.42/1.80 X ), Z ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( Y, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.42/1.80 X ), Y ), 'c_HOL_Oone__class_Oone'( X ) ) ) ) ],
% 1.42/1.80 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.42/1.80 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Ominus__class_Ominus'(
% 1.42/1.80 hAPP( 'c_Suc', Z ), T, 'tc_nat' ) ), hAPP( hAPP(
% 1.42/1.80 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.42/1.80 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Ominus__class_Ominus'( Z
% 1.42/1.80 , T, 'tc_nat' ) ) ), Y ) ), ~( hBOOL( hAPP( 'c_lessequals'( T, 'tc_nat' )
% 1.42/1.80 , Z ) ) ) ],
% 1.42/1.80 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.42/1.80 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), Z, 'tc_nat' ), hAPP(
% 1.42/1.80 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.42/1.80 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.42/1.80 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ) ),
% 1.42/1.80 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.42/1.80 'tc_nat' ), X ), 'c_Divides_Odiv__class_Omod'( Y, Z, 'tc_nat' ) ), Z,
% 1.42/1.80 'tc_nat' ) ) ) ],
% 1.42/1.80 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), X ), T ), X ), ~(
% 1.42/1.80 'c_OrderedGroup_Omonoid__mult'( X, Y, Z ) ) ],
% 1.42/1.80 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.42/1.80 , hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.42/1.80 ), Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z )
% 1.42/1.80 ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ), T ) ) ) ],
% 1.42/1.80 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.42/1.80 , hBOOL( hAPP( 'c_lessequals'( Y, X ), Z ) ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X
% 1.42/1.80 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ) ],
% 1.42/1.80 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.42/1.80 , hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.42/1.80 ), Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T )
% 1.42/1.80 ) ), ~( hBOOL( hAPP( 'c_lessequals'( Z, X ), T ) ) ) ],
% 1.42/1.80 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.42/1.80 , hBOOL( hAPP( 'c_lessequals'( Y, X ), Z ) ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Y ), X
% 1.42/1.80 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ) ) ],
% 1.42/1.80 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ), hBOOL(
% 1.42/1.80 hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z
% 1.42/1.80 ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ), ~(
% 1.42/1.80 hBOOL( hAPP( 'c_lessequals'( Y, X ), T ) ) ) ],
% 1.42/1.80 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ), hBOOL(
% 1.42/1.80 hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z
% 1.42/1.80 ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), ~(
% 1.42/1.80 hBOOL( hAPP( 'c_lessequals'( Z, X ), T ) ) ) ],
% 1.42/1.80 [ hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.42/1.80 'tc_nat' ), X ), Y ), 'tc_nat' ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.42/1.80 'tc_nat' ), Z ), Y ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ),
% 1.42/1.80 Z ) ) ) ],
% 1.42/1.80 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ),
% 1.42/1.80 X ), 'tc_nat' ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z )
% 1.42/1.80 , Y ) ) ) ) ],
% 1.42/1.80 [ hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.42/1.80 'tc_nat' ), X ), Y ), 'tc_nat' ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.42/1.80 'tc_nat' ), X ), Z ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, 'tc_nat' ),
% 1.42/1.80 Z ) ) ) ],
% 1.42/1.80 [ =( 'c_HOL_Ominus__class_Ominus'( X, hAPP( 'c_Suc',
% 1.42/1.80 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ), 'tc_nat' ),
% 1.42/1.80 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.42/1.80 'tc_nat' ), X ), Z ), hAPP( 'c_Suc', Y ), 'tc_nat' ) ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( Z, 'tc_nat' ), Y ) ) ) ],
% 1.42/1.80 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.42/1.80 'c_Lattices_Oupper__semilattice__class_Osup'( 'c_Set_Oinsert'( Y,
% 1.42/1.80 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ), X ),
% 1.42/1.80 'c_SetInterval_Oord__class_OgreaterThanLessThan'( Y, Z, X ), 'tc_fun'( X
% 1.42/1.80 , 'tc_bool' ) ), 'c_SetInterval_Oord__class_OatLeastLessThan'( Y, Z, X )
% 1.42/1.80 ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( Z, X ), Y ) ), =( Z, Y ) ],
% 1.42/1.80 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ), hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( Z, X ), Y ) ), hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ) ],
% 1.42/1.80 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ), hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( Z, X ), Y ) ) ],
% 1.42/1.80 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), =( Z, Y ), hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( Z, X ), Y ) ) ],
% 1.42/1.80 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( Y, X ), Z ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Z, X ),
% 1.42/1.80 Y ) ) ) ],
% 1.42/1.80 [ ~( 'class_RealVector_Ometric__space'( X ) ), ~(
% 1.42/1.80 'class_RealVector_Oreal__normed__algebra__1'( Y ) ), =( Z, T ), ~(
% 1.42/1.80 'c_Lim_OLIM'( U, W, T, Y, X ) ), ~( 'c_Lim_OLIM'( U, W, Z, Y, X ) ) ]
% 1.42/1.80 ,
% 1.42/1.80 [ =( X, Y ), ~( hBOOL( hAPP( 'c_lessequals'( Y, 'tc_nat' ), X ) ) ), ~(
% 1.42/1.80 hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ) ) ],
% 1.42/1.80 [ =( X, Y ), ~( hBOOL( hAPP( 'c_lessequals'( Y, 'tc_Int_Oint' ), X ) ) )
% 1.42/1.80 , ~( hBOOL( hAPP( 'c_lessequals'( X, 'tc_Int_Oint' ), Y ) ) ) ],
% 1.42/1.80 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ), hBOOL(
% 1.42/1.80 hAPP( 'c_HOL_Oord__class_Oless'( Y, 'tc_nat' ), X ) ), =( Y, X ) ],
% 1.42/1.80 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_Int_Oint' ), Y ) ), =(
% 1.42/1.80 Y, X ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, 'tc_Int_Oint' ), X ) )
% 1.42/1.80 ],
% 1.42/1.80 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( Y, 'tc_nat' ), Z ) ), =( Z, Y ), hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( Z, 'tc_nat' ), Y ) ) ],
% 1.42/1.80 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ), hBOOL(
% 1.42/1.80 hAPP( 'c_HOL_Oord__class_Oless'( Y, 'tc_nat' ), X ) ), =( Y, X ) ],
% 1.42/1.80 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( Z, X ), Y ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ),
% 1.42/1.80 Z ) ) ) ],
% 1.42/1.80 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( Z, X ), Y ) ), =( Z, Y ) ],
% 1.42/1.80 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( Z, X ), Y ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ),
% 1.42/1.80 Z ) ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), X ), hAPP( hAPP(
% 1.42/1.80 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.42/1.80 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), X ), Y ) ) ) ]
% 1.42/1.80 ,
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.42/1.80 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.42/1.80 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.42/1.80 Z, X ) ), T ), 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.42/1.80 'c_Power_Opower__class_Opower'( X ), Y ), T ), hAPP( hAPP(
% 1.42/1.80 'c_Power_Opower__class_Opower'( X ), Z ), T ), X ) ) ],
% 1.42/1.80 [ ~( 'class_Orderings_Oorder'( X ) ), =(
% 1.42/1.80 'c_SetInterval_Oord__class_OatLeastAtMost'( Y, Z, X ),
% 1.42/1.80 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ), ~( hBOOL(
% 1.42/1.80 hAPP( 'c_HOL_Oord__class_Oless'( Z, X ), Y ) ) ) ],
% 1.42/1.80 [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), X ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.80 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'(
% 1.42/1.80 X ), Y, X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.80 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL(
% 1.42/1.80 hAPP( 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'(
% 1.42/1.80 'c_HOL_Oone__class_Oone'( X ), Y, X ), X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.42/1.80 ) ) ) ) ],
% 1.42/1.80 [ ~( 'class_Lattices_Olattice'( X ) ), hBOOL( hAPP( 'c_lessequals'(
% 1.42/1.80 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.42/1.80 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ), X ),
% 1.42/1.80 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.42/1.80 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ),
% 1.42/1.80 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T, X ), X ) ) ) ],
% 1.42/1.80 [ hBOOL( hAPP( 'c_lessequals'( 'c_Int_Onumber__class_Onumber__of'( X,
% 1.42/1.80 'tc_nat' ), 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' )
% 1.42/1.80 ) ), ~( hBOOL( hAPP( 'c_lessequals'( X, 'tc_Int_Oint' ), Y ) ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.42/1.80 'class_Int_Onumber__ring'( X ) ), hBOOL( hAPP( 'c_lessequals'( Y,
% 1.42/1.80 'tc_Int_Oint' ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.42/1.80 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.42/1.80 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.42/1.80 'class_Int_Onumber__ring'( X ) ), hBOOL( hAPP( 'c_lessequals'(
% 1.42/1.80 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.42/1.80 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( Y, 'tc_Int_Oint' ), Z ) ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.80 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Oinverse__class_Oinverse'( X ), Y
% 1.42/1.80 ), X ), 'c_HOL_Oone__class_Oone'( X ) ) ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.42/1.80 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.42/1.80 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.42/1.80 'c_SetInterval_Oord__class_OatLeastLessThan'( Y, Z, X ),
% 1.42/1.80 'c_SetInterval_Oord__class_OatLeastAtMost'( Z, T, X ), 'tc_fun'( X,
% 1.42/1.80 'tc_bool' ) ), 'c_SetInterval_Oord__class_OatLeastAtMost'( Y, T, X ) ),
% 1.42/1.80 ~( hBOOL( hAPP( 'c_lessequals'( Z, X ), T ) ) ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( Y, X ), Z ) ) ) ],
% 1.42/1.80 [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), Z, 'tc_nat' ), hAPP(
% 1.42/1.80 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.42/1.80 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ) ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( Z, 'tc_nat' ), Y ) ) ) ],
% 1.42/1.80 [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), Z, 'tc_nat' ), hAPP(
% 1.42/1.80 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.42/1.80 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ) ), Y ) ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( Z, 'tc_nat' ), X ) ) ) ],
% 1.42/1.80 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), hBOOL(
% 1.42/1.80 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.42/1.80 X ), Y ), Z ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.42/1.80 , ~( hBOOL( hAPP( 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.42/1.80 ) ) ) ],
% 1.42/1.80 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), hBOOL(
% 1.42/1.80 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.42/1.80 X ), Y ), Z ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL(
% 1.42/1.80 hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.42/1.80 ) ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.80 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( Y, X ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ) ) ),
% 1.42/1.80 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( T, X ),
% 1.42/1.80 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Z
% 1.42/1.80 , X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ), ~(
% 1.42/1.80 hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.42/1.80 ), Y ), T ), X ), Z ) ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.80 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), T ) ),
% 1.42/1.80 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ),
% 1.42/1.80 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.42/1.80 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ), Y ) ) ),
% 1.42/1.80 ~( hBOOL( hAPP( 'c_lessequals'( Y, X ), hAPP( hAPP(
% 1.42/1.80 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ) ) ],
% 1.42/1.80 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.42/1.80 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.42/1.80 'c_SetInterval_Oord__class_OatLeastLessThan'( Y, Z, X ),
% 1.42/1.80 'c_SetInterval_Oord__class_OatLeastLessThan'( Z, T, X ), 'tc_fun'( X,
% 1.42/1.80 'tc_bool' ) ), 'c_SetInterval_Oord__class_OatLeastLessThan'( Y, T, X ) )
% 1.42/1.80 , ~( hBOOL( hAPP( 'c_lessequals'( Z, X ), T ) ) ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( Y, X ), Z ) ) ) ],
% 1.42/1.80 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), hBOOL( hAPP( hAPP( X, Z ), Y ) ),
% 1.42/1.80 =( Z, Y ), ~( 'c_Ring__and__Field_Oordered__idom'( T, U, W, V0, V1, X, V2
% 1.42/1.80 , V3, V4, V5, V6 ) ) ],
% 1.42/1.80 [ =( hAPP( hAPP( X, hAPP( Y, Z ) ), hAPP( Y, Z ) ), hAPP( hAPP( X, Z ),
% 1.42/1.80 Z ) ), ~( 'c_Ring__and__Field_Oordered__idom'( T, U, W, V0, V1, V2, Y, V3
% 1.42/1.80 , X, V4, V5 ) ) ],
% 1.42/1.80 [ =( hAPP( hAPP( X, hAPP( Y, Z ) ), hAPP( T, Z ) ), Z ), ~(
% 1.42/1.80 'c_Ring__and__Field_Oordered__idom'( U, W, V0, V1, V2, V3, T, V4, X, Y,
% 1.42/1.80 V5 ) ) ],
% 1.42/1.80 [ =( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), hAPP( hAPP( Y, hAPP( X, Z ) ),
% 1.42/1.80 hAPP( X, T ) ) ), ~( 'c_Ring__and__Field_Oordered__idom'( U, W, V0, V1,
% 1.42/1.80 V2, V3, V4, V5, Y, X, V6 ) ) ],
% 1.42/1.80 [ =( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), hAPP( hAPP( Y, hAPP( X, Z ) ),
% 1.42/1.80 hAPP( X, T ) ) ), ~( 'c_Ring__and__Field_Oordered__idom'( U, W, V0, V1,
% 1.42/1.80 V2, V3, X, V4, Y, V5, V6 ) ) ],
% 1.42/1.80 [ =( hAPP( X, hAPP( X, Y ) ), hAPP( X, Y ) ), ~(
% 1.42/1.80 'c_Ring__and__Field_Oordered__idom'( Z, T, U, W, V0, V1, V2, V3, V4, X,
% 1.42/1.80 V5 ) ) ],
% 1.42/1.80 [ ~( 'c_Ring__and__Field_Oordered__idom'( X, Y, Z, T, U, W, V0, V1, V2,
% 1.42/1.80 V3, V4 ) ), =( hAPP( V3, Z ), Z ) ],
% 1.42/1.80 [ ~( 'c_Ring__and__Field_Oordered__idom'( X, Y, hAPP( Z, T ), U, W, V0,
% 1.42/1.80 V1, V2, V3, Z, V4 ) ), =( T, hAPP( Z, T ) ) ],
% 1.42/1.80 [ =( hAPP( X, Y ), hAPP( hAPP( Z, Y ), hAPP( T, Y ) ) ), ~(
% 1.42/1.80 'c_Ring__and__Field_Oordered__idom'( U, W, V0, V1, V2, V3, X, V4, Z, T,
% 1.42/1.80 V5 ) ) ],
% 1.42/1.80 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.42/1.80 'c_Power_Opower__class_Opower'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.42/1.80 'c_Int_OMin', X ) ), Y ), 'c_Int_Onumber__class_Onumber__of'(
% 1.42/1.80 'c_Int_OMin', X ) ), 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ]
% 1.42/1.80 ,
% 1.42/1.80 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( Z, Y ) ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_Lattices_Oupper__semilattice__class_Osup'( Z, X, 'tc_fun'( T,
% 1.42/1.80 'tc_bool' ) ), Y ) ) ) ],
% 1.42/1.80 [ hBOOL( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y,
% 1.42/1.80 'tc_fun'( Z, 'tc_bool' ) ), T ) ), ~( hBOOL( hAPP( Y, T ) ) ) ],
% 1.42/1.80 [ hBOOL( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y,
% 1.42/1.80 'tc_fun'( Z, 'tc_bool' ) ), T ) ), ~( hBOOL( hAPP( X, T ) ) ) ],
% 1.42/1.80 [ ~( hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( 'c_Power_Opower_Opower'( Z,
% 1.42/1.80 T, U ), hAPP( W, Y ) ), V0 ) ) ) ), ~(
% 1.42/1.80 'c_Ring__and__Field_Oordered__idom'( V1, V2, Y, V3, V4, X, W, Z, T, V5, U
% 1.42/1.80 ) ), =( V0, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.42/1.80 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.42/1.80 ), Y ), T ), X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.42/1.80 T ) ) ) ) ],
% 1.42/1.80 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.42/1.80 ), Y ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.42/1.80 ],
% 1.42/1.80 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.42/1.80 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ),
% 1.42/1.80 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.42/1.80 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ),
% 1.42/1.80 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.42/1.80 ), Y ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.42/1.80 ],
% 1.42/1.80 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.42/1.80 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.42/1.80 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), T ), Y ) ), U ) ) ), ~( hBOOL(
% 1.42/1.80 hAPP( 'c_lessequals'( X, 'tc_nat' ), T ) ) ), =( Z, hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.42/1.80 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( T
% 1.42/1.80 , X, 'tc_nat' ) ), Y ) ), U ) ) ],
% 1.42/1.80 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.42/1.80 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.42/1.80 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), T ), Y ) ), U ) ) ), ~( hBOOL(
% 1.42/1.80 hAPP( 'c_lessequals'( T, 'tc_nat' ), X ) ) ), =( hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.42/1.80 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X
% 1.42/1.80 , T, 'tc_nat' ) ), Y ) ), Z ), U ) ],
% 1.42/1.80 [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ),
% 1.42/1.80 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.42/1.80 'tc_nat' ), Y, 'tc_nat' ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, 'tc_nat'
% 1.42/1.80 ), X ) ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.42/1.80 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X )
% 1.42/1.80 , T, X ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oinverse__class_Odivide'(
% 1.42/1.80 Y, T, X ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ) ) ],
% 1.42/1.80 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 1.42/1.80 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X )
% 1.42/1.80 , T, X ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oinverse__class_Odivide'(
% 1.42/1.80 Y, T, X ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ) ) ],
% 1.42/1.80 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( =(
% 1.42/1.80 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.42/1.80 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.42/1.80 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ), =( Z,
% 1.42/1.80 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.80 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( =(
% 1.42/1.80 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.42/1.80 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.42/1.80 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ), =( Y,
% 1.42/1.80 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.80 [ =( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ), hAPP( 'c_Suc',
% 1.42/1.80 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.42/1.80 'tc_nat' ), Y, 'tc_nat' ) ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X
% 1.42/1.80 , 'tc_nat' ), Y ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.80 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), Y ) ) ) ],
% 1.42/1.80 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.42/1.80 'c_HOL_Ominus__class_Ominus'( 'c_Finite__Set_Osetsum'( Y,
% 1.42/1.80 'c_SetInterval_Oord__class_OatLeastLessThan'( Z, T, 'tc_nat' ), 'tc_nat'
% 1.42/1.80 , X ), 'c_Finite__Set_Osetsum'( Y,
% 1.42/1.80 'c_SetInterval_Oord__class_OatLeastLessThan'( Z, U, 'tc_nat' ), 'tc_nat'
% 1.42/1.80 , X ), X ), 'c_Finite__Set_Osetsum'( Y,
% 1.42/1.80 'c_SetInterval_Oord__class_OatLeastLessThan'( U, T, 'tc_nat' ), 'tc_nat'
% 1.42/1.80 , X ) ), ~( hBOOL( hAPP( 'c_lessequals'( U, 'tc_nat' ), T ) ) ), ~( hBOOL(
% 1.42/1.80 hAPP( 'c_lessequals'( Z, 'tc_nat' ), U ) ) ) ],
% 1.42/1.80 [ ~( hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ) ), =( hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.42/1.80 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.42/1.80 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.42/1.80 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Y
% 1.42/1.80 , X, 'tc_nat' ) ), Z ) ), T ) ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.42/1.80 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.42/1.80 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.42/1.80 'c_Power_Opower__class_Opower'( X ), Y ), T ) ), hAPP( hAPP(
% 1.42/1.80 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ) ) ],
% 1.42/1.80 [ hBOOL( hAPP( X, 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ) ),
% 1.42/1.80 ~( hBOOL( hAPP( X, T ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y
% 1.42/1.80 , 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ),
% 1.42/1.80 hAPP( 'c_Suc', T ) ) ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP(
% 1.42/1.80 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ), 'tc_nat' ), Y ) ) ) ]
% 1.42/1.80 ,
% 1.42/1.80 [ =( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ),
% 1.42/1.80 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ) ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.42/1.80 'tc_nat' ), Y ) ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( Y, X ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ) ) ),
% 1.42/1.80 ~( hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.42/1.80 X ), Y ), T ), X ), Z ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.80 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), T ) ),
% 1.42/1.80 ~( hBOOL( hAPP( 'c_lessequals'( Y, X ), hAPP( hAPP(
% 1.42/1.80 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ) ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) )
% 1.42/1.80 ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.80 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( Y, X ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ) ) ),
% 1.42/1.80 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X
% 1.42/1.80 ), X ), T ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP(
% 1.42/1.80 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), Z ) ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.80 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.42/1.80 X ), T ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.80 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( Y, X ), 'c_HOL_Oinverse__class_Odivide'( T, Z, X ) ) ) )
% 1.42/1.80 ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.80 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), T ) ),
% 1.42/1.80 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X
% 1.42/1.80 ), X ), Z ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ), hAPP( hAPP(
% 1.42/1.80 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.80 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( Y, X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z
% 1.42/1.80 ), T ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.80 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ), Z ) ) )
% 1.42/1.80 ],
% 1.42/1.80 [ ~( 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'( X )
% 1.42/1.80 , 'c_Power_Opower_Opower'( 'c_HOL_Oone__class_Oone'( X ),
% 1.42/1.80 'c_HOL_Otimes__class_Otimes'( X ), X ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.42/1.80 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.42/1.80 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ) ) ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ),
% 1.42/1.80 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.42/1.80 , 'tc_nat' ), 'tc_nat' ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ),
% 1.42/1.80 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.42/1.80 , 'tc_nat' ), 'tc_nat' ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.42/1.80 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.42/1.80 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.42/1.80 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ) ) ) ) ],
% 1.42/1.80 [ hBOOL( hAPP( 'c_lessequals'( 'c_Divides_Odiv__class_Omod'( X, Y,
% 1.42/1.80 'tc_nat' ), 'tc_nat' ), Y ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.80 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), Y ) ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.80 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( hAPP( 'c_HOL_Oinverse__class_Oinverse'( X ), Y ), X ),
% 1.42/1.80 'c_HOL_Oone__class_Oone'( X ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X )
% 1.42/1.80 , 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.80 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.42/1.80 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) )
% 1.42/1.80 ), ~( hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.42/1.80 , Y ) ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.80 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ), ~( hBOOL(
% 1.42/1.80 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.42/1.80 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) )
% 1.42/1.80 ) ) ],
% 1.42/1.80 [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ),
% 1.42/1.80 hAPP( 'c_Suc', 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ) ), ~(
% 1.42/1.80 hBOOL( hAPP( 'c_lessequals'( Y, 'tc_nat' ), X ) ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.42/1.80 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), X ), hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.42/1.80 X ), U ), Z ) ), W ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( T, X ), hAPP(
% 1.42/1.80 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.42/1.80 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ominus__class_Ominus'( U, Y, X
% 1.42/1.80 ) ), Z ) ), W ) ) ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( Y, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.42/1.80 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ominus__class_Ominus'( Z
% 1.42/1.80 , T, X ) ), U ) ), W ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.42/1.80 X ), T ), U ) ), Y ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.42/1.80 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ), W ) ) ) ) ]
% 1.42/1.80 ,
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.42/1.80 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), X ), hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.42/1.80 X ), U ), Z ) ), W ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.42/1.80 X ), 'c_HOL_Ominus__class_Ominus'( Y, U, X ) ), Z ) ), T ), X ), W ) ) )
% 1.42/1.80 ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ),
% 1.42/1.80 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.42/1.80 , ~( hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 1.42/1.80 ) ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ),
% 1.42/1.80 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) )
% 1.42/1.80 , ~( hBOOL( hAPP( 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.42/1.80 ) ) ) ],
% 1.42/1.80 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.42/1.80 'c_Power_Opower__class_Opower'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.42/1.80 'c_Int_OMin', X ) ), Y ), 'c_HOL_Oone__class_Oone'( X ) ), ~(
% 1.42/1.80 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.42/1.80 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'(
% 1.42/1.80 Z, 'tc_nat' ) ), ~( hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP(
% 1.42/1.80 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ),
% 1.42/1.80 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z )
% 1.42/1.80 , X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), T ), Z ) ) ), ~(
% 1.42/1.80 hBOOL( hAPP( 'c_lessequals'( Y, X ), T ) ) ),
% 1.42/1.80 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.42/1.80 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.42/1.80 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) )
% 1.42/1.80 ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, 'tc_nat' ), X ) ) ) ]
% 1.42/1.80 ,
% 1.42/1.80 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ), ~( hBOOL(
% 1.42/1.80 hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.42/1.80 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ) ) ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 1.42/1.80 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( =( hAPP(
% 1.42/1.80 'c_HOL_Oinverse__class_Oinverse'( X ), Y ), hAPP(
% 1.42/1.80 'c_HOL_Oinverse__class_Oinverse'( X ), Z ) ) ), =( Y, Z ) ],
% 1.42/1.80 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 1.42/1.80 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 1.42/1.80 , U, X ) ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~(
% 1.42/1.80 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( T, X ), U ) ) ) ],
% 1.42/1.80 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 1.42/1.80 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 1.42/1.80 , U, X ) ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( T, X ), U ) ), ~(
% 1.42/1.80 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ) ) ],
% 1.42/1.80 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 1.42/1.80 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 1.42/1.80 , U, X ) ) ), hBOOL( hAPP( 'c_lessequals'( Z, X ), Y ) ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( U, X ), T ) ) ) ],
% 1.42/1.80 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 1.42/1.80 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 1.42/1.80 , U, X ) ) ), hBOOL( hAPP( 'c_lessequals'( U, X ), T ) ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( Z, X ), Y ) ) ) ],
% 1.42/1.80 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.42/1.80 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.42/1.80 , Y ), 'c_Divides_Odiv__class_Omod'( Z, T, X ) ), T, X ),
% 1.42/1.80 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.42/1.80 , Y ), Z ), T, X ) ) ],
% 1.42/1.80 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.42/1.80 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.42/1.80 , 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ), T ), Z, X ),
% 1.42/1.80 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.42/1.80 , Y ), T ), Z, X ) ) ],
% 1.42/1.80 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.42/1.80 'c_Finite__Set_Osetsum'( Y, 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.42/1.80 Z, T, 'tc_nat' ), 'tc_nat', X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.42/1.80 X ), hAPP( Y, Z ) ), 'c_Finite__Set_Osetsum'( Y,
% 1.42/1.80 'c_SetInterval_Oord__class_OatLeastLessThan'( hAPP( 'c_Suc', Z ), T,
% 1.42/1.80 'tc_nat' ), 'tc_nat', X ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.80 Z, 'tc_nat' ), T ) ) ) ],
% 1.42/1.80 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( Y, hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.42/1.80 X ), 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ), Z ) ),
% 1.42/1.80 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ) ],
% 1.42/1.80 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.42/1.80 X ), 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ), Z ) ),
% 1.42/1.80 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ), Y ) ],
% 1.42/1.80 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.42/1.80 X ), Y ), 'c_Divides_Odiv__class_Odiv'( Z, Y, X ) ) ),
% 1.42/1.80 'c_Divides_Odiv__class_Omod'( Z, Y, X ) ), Z ) ],
% 1.42/1.80 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), =( Y, Z ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( Y, X ), Z ) ) ) ],
% 1.42/1.80 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.42/1.80 Y, X ), Z ) ) ) ],
% 1.42/1.80 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ), =( X, Y
% 1.42/1.80 ), ~( hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ) ) ],
% 1.42/1.80 [ =( X, Y ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y )
% 1.42/1.80 ), ~( hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ) ) ],
% 1.42/1.80 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ), =( X, Y
% 1.42/1.80 ), ~( hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ) ) ],
% 1.42/1.80 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_Int_Oint' ), Y ) ), =(
% 1.42/1.80 X, Y ), ~( hBOOL( hAPP( 'c_lessequals'( X, 'tc_Int_Oint' ), Y ) ) ) ]
% 1.42/1.80 ,
% 1.42/1.80 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), =( Y, Z ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( Y, X ), Z ) ) ) ],
% 1.42/1.80 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.42/1.80 Y, X ), Z ) ) ), =( Y, Z ) ],
% 1.42/1.80 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( Y, X ), Z ) ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.80 Y, X ), Z ) ) ],
% 1.42/1.80 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ), hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.42/1.80 Y, X ), Z ) ) ) ],
% 1.42/1.80 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.42/1.80 Y, X ), Z ) ) ), =( Z, Y ) ],
% 1.42/1.80 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), =( Z, Y ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( Y, X ), Z ) ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.80 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ),
% 1.42/1.80 'c_HOL_Oinverse__class_Odivide'( T, Z, X ) ) ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL(
% 1.42/1.80 hAPP( 'c_lessequals'( Y, X ), T ) ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.80 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ),
% 1.42/1.80 'c_HOL_Oinverse__class_Odivide'( T, Z, X ) ) ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL(
% 1.42/1.80 hAPP( 'c_lessequals'( T, X ), Y ) ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 1.42/1.80 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP(
% 1.42/1.80 'c_HOL_Oinverse__class_Oinverse'( X ), hAPP( hAPP(
% 1.42/1.80 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.42/1.80 'c_Power_Opower__class_Opower'( X ), hAPP(
% 1.42/1.80 'c_HOL_Oinverse__class_Oinverse'( X ), Y ) ), Z ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =(
% 1.42/1.80 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Oone__class_Oone'( X )
% 1.42/1.80 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, Z ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.42/1.80 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.42/1.80 , 'tc_nat' ), 'tc_nat' ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.80 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.42/1.80 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ), X ),
% 1.42/1.80 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.42/1.80 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP(
% 1.42/1.80 hAPP( 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.42/1.80 ) ), Y ) ) ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ) ]
% 1.42/1.80 ,
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X
% 1.42/1.80 ), 'c_HOL_Oinverse__class_Odivide'( T, U, X ) ) ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( U, X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), U ) ) )
% 1.42/1.80 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), T ) ) ), ~( hBOOL(
% 1.42/1.80 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ) ]
% 1.42/1.80 ,
% 1.42/1.80 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.42/1.80 'tc_nat' ), 'tc_nat' ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat'
% 1.42/1.80 ), X ), Y ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.80 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), Y ) ) ) ],
% 1.42/1.80 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.42/1.80 'tc_nat' ), 'tc_nat' ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat'
% 1.42/1.80 ), X ), Y ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.80 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), X ) ) ) ],
% 1.42/1.80 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ),
% 1.42/1.80 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X
% 1.42/1.80 ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ) ) ) ) ]
% 1.42/1.80 ,
% 1.42/1.80 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP(
% 1.42/1.80 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ) ) ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) )
% 1.42/1.80 ],
% 1.42/1.80 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( Y, X ),
% 1.42/1.80 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ) ) ), ~( hBOOL(
% 1.42/1.80 hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ) ) ],
% 1.42/1.80 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( Y, X ),
% 1.42/1.80 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ) ) ), ~( hBOOL(
% 1.42/1.80 hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), T ) ) ) ],
% 1.42/1.80 [ ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ) ), =(
% 1.42/1.80 Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( hBOOL( hAPP( Z,
% 1.42/1.80 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.42/1.80 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), T
% 1.42/1.80 ) ), X ), Y, 'tc_nat' ) ) ) ), hBOOL( hAPP( Z, X ) ) ],
% 1.42/1.80 [ ~( hBOOL( hAPP( 'c_lessequals'( 'c_Int_OPls', 'tc_Int_Oint' ),
% 1.42/1.80 'c_Int_OMin' ) ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( Y, 'tc_nat' ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.42/1.80 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), T ), Y ), X ), hAPP(
% 1.42/1.80 hAPP( 'c_Power_Opower__class_Opower'( X ), T ), Z ) ) ) ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), X ), T ) ) ) ]
% 1.42/1.80 ,
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( Y, 'tc_nat' ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.42/1.80 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), T ), Y ), X ), hAPP(
% 1.42/1.80 hAPP( 'c_Power_Opower__class_Opower'( X ), T ), Z ) ) ) ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), X ), T ) ) ) ]
% 1.42/1.80 ,
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z )
% 1.42/1.80 , X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), T ) ) ), ~(
% 1.42/1.80 hBOOL( hAPP( 'c_lessequals'( Z, 'tc_nat' ), T ) ) ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), X ), Y ) ) ) ]
% 1.42/1.80 ,
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.80 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), X ), hAPP(
% 1.42/1.80 'c_HOL_Oinverse__class_Oinverse'( X ), Y ) ) ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( Y, X ), 'c_HOL_Oone__class_Oone'( X ) ) ) ), ~( hBOOL(
% 1.42/1.80 hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 1.42/1.80 ) ) ) ],
% 1.42/1.80 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oone__class_Oone'(
% 1.42/1.80 'tc_nat' ), 'tc_nat' ) ) ],
% 1.42/1.80 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ), hAPP( 'c_Suc'
% 1.42/1.80 , U ) ), hAPP( hAPP( Y, hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T
% 1.42/1.80 ), U ) ), T ) ), ~( 'c_OrderedGroup_Omonoid__mult'( X, Y, Z ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP(
% 1.42/1.80 'c_HOL_Oinverse__class_Oinverse'( X ), Y ),
% 1.42/1.80 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) )
% 1.42/1.80 , =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.80 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.42/1.80 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.42/1.80 , Y ), Z ), Y, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.42/1.80 'c_Divides_Odiv__class_Odiv'( Z, Y, X ) ), 'c_HOL_Oone__class_Oone'( X )
% 1.42/1.80 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.80 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.42/1.80 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.42/1.80 , Y ), Z ), Z, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.42/1.80 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ), 'c_HOL_Oone__class_Oone'( X )
% 1.42/1.80 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP(
% 1.42/1.80 hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) )
% 1.42/1.80 , 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP(
% 1.42/1.80 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.42/1.80 'c_HOL_Oone__class_Oone'( X ) ) ) ) ],
% 1.42/1.80 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), Z, 'tc_nat' ), hAPP(
% 1.42/1.80 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( X,
% 1.42/1.80 Z, 'tc_nat' ) ), 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ) ),
% 1.42/1.80 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.42/1.80 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X, Z, 'tc_nat' ) ),
% 1.42/1.80 'c_Divides_Odiv__class_Omod'( Y, Z, 'tc_nat' ) ), Z, 'tc_nat' ) ) ) ]
% 1.42/1.80 ,
% 1.42/1.80 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.42/1.80 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.42/1.80 'c_SetInterval_Oord__class_OatLeastAtMost'( Y, Z, X ),
% 1.42/1.80 'c_SetInterval_Oord__class_OgreaterThanLessThan'( Z, T, X ), 'tc_fun'( X
% 1.42/1.80 , 'tc_bool' ) ), 'c_SetInterval_Oord__class_OatLeastLessThan'( Y, T, X )
% 1.42/1.80 ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ), T ) ) ), ~( hBOOL(
% 1.42/1.80 hAPP( 'c_lessequals'( Y, X ), Z ) ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.80 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ),
% 1.42/1.80 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ),
% 1.42/1.80 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ),
% 1.42/1.80 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.80 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), Y ) ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.80 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X
% 1.42/1.80 ), T ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.80 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ), hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.42/1.80 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.42/1.80 X ), Z ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.80 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.42/1.80 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ),
% 1.42/1.80 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ),
% 1.42/1.80 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ),
% 1.42/1.80 'c_HOL_Oinverse__class_Odivide'( T, Z, X ) ) ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.80 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Oinverse__class_Odivide'( Z, T
% 1.42/1.80 , X ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ),
% 1.42/1.80 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( T, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.42/1.80 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.42/1.80 X ), T ) ) ],
% 1.42/1.80 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ),
% 1.42/1.80 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 1.42/1.80 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.42/1.80 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ), ~(
% 1.42/1.80 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 1.42/1.80 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.42/1.80 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ),
% 1.42/1.80 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~(
% 1.42/1.80 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ) ) ],
% 1.42/1.80 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ),
% 1.42/1.80 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~(
% 1.42/1.80 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ],
% 1.42/1.80 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ), ~(
% 1.42/1.80 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 1.42/1.80 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.42/1.80 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ),
% 1.42/1.80 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 1.42/1.80 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.42/1.80 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ), ~(
% 1.42/1.80 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 1.42/1.80 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ) ) ],
% 1.42/1.80 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ), ~(
% 1.42/1.80 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 1.42/1.80 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ],
% 1.42/1.80 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ) ),
% 1.42/1.80 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~(
% 1.42/1.80 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.42/1.80 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ) ), ~(
% 1.42/1.80 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ),
% 1.42/1.80 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.42/1.80 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ),
% 1.42/1.80 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 1.42/1.80 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ) ],
% 1.42/1.80 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ), ~(
% 1.42/1.80 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ),
% 1.42/1.80 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.42/1.80 , Y ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), X ),
% 1.42/1.80 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ), ~( hBOOL(
% 1.42/1.80 hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Oone__class_Oone'( X ) )
% 1.42/1.80 ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.80 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ) ],
% 1.42/1.80 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Ominus__class_Ominus'( X, Y
% 1.42/1.80 , 'tc_nat' ), 'tc_nat' ), Y ), ~( hBOOL( hAPP( 'c_lessequals'( Y,
% 1.42/1.80 'tc_nat' ), X ) ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.42/1.80 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ) ) ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.42/1.80 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ),
% 1.42/1.80 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.42/1.80 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ) ) ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) )
% 1.42/1.80 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.42/1.80 X ), X ), Y ) ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.80 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.42/1.80 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ) ) ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) )
% 1.42/1.80 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.42/1.80 X ), X ), Y ) ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.80 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.42/1.80 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ) ) ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.42/1.80 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ),
% 1.42/1.80 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.80 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Oone__class_Oone'( X ) ) ), ~(
% 1.42/1.80 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), X
% 1.42/1.80 ), hAPP( 'c_HOL_Oinverse__class_Oinverse'( X ), Y ) ) ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.42/1.80 'c_HOL_Oone__class_Oone'( X ) ), X ), X ), Z ) ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Oinverse__class_Odivide'( hAPP(
% 1.42/1.80 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.42/1.80 'c_HOL_Oone__class_Oone'( X ) ), X ) ) ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.42/1.80 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) )
% 1.42/1.80 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) ) ) ],
% 1.42/1.80 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_Int_Oint' ), 'c_Int_OMin' ) ), ~(
% 1.42/1.80 hBOOL( hAPP( 'c_lessequals'( 'c_Int_OBit1'( X ), 'tc_Int_Oint' ),
% 1.42/1.80 'c_Int_OMin' ) ) ) ],
% 1.42/1.80 [ hBOOL( hAPP( 'c_lessequals'( 'c_Int_OBit1'( X ), 'tc_Int_Oint' ),
% 1.42/1.80 'c_Int_OMin' ) ), ~( hBOOL( hAPP( 'c_lessequals'( X, 'tc_Int_Oint' ),
% 1.42/1.80 'c_Int_OMin' ) ) ) ],
% 1.42/1.80 [ =( 'c_HOL_Ominus__class_Ominus'( X, hAPP( 'c_Suc', Y ), 'tc_nat' ),
% 1.42/1.80 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X,
% 1.42/1.80 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.42/1.80 'class_Int_Onumber__ring'( X ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.80 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.42/1.80 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( Y, 'tc_Int_Oint' ), Z ) ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.42/1.80 'class_Int_Onumber__ring'( X ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.80 Y, 'tc_Int_Oint' ), Z ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.80 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.42/1.80 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ) ) ],
% 1.42/1.80 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_Int_Oint' ), Y ) ), ~(
% 1.42/1.80 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.80 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ), 'tc_nat' ),
% 1.42/1.80 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ) ) ) ],
% 1.42/1.80 [ hBOOL( hAPP( 'c_lessequals'( 'c_Divides_Odiv__class_Odiv'( X, Y,
% 1.42/1.80 'tc_nat' ), 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( Z, Y, 'tc_nat' ) )
% 1.42/1.80 ), ~( hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Z ) ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X
% 1.42/1.80 ), 'c_HOL_Oinverse__class_Odivide'( T, Z, X ) ) ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) )
% 1.42/1.80 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), T ) ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X
% 1.42/1.80 ), 'c_HOL_Oinverse__class_Odivide'( T, Z, X ) ) ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.42/1.80 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( T, X ), Y ) ) ) ],
% 1.42/1.80 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), hAPP( hAPP( Y, U ), T ) )
% 1.42/1.80 , hAPP( hAPP( Y, hAPP( hAPP( X, Z ), U ) ), T ) ), ~(
% 1.42/1.80 'c_Groebner__Basis_Ogb__semiring'( X, Y, W, V0, V1, V2 ) ) ],
% 1.42/1.80 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), T ), hAPP( hAPP( Y, hAPP(
% 1.42/1.80 hAPP( X, Z ), U ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, Y, W
% 1.42/1.80 , V0, U, V1 ) ) ],
% 1.42/1.80 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), Y ) ), hAPP( hAPP( Z, hAPP(
% 1.42/1.80 hAPP( X, T ), U ) ), Y ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, Z, W
% 1.42/1.80 , V0, U, V1 ) ) ],
% 1.42/1.80 [ =( hAPP( hAPP( X, Y ), Y ), hAPP( hAPP( Z, hAPP( hAPP( X, T ), T ) ),
% 1.42/1.80 Y ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, Z, U, W, T, V0 ) ) ],
% 1.42/1.80 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.42/1.80 X, T, U, Y, W, V0 ) ) ],
% 1.42/1.80 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.42/1.80 X, T, U, Z, W, V0 ) ) ],
% 1.42/1.80 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 1.42/1.80 'c_Groebner__Basis_Ogb__semiring'( T, X, U, W, V0, V1 ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.42/1.80 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ominus__class_Ominus'( Y, Z, X
% 1.42/1.80 ) ), T ) ), U ), X ), W ) ), ~( hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.42/1.80 X ), Y ), T ) ), U ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.42/1.80 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), W ) ) ) ) ]
% 1.42/1.80 ,
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.80 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ),
% 1.42/1.80 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.42/1.80 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.80 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ),
% 1.42/1.80 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Z, X
% 1.42/1.80 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.42/1.80 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ) ],
% 1.42/1.80 [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( 'c_Suc', X ),
% 1.42/1.80 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ), X ) ],
% 1.42/1.80 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ) ) ],
% 1.42/1.80 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Z ) ) ) ],
% 1.42/1.80 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ), ~( hBOOL(
% 1.42/1.80 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.42/1.80 'tc_nat' ), X ), Z ), 'tc_nat' ), Y ) ) ) ],
% 1.42/1.80 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ) ) ],
% 1.42/1.80 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Z ) ) ) ],
% 1.42/1.80 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =( hAPP(
% 1.42/1.80 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( X ),
% 1.42/1.80 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ) ),
% 1.42/1.80 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ) ) ) ],
% 1.42/1.80 [ hBOOL( hAPP( 'c_lessequals'( hAPP( 'c_Suc', X ), 'tc_nat' ), Y ) ),
% 1.42/1.80 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ) ) ],
% 1.42/1.80 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ), ~( hBOOL(
% 1.42/1.80 hAPP( 'c_lessequals'( hAPP( 'c_Suc', X ), 'tc_nat' ), Y ) ) ) ],
% 1.42/1.80 [ hBOOL( hAPP( 'c_lessequals'( hAPP( 'c_Suc', X ), 'tc_nat' ), Y ) ),
% 1.42/1.80 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ) ) ],
% 1.42/1.80 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ), ~( hBOOL(
% 1.42/1.80 hAPP( 'c_lessequals'( hAPP( 'c_Suc', X ), 'tc_nat' ), Y ) ) ) ],
% 1.42/1.80 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.42/1.80 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( Y, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z )
% 1.42/1.80 , T ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ), Z ) ) ), ~( hBOOL(
% 1.42/1.80 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ) ]
% 1.42/1.80 ,
% 1.42/1.80 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.42/1.80 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( Y, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z )
% 1.42/1.80 , T ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ), T ) ) ), ~( hBOOL(
% 1.42/1.80 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ) ]
% 1.42/1.80 ,
% 1.42/1.80 [ =( 'c_SetInterval_Oord__class_OatLeastLessThan'( X, hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ), 'tc_nat' ),
% 1.42/1.80 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.42/1.80 'c_SetInterval_Oord__class_OatLeastLessThan'( X, Y, 'tc_nat' ),
% 1.42/1.80 'c_SetInterval_Oord__class_OatLeastLessThan'( Y, hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ), 'tc_nat' ), 'tc_fun'(
% 1.42/1.80 'tc_nat', 'tc_bool' ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' )
% 1.42/1.80 , Y ) ) ) ],
% 1.42/1.80 [ hBOOL( hAPP( 'c_lessequals'( 'c_Int_OMin', 'tc_Int_Oint' ),
% 1.42/1.80 'c_Int_OBit0'( X ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.80 'c_Int_OMin', 'tc_Int_Oint' ), X ) ) ) ],
% 1.42/1.80 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_Int_OMin', 'tc_Int_Oint' )
% 1.42/1.80 , X ) ), ~( hBOOL( hAPP( 'c_lessequals'( 'c_Int_OMin', 'tc_Int_Oint' ),
% 1.42/1.80 'c_Int_OBit0'( X ) ) ) ) ],
% 1.42/1.80 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.42/1.80 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ),
% 1.42/1.80 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ),
% 1.42/1.80 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( X, 'tc_Int_Oint' ), 'c_Int_OPls' ) ) ) ],
% 1.42/1.80 [ hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.42/1.80 'tc_nat' ), X ), Y ), 'tc_nat' ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.42/1.80 X, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ) ) ) ), ~(
% 1.42/1.80 hBOOL( hAPP( 'c_lessequals'( Y, 'tc_nat' ), Z ) ) ) ],
% 1.42/1.80 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ),
% 1.42/1.80 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ) ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.42/1.80 Z ), 'tc_nat' ), Y ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Z, 'tc_nat' ),
% 1.42/1.80 Y ) ) ) ],
% 1.42/1.80 [ hBOOL( hAPP( 'c_lessequals'( 'c_Int_OMin', 'tc_Int_Oint' ),
% 1.42/1.80 'c_Int_OBit1'( X ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( 'c_Int_OMin',
% 1.42/1.80 'tc_Int_Oint' ), X ) ) ) ],
% 1.42/1.80 [ hBOOL( hAPP( 'c_lessequals'( 'c_Int_OMin', 'tc_Int_Oint' ), X ) ), ~(
% 1.42/1.80 hBOOL( hAPP( 'c_lessequals'( 'c_Int_OMin', 'tc_Int_Oint' ), 'c_Int_OBit1'(
% 1.42/1.80 X ) ) ) ) ],
% 1.42/1.80 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), hAPP( 'c_Suc',
% 1.42/1.80 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ) ) ],
% 1.42/1.80 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), hAPP( 'c_Suc',
% 1.42/1.80 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ) ) ) ) ],
% 1.42/1.80 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), hAPP( 'c_Suc',
% 1.42/1.80 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ) ) ],
% 1.42/1.80 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.42/1.80 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ), 'tc_nat' ),
% 1.42/1.80 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.42/1.80 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), T ), Y ) ), U ) ) ), ~( hBOOL(
% 1.42/1.80 hAPP( 'c_HOL_Oord__class_Oless'( Z, 'tc_nat' ), hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.42/1.80 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( T
% 1.42/1.80 , X, 'tc_nat' ) ), Y ) ), U ) ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( X,
% 1.42/1.80 'tc_nat' ), T ) ) ) ],
% 1.42/1.80 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.42/1.80 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Y
% 1.42/1.80 , Z, 'tc_nat' ) ), T ) ), U ) ) ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.42/1.80 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T
% 1.42/1.80 ) ), X ), 'tc_nat' ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.42/1.80 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), T ) ), U ) )
% 1.42/1.80 ) ), ~( hBOOL( hAPP( 'c_lessequals'( Z, 'tc_nat' ), Y ) ) ) ],
% 1.42/1.80 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.42/1.80 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ), 'tc_nat' ),
% 1.42/1.80 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.42/1.80 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), T ), Y ) ), U ) ) ), ~( hBOOL(
% 1.42/1.80 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.42/1.80 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.42/1.80 'c_HOL_Ominus__class_Ominus'( X, T, 'tc_nat' ) ), Y ) ), Z ), 'tc_nat' )
% 1.42/1.80 , U ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( T, 'tc_nat' ), X ) ) ) ],
% 1.42/1.80 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.42/1.80 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X
% 1.42/1.80 , Y, 'tc_nat' ) ), Z ) ), T ), 'tc_nat' ), U ) ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.42/1.80 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z
% 1.42/1.80 ) ), T ), 'tc_nat' ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.42/1.80 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ), U ) )
% 1.42/1.80 ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, 'tc_nat' ), X ) ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.42/1.80 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.42/1.80 ), Z ), Y ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.42/1.80 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.42/1.80 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ominus__class_Ominus'( T, Y, X
% 1.42/1.80 ) ), Z ) ), U ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.42/1.80 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ), U ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP(
% 1.42/1.80 'c_HOL_Oinverse__class_Oinverse'( X ), Y ),
% 1.42/1.80 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) )
% 1.42/1.80 ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.42/1.80 'class_Int_Onumber__ring'( X ) ), =( hAPP(
% 1.42/1.80 'c_HOL_Oinverse__class_Oinverse'( X ), Y ),
% 1.42/1.80 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) )
% 1.42/1.80 ],
% 1.42/1.80 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.42/1.80 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), 'c_HOL_Oone__class_Oone'(
% 1.42/1.80 'tc_nat' ) ), Y ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.80 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ),
% 1.42/1.80 'c_HOL_Oinverse__class_Odivide'( Y, T, X ) ) ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP(
% 1.42/1.80 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL(
% 1.42/1.80 hAPP( 'c_lessequals'( Z, X ), T ) ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ),
% 1.42/1.80 'c_HOL_Oinverse__class_Odivide'( Y, T, X ) ) ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP(
% 1.42/1.80 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ), ~( hBOOL(
% 1.42/1.80 hAPP( 'c_lessequals'( T, X ), Z ) ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ),
% 1.42/1.80 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ), =( Z,
% 1.42/1.80 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP(
% 1.42/1.80 hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ) ],
% 1.42/1.80 [ =( hAPP( hAPP( X, hAPP( hAPP( 'c_Power_Opower_Opower'( Y, X, Z ), T )
% 1.42/1.80 , U ) ), T ), hAPP( hAPP( X, T ), hAPP( hAPP( 'c_Power_Opower_Opower'( Y
% 1.42/1.80 , X, Z ), T ), U ) ) ), ~( 'c_OrderedGroup_Omonoid__mult'( Y, X, Z ) ) ]
% 1.42/1.80 ,
% 1.42/1.80 [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( 'c_Suc',
% 1.42/1.80 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ), Z, 'tc_nat' ),
% 1.42/1.80 'c_HOL_Ominus__class_Ominus'( hAPP( 'c_Suc', X ), hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ), 'tc_nat' ) ), ~( hBOOL(
% 1.42/1.80 hAPP( 'c_lessequals'( Y, 'tc_nat' ), X ) ) ) ],
% 1.42/1.80 [ hBOOL( hAPP( 'c_lessequals'( 'c_Int_OBit0'( X ), 'tc_Int_Oint' ),
% 1.42/1.80 'c_Int_OMin' ) ), ~( hBOOL( hAPP( 'c_lessequals'( X, 'tc_Int_Oint' ),
% 1.42/1.80 'c_Int_OMin' ) ) ) ],
% 1.42/1.80 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_Int_Oint' ), 'c_Int_OMin' ) ), ~(
% 1.42/1.80 hBOOL( hAPP( 'c_lessequals'( 'c_Int_OBit0'( X ), 'tc_Int_Oint' ),
% 1.42/1.80 'c_Int_OMin' ) ) ) ],
% 1.42/1.80 [ ~( 'class_Orderings_Oorder'( X ) ), =(
% 1.42/1.80 'c_SetInterval_Oord__class_OgreaterThanLessThan'( Y, Z, X ),
% 1.42/1.80 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ), ~( hBOOL(
% 1.42/1.80 hAPP( 'c_lessequals'( Z, X ), Y ) ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X
% 1.42/1.80 ), 'c_HOL_Oinverse__class_Odivide'( T, U, X ) ) ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( U, X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), U ) ) )
% 1.42/1.80 , ~( hBOOL( hAPP( 'c_lessequals'( Y, X ), T ) ) ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) )
% 1.42/1.80 ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.42/1.80 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.42/1.80 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), hAPP(
% 1.42/1.80 hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), hAPP( hAPP(
% 1.42/1.80 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.42/1.80 'c_HOL_Oone__class_Oone'( X ), Y, X ) ), Z ) ) ],
% 1.42/1.80 [ =( hAPP( 'c_Suc', X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.42/1.80 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), X ) ) ],
% 1.42/1.80 [ =( hAPP( 'c_Suc', X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.42/1.80 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ) ],
% 1.42/1.80 [ hBOOL( hAPP( 'c_lessequals'( 'c_Divides_Odiv__class_Odiv'( X, Y,
% 1.42/1.80 'tc_nat' ), 'tc_nat' ), X ) ) ],
% 1.42/1.80 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ),
% 1.42/1.80 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), T ), ~(
% 1.42/1.80 'c_OrderedGroup_Omonoid__mult'( X, Y, Z ) ) ],
% 1.42/1.80 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ominus__class_Ominus'( Y, Z, X )
% 1.42/1.80 ), Z ), Y ) ],
% 1.42/1.80 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.42/1.80 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.42/1.80 'c_SetInterval_Oord__class_OatLeastLessThan'( Y, Z, X ), 'c_Set_Oinsert'(
% 1.42/1.80 Z, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ), X ),
% 1.42/1.80 'tc_fun'( X, 'tc_bool' ) ), 'c_SetInterval_Oord__class_OatLeastAtMost'( Y
% 1.42/1.80 , Z, X ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ), Z ) ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 1.42/1.80 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP(
% 1.42/1.80 'c_HOL_Oinverse__class_Oinverse'( X ), hAPP(
% 1.42/1.80 'c_HOL_Oinverse__class_Oinverse'( X ), Y ) ), Y ) ],
% 1.42/1.80 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( hBOOL(
% 1.42/1.80 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.42/1.80 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.42/1.80 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.42/1.80 ), =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.42/1.80 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.42/1.80 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.80 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.42/1.80 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.42/1.80 , Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X )
% 1.42/1.80 ), 'c_Divides_Odiv__class_Omod'( Z, T, X ) ), T, X ) ) ],
% 1.42/1.80 [ ~( 'class_OrderedGroup_Olordered__ab__group__add__join'( X ) ), =(
% 1.42/1.80 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.42/1.80 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ) ), T ),
% 1.42/1.80 'c_Lattices_Oupper__semilattice__class_Osup'( hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ],
% 1.42/1.80 [ ~( 'class_OrderedGroup_Olordered__ab__group__add__join'( X ) ), =(
% 1.42/1.80 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.42/1.80 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ) ),
% 1.42/1.80 'c_Lattices_Oupper__semilattice__class_Osup'( hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ) ) ],
% 1.42/1.80 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =( hAPP(
% 1.42/1.80 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.42/1.80 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ) ),
% 1.42/1.80 'c_Lattices_Oupper__semilattice__class_Osup'( hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ) ) ],
% 1.42/1.80 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =( hAPP(
% 1.42/1.80 hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.42/1.80 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ) ), T ),
% 1.42/1.80 'c_Lattices_Oupper__semilattice__class_Osup'( hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ],
% 1.42/1.80 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =(
% 1.42/1.80 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Y, X ), Y ) ],
% 1.42/1.80 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X, X, 'tc_fun'( Y,
% 1.42/1.80 'tc_bool' ) ), X ) ],
% 1.42/1.80 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( Y, X ), T ) ) ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( T, X ), Z ) ) ) ],
% 1.42/1.80 [ ~( 'class_Orderings_Opreorder'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( T, X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( Y, X ), T ) ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.42/1.80 ), Y ), 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ), X ),
% 1.42/1.80 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.42/1.80 , 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'(
% 1.42/1.80 Z, 'tc_nat' ), 'tc_nat' ) ],
% 1.42/1.80 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 1.42/1.80 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.42/1.80 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.42/1.80 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.42/1.80 X ), Y ), Z ) ), T ) ) ],
% 1.42/1.80 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ) ],
% 1.42/1.80 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ) ],
% 1.42/1.80 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 1.42/1.80 [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =( hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.42/1.80 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.42/1.80 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.42/1.80 X ), Y ), Z ) ), T ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.42/1.80 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.42/1.80 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.42/1.80 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.42/1.80 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 1.42/1.80 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.42/1.80 'tc_nat' ), 'tc_nat' ), X ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.80 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), Y ) ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.42/1.80 'tc_nat' ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X )
% 1.42/1.80 ) ) ) ],
% 1.42/1.80 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.42/1.80 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.42/1.80 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.42/1.80 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.42/1.80 'c_Power_Opower__class_Opower'( X ), Y ), T ) ) ) ],
% 1.42/1.80 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( X, 'tc_nat' ), Y ) ) ) ],
% 1.42/1.80 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( X, 'tc_nat' ), Z ) ) ) ],
% 1.42/1.80 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.42/1.80 Z ), 'tc_nat' ), Y ) ) ) ],
% 1.42/1.80 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ),
% 1.42/1.80 X ), 'tc_nat' ), Y ) ) ) ],
% 1.42/1.80 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( X, 'tc_nat' ), Y ) ) ) ],
% 1.42/1.80 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( X, 'tc_nat' ), Z ) ) ) ],
% 1.42/1.80 [ =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y, Z, T ), T ),
% 1.42/1.80 'c_Set_Oinsert'( Y, 'c_Set_Oinsert'( X, Z, T ), T ) ) ],
% 1.42/1.80 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.42/1.80 Y, X ), Z ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ), Y ) )
% 1.42/1.80 ) ],
% 1.42/1.80 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), hBOOL( hAPP( 'c_lessequals'( Z
% 1.42/1.80 , X ), Y ) ) ],
% 1.42/1.80 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.42/1.80 Y, X ), Y ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), Y ) )
% 1.42/1.80 ) ],
% 1.42/1.80 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( Y, X ), Y ) ), hBOOL( hAPP( 'c_lessequals'( Y
% 1.42/1.80 , X ), Y ) ) ],
% 1.42/1.80 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( Z, X ), Y ) ) ) ],
% 1.42/1.80 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( 'c_lessequals'( Y
% 1.42/1.80 , X ), Z ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ), Y ) ) ]
% 1.42/1.80 ,
% 1.42/1.80 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), hBOOL( hAPP( 'c_lessequals'( Z
% 1.42/1.80 , X ), Y ) ) ],
% 1.42/1.80 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.42/1.80 Y, X ), Z ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ), Y ) )
% 1.42/1.80 ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 1.42/1.80 'c_HOL_Ozero__class_Ozero'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y
% 1.42/1.80 , Y, X ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.42/1.80 'c_HOL_Oinverse__class_Odivide'( Y, Y, X ), 'c_HOL_Oone__class_Oone'( X )
% 1.42/1.80 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.42/1.80 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.42/1.80 'c_HOL_Oinverse__class_Odivide'( Y, Y, X ), 'c_HOL_Oone__class_Oone'( X )
% 1.42/1.80 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.80 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.42/1.80 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.42/1.80 , Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_Divides_Odiv__class_Omod'( Z, T
% 1.42/1.80 , X ) ), T, X ) ) ],
% 1.42/1.80 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.42/1.80 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.42/1.80 , Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X )
% 1.42/1.80 ), Z ), T, X ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.80 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ), ~( hBOOL(
% 1.42/1.80 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.42/1.80 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ) ) ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.80 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ), ~( hBOOL(
% 1.42/1.80 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.42/1.80 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ) ) ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.80 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ), ~( hBOOL(
% 1.42/1.80 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.42/1.80 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ) ) ) ) ],
% 1.42/1.80 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), U ), hAPP( hAPP( Y, hAPP(
% 1.42/1.80 hAPP( X, Z ), U ) ), hAPP( hAPP( X, T ), U ) ) ), ~(
% 1.42/1.80 'c_Groebner__Basis_Ogb__semiring'( Y, X, W, V0, V1, V2 ) ) ],
% 1.42/1.80 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.42/1.80 T, X, U, Y, W, V0 ) ) ],
% 1.42/1.80 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.42/1.80 T, X, U, Z, W, V0 ) ) ],
% 1.42/1.80 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.42/1.80 T, X, U, W, Y, V0 ) ) ],
% 1.42/1.80 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.42/1.80 T, X, U, W, Z, V0 ) ) ],
% 1.42/1.80 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 1.42/1.80 , hAPP( hAPP( X, hAPP( hAPP( X, Y ), T ) ), hAPP( hAPP( X, Z ), U ) ) ),
% 1.42/1.80 ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, V0, V1, V2, V3 ) ) ],
% 1.42/1.80 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 1.42/1.80 , hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), hAPP( hAPP( X, T ), U ) ) ) ),
% 1.42/1.80 ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, V0, V1, V2, V3 ) ) ],
% 1.42/1.80 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 1.42/1.80 , hAPP( hAPP( X, T ), hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), U ) ) ),
% 1.42/1.80 ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, V0, V1, V2, V3 ) ) ],
% 1.42/1.80 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, hAPP(
% 1.42/1.80 hAPP( X, Y ), T ) ), Z ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, W
% 1.42/1.80 , V0, V1, V2 ) ) ],
% 1.42/1.80 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, Y ),
% 1.42/1.80 hAPP( hAPP( X, Z ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X,
% 1.42/1.80 W, V0, V1, V2 ) ) ],
% 1.42/1.80 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 1.42/1.80 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, W
% 1.42/1.80 , V0, V1, V2 ) ) ],
% 1.42/1.80 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, Z ),
% 1.42/1.80 hAPP( hAPP( X, Y ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X,
% 1.42/1.80 W, V0, V1, V2 ) ) ],
% 1.42/1.80 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 1.42/1.80 , hAPP( hAPP( X, hAPP( hAPP( X, Y ), T ) ), hAPP( hAPP( X, Z ), U ) ) ),
% 1.42/1.80 ~( 'c_Groebner__Basis_Ogb__semiring'( X, W, V0, V1, V2, V3 ) ) ],
% 1.42/1.80 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, Y ),
% 1.42/1.80 hAPP( hAPP( X, Z ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U,
% 1.42/1.80 W, V0, V1, V2 ) ) ],
% 1.42/1.80 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, Z ),
% 1.42/1.80 hAPP( hAPP( X, Y ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U,
% 1.42/1.80 W, V0, V1, V2 ) ) ],
% 1.42/1.80 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, hAPP(
% 1.42/1.80 hAPP( X, Y ), T ) ), Z ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U, W
% 1.42/1.80 , V0, V1, V2 ) ) ],
% 1.42/1.80 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 1.42/1.80 'c_Groebner__Basis_Ogb__semiring'( X, T, U, W, V0, V1 ) ) ],
% 1.42/1.80 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 1.42/1.80 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U, W
% 1.42/1.80 , V0, V1, V2 ) ) ],
% 1.42/1.80 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.42/1.80 X, T, U, Y, W, V0 ) ) ],
% 1.42/1.80 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 1.42/1.80 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U, W
% 1.42/1.80 , V0, V1, V2 ) ) ],
% 1.42/1.80 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 1.42/1.80 'c_Groebner__Basis_Ogb__semiring'( X, T, U, W, V0, V1 ) ) ],
% 1.42/1.80 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.42/1.80 T, X, U, Y, W, V0 ) ) ],
% 1.42/1.80 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.42/1.80 T, X, U, W, Y, V0 ) ) ],
% 1.42/1.80 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 1.42/1.80 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, W
% 1.42/1.80 , V0, V1, V2 ) ) ],
% 1.42/1.80 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 1.42/1.80 'c_Groebner__Basis_Ogb__semiring'( T, X, U, W, V0, V1 ) ) ],
% 1.42/1.80 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), U ) ), hAPP( hAPP( Z, hAPP(
% 1.42/1.80 hAPP( X, Y ), T ) ), hAPP( hAPP( X, Y ), U ) ) ), ~(
% 1.42/1.80 'c_Groebner__Basis_Ogb__semiring'( Z, X, W, V0, V1, V2 ) ) ],
% 1.42/1.80 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), U ), hAPP( hAPP( Y, hAPP(
% 1.42/1.80 hAPP( X, Z ), U ) ), hAPP( hAPP( X, T ), U ) ) ), ~(
% 1.42/1.80 'c_Groebner__Basis_Ogb__semiring'( W, Y, X, V0, V1, V2 ) ) ],
% 1.42/1.80 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 1.42/1.80 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ),
% 1.42/1.80 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'(
% 1.42/1.80 'c_Divides_Odiv__class_Omod'( Y, T, X ), 'c_Divides_Odiv__class_Omod'( Z
% 1.42/1.80 , T, X ), X ), T, X ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.42/1.80 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ) ) ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) )
% 1.42/1.80 , ~( hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 1.42/1.80 ) ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.42/1.80 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ) ) ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.42/1.80 , ~( hBOOL( hAPP( 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.42/1.80 ) ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.42/1.80 'c_HOL_Oinverse__class_Odivide'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y
% 1.42/1.80 ) ],
% 1.42/1.80 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.42/1.80 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ) ) ), =( X, Z
% 1.42/1.80 ) ],
% 1.42/1.80 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.42/1.80 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ), =( Y, Z
% 1.42/1.80 ) ],
% 1.42/1.80 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.42/1.80 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ), =( Y, Z
% 1.42/1.80 ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.42/1.80 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP(
% 1.42/1.80 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 1.42/1.80 [ ~( 'class_OrderedGroup_Ocancel__ab__semigroup__add'( X ) ), ~( =( hAPP(
% 1.42/1.80 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 1.42/1.80 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =( hAPP(
% 1.42/1.80 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 1.42/1.80 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =( hAPP(
% 1.42/1.80 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ), =( Y, T ) ],
% 1.42/1.80 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), hBOOL(
% 1.42/1.80 hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.42/1.80 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) )
% 1.42/1.80 , ~( hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 1.42/1.80 ) ) ) ],
% 1.42/1.80 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), hBOOL(
% 1.42/1.80 hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.42/1.80 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL(
% 1.42/1.80 hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 1.42/1.80 ) ) ) ],
% 1.42/1.80 [ ~( 'class_Lattices_Olattice'( X ) ), hBOOL( hAPP( 'c_lessequals'(
% 1.42/1.80 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.42/1.80 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ),
% 1.42/1.80 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T, X ), X ), X ),
% 1.42/1.80 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.42/1.80 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ) ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP(
% 1.42/1.80 hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ), =( Y,
% 1.42/1.80 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'(
% 1.42/1.80 Z, 'tc_nat' ) ) ],
% 1.42/1.80 [ ~( 'class_Lattices_Olattice'( X ) ), hBOOL( hAPP( 'c_lessequals'( Y, X
% 1.42/1.80 ), 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ) ) ) ],
% 1.42/1.80 [ ~( 'class_Lattices_Olattice'( X ) ), hBOOL( hAPP( 'c_lessequals'( Y, X
% 1.42/1.80 ), 'c_Lattices_Oupper__semilattice__class_Osup'( Z, Y, X ) ) ) ],
% 1.42/1.80 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ),
% 1.42/1.80 X ), T ) ), ~( hBOOL( hAPP( 'c_lessequals'( Z, X ), T ) ) ), ~( hBOOL(
% 1.42/1.80 hAPP( 'c_lessequals'( Y, X ), T ) ) ) ],
% 1.42/1.80 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( Y, X ), 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.42/1.80 Z, X ) ) ) ],
% 1.42/1.80 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( Y, X ), 'c_Lattices_Oupper__semilattice__class_Osup'( Z,
% 1.42/1.80 Y, X ) ) ) ],
% 1.42/1.80 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ),
% 1.42/1.80 X ), T ) ), ~( hBOOL( hAPP( 'c_lessequals'( Z, X ), T ) ) ), ~( hBOOL(
% 1.42/1.80 hAPP( 'c_lessequals'( Y, X ), T ) ) ) ],
% 1.42/1.80 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ),
% 1.42/1.80 X ), T ) ), ~( hBOOL( hAPP( 'c_lessequals'( Z, X ), T ) ) ), ~( hBOOL(
% 1.42/1.80 hAPP( 'c_lessequals'( Y, X ), T ) ) ) ],
% 1.42/1.80 [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ), 'tc_nat' ),
% 1.42/1.80 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ) ) ],
% 1.42/1.80 [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ), 'tc_nat' ),
% 1.42/1.80 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ) ],
% 1.42/1.80 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( 'c_Power_Opower_Opower'( Z, T,
% 1.42/1.80 U ), hAPP( W, V0 ) ), V1 ) ) ), =( V0, Y ), ~(
% 1.42/1.80 'c_Ring__and__Field_Oordered__idom'( V2, V3, Y, V4, V5, X, W, Z, T, V6, U
% 1.42/1.80 ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.80 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), T ) ),
% 1.42/1.80 ~( hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), T )
% 1.42/1.80 ) ), ~( hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP(
% 1.42/1.80 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ), Y ) ) ), hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ]
% 1.42/1.80 ,
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.80 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), T ) ),
% 1.42/1.80 ~( hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), T )
% 1.42/1.80 ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ),
% 1.42/1.80 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X
% 1.42/1.80 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.80 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( Y, X ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ) ) ),
% 1.42/1.80 ~( hBOOL( hAPP( 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.42/1.80 ) ), ~( hBOOL( hAPP( 'c_lessequals'( Z, X ), hAPP( hAPP(
% 1.42/1.80 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ), hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ]
% 1.42/1.80 ,
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.80 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( Y, X ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ) ) ),
% 1.42/1.80 ~( hBOOL( hAPP( 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.42/1.80 ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( T, X ),
% 1.42/1.80 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( hAPP(
% 1.42/1.80 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), Z ) ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z )
% 1.42/1.80 , X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), T ) ) ), ~(
% 1.42/1.80 hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), X ), Y ) ) )
% 1.42/1.80 , ~( hBOOL( hAPP( 'c_lessequals'( Z, 'tc_nat' ), T ) ) ) ],
% 1.42/1.80 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_Divides_Odiv__class_Omod'(
% 1.42/1.80 X, Y, 'tc_nat' ), 'tc_nat' ), Y ) ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.42/1.80 'tc_nat' ), Y ) ) ) ],
% 1.42/1.80 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.42/1.80 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y )
% 1.42/1.80 , 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ),
% 1.42/1.80 =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP(
% 1.42/1.80 'c_HOL_Oinverse__class_Oinverse'( X ), Y ) ) ) ) ],
% 1.42/1.80 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 1.42/1.80 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ),
% 1.42/1.80 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'(
% 1.42/1.80 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z, X ), T, X ) ) ],
% 1.42/1.80 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 1.42/1.80 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ),
% 1.42/1.80 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( Y,
% 1.42/1.80 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.42/1.80 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.42/1.80 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ) ) ), ~(
% 1.42/1.80 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.42/1.80 , 'tc_nat' ), 'tc_nat' ) ) ],
% 1.42/1.80 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =( hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) ) ), =( hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), U ) ],
% 1.42/1.80 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.42/1.80 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), hAPP( hAPP(
% 1.42/1.80 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X
% 1.42/1.80 , 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ), Y ) ) ), =( X,
% 1.42/1.80 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.42/1.80 ), Y ), hAPP( 'c_Suc', Z ) ), X ), 'c_HOL_Oone__class_Oone'( X ) ) ),
% 1.42/1.80 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ),
% 1.42/1.80 'c_HOL_Oone__class_Oone'( X ) ) ) ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) )
% 1.42/1.80 ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) )
% 1.42/1.80 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.42/1.80 'c_HOL_Oinverse__class_Oinverse'( X ), Z ), X ), hAPP(
% 1.42/1.80 'c_HOL_Oinverse__class_Oinverse'( X ), Y ) ) ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Oinverse__class_Oinverse'( X ), Y
% 1.42/1.80 ), X ), hAPP( 'c_HOL_Oinverse__class_Oinverse'( X ), Z ) ) ), ~( hBOOL(
% 1.42/1.80 hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z
% 1.42/1.80 ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ), Y ) ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.42/1.80 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.42/1.80 'c_HOL_Oinverse__class_Oinverse'( X ), Z ), X ), hAPP(
% 1.42/1.80 'c_HOL_Oinverse__class_Oinverse'( X ), Y ) ) ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Oinverse__class_Oinverse'( X ), Y
% 1.42/1.80 ), X ), hAPP( 'c_HOL_Oinverse__class_Oinverse'( X ), Z ) ) ), ~( hBOOL(
% 1.42/1.80 hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.42/1.80 ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ), Y ) ) ) ],
% 1.42/1.80 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), hBOOL(
% 1.42/1.80 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL(
% 1.42/1.80 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ) ]
% 1.42/1.80 ,
% 1.42/1.80 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'(
% 1.42/1.80 X, Y, 'tc_nat' ), 'tc_nat' ), hAPP( 'c_Suc', X ) ) ) ],
% 1.42/1.80 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.42/1.80 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.42/1.80 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.42/1.80 ), Z ) ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.42/1.80 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.42/1.80 ), T ) ) ) ],
% 1.42/1.80 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.42/1.80 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( X ), X ), hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.42/1.80 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.42/1.80 ), T ) ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.42/1.80 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Z
% 1.42/1.80 ), T ) ) ) ],
% 1.42/1.80 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), hAPP( 'c_Suc',
% 1.42/1.80 Y ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ) ) ],
% 1.42/1.80 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), hAPP( 'c_Suc', Y ) ) ) ) ],
% 1.42/1.80 [ ~( hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), X ) ) ), hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), hAPP( 'c_Suc', X ) ) ) ],
% 1.42/1.80 [ hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.42/1.80 'tc_nat' ), X ), Y ), 'tc_nat' ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.42/1.80 'tc_nat' ), Z ), T ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, 'tc_nat' ),
% 1.42/1.80 T ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Z ) ) ) ],
% 1.42/1.80 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ), hBOOL(
% 1.42/1.80 hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z
% 1.42/1.80 ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) ) ), ~(
% 1.42/1.80 hBOOL( hAPP( 'c_lessequals'( Z, X ), U ) ) ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( Y, X ), T ) ) ) ],
% 1.42/1.80 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.42/1.80 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.42/1.80 'c_SetInterval_Oord__class_OgreaterThanLessThan'( Y, Z, X ),
% 1.42/1.80 'c_SetInterval_Oord__class_OatLeastLessThan'( Z, T, X ), 'tc_fun'( X,
% 1.42/1.80 'tc_bool' ) ), 'c_SetInterval_Oord__class_OgreaterThanLessThan'( Y, T, X
% 1.42/1.80 ) ), ~( hBOOL( hAPP( 'c_lessequals'( Z, X ), T ) ) ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.80 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ), ~( hBOOL(
% 1.42/1.80 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP(
% 1.42/1.80 'c_HOL_Oinverse__class_Oinverse'( X ), Y ) ) ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.80 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP(
% 1.42/1.80 'c_HOL_Oinverse__class_Oinverse'( X ), Y ) ) ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ) ],
% 1.42/1.80 [ ~( hBOOL( hAPP( X, 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ), Y, 'tc_nat' ) ) ) ),
% 1.42/1.80 hBOOL( hAPP( X, Z ) ) ],
% 1.42/1.80 [ ~( hBOOL( hAPP( X, 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ), Y, 'tc_nat' ) ) ) ),
% 1.42/1.80 hBOOL( hAPP( X, Z ) ) ],
% 1.42/1.80 [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.42/1.80 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.42/1.80 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), T ), Y ) ), U ), 'tc_nat' ),
% 1.42/1.80 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.42/1.80 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.42/1.80 'c_HOL_Ominus__class_Ominus'( X, T, 'tc_nat' ) ), Y ) ), Z ), U, 'tc_nat'
% 1.42/1.80 ) ), ~( hBOOL( hAPP( 'c_lessequals'( T, 'tc_nat' ), X ) ) ) ],
% 1.42/1.80 [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.42/1.80 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.42/1.80 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), T ), Y ) ), U ), 'tc_nat' ),
% 1.42/1.80 'c_HOL_Ominus__class_Ominus'( Z, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.42/1.80 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.42/1.80 'c_HOL_Ominus__class_Ominus'( T, X, 'tc_nat' ) ), Y ) ), U ), 'tc_nat' )
% 1.42/1.80 ), ~( hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), T ) ) ) ],
% 1.42/1.80 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ),
% 1.42/1.80 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( X,
% 1.42/1.80 Y, 'tc_nat' ) ), 'c_Divides_Odiv__class_Odiv'( hAPP( 'c_Suc',
% 1.42/1.80 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ) ),
% 1.42/1.80 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.42/1.80 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ),
% 1.42/1.80 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 1.42/1.80 'tc_nat' ) ), Y, 'tc_nat' ) ), Y, 'tc_nat' ) ) ) ],
% 1.42/1.80 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ), ~( hBOOL(
% 1.42/1.80 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ) ) ) ) ],
% 1.42/1.80 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ) ) ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.42/1.80 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'(
% 1.42/1.80 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ), 'tc_nat' ) ), ~( hBOOL(
% 1.42/1.80 hAPP( 'c_lessequals'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y
% 1.42/1.80 ), 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ), X ),
% 1.42/1.80 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.80 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.42/1.80 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.80 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), X
% 1.42/1.80 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.80 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'(
% 1.42/1.80 'c_HOL_Oone__class_Oone'( X ), Y, X ), X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.42/1.80 ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ),
% 1.42/1.80 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.42/1.80 [ ~( 'class_RealVector_Oreal__field'( X ) ), =(
% 1.42/1.80 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.42/1.80 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.42/1.80 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X ), W, X ), hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.42/1.80 X ), Y ), 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ominus__class_Ominus'(
% 1.42/1.80 Z, U, X ), W, X ) ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.42/1.80 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ominus__class_Ominus'( Y, T, X )
% 1.42/1.80 , W, X ) ), U ) ) ) ],
% 1.42/1.80 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.42/1.80 'c_Divides_Odiv__class_Omod'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), Z
% 1.42/1.80 , X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 1.42/1.80 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.42/1.80 'c_Divides_Odiv__class_Odiv'( Y, Y, X ), 'c_HOL_Oone__class_Oone'( X ) )
% 1.42/1.80 , =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.80 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_Int_OMin', 'tc_Int_Oint' )
% 1.42/1.80 , 'c_Int_OPls' ) ) ],
% 1.42/1.80 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_Int_Oint' ), 'c_Int_OMin' ) ), ~(
% 1.42/1.80 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_Int_OBit0'( X ), 'tc_Int_Oint'
% 1.42/1.80 ), 'c_Int_OMin' ) ) ) ],
% 1.42/1.80 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_Int_OBit0'( X ),
% 1.42/1.80 'tc_Int_Oint' ), 'c_Int_OMin' ) ), ~( hBOOL( hAPP( 'c_lessequals'( X,
% 1.42/1.80 'tc_Int_Oint' ), 'c_Int_OMin' ) ) ) ],
% 1.42/1.80 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.42/1.80 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ),
% 1.42/1.80 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'(
% 1.42/1.80 'tc_nat' ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_Int_Oint'
% 1.42/1.80 ), 'c_Int_OPls' ) ) ) ],
% 1.42/1.80 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.42/1.80 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( Y, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.42/1.80 X ), Z ), T ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ), T ) ) ), ~(
% 1.42/1.80 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.42/1.80 X ), Z ) ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.80 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ), ~( hBOOL(
% 1.42/1.80 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.42/1.80 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ) ) ) ) ],
% 1.42/1.80 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.42/1.80 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( Y, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.42/1.80 X ), Z ), T ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), T )
% 1.42/1.80 ) ), ~( hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.42/1.80 ), Z ) ) ) ],
% 1.42/1.80 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ), 'tc_nat'
% 1.42/1.80 ), 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ) ) ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( Z, 'tc_nat' ), Y ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Z
% 1.42/1.80 , 'tc_nat' ), X ) ) ) ],
% 1.42/1.80 [ hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.42/1.80 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ) )
% 1.42/1.80 ), ~( hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Z ) ) ), ~( hBOOL(
% 1.42/1.80 hAPP( 'c_lessequals'( Y, 'tc_nat' ), Z ) ) ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( Y, 'tc_nat' ), X ) ) ) ],
% 1.42/1.80 [ hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.42/1.80 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ) )
% 1.42/1.80 ), ~( hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Z ) ) ) ],
% 1.42/1.80 [ hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.42/1.80 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ) )
% 1.42/1.80 ), ~( hBOOL( hAPP( 'c_lessequals'( Z, 'tc_nat' ), Y ) ) ) ],
% 1.42/1.80 [ =( 'c_HOL_Ominus__class_Ominus'( X, hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ),
% 1.42/1.80 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.42/1.80 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.42/1.80 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ), 'tc_nat' ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z )
% 1.42/1.80 , X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), T ), Z ) ) ), ~(
% 1.42/1.80 hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) )
% 1.42/1.80 ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ), T ) ) ) ],
% 1.42/1.80 [ ~( =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 1.42/1.80 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ) ) ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( Y, 'tc_nat' ), Z ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y
% 1.42/1.80 , 'tc_nat' ), X ) ) ), =( X, Z ) ],
% 1.42/1.80 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 1.42/1.80 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ominus__class_Ominus'( Z
% 1.42/1.80 , T, X ) ) ), =( Z, T ) ],
% 1.42/1.80 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 1.42/1.80 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 1.42/1.80 , T, X ) ) ), =( Y, Z ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.80 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), X ), Y ) ), hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL(
% 1.42/1.80 hAPP( 'c_lessequals'( hAPP( 'c_HOL_Oinverse__class_Oinverse'( X ), Y ), X
% 1.42/1.80 ), 'c_HOL_Oone__class_Oone'( X ) ) ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.42/1.80 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), =( Y,
% 1.42/1.80 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hBOOL( hAPP( 'c_lessequals'(
% 1.42/1.80 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ),
% 1.42/1.80 'c_HOL_Ozero__class_Ozero'( X ) ), Y ), X ), 'c_HOL_Ozero__class_Ozero'(
% 1.42/1.80 X ) ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.42/1.80 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.42/1.80 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ),
% 1.42/1.80 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.42/1.80 'c_HOL_Ozero__class_Ozero'( X ) ), hBOOL( hAPP( 'c_lessequals'( Y, X ),
% 1.42/1.80 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( hAPP(
% 1.42/1.80 hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ),
% 1.42/1.80 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.42/1.80 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =(
% 1.42/1.80 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.42/1.80 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ),
% 1.42/1.80 'c_Lattices_Oupper__semilattice__class_Osup'( Z,
% 1.42/1.80 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T, X ), X ) ) ],
% 1.42/1.80 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =(
% 1.42/1.80 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.42/1.80 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), T, X ),
% 1.42/1.80 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.42/1.80 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ) ) ],
% 1.42/1.80 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.42/1.80 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 1.42/1.80 'tc_bool' ) ), T, 'tc_fun'( Z, 'tc_bool' ) ),
% 1.42/1.80 'c_Lattices_Oupper__semilattice__class_Osup'( X,
% 1.42/1.80 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T, 'tc_fun'( Z,
% 1.42/1.80 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.42/1.80 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X,
% 1.42/1.80 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, 'tc_fun'( T,
% 1.42/1.80 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ),
% 1.42/1.80 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.42/1.80 'c_Lattices_Oupper__semilattice__class_Osup'( X, Z, 'tc_fun'( T,
% 1.42/1.80 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 1.42/1.80 [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 1.42/1.80 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.42/1.80 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ),
% 1.42/1.80 'c_Lattices_Oupper__semilattice__class_Osup'( Z,
% 1.42/1.80 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T, X ), X ) ) ],
% 1.42/1.80 [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 1.42/1.80 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.42/1.80 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), T, X ),
% 1.42/1.80 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.42/1.80 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ) ) ],
% 1.42/1.80 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.42/1.80 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.42/1.80 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X
% 1.42/1.80 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.42/1.80 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.42/1.80 X ), 'c_HOL_Ominus__class_Ominus'( Y, T, X ) ),
% 1.42/1.80 'c_HOL_Ominus__class_Ominus'( Z, U, X ) ) ), hAPP( hAPP(
% 1.42/1.80 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ominus__class_Ominus'( Y, T, X
% 1.42/1.80 ) ), U ) ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.42/1.80 'c_HOL_Ominus__class_Ominus'( Z, U, X ) ) ) ) ],
% 1.42/1.80 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Ominus__class_Ominus'( X, Y
% 1.42/1.80 , 'tc_nat' ), 'tc_nat' ), 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat'
% 1.42/1.80 ), 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.42/1.80 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Ominus__class_Ominus'( X, Y
% 1.42/1.80 , 'tc_nat' ), 'tc_nat' ), ~( 'c_Parity_Oeven__odd__class_Oeven'( Y,
% 1.42/1.80 'tc_nat' ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ]
% 1.42/1.80 ,
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.42/1.80 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ), ~(
% 1.42/1.80 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.42/1.80 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ), ~(
% 1.42/1.80 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 1.42/1.80 'class_OrderedGroup_Omonoid__mult'( X ) ), hBOOL( hAPP( 'c_lessequals'(
% 1.42/1.80 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.42/1.80 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ), ~(
% 1.42/1.80 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.80 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ),
% 1.42/1.80 ~( hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), X ), hAPP(
% 1.42/1.80 'c_HOL_Oinverse__class_Oinverse'( X ), Y ) ) ) ) ],
% 1.42/1.80 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( =(
% 1.42/1.80 'c_SetInterval_Oord__class_OlessThan'( Y, X ),
% 1.42/1.80 'c_SetInterval_Oord__class_OlessThan'( Z, X ) ) ), =( Y, Z ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), X ), hAPP( hAPP(
% 1.42/1.80 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.42/1.80 'tc_nat' ), Z ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.80 'c_HOL_Oone__class_Oone'( X ), X ), Y ) ) ) ],
% 1.42/1.80 [ hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.42/1.80 'tc_nat' ), 'tc_nat' ), X ) ) ],
% 1.42/1.80 [ ~( 'class_Orderings_Oorder'( X ) ), =(
% 1.42/1.80 'c_SetInterval_Oord__class_OatLeastAtMost'( Y, Y, X ), 'c_Set_Oinsert'( Y
% 1.42/1.80 , 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ), X ) ) ]
% 1.42/1.80 ,
% 1.42/1.80 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), hBOOL(
% 1.42/1.80 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.42/1.80 X ), Y ), Z ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.42/1.80 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ),
% 1.42/1.80 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.42/1.80 ), Y ), Z ), X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), T ),
% 1.42/1.80 Z ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.80 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), Z ) ) ), ~( hBOOL(
% 1.42/1.80 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ), ~(
% 1.42/1.80 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), T ) ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.42/1.80 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Ominus__class_Ominus'( Z
% 1.42/1.80 , T, 'tc_nat' ) ), 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.42/1.80 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.42/1.80 'c_Power_Opower__class_Opower'( X ), Y ), T ), X ) ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( T, 'tc_nat' ), Z ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.42/1.80 X ) ) ],
% 1.42/1.80 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.42/1.80 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.42/1.80 , Y ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ),
% 1.42/1.80 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ominus__class_Ominus'(
% 1.42/1.80 Y, T, X ) ), 'c_HOL_Ominus__class_Ominus'( Z, U, X ) ) ) ],
% 1.42/1.80 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.42/1.80 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'(
% 1.42/1.80 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.42/1.80 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.42/1.80 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 1.42/1.80 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ) ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( Y, 'tc_nat' ), Z ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y
% 1.42/1.80 , 'tc_nat' ), X ) ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.80 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( hAPP( 'c_HOL_Oinverse__class_Oinverse'( X ), Y ), X ),
% 1.42/1.80 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X
% 1.42/1.80 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.80 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL(
% 1.42/1.80 hAPP( 'c_lessequals'( hAPP( 'c_HOL_Oinverse__class_Oinverse'( X ), Y ), X
% 1.42/1.80 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.42/1.80 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'(
% 1.42/1.80 X, Y, 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y,
% 1.42/1.80 'tc_nat' ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, 'tc_nat' ), X ) ) ),
% 1.42/1.80 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Z ) ) ) ],
% 1.42/1.80 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Ominus__class_Ominus'( X
% 1.42/1.80 , 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ), ~(
% 1.42/1.80 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.42/1.80 'tc_nat' ), X ) ) ) ],
% 1.42/1.80 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ),
% 1.42/1.80 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Ominus__class_Ominus'( X,
% 1.42/1.80 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ), 'tc_nat' ), ~( hBOOL(
% 1.42/1.80 hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.42/1.80 'tc_nat' ), X ) ) ) ],
% 1.42/1.80 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.42/1.80 'tc_nat' ), 'tc_nat' ), X ) ), 'c_Parity_Oeven__odd__class_Oeven'( X,
% 1.42/1.80 'tc_nat' ) ],
% 1.42/1.80 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_OrderedGroup_Omonoid__mult'( Z
% 1.42/1.80 , X, T ) ) ],
% 1.42/1.80 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_OrderedGroup_Omonoid__mult'( Y
% 1.42/1.80 , X, T ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.42/1.80 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.42/1.80 , 'tc_nat' ), 'tc_nat' ), hBOOL( hAPP( 'c_lessequals'( Z, X ),
% 1.42/1.80 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( hAPP(
% 1.42/1.80 hAPP( 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.42/1.80 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ), X ),
% 1.42/1.80 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.42/1.80 [ hBOOL( hAPP( 'c_Set_Oinsert'( X, Y, Z ), T ) ), ~( hBOOL( hAPP( Y, T )
% 1.42/1.80 ) ) ],
% 1.42/1.80 [ ~( 'class_Int_Onumber__ring'( X ) ), ~( 'c_Int_Oiszero'(
% 1.42/1.80 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OMin', X ), X ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.42/1.80 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( =( hAPP(
% 1.42/1.80 'c_HOL_Oinverse__class_Oinverse'( X ), Y ), 'c_HOL_Oone__class_Oone'( X )
% 1.42/1.80 ) ), =( Y, 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.80 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), X ), Y ) ),
% 1.42/1.80 hBOOL( hAPP( 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.42/1.80 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.42/1.80 'c_HOL_Oinverse__class_Oinverse'( X ), Y ), X ), 'c_HOL_Oone__class_Oone'(
% 1.42/1.80 X ) ) ) ) ],
% 1.42/1.80 [ hBOOL( hAPP( 'c_lessequals'( 'c_Divides_Odiv__class_Omod'( X, Y,
% 1.42/1.80 'tc_nat' ), 'tc_nat' ), X ) ) ],
% 1.42/1.80 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ),
% 1.42/1.80 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.42/1.80 'tc_nat' ), Y ), X ), Z, 'tc_nat' ) ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.42/1.80 Z, 'tc_nat' ), Y ) ) ) ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP(
% 1.42/1.80 'c_HOL_Oinverse__class_Oinverse'( X ), Y ) ) ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) )
% 1.42/1.80 ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.80 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP(
% 1.42/1.80 'c_HOL_Oinverse__class_Oinverse'( X ), Y ) ) ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) )
% 1.42/1.80 ],
% 1.42/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.80 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ),
% 1.42/1.80 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X
% 1.42/1.80 ), X ), hAPP( 'c_HOL_Oinverse__class_Oinverse'( X ), Y ) ) ) ) ],
% 1.42/1.80 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ),
% 1.42/1.80 'tc_Int_Oint' ), 'c_Int_OMin' ) ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( X, 'tc_Int_Oint' ), 'c_Int_OMin' ) ) ) ],
% 1.42/1.80 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_Int_Oint' ),
% 1.42/1.80 'c_Int_OMin' ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.80 'c_Int_OBit1'( X ), 'tc_Int_Oint' ), 'c_Int_OMin' ) ) ) ],
% 1.42/1.80 [ hBOOL( hAPP( 'c_lessequals'( 'c_Int_OMin', 'tc_Int_Oint' ),
% 1.42/1.80 'c_Int_OPls' ) ) ],
% 1.42/1.80 [ =( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ),
% 1.42/1.80 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( hBOOL( hAPP(
% 1.42/1.80 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ) ) ],
% 1.42/1.80 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), T ) ), hBOOL( hAPP(
% 1.42/1.80 hAPP( U, T ), W ) ), ~( hBOOL( hAPP( hAPP( X, Z ), V0 ) ) ), ~(
% 1.42/1.80 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, U, X, V4, V0, Y, V5,
% 1.42/1.80 V6 ) ) ],
% 1.42/1.80 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), T ) ), ~( hBOOL( hAPP(
% 1.42/1.80 hAPP( X, U ), Z ) ) ), hBOOL( hAPP( hAPP( W, V0 ), T ) ), ~(
% 1.42/1.80 'c_Ring__and__Field_Oordered__idom'( V1, V2, V0, V3, W, X, V4, U, Y, V5,
% 1.42/1.80 V6 ) ) ],
% 1.42/1.80 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), Y ) ) ), hBOOL( hAPP(
% 1.42/1.80 hAPP( U, Y ), W ) ), ~( hBOOL( hAPP( hAPP( X, V0 ), T ) ) ), ~(
% 1.42/1.80 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, U, X, V4, V0, Z, V5,
% 1.42/1.80 V6 ) ) ],
% 1.42/1.80 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), Y ) ) ), ~( hBOOL( hAPP(
% 1.42/1.80 hAPP( X, T ), U ) ) ), hBOOL( hAPP( hAPP( W, V0 ), Y ) ), ~(
% 1.42/1.80 'c_Ring__and__Field_Oordered__idom'( V1, V2, V0, V3, W, X, V4, U, Z, V5,
% 1.42/1.80 V6 ) ) ],
% 1.42/1.80 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), Z ) ), hBOOL( hAPP(
% 1.42/1.80 hAPP( U, Z ), W ) ), ~( hBOOL( hAPP( hAPP( X, T ), V0 ) ) ), ~(
% 1.42/1.80 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, U, X, V4, V0, Y, V5,
% 1.42/1.80 V6 ) ) ],
% 1.42/1.80 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), Z ) ), ~( hBOOL( hAPP(
% 1.42/1.80 hAPP( X, U ), T ) ) ), hBOOL( hAPP( hAPP( W, V0 ), Z ) ), ~(
% 1.42/1.80 'c_Ring__and__Field_Oordered__idom'( V1, V2, V0, V3, W, X, V4, U, Y, V5,
% 1.42/1.80 V6 ) ) ],
% 1.42/1.80 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, Y ), T ) ) ), hBOOL( hAPP(
% 1.42/1.80 hAPP( U, Y ), W ) ), ~( hBOOL( hAPP( hAPP( X, V0 ), T ) ) ), ~(
% 1.42/1.80 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, U, X, V4, V0, Z, V5,
% 1.42/1.80 V6 ) ) ],
% 1.42/1.80 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, Y ), T ) ) ), ~( hBOOL( hAPP(
% 1.42/1.80 hAPP( X, T ), U ) ) ), hBOOL( hAPP( hAPP( W, V0 ), Y ) ), ~(
% 1.42/1.80 'c_Ring__and__Field_Oordered__idom'( V1, V2, V0, V3, W, X, V4, U, Z, V5,
% 1.42/1.80 V6 ) ) ],
% 1.42/1.80 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), T ) ), hBOOL( hAPP(
% 1.42/1.80 hAPP( U, T ), W ) ), ~( hBOOL( hAPP( hAPP( X, Z ), V0 ) ) ), ~(
% 1.42/1.80 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, X, U, V4, V0, Y, V5,
% 1.42/1.80 V6 ) ) ],
% 1.42/1.80 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), T ) ), ~( hBOOL( hAPP(
% 1.42/1.80 hAPP( X, U ), Z ) ) ), hBOOL( hAPP( hAPP( W, V0 ), T ) ), ~(
% 1.42/1.80 'c_Ring__and__Field_Oordered__idom'( V1, V2, V0, V3, X, W, V4, U, Y, V5,
% 1.42/1.80 V6 ) ) ],
% 1.42/1.80 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), Y ) ) ), hBOOL( hAPP(
% 1.42/1.80 hAPP( U, Y ), W ) ), ~( hBOOL( hAPP( hAPP( X, V0 ), T ) ) ), ~(
% 1.42/1.80 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, X, U, V4, V0, Z, V5,
% 1.42/1.80 V6 ) ) ],
% 1.42/1.80 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), Y ) ) ), ~( hBOOL( hAPP(
% 1.42/1.80 hAPP( X, T ), U ) ) ), hBOOL( hAPP( hAPP( W, V0 ), Y ) ), ~(
% 1.42/1.80 'c_Ring__and__Field_Oordered__idom'( V1, V2, V0, V3, X, W, V4, U, Z, V5,
% 1.42/1.80 V6 ) ) ],
% 1.42/1.80 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), Z ) ), hBOOL( hAPP(
% 1.42/1.80 hAPP( U, Z ), W ) ), ~( hBOOL( hAPP( hAPP( X, T ), V0 ) ) ), ~(
% 1.42/1.80 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, X, U, V4, V0, Y, V5,
% 1.42/1.80 V6 ) ) ],
% 1.42/1.80 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), Z ) ), ~( hBOOL( hAPP(
% 1.42/1.81 hAPP( X, U ), T ) ) ), hBOOL( hAPP( hAPP( W, V0 ), Z ) ), ~(
% 1.42/1.81 'c_Ring__and__Field_Oordered__idom'( V1, V2, V0, V3, X, W, V4, U, Y, V5,
% 1.42/1.81 V6 ) ) ],
% 1.42/1.81 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, Y ), T ) ) ), hBOOL( hAPP(
% 1.42/1.81 hAPP( U, Y ), W ) ), ~( hBOOL( hAPP( hAPP( X, V0 ), T ) ) ), ~(
% 1.42/1.81 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, X, U, V4, V0, Z, V5,
% 1.42/1.81 V6 ) ) ],
% 1.42/1.81 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, Y ), T ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 hAPP( X, T ), U ) ) ), hBOOL( hAPP( hAPP( W, V0 ), Y ) ), ~(
% 1.42/1.81 'c_Ring__and__Field_Oordered__idom'( V1, V2, V0, V3, X, W, V4, U, Z, V5,
% 1.42/1.81 V6 ) ) ],
% 1.42/1.81 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( Z, T ) ) ), ~( hBOOL( hAPP( hAPP( X,
% 1.42/1.81 Y ), T ) ) ), ~( 'c_Ring__and__Field_Oordered__idom'( U, W, Y, V0, V1, X
% 1.42/1.81 , V2, V3, V4, Z, V5 ) ) ],
% 1.42/1.81 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( X, Y ), hAPP(
% 1.42/1.81 T, Z ) ) ) ), ~( 'c_Ring__and__Field_Oordered__idom'( U, W, Y, V0, V1, X
% 1.42/1.81 , V2, V3, V4, T, V5 ) ) ],
% 1.42/1.81 [ hBOOL( hAPP( hAPP( X, hAPP( Y, Z ) ), T ) ), ~( hBOOL( hAPP( hAPP( X,
% 1.42/1.81 Z ), T ) ) ), ~( 'c_Ring__and__Field_Oordered__idom'( U, W, T, V0, V1, X
% 1.42/1.81 , V2, V3, V4, Y, V5 ) ) ],
% 1.42/1.81 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( X, hAPP( T, Y
% 1.42/1.81 ) ), Z ) ) ), ~( 'c_Ring__and__Field_Oordered__idom'( U, W, Z, V0, V1, X
% 1.42/1.81 , V2, V3, V4, T, V5 ) ) ],
% 1.42/1.81 [ ~( 'class_RealVector_Oreal__normed__div__algebra'( X ) ), 'c_Lim_OLIM'(
% 1.42/1.81 'c_HOL_Oinverse__class_Oinverse'( X ), Y, hAPP(
% 1.42/1.81 'c_HOL_Oinverse__class_Oinverse'( X ), Y ), X, X ), =( Y,
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.81 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =(
% 1.42/1.81 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ),
% 1.42/1.81 'c_Lattices_Oupper__semilattice__class_Osup'( Z, Y, X ) ) ],
% 1.42/1.81 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 1.42/1.81 'tc_bool' ) ), 'c_Lattices_Oupper__semilattice__class_Osup'( Y, X,
% 1.42/1.81 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.42/1.81 [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 1.42/1.81 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ),
% 1.42/1.81 'c_Lattices_Oupper__semilattice__class_Osup'( Z, Y, X ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ),
% 1.42/1.81 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ),
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), X
% 1.42/1.81 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.42/1.81 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ),
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X
% 1.42/1.81 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ),
% 1.42/1.81 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.42/1.81 X ), Z ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.81 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), X ),
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.42/1.81 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.42/1.81 X ), Y ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.81 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ),
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =( hAPP( hAPP(
% 1.42/1.81 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.42/1.81 'c_Power_Opower__class_Opower'( X ), T ), Z ) ) ), =( Y, T ), ~( hBOOL(
% 1.42/1.81 hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.42/1.81 'tc_nat' ), Z ) ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ) ],
% 1.42/1.81 [ =( 'c_Set_Oinsert'( X, Y, Z ),
% 1.42/1.81 'c_Lattices_Oupper__semilattice__class_Osup'( 'c_Set_Oinsert'( X,
% 1.42/1.81 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Y,
% 1.42/1.81 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.42/1.81 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =(
% 1.42/1.81 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.42/1.81 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), X ),
% 1.42/1.81 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ) ) ],
% 1.42/1.81 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X,
% 1.42/1.81 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 1.42/1.81 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ),
% 1.42/1.81 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 1.42/1.81 'tc_bool' ) ) ) ],
% 1.42/1.81 [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 1.42/1.81 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.42/1.81 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), X ),
% 1.42/1.81 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ) ) ],
% 1.42/1.81 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Ominus__class_Ominus'( X, Y
% 1.42/1.81 , 'tc_nat' ), 'tc_nat' ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X,
% 1.42/1.81 'tc_nat' ), Y ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.42/1.81 'c_Groebner__Basis_Ogb__semiring'( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( X ), 'c_Power_Opower__class_Opower'( X ),
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ), X ) ]
% 1.42/1.81 ,
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( 'c_Finite__Set_Osetsum'(
% 1.42/1.81 hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.42/1.81 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.42/1.81 'tc_nat' ), Z, 'tc_nat' ), 'tc_nat', X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.42/1.81 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_Power_Opower__class_Opower'(
% 1.42/1.81 X ), Y ), Z ), 'c_HOL_Oone__class_Oone'( X ), X ),
% 1.42/1.81 'c_HOL_Ominus__class_Ominus'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), X )
% 1.42/1.81 ), =( Y, 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.42/1.81 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( 'c_Power_Opower_Opower'( Z, T,
% 1.42/1.81 U ), hAPP( W, V0 ) ), V1 ) ) ), ~( 'c_Ring__and__Field_Oordered__idom'(
% 1.42/1.81 V2, V3, Y, V4, X, V5, W, Z, T, V6, U ) ) ],
% 1.42/1.81 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.42/1.81 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.42/1.81 , Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), Z, X )
% 1.42/1.81 , 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 1.42/1.81 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.42/1.81 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.42/1.81 , Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), T, X )
% 1.42/1.81 , 'c_Divides_Odiv__class_Omod'( Y, T, X ) ) ],
% 1.42/1.81 [ =( hAPP( X, Y ), hAPP( Z, T ) ), ~( hBOOL( hAPP( hAPP( U, Y ), W ) ) )
% 1.42/1.81 , ~( 'c_Ring__and__Field_Oordered__idom'( V0, Z, W, V1, V2, U, V3, T, V4
% 1.42/1.81 , X, V5 ) ) ],
% 1.42/1.81 [ =( hAPP( X, Y ), Z ), ~( hBOOL( hAPP( hAPP( T, U ), Y ) ) ), ~(
% 1.42/1.81 'c_Ring__and__Field_Oordered__idom'( W, V0, U, V1, V2, T, V3, Z, V4, X,
% 1.42/1.81 V5 ) ) ],
% 1.42/1.81 [ ~( =( hAPP( X, Y ), hAPP( Z, T ) ) ), ~(
% 1.42/1.81 'c_Ring__and__Field_Oordered__idom'( U, Z, W, V0, V1, V2, V3, T, V4, X,
% 1.42/1.81 V5 ) ), hBOOL( hAPP( hAPP( V2, Y ), W ) ) ],
% 1.42/1.81 [ =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.42/1.81 X, 'tc_nat' ), Y ) ) ) ],
% 1.42/1.81 [ ~( =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), hBOOL( hAPP( 'c_lessequals'(
% 1.42/1.81 X, 'tc_nat' ), Y ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.42/1.81 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.42/1.81 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP( hAPP(
% 1.42/1.81 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.42/1.81 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.42/1.81 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), hAPP( hAPP(
% 1.42/1.81 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.42/1.81 X ), 'c_HOL_Ominus__class_Ominus'( Y, U, X ) ), Z ) ), T ) ) ) ],
% 1.42/1.81 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X, 'c_Set_Oinsert'( Y
% 1.42/1.81 , Z, T ), 'tc_fun'( T, 'tc_bool' ) ), 'c_Set_Oinsert'( Y,
% 1.42/1.81 'c_Lattices_Oupper__semilattice__class_Osup'( X, Z, 'tc_fun'( T,
% 1.42/1.81 'tc_bool' ) ), T ) ) ],
% 1.42/1.81 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( 'c_Set_Oinsert'( X, Y
% 1.42/1.81 , Z ), T, 'tc_fun'( Z, 'tc_bool' ) ), 'c_Set_Oinsert'( X,
% 1.42/1.81 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T, 'tc_fun'( Z,
% 1.42/1.81 'tc_bool' ) ), Z ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), X ), hAPP( hAPP(
% 1.42/1.81 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), X ), Y ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =( hAPP( hAPP(
% 1.42/1.81 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.42/1.81 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.42/1.81 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), W ) ) ), =( hAPP(
% 1.42/1.81 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ominus__class_Ominus'( Y, U, X
% 1.42/1.81 ) ), Z ) ), T ), W ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =( hAPP( hAPP(
% 1.42/1.81 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.42/1.81 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.42/1.81 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), W ) ) ), =( T, hAPP(
% 1.42/1.81 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ominus__class_Ominus'( U, Y, X
% 1.42/1.81 ) ), Z ) ), W ) ) ],
% 1.42/1.81 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 1.42/1.81 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.42/1.81 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.42/1.81 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ), Z ) ),
% 1.42/1.81 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ), T ), hAPP( hAPP(
% 1.42/1.81 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ],
% 1.42/1.81 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 1.42/1.81 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.42/1.81 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.42/1.81 'c_Divides_Odiv__class_Odiv'( Z, Y, X ) ) ), 'c_Divides_Odiv__class_Omod'(
% 1.42/1.81 Z, Y, X ) ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T )
% 1.42/1.81 ) ],
% 1.42/1.81 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_Int_OMin', 'tc_Int_Oint' )
% 1.42/1.81 , X ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_Int_OMin',
% 1.42/1.81 'tc_Int_Oint' ), 'c_Int_OBit0'( X ) ) ) ) ],
% 1.42/1.81 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_Int_OMin', 'tc_Int_Oint' )
% 1.42/1.81 , 'c_Int_OBit0'( X ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.81 'c_Int_OMin', 'tc_Int_Oint' ), X ) ) ) ],
% 1.42/1.81 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_Int_OMin', 'tc_Int_Oint' )
% 1.42/1.81 , X ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_Int_OMin',
% 1.42/1.81 'tc_Int_Oint' ), 'c_Int_OBit1'( X ) ) ) ) ],
% 1.42/1.81 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_Int_OMin', 'tc_Int_Oint' )
% 1.42/1.81 , 'c_Int_OBit1'( X ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.81 'c_Int_OMin', 'tc_Int_Oint' ), X ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.42/1.81 ), Y ), Z ), X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.42/1.81 T ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ),
% 1.42/1.81 'c_HOL_Oone__class_Oone'( X ) ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) )
% 1.42/1.81 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( T, 'tc_nat' ), Z ) ) ) ]
% 1.42/1.81 ,
% 1.42/1.81 [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ),
% 1.42/1.81 'c_HOL_Ominus__class_Ominus'( X, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.42/1.81 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ) ), Y ),
% 1.42/1.81 'tc_nat' ) ) ],
% 1.42/1.81 [ =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( X, Y, Z ), Z ),
% 1.42/1.81 'c_Set_Oinsert'( X, Y, Z ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_lessequals'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z )
% 1.42/1.81 , X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), T ) ) ), ~(
% 1.42/1.81 hBOOL( hAPP( 'c_lessequals'( Y, X ), 'c_HOL_Oone__class_Oone'( X ) ) ) )
% 1.42/1.81 , ~( hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 1.42/1.81 ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( T, 'tc_nat' ), Z ) ) ) ],
% 1.42/1.81 [ hBOOL( hAPP( X, Y ) ), =( Z, Y ), ~( hBOOL( hAPP( 'c_Set_Oinsert'( Z,
% 1.42/1.81 X, T ), Y ) ) ) ],
% 1.42/1.81 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), X, 'tc_nat' ),
% 1.42/1.81 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat'
% 1.42/1.81 ), X ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( 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 ), Z ), Y ) ) ],
% 1.42/1.81 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.42/1.81 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ) ), ~(
% 1.42/1.81 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, 'tc_nat' ), Y ) ) ), hBOOL(
% 1.42/1.81 hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), T ) ) ],
% 1.42/1.81 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), hAPP(
% 1.42/1.81 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( 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 ), Z ), Y ) ) ],
% 1.42/1.81 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( 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 ), Z ), Y ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP(
% 1.42/1.81 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ), ~( hBOOL(
% 1.42/1.81 hAPP( 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ),
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ), hBOOL( hAPP(
% 1.42/1.81 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ), ~( hBOOL(
% 1.42/1.81 hAPP( 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), X ),
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP(
% 1.42/1.81 'c_lessequals'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL(
% 1.42/1.81 hAPP( 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ),
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ), hBOOL( hAPP(
% 1.42/1.81 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL(
% 1.42/1.81 hAPP( 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), X ),
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.42/1.81 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'(
% 1.42/1.81 X, Y, 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, Z,
% 1.42/1.81 'tc_nat' ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, 'tc_nat' )
% 1.42/1.81 , X ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, 'tc_nat' ), Y )
% 1.42/1.81 ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_lessequals'( Y, X ), Z ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_lessequals'( hAPP( 'c_HOL_Oinverse__class_Oinverse'( X ), Z ), X ),
% 1.42/1.81 hAPP( 'c_HOL_Oinverse__class_Oinverse'( X ), Y ) ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_lessequals'( hAPP( 'c_HOL_Oinverse__class_Oinverse'( X ), Y ), X ),
% 1.42/1.81 hAPP( 'c_HOL_Oinverse__class_Oinverse'( X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) )
% 1.42/1.81 , ~( hBOOL( hAPP( 'c_lessequals'( Z, X ), Y ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_lessequals'( Y, X ), Z ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.81 Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_lessequals'( hAPP( 'c_HOL_Oinverse__class_Oinverse'( X ), Z ), X ),
% 1.42/1.81 hAPP( 'c_HOL_Oinverse__class_Oinverse'( X ), Y ) ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_lessequals'( hAPP( 'c_HOL_Oinverse__class_Oinverse'( X ), Y ), X ),
% 1.42/1.81 hAPP( 'c_HOL_Oinverse__class_Oinverse'( X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.42/1.81 , ~( hBOOL( hAPP( 'c_lessequals'( Z, X ), Y ) ) ) ],
% 1.42/1.81 [ hBOOL( hAPP( 'c_lessequals'( 'c_Divides_Odiv__class_Odiv'( X, Y,
% 1.42/1.81 'tc_nat' ), 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( X, Z, 'tc_nat' ) )
% 1.42/1.81 ), ~( hBOOL( hAPP( 'c_lessequals'( Z, 'tc_nat' ), Y ) ) ), ~( hBOOL(
% 1.42/1.81 hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.42/1.81 'tc_nat' ), Z ) ) ) ],
% 1.42/1.81 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.42/1.81 'c_Divides_Odiv__class_Odiv'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), Z
% 1.42/1.81 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.81 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), hAPP( hAPP( Y, Z ), U ) )
% 1.42/1.81 , hAPP( hAPP( Y, Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.42/1.81 , T ), U ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, Y, V0, V1, V2
% 1.42/1.81 ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_lessequals'( hAPP( 'c_HOL_Oinverse__class_Oinverse'( X ), Y ), X ),
% 1.42/1.81 'c_HOL_Oone__class_Oone'( X ) ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.42/1.81 'c_HOL_Oone__class_Oone'( X ), X ), Y ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.42/1.81 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.42/1.81 X ), 'c_HOL_Oone__class_Oone'( X ) ), 'c_HOL_Oone__class_Oone'( X ) ) ),
% 1.42/1.81 Y ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.42/1.81 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.42/1.81 'c_HOL_Ominus__class_Ominus'( Y, Z, X ) ), T ) ), U ), X ), W ) ), ~(
% 1.42/1.81 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.42/1.81 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.42/1.81 X ), Y ), T ) ), U ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.42/1.81 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), W ) ) ) ) ]
% 1.42/1.81 ,
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.42/1.81 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), X ), hAPP(
% 1.42/1.81 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), W ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.42/1.81 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.42/1.81 'c_HOL_Ominus__class_Ominus'( Y, U, X ) ), Z ) ), T ), X ), W ) ) ) ]
% 1.42/1.81 ,
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( Y, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.42/1.81 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.42/1.81 'c_HOL_Ominus__class_Ominus'( Z, T, X ) ), U ) ), W ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.42/1.81 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), Y ), X ), hAPP(
% 1.42/1.81 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ), W ) ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.42/1.81 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), X ), hAPP(
% 1.42/1.81 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), W ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( T, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.42/1.81 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.42/1.81 'c_HOL_Ominus__class_Ominus'( U, Y, X ) ), Z ) ), W ) ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.42/1.81 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Oone__class_Oone'(
% 1.42/1.81 'tc_nat' ) ), Y ) ],
% 1.42/1.81 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.42/1.81 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Oone__class_Oone'(
% 1.42/1.81 'tc_nat' ) ), Y ) ],
% 1.42/1.81 [ ~( hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ) ), =( hAPP( hAPP(
% 1.42/1.81 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.42/1.81 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Y
% 1.42/1.81 , X, 'tc_nat' ) ), Z ) ), T ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.42/1.81 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z
% 1.42/1.81 ) ), T ) ) ],
% 1.42/1.81 [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 1.42/1.81 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.42/1.81 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 1.42/1.81 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 1.42/1.81 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.42/1.81 , U ), Y ), Z, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.42/1.81 'c_HOL_Oplus__class_Oplus'( X ), W ), T ), Z, X ) ) ],
% 1.42/1.81 [ hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.42/1.81 'tc_nat' ), 'tc_nat' ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'( X,
% 1.42/1.81 'tc_nat' ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y )
% 1.42/1.81 ) ) ) ],
% 1.42/1.81 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), hAPP( hAPP(
% 1.42/1.81 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ), 'tc_nat'
% 1.42/1.81 ), Y ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP(
% 1.42/1.81 hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) )
% 1.42/1.81 ],
% 1.42/1.81 [ ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ) ), =(
% 1.42/1.81 Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( hBOOL( hAPP( Z,
% 1.42/1.81 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.42/1.81 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), T
% 1.42/1.81 ) ), X ), Y, 'tc_nat' ) ) ) ), hBOOL( hAPP( Z, T ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), X ),
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.42/1.81 [ hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.42/1.81 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.42/1.81 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ), Z ) ), T ), 'tc_nat' )
% 1.42/1.81 , U ) ), ~( hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP(
% 1.42/1.81 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), T ), 'tc_nat' ),
% 1.42/1.81 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ), U ) ) ) ), ~( hBOOL(
% 1.42/1.81 hAPP( 'c_lessequals'( Y, 'tc_nat' ), X ) ) ) ],
% 1.42/1.81 [ hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.42/1.81 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y
% 1.42/1.81 ) ), Z ), 'tc_nat' ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.42/1.81 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), T ), Y ) ), U ) )
% 1.42/1.81 ), ~( hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP(
% 1.42/1.81 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X
% 1.42/1.81 , T, 'tc_nat' ) ), Y ) ), Z ), 'tc_nat' ), U ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_lessequals'( T, 'tc_nat' ), X ) ) ) ],
% 1.42/1.81 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), hAPP( hAPP(
% 1.42/1.81 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Y
% 1.42/1.81 , Z, 'tc_nat' ) ), T ) ), U ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( hAPP(
% 1.42/1.81 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ), X ), 'tc_nat' ),
% 1.42/1.81 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), T ) ), U ) ) ) ), ~( hBOOL(
% 1.42/1.81 hAPP( 'c_lessequals'( Z, 'tc_nat' ), Y ) ) ) ],
% 1.42/1.81 [ hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.42/1.81 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y
% 1.42/1.81 ) ), Z ), 'tc_nat' ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.42/1.81 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), T ), Y ) ), U ) )
% 1.42/1.81 ), ~( hBOOL( hAPP( 'c_lessequals'( Z, 'tc_nat' ), hAPP( hAPP(
% 1.42/1.81 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( T
% 1.42/1.81 , X, 'tc_nat' ) ), Y ) ), U ) ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( X,
% 1.42/1.81 'tc_nat' ), T ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =( hAPP(
% 1.42/1.81 'c_HOL_Oinverse__class_Oinverse'( X ), hAPP( hAPP(
% 1.42/1.81 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.42/1.81 'c_Power_Opower__class_Opower'( X ), hAPP(
% 1.42/1.81 'c_HOL_Oinverse__class_Oinverse'( X ), Y ) ), Z ) ), =( Y,
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.42/1.81 'c_HOL_Oone__class_Oone'( X ) ) ) ],
% 1.42/1.81 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.42/1.81 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ) ), Y ),
% 1.42/1.81 'c_HOL_Ominus__class_Ominus'( X, 'c_Divides_Odiv__class_Omod'( X, Y,
% 1.42/1.81 'tc_nat' ), 'tc_nat' ) ) ],
% 1.42/1.81 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.42/1.81 'c_Divides_Odiv__class_Odiv'( Y, X, 'tc_nat' ) ),
% 1.42/1.81 'c_HOL_Ominus__class_Ominus'( Y, 'c_Divides_Odiv__class_Omod'( Y, X,
% 1.42/1.81 'tc_nat' ), 'tc_nat' ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.42/1.81 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.42/1.81 X ), Y ), Z ) ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP(
% 1.42/1.81 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Oone__class_Oone'( X )
% 1.42/1.81 ) ), Z ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.42/1.81 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ), hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.42/1.81 X ), Z ), 'c_HOL_Oone__class_Oone'( X ) ) ), Y ) ) ],
% 1.42/1.81 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z
% 1.42/1.81 , 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.42/1.81 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ), ~(
% 1.42/1.81 hBOOL( hAPP( 'c_lessequals'( Z, 'tc_nat' ), Y ) ) ) ],
% 1.42/1.81 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.42/1.81 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.42/1.81 'c_HOL_Oplus__class_Oplus'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.42/1.81 Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.81 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), hAPP(
% 1.42/1.81 'c_Suc', hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.42/1.81 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 1.42/1.81 'tc_nat' ) ), Y ) ) ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ]
% 1.42/1.81 ,
% 1.42/1.81 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'(
% 1.42/1.81 X, Y, 'tc_nat' ), 'tc_nat' ), Z ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Z ) ) ) ],
% 1.42/1.81 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.42/1.81 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Oone__class_Oone'( X ), X ),
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_lessequals'( Y, X ), 'c_HOL_Oone__class_Oone'( X ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), X ), hAPP(
% 1.42/1.81 'c_HOL_Oinverse__class_Oinverse'( X ), Y ) ) ) ) ],
% 1.42/1.81 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( Y, X ), Y ) ) ) ],
% 1.42/1.81 [ ~( 'class_Orderings_Oorder'( X ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( Y, X ), Y ) ) ) ],
% 1.42/1.81 [ ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), X ) ) ) ]
% 1.42/1.81 ,
% 1.42/1.81 [ ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), X ) ) ) ]
% 1.42/1.81 ,
% 1.42/1.81 [ ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_Int_Oint' ), X ) ) )
% 1.42/1.81 ],
% 1.42/1.81 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( Y, X ), Y ) ) ) ],
% 1.42/1.81 [ ~( 'class_Orderings_Opreorder'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), hBOOL( hAPP( 'c_lessequals'( Z
% 1.42/1.81 , X ), Y ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ), Z ) ) ) ],
% 1.42/1.81 [ ~( hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), hAPP( hAPP(
% 1.42/1.81 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ) ) ) ), =(
% 1.42/1.81 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.42/1.81 'tc_nat' ), Y ), X ), X, 'tc_nat' ), Y ) ],
% 1.42/1.81 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), hBOOL(
% 1.42/1.81 hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.42/1.81 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) )
% 1.42/1.81 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.42/1.81 X ), X ), Y ) ) ) ],
% 1.42/1.81 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), hAPP( hAPP(
% 1.42/1.81 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.42/1.81 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), hAPP( hAPP(
% 1.42/1.81 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.42/1.81 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), hAPP( hAPP(
% 1.42/1.81 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ) ) ) ],
% 1.42/1.81 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), hAPP( hAPP(
% 1.42/1.81 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), X ),
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.42/1.81 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.42/1.81 'c_HOL_Oinverse__class_Oinverse'( X ), Y ), X ),
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Oinverse__class_Oinverse'( X ), Y
% 1.42/1.81 ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.42/1.81 ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Oinverse__class_Oinverse'( X ), Y
% 1.42/1.81 ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.42/1.81 ],
% 1.42/1.81 [ =( hAPP( hAPP( X, Y ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), Y ),
% 1.42/1.81 ~( 'c_Groebner__Basis_Ogb__semiring'( Z, T, X, U, W, V0 ) ) ],
% 1.42/1.81 [ ~( 'class_Divides_Oring__div'( X ) ), ~( =(
% 1.42/1.81 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.42/1.81 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 1.42/1.81 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 1.42/1.81 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 1.42/1.81 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( W, T,
% 1.42/1.81 X ), Z, X ) ) ],
% 1.42/1.81 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), X ),
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X
% 1.42/1.81 ), Z ) ) ) ],
% 1.42/1.81 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_lessequals'( Y, X ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.42/1.81 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 1.42/1.81 X ) ) ) ) ],
% 1.42/1.81 [ =( X, hAPP( 'c_Suc', 'c_HOL_Ominus__class_Ominus'( X,
% 1.42/1.81 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.42/1.81 'tc_nat' ), X ) ) ) ],
% 1.42/1.81 [ =( hAPP( 'c_Suc', 'c_HOL_Ominus__class_Ominus'( X,
% 1.42/1.81 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ), X ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.42/1.81 'tc_nat' ), X ) ) ) ],
% 1.42/1.81 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.42/1.81 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ), hAPP( hAPP(
% 1.42/1.81 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( Y, 'tc_nat' ), T ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Z ) ) ) ],
% 1.42/1.81 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.42/1.81 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.42/1.81 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), hAPP( hAPP(
% 1.42/1.81 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( Z, X ), U ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( Y, X ), T ) ) ) ],
% 1.42/1.81 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP( 'c_lessequals'( Y, X
% 1.42/1.81 ), Z ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ) ) ]
% 1.42/1.81 ,
% 1.42/1.81 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ) ) ],
% 1.42/1.81 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.42/1.81 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ), Y, 'tc_nat' )
% 1.42/1.81 , 'c_Divides_Odiv__class_Omod'( Z, Y, 'tc_nat' ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_lessequals'( Y, X ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ) ) ),
% 1.42/1.81 ~( hBOOL( hAPP( 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.42/1.81 ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( T, X ),
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ]
% 1.42/1.81 ,
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.42/1.81 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.42/1.81 X ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ),
% 1.42/1.81 'c_HOL_Oinverse__class_Odivide'( T, Z, X ) ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), T ) ),
% 1.42/1.81 ~( hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), T )
% 1.42/1.81 ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ),
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ]
% 1.42/1.81 ,
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ), hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.42/1.81 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.42/1.81 X ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.42/1.81 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), Y ) ) ) ],
% 1.42/1.81 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.42/1.81 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.42/1.81 , Y ), Z ), Z, X ), Y ) ],
% 1.42/1.81 [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.42/1.81 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), X, 'tc_nat' ), Y ) ]
% 1.42/1.81 ,
% 1.42/1.81 [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.42/1.81 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), Y, 'tc_nat' ), X ) ]
% 1.42/1.81 ,
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.42/1.81 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.42/1.81 X ), Y ), Z ), T, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.42/1.81 'c_HOL_Oinverse__class_Odivide'( Y, T, X ) ),
% 1.42/1.81 'c_HOL_Oinverse__class_Odivide'( Z, T, X ) ) ) ],
% 1.42/1.81 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 1.42/1.81 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.42/1.81 X ), Y ), Z ), T, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.42/1.81 'c_HOL_Oinverse__class_Odivide'( Y, T, X ) ),
% 1.42/1.81 'c_HOL_Oinverse__class_Odivide'( Z, T, X ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), X ), hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), X ), Z ) ) ),
% 1.42/1.81 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X )
% 1.42/1.81 , X ), Y ) ) ) ],
% 1.42/1.81 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.42/1.81 'c_Divides_Odiv__class_Odiv'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y )
% 1.42/1.81 ],
% 1.42/1.81 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.42/1.81 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.42/1.81 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), hAPP( hAPP(
% 1.42/1.81 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_lessequals'( Z, X ), U ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( Y, X ), T ) ) ) ],
% 1.42/1.81 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.42/1.81 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.42/1.81 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), hAPP( hAPP(
% 1.42/1.81 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( Z, X ), U ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_lessequals'( Y, X ), T ) ) ) ],
% 1.42/1.81 [ ~( =( 'c_Divides_Odiv__class_Omod'( X,
% 1.42/1.81 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit0'(
% 1.42/1.81 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' ), 'tc_nat' ),
% 1.42/1.81 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.42/1.81 'c_Int_OPls' ) ), 'tc_nat' ) ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'(
% 1.42/1.81 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Ominus__class_Ominus'( X,
% 1.42/1.81 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ),
% 1.42/1.81 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.81 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ) ],
% 1.42/1.81 [ ~( =( 'c_Divides_Odiv__class_Omod'( X,
% 1.42/1.81 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit0'(
% 1.42/1.81 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' ), 'tc_nat' ),
% 1.42/1.81 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ),
% 1.42/1.81 'c_Parity_Oeven__odd__class_Oeven'( 'c_Divides_Odiv__class_Odiv'(
% 1.42/1.81 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 1.42/1.81 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.42/1.81 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ]
% 1.42/1.81 ,
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.42/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), 'c_Int_Oiszero'(
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~( =( hAPP(
% 1.42/1.81 'c_HOL_Oinverse__class_Oinverse'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X
% 1.42/1.81 ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 1.42/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( =( hAPP(
% 1.42/1.81 'c_HOL_Oinverse__class_Oinverse'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X
% 1.42/1.81 ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =( Y,
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_Int_Oiszero'( Y, X ) ) ],
% 1.42/1.81 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.42/1.81 'c_Divides_Odiv__class_Omod'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.42/1.81 ) ],
% 1.42/1.81 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.42/1.81 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 1.42/1.81 ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =(
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =( hAPP(
% 1.42/1.81 'c_HOL_Oinverse__class_Oinverse'( X ), hAPP(
% 1.42/1.81 'c_HOL_Oinverse__class_Oinverse'( X ), Y ) ), Y ), =( Y,
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.42/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.42/1.81 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.42/1.81 ,
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP(
% 1.42/1.81 'c_HOL_Oinverse__class_Oinverse'( X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.42/1.81 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 1.42/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP(
% 1.42/1.81 'c_HOL_Oinverse__class_Oinverse'( X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.42/1.81 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~( =( hAPP(
% 1.42/1.81 'c_HOL_Oinverse__class_Oinverse'( X ), Y ), hAPP(
% 1.42/1.81 'c_HOL_Oinverse__class_Oinverse'( X ), Z ) ) ), =( Y, Z ), =( Z,
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.42/1.81 ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oring__1__no__zero__divisors'( X ) ), ~(
% 1.42/1.81 =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ),
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.42/1.81 ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.42/1.81 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.42/1.81 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.42/1.81 ), ~( =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ),
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.42/1.81 ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =(
% 1.42/1.81 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.42/1.81 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.42/1.81 'c_Divides_Odiv__class_Odiv'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.81 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.42/1.81 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.81 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), ~( =( hAPP(
% 1.42/1.81 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.42/1.81 ) ) ],
% 1.42/1.81 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.42/1.81 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.42/1.81 ) ],
% 1.42/1.81 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.42/1.81 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.42/1.81 ) ],
% 1.42/1.81 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.42/1.81 'c_HOL_Ominus__class_Ominus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 1.42/1.81 ) ],
% 1.42/1.81 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.42/1.81 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.42/1.81 ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.42/1.81 X ) ), =( 'c_HOL_Ominus__class_Ominus'( Y, Y, X ),
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.42/1.81 X ) ), ~( =( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) )
% 1.42/1.81 , =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.81 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.42/1.81 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.81 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =( hAPP(
% 1.42/1.81 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.42/1.81 , 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.42/1.81 ,
% 1.42/1.81 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 1.42/1.81 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.42/1.81 ) ), =( Y, Z ) ],
% 1.42/1.81 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 1.42/1.81 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.42/1.81 ) ), =( Y, Z ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.42/1.81 X ) ), ~( =( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, Z ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.42/1.81 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.42/1.81 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.42/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.42/1.81 'c_HOL_Oinverse__class_Odivide'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.42/1.81 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.42/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.42/1.81 'c_HOL_Oinverse__class_Odivide'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.42/1.81 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.81 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 1.42/1.81 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.42/1.81 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.81 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 1.42/1.81 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.42/1.81 Y ) ],
% 1.42/1.81 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 1.42/1.81 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.42/1.81 Y ) ],
% 1.42/1.81 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.42/1.81 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.42/1.81 Y ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.42/1.81 X ) ), =( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.42/1.81 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.42/1.81 Y ) ],
% 1.42/1.81 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.42/1.81 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.42/1.81 Y ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.42/1.81 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.42/1.81 Y ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.42/1.81 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.42/1.81 Y ) ],
% 1.42/1.81 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), ~(
% 1.42/1.81 'class_RealVector_Ometric__space'( Y ) ), 'c_Lim_OLIM'( 'c_COMBB'( Z,
% 1.42/1.81 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), X, Y, X ),
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ), hAPP( Z, T ), X, Y ), ~( 'c_Lim_OLIM'( Z
% 1.42/1.81 , T, hAPP( Z, T ), X, Y ) ) ],
% 1.42/1.81 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), ~(
% 1.42/1.81 'class_RealVector_Ometric__space'( Y ) ), 'c_Lim_OLIM'( Z, T, hAPP( Z, T
% 1.42/1.81 ), X, Y ), ~( 'c_Lim_OLIM'( 'c_COMBB'( Z, hAPP(
% 1.42/1.81 'c_HOL_Oplus__class_Oplus'( X ), T ), X, Y, X ),
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ), hAPP( Z, T ), X, Y ) ) ],
% 1.42/1.81 [ ~( 'class_RealVector_Ometric__space'( X ) ), ~(
% 1.42/1.81 'class_RealVector_Oreal__normed__vector'( Y ) ), 'c_Lim_OLIM'( 'c_COMBB'(
% 1.42/1.81 Z, hAPP( 'c_HOL_Oplus__class_Oplus'( Y ), T ), Y, X, Y ),
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( Y ), U, Y, X ), ~( 'c_Lim_OLIM'( Z, T, U, Y,
% 1.42/1.81 X ) ) ],
% 1.42/1.81 [ ~( 'class_RealVector_Ometric__space'( X ) ), ~(
% 1.42/1.81 'class_RealVector_Oreal__normed__vector'( Y ) ), 'c_Lim_OLIM'( Z, T, U, Y
% 1.42/1.81 , X ), ~( 'c_Lim_OLIM'( 'c_COMBB'( Z, hAPP( 'c_HOL_Oplus__class_Oplus'( Y
% 1.42/1.81 ), T ), Y, X, Y ), 'c_HOL_Ozero__class_Ozero'( Y ), U, Y, X ) ) ],
% 1.42/1.81 [ ~( 'class_RealVector_Oreal__normed__div__algebra'( X ) ), ~(
% 1.42/1.81 'class_RealVector_Ometric__space'( Y ) ), 'c_Lim_OLIM'( 'c_COMBB'(
% 1.42/1.81 'c_HOL_Oinverse__class_Oinverse'( X ), Z, X, X, Y ), T, hAPP(
% 1.42/1.81 'c_HOL_Oinverse__class_Oinverse'( X ), U ), Y, X ), =( U,
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_Lim_OLIM'( Z, T, U, Y, X ) ) ]
% 1.42/1.81 ,
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 1.42/1.81 'c_HOL_Ominus__class_Ominus'( hAPP( 'c_HOL_Oinverse__class_Oinverse'( X )
% 1.42/1.81 , Y ), hAPP( 'c_HOL_Oinverse__class_Oinverse'( X ), Z ), X ), hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_HOL_Oinverse__class_Oinverse'(
% 1.42/1.81 X ), Y ) ), 'c_HOL_Ominus__class_Ominus'( Z, Y, X ) ) ), hAPP(
% 1.42/1.81 'c_HOL_Oinverse__class_Oinverse'( X ), Z ) ) ), =( Z,
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.42/1.81 ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.42/1.81 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.42/1.81 X ), Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U
% 1.42/1.81 ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ), ~( hBOOL(
% 1.42/1.81 hAPP( 'c_lessequals'( Z, X ), U ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( Y, X ), T ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.42/1.81 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.42/1.81 X ), Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U
% 1.42/1.81 ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.42/1.81 X ), Z ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( Z, X ), U ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_lessequals'( Y, X ), T ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X
% 1.42/1.81 ), 'c_HOL_Oinverse__class_Odivide'( Y, T, X ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP(
% 1.42/1.81 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.42/1.81 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ), T ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X
% 1.42/1.81 ), 'c_HOL_Oinverse__class_Odivide'( Y, T, X ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP(
% 1.42/1.81 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) )
% 1.42/1.81 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( T, X ), Z ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.42/1.81 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.42/1.81 ) ), 'c_HOL_Oinverse__class_Odivide'( T, U, X ) ),
% 1.42/1.81 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.42/1.81 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), U ) ), hAPP(
% 1.42/1.81 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ), hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ), X ) ), =( U,
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.42/1.81 ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Oinverse__class_Odivide'( Z, T
% 1.42/1.81 , X ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ),
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( T, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.42/1.81 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), Z ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Oinverse__class_Odivide'( Z, T
% 1.42/1.81 , X ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ),
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( Z, X ), hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ), hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ]
% 1.42/1.81 ,
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Oinverse__class_Odivide'( Z, T
% 1.42/1.81 , X ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( T, X ),
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( Z, X ), hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ), hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ]
% 1.42/1.81 ,
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( Y, X ), hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( T, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.42/1.81 , hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X )
% 1.42/1.81 , X ), T ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ),
% 1.42/1.81 'c_HOL_Oinverse__class_Odivide'( Y, T, X ) ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X
% 1.42/1.81 ), T ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ), hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.42/1.81 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X
% 1.42/1.81 ), T ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.42/1.81 , T ), Z ), X ), Y ) ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X
% 1.42/1.81 ), T ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ),
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.42/1.81 , T ), Z ), X ), Y ) ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.42/1.81 , Y ), Z ), X ), T ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X )
% 1.42/1.81 , 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ),
% 1.42/1.81 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.81 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), Y ) ) ) ],
% 1.42/1.81 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.42/1.81 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.42/1.81 , Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), Z, X )
% 1.42/1.81 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ),
% 1.42/1.81 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ) ), =( Z,
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.81 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.42/1.81 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.42/1.81 , Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), T, X )
% 1.42/1.81 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ),
% 1.42/1.81 'c_Divides_Odiv__class_Odiv'( Y, T, X ) ) ), =( T,
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.42/1.81 X ), Y ) ), ~( hBOOL( hAPP( 'c_lessequals'( Z, X ),
% 1.42/1.81 'c_HOL_Oone__class_Oone'( X ) ) ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.42/1.81 X ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ),
% 1.42/1.81 'c_HOL_Oone__class_Oone'( X ) ) ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.42/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.42/1.81 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Oinverse__class_Odivide'( Z
% 1.42/1.81 , T, X ) ), 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.42/1.81 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), T, X ) ), =( T,
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.42/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.42/1.81 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.42/1.81 ) ), T ), 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.42/1.81 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ), Z, X ) ), =( Z,
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =( hAPP( hAPP(
% 1.42/1.81 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Oinverse__class_Oinverse'(
% 1.42/1.81 X ), Y ) ), hAPP( 'c_HOL_Oinverse__class_Oinverse'( X ), Z ) ), hAPP(
% 1.42/1.81 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_HOL_Oinverse__class_Oinverse'(
% 1.42/1.81 X ), Y ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) ),
% 1.42/1.81 hAPP( 'c_HOL_Oinverse__class_Oinverse'( X ), Z ) ) ), =( Z,
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.42/1.81 ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.42/1.81 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Oinverse__class_Oinverse'(
% 1.42/1.81 X ), Y ) ), hAPP( 'c_HOL_Oinverse__class_Oinverse'( X ), Z ) ), hAPP(
% 1.42/1.81 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.42/1.81 X ), Y ), Z ) ), hAPP( 'c_HOL_Oinverse__class_Oinverse'( X ), Y ) ) ),
% 1.42/1.81 hAPP( 'c_HOL_Oinverse__class_Oinverse'( X ), Z ) ) ), =( Z,
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.42/1.81 ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Oinverse__class_Odivide'( Z, T
% 1.42/1.81 , X ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ),
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( Z, X ), hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.42/1.81 , Y ), T ), X ), Z ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Oinverse__class_Odivide'( Z, T
% 1.42/1.81 , X ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( T, X ),
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( Z, X ), hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.42/1.81 , Y ), T ), X ), Z ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X
% 1.42/1.81 ), T ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.42/1.81 , T ), Z ), X ), Y ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X
% 1.42/1.81 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X
% 1.42/1.81 ), T ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ),
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.42/1.81 , T ), Z ), X ), Y ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X
% 1.42/1.81 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =( hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP(
% 1.42/1.81 'c_HOL_Oinverse__class_Oinverse'( X ), Y ) ), 'c_HOL_Oone__class_Oone'( X
% 1.42/1.81 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =( hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_HOL_Oinverse__class_Oinverse'(
% 1.42/1.81 X ), Y ) ), Y ), 'c_HOL_Oone__class_Oone'( X ) ), =( Y,
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_HOL_Oinverse__class_Oinverse'(
% 1.42/1.81 X ), Y ) ), Y ), 'c_HOL_Oone__class_Oone'( X ) ), =( Y,
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.42/1.81 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X )
% 1.42/1.81 , 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ),
% 1.42/1.81 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( X ), Y ), U ), hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ), hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ), X ) ), =( U,
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.42/1.81 ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( hBOOL(
% 1.42/1.81 hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.42/1.81 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ), hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.42/1.81 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.42/1.81 X ), Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U
% 1.42/1.81 ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.42/1.81 X ), Z ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'(
% 1.42/1.81 X ), X ), Y ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ), U )
% 1.42/1.81 ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), T ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Oinverse__class_Odivide'( Z, T
% 1.42/1.81 , X ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) )
% 1.42/1.81 ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X
% 1.42/1.81 ), T ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) )
% 1.42/1.81 ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Oinverse__class_Odivide'( Z, T
% 1.42/1.81 , X ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.42/1.81 , Y ), T ), X ), Z ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.42/1.81 , Y ), Z ), X ), T ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Oinverse__class_Odivide'( T, Z
% 1.42/1.81 , X ) ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X
% 1.42/1.81 ), T ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( Y, X ), hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ) ) ],
% 1.42/1.81 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_Int_Oint' ), Y ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( X, 'tc_Int_Oint' ), Y ) ) ) ],
% 1.42/1.81 [ ~( 'class_Orderings_Opreorder'( X ) ), hBOOL( hAPP( 'c_lessequals'( Y
% 1.42/1.81 , X ), Z ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ) )
% 1.42/1.81 ],
% 1.42/1.81 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ) ) ],
% 1.42/1.81 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =(
% 1.42/1.81 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), Z ), ~( hBOOL(
% 1.42/1.81 hAPP( 'c_lessequals'( Y, X ), Z ) ) ) ],
% 1.42/1.81 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), ~( =(
% 1.42/1.81 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), Z ) ), hBOOL(
% 1.42/1.81 hAPP( 'c_lessequals'( Y, X ), Z ) ) ],
% 1.42/1.81 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =(
% 1.42/1.81 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), Y ), ~( hBOOL(
% 1.42/1.81 hAPP( 'c_lessequals'( Z, X ), Y ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.42/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP(
% 1.42/1.81 'c_HOL_Oinverse__class_Oinverse'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.42/1.81 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), X ), hAPP(
% 1.42/1.81 'c_HOL_Oinverse__class_Oinverse'( X ), Y ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Oone__class_Oone'( X ) ) ) ),
% 1.42/1.81 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X
% 1.42/1.81 ), X ), Y ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =( hAPP(
% 1.42/1.81 'c_HOL_Oinverse__class_Oinverse'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.42/1.81 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.42/1.81 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL(
% 1.42/1.81 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ) ]
% 1.42/1.81 ,
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.42/1.81 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_lessequals'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL(
% 1.42/1.81 hAPP( 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ]
% 1.42/1.81 ,
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ),
% 1.42/1.81 'c_HOL_Oinverse__class_Odivide'( T, U, X ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_lessequals'( U, X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), U ) ) )
% 1.42/1.81 , ~( hBOOL( hAPP( 'c_lessequals'( Y, X ), T ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), X ), hAPP( hAPP(
% 1.42/1.81 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ) ) ), ~(
% 1.42/1.81 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), X
% 1.42/1.81 ), Y ) ) ) ],
% 1.42/1.81 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), X ),
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ) ) ],
% 1.42/1.81 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), X ),
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.42/1.81 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.42/1.81 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.42/1.81 'c_SetInterval_Oord__class_OlessThan'( Y, X ),
% 1.42/1.81 'c_SetInterval_Oord__class_OatLeastLessThan'( Y, Z, X ), 'tc_fun'( X,
% 1.42/1.81 'tc_bool' ) ), 'c_SetInterval_Oord__class_OlessThan'( Z, X ) ), ~( hBOOL(
% 1.42/1.81 hAPP( 'c_lessequals'( Y, X ), Z ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.42/1.81 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), hBOOL( hAPP(
% 1.42/1.81 'c_lessequals'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL(
% 1.42/1.81 hAPP( 'c_lessequals'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Z
% 1.42/1.81 ), Y ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.42/1.81 'c_HOL_Oone__class_Oone'( X ) ) ) ],
% 1.42/1.81 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.42/1.81 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ), Y ), X ), ~( hBOOL(
% 1.42/1.81 hAPP( 'c_lessequals'( Y, 'tc_nat' ), X ) ) ) ],
% 1.42/1.81 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.42/1.81 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ) ), Y ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_lessequals'( X, 'tc_nat' ), Y ) ) ) ],
% 1.42/1.81 [ ~( hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ) ), =( Y, hAPP(
% 1.42/1.81 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.42/1.81 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ) ), X ) ) ],
% 1.42/1.81 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( =(
% 1.42/1.81 'c_SetInterval_Oord__class_OatLeast'( Y, X ),
% 1.42/1.81 'c_SetInterval_Oord__class_OatLeast'( Z, X ) ) ), =( Y, Z ) ],
% 1.42/1.81 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.42/1.81 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ), Z ),
% 1.42/1.81 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.42/1.81 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y
% 1.42/1.81 , 'tc_nat' ), X ) ) ) ],
% 1.42/1.81 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.42/1.81 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ),
% 1.42/1.81 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.42/1.81 'tc_nat' ), X ), Y ), Z, 'tc_nat' ) ), ~( hBOOL( hAPP( 'c_lessequals'( Z
% 1.42/1.81 , 'tc_nat' ), Y ) ) ) ],
% 1.42/1.81 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_Divides_Odiv__class_Odiv'(
% 1.42/1.81 X, Y, 'tc_nat' ), 'tc_nat' ), X ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.42/1.81 'tc_nat' ), X ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.81 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ), Y ) ) ) ],
% 1.42/1.81 [ ~( 'class_Orderings_Oorder'( X ) ), ~( =(
% 1.42/1.81 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ),
% 1.42/1.81 'c_SetInterval_Oord__class_OatLeastAtMost'( Y, Z, X ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_lessequals'( Y, X ), Z ) ) ) ],
% 1.42/1.81 [ ~( 'class_Orderings_Oorder'( X ) ), =( 'c_Orderings_Obot__class_Obot'(
% 1.42/1.81 'tc_fun'( X, 'tc_bool' ) ), 'c_SetInterval_Oord__class_OatLeastAtMost'( Y
% 1.42/1.81 , Z, X ) ), hBOOL( hAPP( 'c_lessequals'( Y, X ), Z ) ) ],
% 1.42/1.81 [ ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', 'tc_Int_Oint'
% 1.42/1.81 ), 'c_Int_OMin' ) ) ) ],
% 1.42/1.81 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP(
% 1.42/1.81 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.42/1.81 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), T ), hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), U ) ) ) ), =(
% 1.42/1.81 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ),
% 1.42/1.81 'c_Divides_Odiv__class_Omod'( T, Y, 'tc_nat' ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =( hAPP( hAPP(
% 1.42/1.81 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.42/1.81 'c_Power_Opower__class_Opower'( X ), Y ), T ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), X ), Y ) ) ),
% 1.42/1.81 =( Z, T ) ],
% 1.42/1.81 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'class_Int_Onumber'( X ) ),
% 1.42/1.81 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.81 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.42/1.81 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_lessequals'( 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ),
% 1.42/1.81 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ) ) ],
% 1.42/1.81 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'class_Int_Onumber'( X ) ),
% 1.42/1.81 hBOOL( hAPP( 'c_lessequals'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.42/1.81 X ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ), hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ), X
% 1.42/1.81 ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP(
% 1.42/1.81 hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.42/1.81 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) )
% 1.42/1.81 , 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'(
% 1.42/1.81 Z, 'tc_nat' ), 'tc_nat' ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.42/1.81 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP(
% 1.42/1.81 'c_HOL_Oinverse__class_Oinverse'( X ), Z ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.42/1.81 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.42/1.81 Z, X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP(
% 1.42/1.81 'c_HOL_Oinverse__class_Oinverse'( X ), Z ) ) ) ],
% 1.42/1.81 [ hBOOL( hAPP( 'c_Set_Oinsert'( X, Y, Z ), X ) ) ],
% 1.42/1.81 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'(
% 1.42/1.81 X, Y, 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y,
% 1.42/1.81 'tc_nat' ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' )
% 1.42/1.81 , Z ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, 'tc_nat' ), Z ) ) ), ~(
% 1.42/1.81 hBOOL( hAPP( 'c_lessequals'( Y, 'tc_nat' ), X ) ) ) ],
% 1.42/1.81 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ), ~( hBOOL(
% 1.42/1.81 hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Z,
% 1.42/1.81 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) )
% 1.42/1.81 ) ), ~( hBOOL( hAPP( 'c_lessequals'( Z, 'tc_nat' ), Y ) ) ), ~( hBOOL(
% 1.42/1.81 hAPP( 'c_lessequals'( Z, 'tc_nat' ), X ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ),
% 1.42/1.81 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X
% 1.42/1.81 ), X ), 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ),
% 1.42/1.81 Y, X ) ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.42/1.81 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) )
% 1.42/1.81 ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.42/1.81 X ), X ), Y ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( 'class_Int_Onumber'( X )
% 1.42/1.81 ), =( hAPP( 'c_HOL_Oinverse__class_Oinverse'( X ),
% 1.42/1.81 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 1.42/1.81 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ),
% 1.42/1.81 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.42/1.81 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL(
% 1.42/1.81 hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y
% 1.42/1.81 ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.42/1.81 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X
% 1.42/1.81 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.42/1.81 Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( Y, 'tc_nat' ), Z ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.42/1.81 ), T ), Y ), X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), T ),
% 1.42/1.81 Z ) ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.81 'c_HOL_Oone__class_Oone'( X ), X ), T ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.42/1.81 ), Y ), Z ), X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.42/1.81 T ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.81 'c_HOL_Oone__class_Oone'( X ), X ), Y ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( Z, 'tc_nat' ), T ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( Y, 'tc_nat' ), Z ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.42/1.81 ), T ), Y ), X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), T ),
% 1.42/1.81 Z ) ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.81 'c_HOL_Oone__class_Oone'( X ), X ), T ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.42/1.81 ), Y ), Z ), X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.42/1.81 T ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, 'tc_nat' ), T ) )
% 1.42/1.81 ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'(
% 1.42/1.81 X ), X ), Y ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.42/1.81 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_lessequals'(
% 1.42/1.81 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.42/1.81 'c_HOL_Oinverse__class_Odivide'( Z, T, X ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_lessequals'( 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( T, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.42/1.81 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.42/1.81 X ), T ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.42/1.81 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_lessequals'(
% 1.42/1.81 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.42/1.81 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.42/1.81 X ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.42/1.81 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.42/1.81 'c_HOL_Oinverse__class_Odivide'( T, Z, X ) ) ) ) ],
% 1.42/1.81 [ ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.42/1.81 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ), Y ) ) ) ]
% 1.42/1.81 ,
% 1.42/1.81 [ ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.42/1.81 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ), X ) ) ) ]
% 1.42/1.81 ,
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.42/1.81 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.42/1.81 Z, X ) ), T ), 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.42/1.81 'c_Power_Opower__class_Opower'( X ), Y ), T ), hAPP( hAPP(
% 1.42/1.81 'c_Power_Opower__class_Opower'( X ), Z ), T ), X ) ), =( Z,
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.81 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ),
% 1.42/1.81 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.42/1.81 'tc_nat' ), X ), Z ), 'tc_nat' ), Y ) ) ) ],
% 1.42/1.81 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.42/1.81 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ), Z ) ), ~(
% 1.42/1.81 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ),
% 1.42/1.81 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ) ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.42/1.81 X ), T ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ),
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ),
% 1.42/1.81 ~( hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X
% 1.42/1.81 ), X ), Y ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), T ) ),
% 1.42/1.81 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ),
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.42/1.81 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ), Y ) ) ),
% 1.42/1.81 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.42/1.81 X ), Z ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_lessequals'( Y, X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z
% 1.42/1.81 ), T ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( T, X ),
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ),
% 1.42/1.81 ~( hBOOL( hAPP( 'c_lessequals'( Z, X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.42/1.81 Y, T, X ) ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_lessequals'( Y, X ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ) ) ),
% 1.42/1.81 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( T, X ),
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Z
% 1.42/1.81 , X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ),
% 1.42/1.81 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.42/1.81 X ), T ) ) ],
% 1.42/1.81 [ ~( 'c_Ring__and__Field_Oordered__idom'( X, Y, Z, T, U, W, V0, hAPP( V1
% 1.42/1.81 , V2 ), V3, V1, V4 ) ), hBOOL( hAPP( hAPP( W, Z ), V2 ) ) ],
% 1.42/1.81 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.42/1.81 ), ~( hBOOL( hAPP( hAPP( X, W ), hAPP( hAPP( V0, W ), Z ) ) ) ), ~(
% 1.42/1.81 'c_Ring__and__Field_Oordered__idom'( V1, V2, U, V3, X, T, V4, Y, V0, V5,
% 1.42/1.81 V6 ) ) ],
% 1.42/1.81 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.42/1.81 ), ~( hBOOL( hAPP( hAPP( X, U ), hAPP( hAPP( V0, U ), Y ) ) ) ), ~(
% 1.42/1.81 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, X, T, V4, Z, V0, V5,
% 1.42/1.81 V6 ) ) ],
% 1.42/1.81 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, Y ), T ) ) ), hBOOL( hAPP(
% 1.42/1.81 hAPP( U, Y ), W ) ), hBOOL( hAPP( hAPP( U, W ), Y ) ), ~(
% 1.42/1.81 'c_Ring__and__Field_Oordered__idom'( V0, V1, W, V2, X, U, V3, V4, Z, V5,
% 1.42/1.81 V6 ) ) ],
% 1.42/1.81 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, Y ), T ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 hAPP( X, T ), U ) ) ), ~( hBOOL( hAPP( hAPP( X, U ), T ) ) ), ~(
% 1.42/1.81 'c_Ring__and__Field_Oordered__idom'( W, V0, V1, V2, X, V3, V4, U, Z, V5,
% 1.42/1.81 V6 ) ) ],
% 1.42/1.81 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.42/1.81 ), ~( hBOOL( hAPP( hAPP( X, hAPP( hAPP( V0, W ), Y ) ), W ) ) ), ~(
% 1.42/1.81 'c_Ring__and__Field_Oordered__idom'( V1, V2, U, V3, X, T, V4, Z, V0, V5,
% 1.42/1.81 V6 ) ) ],
% 1.42/1.81 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.42/1.81 ), ~( hBOOL( hAPP( hAPP( X, hAPP( hAPP( V0, U ), Z ) ), U ) ) ), ~(
% 1.42/1.81 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, X, T, V4, Y, V0, V5,
% 1.42/1.81 V6 ) ) ],
% 1.42/1.81 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), Z ) ), hBOOL( hAPP(
% 1.42/1.81 hAPP( U, Z ), W ) ), hBOOL( hAPP( hAPP( U, W ), Z ) ), ~(
% 1.42/1.81 'c_Ring__and__Field_Oordered__idom'( V0, V1, W, V2, X, U, V3, V4, Y, V5,
% 1.42/1.81 V6 ) ) ],
% 1.42/1.81 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), Z ) ), ~( hBOOL( hAPP(
% 1.42/1.81 hAPP( X, U ), T ) ) ), ~( hBOOL( hAPP( hAPP( X, T ), U ) ) ), ~(
% 1.42/1.81 'c_Ring__and__Field_Oordered__idom'( W, V0, V1, V2, X, V3, V4, U, Y, V5,
% 1.42/1.81 V6 ) ) ],
% 1.42/1.81 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.42/1.81 ), ~( hBOOL( hAPP( hAPP( X, W ), hAPP( hAPP( V0, Z ), W ) ) ) ), ~(
% 1.42/1.81 'c_Ring__and__Field_Oordered__idom'( V1, V2, U, V3, X, T, V4, Y, V0, V5,
% 1.42/1.81 V6 ) ) ],
% 1.42/1.81 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.42/1.81 ), ~( hBOOL( hAPP( hAPP( X, U ), hAPP( hAPP( V0, Y ), U ) ) ) ), ~(
% 1.42/1.81 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, X, T, V4, Z, V0, V5,
% 1.42/1.81 V6 ) ) ],
% 1.42/1.81 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), Y ) ) ), hBOOL( hAPP(
% 1.42/1.81 hAPP( U, Y ), W ) ), hBOOL( hAPP( hAPP( U, W ), Y ) ), ~(
% 1.42/1.81 'c_Ring__and__Field_Oordered__idom'( V0, V1, W, V2, X, U, V3, V4, Z, V5,
% 1.42/1.81 V6 ) ) ],
% 1.42/1.81 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), Y ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 hAPP( X, T ), U ) ) ), ~( hBOOL( hAPP( hAPP( X, U ), T ) ) ), ~(
% 1.42/1.81 'c_Ring__and__Field_Oordered__idom'( W, V0, V1, V2, X, V3, V4, U, Z, V5,
% 1.42/1.81 V6 ) ) ],
% 1.42/1.81 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.42/1.81 ), ~( hBOOL( hAPP( hAPP( X, hAPP( hAPP( V0, Y ), W ) ), W ) ) ), ~(
% 1.42/1.81 'c_Ring__and__Field_Oordered__idom'( V1, V2, U, V3, X, T, V4, Z, V0, V5,
% 1.42/1.81 V6 ) ) ],
% 1.42/1.81 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.42/1.81 ), ~( hBOOL( hAPP( hAPP( X, hAPP( hAPP( V0, Z ), U ) ), U ) ) ), ~(
% 1.42/1.81 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, X, T, V4, Y, V0, V5,
% 1.42/1.81 V6 ) ) ],
% 1.42/1.81 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), T ) ), hBOOL( hAPP(
% 1.42/1.81 hAPP( U, T ), W ) ), hBOOL( hAPP( hAPP( U, W ), T ) ), ~(
% 1.42/1.81 'c_Ring__and__Field_Oordered__idom'( V0, V1, W, V2, X, U, V3, V4, Y, V5,
% 1.42/1.81 V6 ) ) ],
% 1.42/1.81 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), T ) ), ~( hBOOL( hAPP(
% 1.42/1.81 hAPP( X, U ), Z ) ) ), ~( hBOOL( hAPP( hAPP( X, Z ), U ) ) ), ~(
% 1.42/1.81 'c_Ring__and__Field_Oordered__idom'( W, V0, V1, V2, X, V3, V4, U, Y, V5,
% 1.42/1.81 V6 ) ) ],
% 1.42/1.81 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.42/1.81 ), ~( hBOOL( hAPP( hAPP( X, W ), hAPP( hAPP( V0, W ), Z ) ) ) ), ~(
% 1.42/1.81 'c_Ring__and__Field_Oordered__idom'( V1, V2, U, V3, T, X, V4, Y, V0, V5,
% 1.42/1.81 V6 ) ) ],
% 1.42/1.81 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.42/1.81 ), ~( hBOOL( hAPP( hAPP( X, U ), hAPP( hAPP( V0, U ), Y ) ) ) ), ~(
% 1.42/1.81 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, T, X, V4, Z, V0, V5,
% 1.42/1.81 V6 ) ) ],
% 1.42/1.81 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, Y ), T ) ) ), hBOOL( hAPP(
% 1.42/1.81 hAPP( U, Y ), W ) ), hBOOL( hAPP( hAPP( U, W ), Y ) ), ~(
% 1.42/1.81 'c_Ring__and__Field_Oordered__idom'( V0, V1, W, V2, U, X, V3, V4, Z, V5,
% 1.42/1.81 V6 ) ) ],
% 1.42/1.81 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, Y ), T ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 hAPP( X, T ), U ) ) ), ~( hBOOL( hAPP( hAPP( X, U ), T ) ) ), ~(
% 1.42/1.81 'c_Ring__and__Field_Oordered__idom'( W, V0, V1, V2, V3, X, V4, U, Z, V5,
% 1.42/1.81 V6 ) ) ],
% 1.42/1.81 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.42/1.81 ), ~( hBOOL( hAPP( hAPP( X, hAPP( hAPP( V0, W ), Y ) ), W ) ) ), ~(
% 1.42/1.81 'c_Ring__and__Field_Oordered__idom'( V1, V2, U, V3, T, X, V4, Z, V0, V5,
% 1.42/1.81 V6 ) ) ],
% 1.42/1.81 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.42/1.81 ), ~( hBOOL( hAPP( hAPP( X, hAPP( hAPP( V0, U ), Z ) ), U ) ) ), ~(
% 1.42/1.81 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, T, X, V4, Y, V0, V5,
% 1.42/1.81 V6 ) ) ],
% 1.42/1.81 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), Z ) ), hBOOL( hAPP(
% 1.42/1.81 hAPP( U, Z ), W ) ), hBOOL( hAPP( hAPP( U, W ), Z ) ), ~(
% 1.42/1.81 'c_Ring__and__Field_Oordered__idom'( V0, V1, W, V2, U, X, V3, V4, Y, V5,
% 1.42/1.81 V6 ) ) ],
% 1.42/1.81 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), Z ) ), ~( hBOOL( hAPP(
% 1.42/1.81 hAPP( X, U ), T ) ) ), ~( hBOOL( hAPP( hAPP( X, T ), U ) ) ), ~(
% 1.42/1.81 'c_Ring__and__Field_Oordered__idom'( W, V0, V1, V2, V3, X, V4, U, Y, V5,
% 1.42/1.81 V6 ) ) ],
% 1.42/1.81 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.42/1.81 ), ~( hBOOL( hAPP( hAPP( X, W ), hAPP( hAPP( V0, Z ), W ) ) ) ), ~(
% 1.42/1.81 'c_Ring__and__Field_Oordered__idom'( V1, V2, U, V3, T, X, V4, Y, V0, V5,
% 1.42/1.81 V6 ) ) ],
% 1.42/1.81 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.42/1.81 ), ~( hBOOL( hAPP( hAPP( X, U ), hAPP( hAPP( V0, Y ), U ) ) ) ), ~(
% 1.42/1.81 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, T, X, V4, Z, V0, V5,
% 1.42/1.81 V6 ) ) ],
% 1.42/1.81 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), Y ) ) ), hBOOL( hAPP(
% 1.42/1.81 hAPP( U, Y ), W ) ), hBOOL( hAPP( hAPP( U, W ), Y ) ), ~(
% 1.42/1.81 'c_Ring__and__Field_Oordered__idom'( V0, V1, W, V2, U, X, V3, V4, Z, V5,
% 1.42/1.81 V6 ) ) ],
% 1.42/1.81 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), Y ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 hAPP( X, T ), U ) ) ), ~( hBOOL( hAPP( hAPP( X, U ), T ) ) ), ~(
% 1.42/1.81 'c_Ring__and__Field_Oordered__idom'( W, V0, V1, V2, V3, X, V4, U, Z, V5,
% 1.42/1.81 V6 ) ) ],
% 1.42/1.81 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.42/1.81 ), ~( hBOOL( hAPP( hAPP( X, hAPP( hAPP( V0, Y ), W ) ), W ) ) ), ~(
% 1.42/1.81 'c_Ring__and__Field_Oordered__idom'( V1, V2, U, V3, T, X, V4, Z, V0, V5,
% 1.42/1.81 V6 ) ) ],
% 1.42/1.81 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.42/1.81 ), ~( hBOOL( hAPP( hAPP( X, hAPP( hAPP( V0, Z ), U ) ), U ) ) ), ~(
% 1.42/1.81 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, T, X, V4, Y, V0, V5,
% 1.42/1.81 V6 ) ) ],
% 1.42/1.81 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), T ) ), hBOOL( hAPP(
% 1.42/1.81 hAPP( U, T ), W ) ), hBOOL( hAPP( hAPP( U, W ), T ) ), ~(
% 1.42/1.81 'c_Ring__and__Field_Oordered__idom'( V0, V1, W, V2, U, X, V3, V4, Y, V5,
% 1.42/1.81 V6 ) ) ],
% 1.42/1.81 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), T ) ), ~( hBOOL( hAPP(
% 1.42/1.81 hAPP( X, U ), Z ) ) ), ~( hBOOL( hAPP( hAPP( X, Z ), U ) ) ), ~(
% 1.42/1.81 'c_Ring__and__Field_Oordered__idom'( W, V0, V1, V2, V3, X, V4, U, Y, V5,
% 1.42/1.81 V6 ) ) ],
% 1.42/1.81 [ ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_Int_OMin', 'tc_Int_Oint'
% 1.42/1.81 ), 'c_Int_OMin' ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X
% 1.42/1.81 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) )
% 1.42/1.81 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ),
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X
% 1.42/1.81 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.42/1.81 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.42/1.81 X ), X ), Y ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X
% 1.42/1.81 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.42/1.81 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.42/1.81 X ), X ), Y ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X
% 1.42/1.81 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) )
% 1.42/1.81 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ),
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.42/1.81 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.42/1.81 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ), hAPP( hAPP(
% 1.42/1.81 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Z ) ) ) ],
% 1.42/1.81 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ), ~( hBOOL(
% 1.42/1.81 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.42/1.81 'tc_nat' ), Z ), X ), 'tc_nat' ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.42/1.81 'tc_nat' ), Z ), Y ) ) ) ) ],
% 1.42/1.81 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.42/1.81 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ), hAPP( hAPP(
% 1.42/1.81 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( Y, 'tc_nat' ), Z ) ) ) ],
% 1.42/1.81 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.42/1.81 , hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T
% 1.42/1.81 ), Y ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ) )
% 1.42/1.81 ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( Y, X ), hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) )
% 1.42/1.81 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.81 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ), Z ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ), hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ), X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.42/1.81 ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( hBOOL(
% 1.42/1.81 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.42/1.81 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP(
% 1.42/1.81 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ), X ),
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.42/1.81 hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ), ~( hBOOL(
% 1.42/1.81 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.42/1.81 X ), Y ), T ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T
% 1.42/1.81 ) ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.42/1.81 hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ), ~( hBOOL(
% 1.42/1.81 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.42/1.81 X ), T ), Y ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z
% 1.42/1.81 ) ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.42/1.81 , Y ), T ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T )
% 1.42/1.81 ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.42/1.81 , T ), Y ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.42/1.81 ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.42/1.81 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.42/1.81 X ), Y ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z )
% 1.42/1.81 ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.42/1.81 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.42/1.81 X ), Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U
% 1.42/1.81 ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.42/1.81 X ), Z ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( Z, X ), U ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( Y, X ), T ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.42/1.81 hAPP( 'c_lessequals'( Y, X ), Z ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) )
% 1.42/1.81 , ~( hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.42/1.81 hAPP( 'c_lessequals'( Y, X ), Z ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) )
% 1.42/1.81 , ~( hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ), hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.42/1.81 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ), ~(
% 1.42/1.81 hBOOL( hAPP( 'c_lessequals'( Z, X ), T ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) )
% 1.42/1.81 ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_lessequals'( Y, X ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ), hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) )
% 1.42/1.81 ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.42/1.81 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ), ~(
% 1.42/1.81 hBOOL( hAPP( 'c_lessequals'( T, X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.42/1.81 ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_lessequals'( Y, X ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ), hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ) ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( T, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.42/1.81 ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( Y,
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ) ), ~( hBOOL( hAPP( 'c_lessequals'( hAPP(
% 1.42/1.81 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ), hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), X ),
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( Y,
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ) ), ~( hBOOL( hAPP( 'c_lessequals'( hAPP(
% 1.42/1.81 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ), X ),
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP(
% 1.42/1.81 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ) ) ), =( Z,
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP(
% 1.42/1.81 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ) ) ), =( Y,
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_lessequals'( Y, X ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ) ) ),
% 1.42/1.81 ~( hBOOL( hAPP( 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.42/1.81 ) ), ~( hBOOL( hAPP( 'c_lessequals'( Z, X ), hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ),
% 1.42/1.81 X ), Z ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), T ) ),
% 1.42/1.81 ~( hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), T )
% 1.42/1.81 ) ), ~( hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ), Y ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_lessequals'( Y, X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T
% 1.42/1.81 ), Z ) ) ) ) ],
% 1.42/1.81 [ ~( 'class_RealVector_Ometric__space'( X ) ), ~(
% 1.42/1.81 'class_RealVector_Ometric__space'( Y ) ), ~(
% 1.42/1.81 'class_RealVector_Ometric__space'( Z ) ), 'c_Lim_OLIM'( 'c_COMBB'( T, U,
% 1.42/1.81 X, Y, Z ), W, hAPP( T, V0 ), Z, Y ), ~( 'c_Lim_OLIM'( U, W, V0, Z, X ) )
% 1.42/1.81 , ~( 'c_Lim_OLIM'( T, V0, hAPP( T, V0 ), X, Y ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.42/1.81 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.81 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.42/1.81 'c_HOL_Oinverse__class_Odivide'( Z, T, X ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ), X
% 1.42/1.81 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( T, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.42/1.81 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.42/1.81 X ), T ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.42/1.81 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.81 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.42/1.81 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.42/1.81 X ), Z ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.81 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.42/1.81 'c_HOL_Oinverse__class_Odivide'( T, Z, X ) ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.42/1.81 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.81 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ),
% 1.42/1.81 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.42/1.81 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ) ), hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.42/1.81 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.42/1.81 X ), Z ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.42/1.81 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.42/1.81 Y, X ) ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ),
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ),
% 1.42/1.81 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.81 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ),
% 1.42/1.81 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.42/1.81 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X
% 1.42/1.81 ), 'c_HOL_Oinverse__class_Odivide'( Z,
% 1.42/1.81 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.42/1.81 , hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.81 'c_Int_Onumber__class_Onumber__of'( T, X ), X ),
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.42/1.81 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.42/1.81 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X
% 1.42/1.81 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ), X
% 1.42/1.81 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.42/1.81 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Oinverse__class_Odivide'( T,
% 1.42/1.81 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.42/1.81 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.81 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.42/1.81 , X ), X ), X ), T ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ), hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ), X
% 1.42/1.81 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.42/1.81 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.42/1.81 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ), hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ), X
% 1.42/1.81 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.42/1.81 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( T,
% 1.42/1.81 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), X ), Y ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.42/1.81 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_lessequals'(
% 1.42/1.81 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ),
% 1.42/1.81 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.42/1.81 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.42/1.81 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ), Y ) ) ), hBOOL(
% 1.42/1.81 hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z
% 1.42/1.81 ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.42/1.81 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_lessequals'(
% 1.42/1.81 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ),
% 1.42/1.81 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.42/1.81 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ) ), hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.42/1.81 ~( hBOOL( hAPP( 'c_lessequals'( Y, X ), hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( T
% 1.42/1.81 , X ) ), Z ) ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.42/1.81 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_lessequals'( Y, X ),
% 1.42/1.81 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.42/1.81 , X ), X ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ),
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Z
% 1.42/1.81 , X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.42/1.81 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ) ) ), hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.42/1.81 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.42/1.81 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_lessequals'(
% 1.42/1.81 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.42/1.81 , X ), X ), X ), T ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.42/1.81 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ), Y ) ) ), hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.42/1.81 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.42/1.81 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_lessequals'( Y, X ), hAPP(
% 1.42/1.81 hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.42/1.81 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( T, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.42/1.81 , hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X )
% 1.42/1.81 , X ), T ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.42/1.81 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ),
% 1.42/1.81 'c_HOL_Oinverse__class_Odivide'( Y, T, X ) ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.42/1.81 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_lessequals'(
% 1.42/1.81 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.42/1.81 'c_HOL_Oinverse__class_Odivide'( Z, T, X ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( T, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.42/1.81 , ~( hBOOL( hAPP( 'c_lessequals'( Z, X ), hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.42/1.81 , X ) ), T ) ) ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.42/1.81 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_lessequals'( Y, X ),
% 1.42/1.81 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.42/1.81 , X ), X ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.81 'c_Int_Onumber__class_Onumber__of'( T, X ), X ),
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Z
% 1.42/1.81 , X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.42/1.81 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ) ) ), hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.42/1.81 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.42/1.81 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_lessequals'( Y, X ), hAPP(
% 1.42/1.81 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.42/1.81 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X ), X
% 1.42/1.81 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.42/1.81 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_lessequals'( Z, X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.42/1.81 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.42/1.81 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_lessequals'(
% 1.42/1.81 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.42/1.81 , X ), X ), X ), T ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.81 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ),
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.42/1.81 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.42/1.81 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ), Y ) ) ), hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.42/1.81 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.42/1.81 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.42/1.81 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ), T ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ), X
% 1.42/1.81 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.42/1.81 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( T,
% 1.42/1.81 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), X ), Y ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.42/1.81 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_lessequals'(
% 1.42/1.81 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ),
% 1.42/1.81 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.42/1.81 , ~( hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( T
% 1.42/1.81 , X ) ), Z ), X ), Y ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ), hAPP(
% 1.42/1.81 hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.42/1.81 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ) ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.42/1.81 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_lessequals'( Y, X ),
% 1.42/1.81 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.42/1.81 , X ), X ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.81 'c_Int_Onumber__class_Onumber__of'( T, X ), X ),
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Z
% 1.42/1.81 , X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.42/1.81 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.42/1.81 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), Z ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.42/1.81 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_lessequals'(
% 1.42/1.81 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.42/1.81 , X ), X ), X ), T ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.81 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ),
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.42/1.81 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.42/1.81 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ), Y ) ) ), ~( hBOOL(
% 1.42/1.81 hAPP( 'c_lessequals'( Y, X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.42/1.81 ), T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.42/1.81 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_lessequals'( Y, X ), hAPP(
% 1.42/1.81 hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.42/1.81 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) )
% 1.42/1.81 , ~( hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( Y, T,
% 1.42/1.81 X ), X ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.42/1.81 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_lessequals'(
% 1.42/1.81 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ),
% 1.42/1.81 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) )
% 1.42/1.81 , ~( hBOOL( hAPP( 'c_lessequals'( Y, X ), hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( T
% 1.42/1.81 , X ) ), Z ) ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.42/1.81 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_lessequals'( Y, X ),
% 1.42/1.81 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.42/1.81 , X ), X ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ),
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X ), X
% 1.42/1.81 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.42/1.81 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.42/1.81 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), Z ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.42/1.81 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_lessequals'(
% 1.42/1.81 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.42/1.81 , X ), X ), X ), T ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ), hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ), X
% 1.42/1.81 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.42/1.81 Y, X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.42/1.81 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.42/1.81 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_lessequals'(
% 1.42/1.81 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.42/1.81 'c_HOL_Oinverse__class_Odivide'( Z, T, X ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_lessequals'( 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Z
% 1.42/1.81 , X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.42/1.81 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ) ) ) ), hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ]
% 1.42/1.81 ,
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.42/1.81 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_lessequals'(
% 1.42/1.81 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.42/1.81 'c_HOL_Oinverse__class_Odivide'( Z, T, X ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_lessequals'( 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( T, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.42/1.81 ~( hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.42/1.81 X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ), Z ) ) ) ]
% 1.42/1.81 ,
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.42/1.81 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.42/1.81 , X ) ), Z ), X ), T ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_lessequals'( 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.42/1.81 'c_HOL_Oinverse__class_Odivide'( T, Z, X ) ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.42/1.81 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_lessequals'(
% 1.42/1.81 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.42/1.81 'c_HOL_Oinverse__class_Odivide'( Z, T, X ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) )
% 1.42/1.81 , ~( hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.42/1.81 , X ) ), T ), X ), Z ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.42/1.81 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_lessequals'(
% 1.42/1.81 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.42/1.81 'c_HOL_Oinverse__class_Odivide'( Z, T, X ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( T, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.42/1.81 , ~( hBOOL( hAPP( 'c_lessequals'( Z, X ), hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.42/1.81 , X ) ), T ) ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.42/1.81 , X ) ), T ), X ), Z ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.42/1.81 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.42/1.81 , X ) ), Z ), X ), T ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X
% 1.42/1.81 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ),
% 1.42/1.81 ~( hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X
% 1.42/1.81 ), X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.42/1.81 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_lessequals'(
% 1.42/1.81 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ),
% 1.42/1.81 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.42/1.81 , ~( hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( T
% 1.42/1.81 , X ) ), Z ), X ), Y ) ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.42/1.81 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_lessequals'( Y, X ),
% 1.42/1.81 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.42/1.81 , X ), X ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.42/1.81 T, X ) ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.42/1.81 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), Z ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.42/1.81 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.42/1.81 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ), T ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.42/1.81 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_lessequals'( Y, X ), 'c_HOL_Oinverse__class_Odivide'( T,
% 1.42/1.81 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.42/1.81 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_lessequals'(
% 1.42/1.81 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.42/1.81 , X ), X ), X ), T ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.42/1.81 Z, X ) ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ), hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.42/1.81 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.42/1.81 'class_Int_Onumber'( X ) ), hBOOL( hAPP( 'c_lessequals'( Y, X ), hAPP(
% 1.42/1.81 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.42/1.81 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.42/1.81 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.42/1.81 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), X ), Z ) ) ) ],
% 1.42/1.81 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.42/1.81 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.42/1.81 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X
% 1.42/1.81 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.42/1.81 'c_Divides_Odiv__class_Omod'( Y, T, X ) ), Z ) ) ],
% 1.42/1.81 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.42/1.81 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.42/1.81 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X
% 1.42/1.81 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.42/1.81 'c_Divides_Odiv__class_Omod'( Z, T, X ) ) ) ],
% 1.42/1.81 [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 1.42/1.81 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.42/1.81 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 1.42/1.81 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 1.42/1.81 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.42/1.81 ), U ), Y ), Z, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( X ), W ), T ), Z, X ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.42/1.81 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 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 ), T ), U ) ), hAPP( hAPP(
% 1.42/1.81 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.42/1.81 X ), Y ), U ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.42/1.81 ) ) ), =( Z, U ), =( Y, T ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.42/1.81 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 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 ), T ), U ) ), hAPP( hAPP(
% 1.42/1.81 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.42/1.81 X ), Y ), U ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.42/1.81 ) ) ), =( Z, U ), =( Y, T ) ],
% 1.42/1.81 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.42/1.81 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), Y ), hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.42/1.81 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.42/1.81 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.42/1.81 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.42/1.81 ), Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X
% 1.42/1.81 ) ), 'c_Divides_Odiv__class_Omod'( Z, T, X ) ), T, X ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.42/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP(
% 1.42/1.81 'c_HOL_Oinverse__class_Oinverse'( 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_Oinverse__class_Oinverse'(
% 1.42/1.81 X ), Y ) ), hAPP( 'c_HOL_Oinverse__class_Oinverse'( X ), Z ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( Z, X ), Y ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.42/1.81 , Z ), T ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.42/1.81 ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( Z, X ), Y ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.42/1.81 , T ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y )
% 1.42/1.81 ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.42/1.81 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.42/1.81 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.42/1.81 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.42/1.81 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Ocomm__semiring'( X ) ), =( hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.42/1.81 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.42/1.81 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.42/1.81 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.42/1.81 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.42/1.81 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.42/1.81 ) ) ],
% 1.42/1.81 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.42/1.81 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.42/1.81 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.42/1.81 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.42/1.81 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.42/1.81 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.42/1.81 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.42/1.81 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.42/1.81 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.42/1.81 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.42/1.81 ) ) ],
% 1.42/1.81 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.42/1.81 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.42/1.81 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.42/1.81 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.42/1.81 ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.42/1.81 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.42/1.81 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.42/1.81 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =( hAPP( hAPP(
% 1.42/1.81 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.42/1.81 'c_Power_Opower__class_Opower'( X ), Y ), T ) ), hAPP( hAPP(
% 1.42/1.81 'c_Power_Opower__class_Opower'( X ), Z ), T ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.42/1.81 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.42/1.81 'c_Power_Opower__class_Opower'( X ), Y ), T ) ), hAPP( hAPP(
% 1.42/1.81 'c_Power_Opower__class_Opower'( X ), Z ), T ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.42/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z
% 1.42/1.81 , X ) ), 'c_HOL_Oinverse__class_Odivide'( T, U, X ) ),
% 1.42/1.81 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.42/1.81 X ), Y ), T ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ), X
% 1.42/1.81 ) ) ],
% 1.42/1.81 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), 'c_Lim_OLIM'(
% 1.42/1.81 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z, hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X, X ) ],
% 1.42/1.81 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.42/1.81 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.42/1.81 ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ), T ), Z, X ),
% 1.42/1.81 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.42/1.81 ), Y ), T ), Z, X ) ) ],
% 1.42/1.81 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.42/1.81 Y ) ],
% 1.42/1.81 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 1.42/1.81 Y ) ],
% 1.42/1.81 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =( hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 1.42/1.81 Y ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 1.42/1.81 Y ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.42/1.81 Y ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 1.42/1.81 Y ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.42/1.81 X ) ), =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 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 ), Y ), T ) ), hAPP( hAPP(
% 1.42/1.81 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.42/1.81 X ), Y ), T ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z )
% 1.42/1.81 ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.42/1.81 X ) ), =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 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 ), Y ), T ) ), hAPP( hAPP(
% 1.42/1.81 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.42/1.81 X ), Y ), T ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z )
% 1.42/1.81 ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), =( hAPP( hAPP(
% 1.42/1.81 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.42/1.81 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ), U ) ), hAPP( hAPP(
% 1.42/1.81 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.42/1.81 X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ), U )
% 1.42/1.81 ) ],
% 1.42/1.81 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ominus__class_Ominus'( Z,
% 1.42/1.81 T, X ) ), 'c_HOL_Ominus__class_Ominus'( 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 ), Y ), T ), X ) ) ],
% 1.42/1.81 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ominus__class_Ominus'( Z,
% 1.42/1.81 T, X ) ), 'c_HOL_Ominus__class_Ominus'( 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 ), Y ), T ), X ) ) ],
% 1.42/1.81 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ominus__class_Ominus'( Y, Z, X
% 1.42/1.81 ) ), T ), 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ) ],
% 1.42/1.81 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ominus__class_Ominus'( Y, Z, X
% 1.42/1.81 ) ), T ), 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ) ],
% 1.42/1.81 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.42/1.81 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.42/1.81 ), Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_Divides_Odiv__class_Omod'( Z,
% 1.42/1.81 T, X ) ), T, X ) ) ],
% 1.42/1.81 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.42/1.81 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.42/1.81 ), Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X
% 1.42/1.81 ) ), Z ), T, X ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.42/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z
% 1.42/1.81 , X ) ), T ), 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), Z, X ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_lessequals'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), 'c_HOL_Ozero__class_Ozero'(
% 1.42/1.81 X ) ) ) ) ],
% 1.42/1.81 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.42/1.81 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.42/1.81 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.42/1.81 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.42/1.81 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.42/1.81 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( X ) )
% 1.42/1.81 ],
% 1.42/1.81 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.42/1.81 , hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.42/1.81 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), hAPP( hAPP(
% 1.42/1.81 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( Z, X ), T ) ) ) ],
% 1.42/1.81 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.42/1.81 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.42/1.81 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), hAPP( hAPP(
% 1.42/1.81 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( Z, X ), T ) ) ) ],
% 1.42/1.81 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.42/1.81 , hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.42/1.81 ), T ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) )
% 1.42/1.81 ],
% 1.42/1.81 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.42/1.81 , hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.42/1.81 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), hAPP( hAPP(
% 1.42/1.81 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( Y, X ), T ) ) ) ],
% 1.42/1.81 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.42/1.81 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.42/1.81 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), hAPP( hAPP(
% 1.42/1.81 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( Y, X ), T ) ) ) ],
% 1.42/1.81 [ ~( 'class_Orderings_Opreorder'( X ) ), hBOOL( hAPP( 'c_lessequals'( Y
% 1.42/1.81 , X ), Y ) ) ],
% 1.42/1.81 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP( 'c_lessequals'( Y, X
% 1.42/1.81 ), Y ) ) ],
% 1.42/1.81 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), X ) ) ],
% 1.42/1.81 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_Int_Oint' ), Y ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_lessequals'( Z, 'tc_Int_Oint' ), Y ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_lessequals'( X, 'tc_Int_Oint' ), Z ) ) ) ],
% 1.42/1.81 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_lessequals'( Z, 'tc_nat' ), Y ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( X
% 1.42/1.81 , 'tc_nat' ), Z ) ) ) ],
% 1.42/1.81 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_Int_Oint' ), X ) ) ],
% 1.42/1.81 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), X ) ) ],
% 1.42/1.81 [ ~( 'class_Orderings_Opreorder'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( T, X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_lessequals'( Y, X ), T ) ) ) ],
% 1.42/1.81 [ ~( 'class_Orderings_Opreorder'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.42/1.81 T, X ), Z ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), T ) )
% 1.42/1.81 ) ],
% 1.42/1.81 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_lessequals'( Y, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z )
% 1.42/1.81 , T ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( U, X ), T ) ) ), ~( hBOOL(
% 1.42/1.81 hAPP( 'c_lessequals'( Y, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.42/1.81 , Z ), U ) ) ) ) ],
% 1.42/1.81 [ ~( 'class_Orderings_Opreorder'( X ) ), hBOOL( hAPP( 'c_lessequals'( Y
% 1.42/1.81 , X ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'( T, X ), Z ) ) ), ~( hBOOL(
% 1.42/1.81 hAPP( 'c_lessequals'( Y, X ), T ) ) ) ],
% 1.42/1.81 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), hBOOL(
% 1.42/1.81 hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z
% 1.42/1.81 ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_lessequals'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL(
% 1.42/1.81 hAPP( 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ]
% 1.42/1.81 ,
% 1.42/1.81 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( Y, X ), T ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_lessequals'( T, X ), Z ) ) ) ],
% 1.42/1.81 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.42/1.81 Y, X ), T ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( T, X ), Z ) )
% 1.42/1.81 ) ],
% 1.42/1.81 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP( 'c_lessequals'( Y, X
% 1.42/1.81 ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ), T ) ) ), ~( hBOOL(
% 1.42/1.81 hAPP( 'c_lessequals'( T, X ), Z ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Oinverse__class_Oinverse'( X ), Y
% 1.42/1.81 ), X ), 'c_HOL_Oone__class_Oone'( X ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), X ), Y ) ) ) ]
% 1.42/1.81 ,
% 1.42/1.81 [ hBOOL( hAPP( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( hBOOL(
% 1.42/1.81 hAPP( 'c_HOL_Oord__class_Oless'( Y, 'tc_nat' ), Z ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 X, 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ) ) ) ],
% 1.42/1.81 [ =( X, Y ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ),
% 1.42/1.81 hAPP( 'c_Suc', Y ) ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, 'tc_nat' ),
% 1.42/1.81 X ) ) ) ],
% 1.42/1.81 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ),
% 1.42/1.81 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( Y, 'tc_nat' ), X ) ), ~(
% 1.42/1.81 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Ominus__class_Ominus'( Y, X,
% 1.42/1.81 'tc_nat' ), 'tc_nat' ) ) ],
% 1.42/1.81 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ),
% 1.42/1.81 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ), ~(
% 1.42/1.81 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.42/1.81 'tc_nat' ), 'tc_nat' ) ) ],
% 1.42/1.81 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 1.42/1.81 'c_HOL_Oplus__class_Oplus'( X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X )
% 1.42/1.81 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.42/1.81 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ), Z ) ), Y ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP(
% 1.42/1.81 hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.42/1.81 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ) ) ), =( Y,
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'(
% 1.42/1.81 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), ~( 'c_Int_Oiszero'(
% 1.42/1.81 'c_HOL_Oone__class_Oone'( X ), X ) ) ],
% 1.42/1.81 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'(
% 1.42/1.81 X, Y, 'tc_nat' ), 'tc_nat' ), X ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.42/1.81 'tc_nat' ), X ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), Y ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.42/1.81 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), hBOOL( hAPP(
% 1.42/1.81 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ), ~( hBOOL(
% 1.42/1.81 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.42/1.81 'c_Power_Opower__class_Opower'( X ), Z ), Y ) ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.42/1.81 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ),
% 1.42/1.81 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ), ~( hBOOL(
% 1.42/1.81 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.42/1.81 '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 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.42/1.81 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ),
% 1.42/1.81 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ),
% 1.42/1.81 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.42/1.81 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ) ],
% 1.42/1.81 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.42/1.81 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ) ), Y ), hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( Y, 'tc_nat' ), X ) ) ],
% 1.42/1.81 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.42/1.81 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.42/1.81 'c_SetInterval_Oord__class_OatLeastLessThan'( Y, Z, X ),
% 1.42/1.81 'c_SetInterval_Oord__class_OatLeast'( Z, X ), 'tc_fun'( X, 'tc_bool' ) )
% 1.42/1.81 , 'c_SetInterval_Oord__class_OatLeast'( Y, X ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_lessequals'( Y, X ), Z ) ) ) ],
% 1.42/1.81 [ ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.42/1.81 'tc_nat' ), 'tc_nat' ), X ) ) ), hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.42/1.81 'c_Divides_Odiv__class_Odiv'( Y, X, 'tc_nat' ) ), 'tc_nat' ), Y ) ) ]
% 1.42/1.81 ,
% 1.42/1.81 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( Z, X ), Y ) ) ) ],
% 1.42/1.81 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( Z, X ), Y ) ) ) ],
% 1.42/1.81 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( 'c_lessequals'( Y
% 1.42/1.81 , X ), Z ) ), hBOOL( hAPP( 'c_lessequals'( Z, X ), Y ) ) ],
% 1.42/1.81 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ), hBOOL( hAPP(
% 1.42/1.81 'c_lessequals'( Y, 'tc_nat' ), X ) ) ],
% 1.42/1.81 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_Int_Oint' ), Y ) ), hBOOL( hAPP(
% 1.42/1.81 'c_lessequals'( Y, 'tc_Int_Oint' ), X ) ) ],
% 1.42/1.81 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( Z, X ), Y ) ) ) ],
% 1.42/1.81 [ ~( 'class_Orderings_Oorder'( X ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( Z, X ), Y ) ) ) ],
% 1.42/1.81 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', 'tc_Int_Oint' )
% 1.42/1.81 , X ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ),
% 1.42/1.81 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ) ) ) ],
% 1.42/1.81 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.42/1.81 'tc_nat' ), 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' )
% 1.42/1.81 ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_Int_OPls',
% 1.42/1.81 'tc_Int_Oint' ), X ) ) ) ],
% 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 [ ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.42/1.81 'tc_nat' ), 'tc_nat' ), X ) ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.81 Y, 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X )
% 1.42/1.81 , hAPP( 'c_Suc', 'c_Divides_Odiv__class_Odiv'( Y, X, 'tc_nat' ) ) ) ) ) ]
% 1.42/1.81 ,
% 1.42/1.81 [ =( hAPP( 'c_Suc', hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' )
% 1.42/1.81 , hAPP( 'c_Suc', 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 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ),
% 1.42/1.81 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.42/1.81 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( Y, hAPP( hAPP( Y, T ), T ) )
% 1.42/1.81 , T ) ), ~( 'c_OrderedGroup_Omonoid__mult'( X, Y, Z ) ) ],
% 1.42/1.81 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.42/1.81 'c_Finite__Set_Osetsum'( Y, 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.42/1.81 Z, hAPP( 'c_Suc', T ), 'tc_nat' ), 'tc_nat', X ),
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( T, 'tc_nat' ), Z ) ) ) ],
% 1.42/1.81 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), 'c_Series_Osums'(
% 1.42/1.81 Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( Y,
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), X ), ~( 'c_Series_Osums'(
% 1.42/1.81 'c_COMBB'( Y, 'c_Suc', 'tc_nat', X, 'tc_nat' ), Z, X ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.42/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.42/1.81 'class_Int_Onumber__ring'( X ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.42/1.81 'c_HOL_Oone__class_Oone'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.42/1.81 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), X ), X ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.42/1.81 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.42/1.81 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.81 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.42/1.81 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.42/1.81 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.81 'c_Int_OPls' ) ), 'tc_nat' ) ) ), X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.42/1.81 ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.42/1.81 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.42/1.81 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.42/1.81 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.81 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.42/1.81 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.42/1.81 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.81 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP(
% 1.42/1.81 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.42/1.81 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.42/1.81 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.81 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.42/1.81 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.42/1.81 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.81 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.42/1.81 ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP(
% 1.42/1.81 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.42/1.81 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.42/1.81 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.81 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.42/1.81 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.42/1.81 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.81 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 1.42/1.81 ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP(
% 1.42/1.81 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.42/1.81 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.42/1.81 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.81 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.42/1.81 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.42/1.81 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.81 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.42/1.81 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.42/1.81 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.81 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.42/1.81 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.42/1.81 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.81 'c_Int_OPls' ) ), 'tc_nat' ) ) ), X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.42/1.81 ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ) ), ~( hBOOL( hAPP( 'c_lessequals'( hAPP(
% 1.42/1.81 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.42/1.81 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.42/1.81 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.81 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.42/1.81 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.42/1.81 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.81 'c_Int_OPls' ) ), 'tc_nat' ) ) ), X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.42/1.81 ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ) ), ~( hBOOL( hAPP( 'c_lessequals'( hAPP(
% 1.42/1.81 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.42/1.81 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.42/1.81 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.81 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.42/1.81 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.42/1.81 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.81 'c_Int_OPls' ) ), 'tc_nat' ) ) ), X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.42/1.81 ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.42/1.81 ), Y ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.81 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), hAPP( hAPP(
% 1.42/1.81 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.42/1.81 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.81 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ) ],
% 1.42/1.81 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.42/1.81 'tc_nat' ), 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( X,
% 1.42/1.81 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.81 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat'
% 1.42/1.81 ), X ) ) ) ],
% 1.42/1.81 [ ~( =( 'c_Divides_Odiv__class_Omod'( X,
% 1.42/1.81 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.81 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oone__class_Oone'(
% 1.42/1.81 'tc_nat' ) ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ),
% 1.42/1.81 'c_Divides_Odiv__class_Omod'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.42/1.81 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) )
% 1.42/1.81 ) ],
% 1.42/1.81 [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.42/1.81 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ),
% 1.42/1.81 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.42/1.81 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X,
% 1.42/1.81 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.81 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.42/1.81 , T ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y )
% 1.42/1.81 ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( T, X ),
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.42/1.81 , Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.42/1.81 ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( T, X ), Z ) ) ), ~(
% 1.42/1.81 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ),
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.42/1.81 , T ), Y ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.42/1.81 ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.42/1.81 , Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.42/1.81 ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ), T ) ) ), ~(
% 1.42/1.81 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.42/1.81 X ), Y ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.42/1.81 , Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.42/1.81 ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ),
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( T, X ), Z ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.42/1.81 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.42/1.81 X ), Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T
% 1.42/1.81 ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( Z, X ), T ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.42/1.81 , Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.42/1.81 ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ), T ) ) ), ~(
% 1.42/1.81 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.42/1.81 X ), Y ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.42/1.81 , Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.42/1.81 ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( T, X ), Z ) ) ), ~(
% 1.42/1.81 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ),
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.42/1.81 , Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.42/1.81 ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ),
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( T, X ), Y ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.42/1.81 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.42/1.81 X ), Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z
% 1.42/1.81 ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( Y, X ), T ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.42/1.81 , Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.42/1.81 ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), T ) ) ), ~(
% 1.42/1.81 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.42/1.81 X ), Z ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.42/1.81 , Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.42/1.81 ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( T, X ), Y ) ) ), ~(
% 1.42/1.81 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ),
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__comm__semiring__strict'( X ) ),
% 1.42/1.81 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) )
% 1.42/1.81 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ), T ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.42/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.42/1.81 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.42/1.81 X ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X
% 1.42/1.81 ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ) ), =( Y,
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.42/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.42/1.81 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.42/1.81 X ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X
% 1.42/1.81 ), 'c_HOL_Oinverse__class_Odivide'( Y, T, X ) ), =( Z,
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP(
% 1.42/1.81 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.42/1.81 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ),
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.42/1.81 hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.42/1.81 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ), ~( hBOOL(
% 1.42/1.81 hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z
% 1.42/1.81 ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.42/1.81 hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 1.42/1.81 ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP(
% 1.42/1.81 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.42/1.81 hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 1.42/1.81 ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP(
% 1.42/1.81 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ) ) ],
% 1.42/1.81 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.42/1.81 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.42/1.81 ), Y ), Z ), Y, X ), Z ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.81 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.42/1.81 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.42/1.81 ), Y ), Z ), Z, X ), Y ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.42/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.42/1.81 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.42/1.81 X ), Y ), Z ), Z, X ), Y ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.42/1.81 ,
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.42/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( Y,
% 1.42/1.81 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.42/1.81 X ), Y ), Z ), Z, X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'(
% 1.42/1.81 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), Y, X ), Z ) ]
% 1.42/1.81 ,
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Oinverse__class_Odivide'(
% 1.42/1.81 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), Y, X ) ) ],
% 1.42/1.81 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.42/1.81 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.42/1.81 ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ), hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z )
% 1.42/1.81 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP(
% 1.42/1.81 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ), ~( hBOOL(
% 1.42/1.81 hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y )
% 1.42/1.81 , Z ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ), hBOOL( hAPP(
% 1.42/1.81 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ), ~( hBOOL(
% 1.42/1.81 hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z )
% 1.42/1.81 , Y ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP(
% 1.42/1.81 'c_lessequals'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL(
% 1.42/1.81 hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y )
% 1.42/1.81 , Z ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ), hBOOL( hAPP(
% 1.42/1.81 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL(
% 1.42/1.81 hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z )
% 1.42/1.81 , Y ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.42/1.81 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.42/1.81 X ), Y ), Z ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) )
% 1.42/1.81 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ),
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.42/1.81 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.42/1.81 X ), Y ), Z ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.42/1.81 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.42/1.81 X ), X ), Y ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.42/1.81 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.42/1.81 X ), Y ), Z ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.42/1.81 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.42/1.81 X ), X ), Z ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Omult__mono1'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.42/1.81 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ), ~(
% 1.42/1.81 hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) )
% 1.42/1.81 ), ~( hBOOL( hAPP( 'c_lessequals'( Z, X ), T ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.42/1.81 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ), ~(
% 1.42/1.81 hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) )
% 1.42/1.81 ), ~( hBOOL( hAPP( 'c_lessequals'( Z, X ), T ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP(
% 1.42/1.81 hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP(
% 1.42/1.81 hAPP( 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.42/1.81 ) ), Y ) ) ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.42/1.81 ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_lessequals'( Y, X ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_lessequals'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.42/1.81 hAPP( 'c_Suc', T ) ), X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.42/1.81 ), Z ), hAPP( 'c_Suc', T ) ) ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =( hAPP( hAPP(
% 1.42/1.81 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ), hAPP(
% 1.42/1.81 hAPP( 'c_Power_Opower__class_Opower'( X ), T ), hAPP( 'c_Suc', Z ) ) ) )
% 1.42/1.81 , =( Y, T ), ~( hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'(
% 1.42/1.81 X ), X ), T ) ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ) ],
% 1.42/1.81 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.42/1.81 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.42/1.81 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), hAPP( 'c_Suc', Z ) ), hAPP(
% 1.42/1.81 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.42/1.81 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.42/1.81 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), Z ) ) ) ],
% 1.42/1.81 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.42/1.81 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.42/1.81 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), hAPP( 'c_Suc', Z ) ), hAPP(
% 1.42/1.81 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.42/1.81 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.42/1.81 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), Z ) ), Y ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ) ), hBOOL( hAPP( 'c_lessequals'( Y, X ),
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( hAPP(
% 1.42/1.81 hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.42/1.81 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ), X ),
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.42/1.81 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.42/1.81 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.42/1.81 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ), X ),
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.42/1.81 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP(
% 1.42/1.81 hAPP( 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.42/1.81 ) ), 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ) ) ) ), ~(
% 1.42/1.81 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.42/1.81 , 'tc_nat' ), 'tc_nat' ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ),
% 1.42/1.81 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.42/1.81 , 'tc_nat' ), 'tc_nat' ), =( 'c_Int_Onumber__class_Onumber__of'( Z,
% 1.42/1.81 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP(
% 1.42/1.81 hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.42/1.81 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ) ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP(
% 1.42/1.81 'c_lessequals'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.42/1.81 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ), X ),
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X
% 1.42/1.81 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ),
% 1.42/1.81 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.42/1.81 , 'tc_nat' ), 'tc_nat' ), =( 'c_Int_Onumber__class_Onumber__of'( Z,
% 1.42/1.81 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.42/1.81 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.42/1.81 , 'tc_nat' ), 'tc_nat' ) ), =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.42/1.81 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hBOOL( hAPP(
% 1.42/1.81 'c_lessequals'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ),
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.42/1.81 , 'tc_nat' ) ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.42/1.81 [ ~( hBOOL( hAPP( X, 'c_Divides_Odiv__class_Omod'( Y,
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ) ), hBOOL( hAPP( X
% 1.42/1.81 , Y ) ) ],
% 1.42/1.81 [ ~( hBOOL( hAPP( X, Y ) ) ), hBOOL( hAPP( X,
% 1.42/1.81 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.42/1.81 'tc_nat' ) ) ) ],
% 1.42/1.81 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ),
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ],
% 1.42/1.81 [ hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.42/1.81 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.42/1.81 [ ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.42/1.81 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ]
% 1.42/1.81 ,
% 1.42/1.81 [ ~( hBOOL( hAPP( X, 'c_Divides_Odiv__class_Odiv'( Y,
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ) ), hBOOL( hAPP( X
% 1.42/1.81 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.42/1.81 [ ~( hBOOL( hAPP( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), hBOOL(
% 1.42/1.81 hAPP( X, 'c_Divides_Odiv__class_Odiv'( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.42/1.81 'tc_nat' ), 'tc_nat' ) ) ) ],
% 1.42/1.81 [ hBOOL( hAPP( X, 'c_Divides_Odiv__class_Odiv'( Y,
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ), ~( hBOOL( hAPP( X
% 1.42/1.81 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.42/1.81 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.42/1.81 'tc_nat' ), 'tc_nat' ), X ) ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.42/1.81 ) ) ],
% 1.42/1.81 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Ozero__class_Ozero'(
% 1.42/1.81 'tc_nat' ), 'tc_nat' ) ],
% 1.42/1.81 [ ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ),
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.42/1.81 [ ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ),
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.42/1.81 [ =( hAPP( hAPP( X, Y ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Z ),
% 1.42/1.81 ~( 'c_Groebner__Basis_Ogb__semiring'( T, U, X, W, Z, V0 ) ) ],
% 1.42/1.81 [ ~( =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( =(
% 1.42/1.81 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ),
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y, X ) ],
% 1.42/1.81 [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_lessequals'( X, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) )
% 1.42/1.81 ) ],
% 1.42/1.81 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.42/1.81 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.42/1.81 [ =( 'c_HOL_Ominus__class_Ominus'( X, X, 'tc_nat' ),
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.42/1.81 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Ozero__class_Ozero'(
% 1.42/1.81 'tc_nat' ), 'tc_nat' ), X ) ],
% 1.42/1.81 [ ~( =( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y )
% 1.42/1.81 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.42/1.81 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), X
% 1.42/1.81 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.42/1.81 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.42/1.81 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.42/1.81 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.42/1.81 ), X, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.42/1.81 [ hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.42/1.81 'tc_nat' ), X ) ) ],
% 1.42/1.81 [ =( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.42/1.81 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ],
% 1.42/1.81 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), X ) ],
% 1.42/1.81 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.42/1.81 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( Y ), X ), hAPP( hAPP(
% 1.42/1.81 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.42/1.81 X ), 'c_HOL_Oone__class_Oone'( X ) ), 'c_Int_Onumber__class_Onumber__of'(
% 1.42/1.81 Y, X ) ) ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ) ],
% 1.42/1.81 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.42/1.81 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.42/1.81 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), hAPP( hAPP(
% 1.42/1.81 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.42/1.81 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.42/1.81 'c_HOL_Oplus__class_Oplus'( X ), X ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.42/1.81 ), Z ) ), T ) ) ],
% 1.42/1.81 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'(
% 1.42/1.81 X, hAPP( 'c_Suc', Y ), 'tc_nat' ), 'tc_nat' ), X ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.42/1.81 'tc_nat' ), X ) ) ) ],
% 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 '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' ) ), ~(
% 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_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_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 [ =( hAPP( 'c_Suc', 'c_HOL_Ominus__class_Ominus'( X, hAPP( 'c_Suc',
% 1.42/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ), X ), ~( hBOOL(
% 1.42/1.81 hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.42/1.81 'tc_nat' ), 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 'class_Int_Onumber__ring'( X ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.81 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ), 'c_HOL_Oone__class_Oone'(
% 1.42/1.81 X ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, 'tc_Int_Oint' ),
% 1.42/1.81 'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.42/1.81 'class_Int_Onumber__ring'( X ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.81 Y, 'tc_Int_Oint' ), 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ), X
% 1.42/1.81 ), 'c_HOL_Oone__class_Oone'( X ) ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.42/1.81 'class_Int_Onumber__ring'( X ) ), hBOOL( hAPP( 'c_lessequals'(
% 1.42/1.81 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ), 'c_HOL_Oone__class_Oone'(
% 1.42/1.81 X ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, 'tc_Int_Oint' ),
% 1.42/1.81 'c_Int_OBit1'( 'c_Int_OPls' ) ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.42/1.81 'class_Int_Onumber__ring'( X ) ), hBOOL( hAPP( 'c_lessequals'( Y,
% 1.42/1.81 'tc_Int_Oint' ), 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_lessequals'( 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.42/1.81 'c_HOL_Oone__class_Oone'( X ) ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.42/1.81 'class_Int_Onumber__ring'( X ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.81 'c_HOL_Oone__class_Oone'( X ), X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.42/1.81 , X ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'(
% 1.42/1.81 'c_Int_OPls' ), 'tc_Int_Oint' ), Y ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.42/1.81 'class_Int_Onumber__ring'( X ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.81 'c_Int_OBit1'( 'c_Int_OPls' ), 'tc_Int_Oint' ), Y ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), X ),
% 1.42/1.81 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.42/1.81 'class_Int_Onumber__ring'( X ) ), hBOOL( hAPP( 'c_lessequals'(
% 1.42/1.81 'c_HOL_Oone__class_Oone'( X ), X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.42/1.81 , X ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( 'c_Int_OBit1'( 'c_Int_OPls' )
% 1.42/1.81 , 'tc_Int_Oint' ), Y ) ) ) ],
% 1.42/1.81 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.42/1.81 'class_Int_Onumber__ring'( X ) ), hBOOL( hAPP( 'c_lessequals'(
% 1.42/1.81 'c_Int_OBit1'( 'c_Int_OPls' ), 'tc_Int_Oint' ), Y ) ), ~( hBOOL( hAPP(
% 1.42/1.81 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), X ),
% 1.42/1.81 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ) ) ],
% 1.42/1.81 [ ~( 'class_Lattices_Obounded__lattice'( X ) ), =(
% 1.42/1.81 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.42/1.81 'c_Orderings_Obot__class_Obot'( X ), X ), Y ) ],
% 1.42/1.81 [ ~( 'class_Lattices_Obounded__lattice'( X ) ), =(
% 1.42/1.81 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.42/1.81 'c_Orderings_Obot__class_Obot'( X ), Y, X ), Y ) ],
% 1.42/1.81 [ ~( 'class_Orderings_Obot'( X ) ), hBOOL( hAPP( 'c_lessequals'(
% 1.42/1.81 'c_Orderings_Obot__class_Obot'( X ), X ), Y ) ) ],
% 1.42/1.81 [ ~( 'class_Lattices_Obounded__lattice'( X ) ), ~( =(
% 1.42/1.81 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ),
% 1.42/1.81 'c_Orderings_Obot__class_Obot'( X ) ) ), =( Z,
% 1.42/1.81 'c_Orderings_Obot__class_Obot'( X ) ) ],
% 1.42/1.81 [ ~( 'class_Lattices_Obounded__lattice'( X ) ), ~( =(
% 1.42/1.81 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ),
% 1.42/1.81 'c_Orderings_Obot__class_Obot'( X ) ) ), =( Y,
% 1.42/1.81 'c_Orderings_Obot__class_Obot'( X ) ) ],
% 1.42/1.81 [ ~( =( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ),
% 1.42/1.82 'c_Set_Oinsert'( Y, Z, X ) ) ) ],
% 1.42/1.82 [ =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y,
% 1.42/1.82 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ),
% 1.42/1.82 'c_Set_Oinsert'( Y, 'c_Set_Oinsert'( X, 'c_Orderings_Obot__class_Obot'(
% 1.42/1.82 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ) ) ],
% 1.42/1.82 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.42/1.82 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ),
% 1.42/1.82 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ), 'tc_fun'( X,
% 1.42/1.82 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) )
% 1.42/1.82 ) ],
% 1.42/1.82 [ ~( =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y,
% 1.42/1.82 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ),
% 1.42/1.82 'c_Set_Oinsert'( T, 'c_Set_Oinsert'( U, 'c_Orderings_Obot__class_Obot'(
% 1.42/1.82 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ) ) ), =( X, U ), =( X, T ) ],
% 1.42/1.82 [ ~( =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y,
% 1.42/1.82 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ),
% 1.42/1.82 'c_Set_Oinsert'( T, 'c_Set_Oinsert'( U, 'c_Orderings_Obot__class_Obot'(
% 1.42/1.82 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ) ) ), =( Y, T ), =( X, T ) ],
% 1.42/1.82 [ ~( =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y,
% 1.42/1.82 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ),
% 1.42/1.82 'c_Set_Oinsert'( T, 'c_Set_Oinsert'( U, 'c_Orderings_Obot__class_Obot'(
% 1.42/1.82 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ) ) ), =( X, U ), =( Y, U ) ],
% 1.42/1.82 [ ~( =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y,
% 1.42/1.82 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ),
% 1.42/1.82 'c_Set_Oinsert'( T, 'c_Set_Oinsert'( U, 'c_Orderings_Obot__class_Obot'(
% 1.42/1.82 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ) ) ), =( Y, T ), =( Y, U ) ],
% 1.42/1.82 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.42/1.82 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ), Y, 'tc_fun'(
% 1.42/1.82 X, 'tc_bool' ) ), Y ) ],
% 1.42/1.82 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X,
% 1.42/1.82 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ), 'tc_fun'( Y,
% 1.42/1.82 'tc_bool' ) ), X ) ],
% 1.42/1.82 [ ~( =( 'c_Set_Oinsert'( X, Y, Z ), 'c_Orderings_Obot__class_Obot'(
% 1.42/1.82 'tc_fun'( Z, 'tc_bool' ) ) ) ) ],
% 1.42/1.82 [ ~( =( 'c_Set_Oinsert'( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y
% 1.42/1.82 , 'tc_bool' ) ), Y ), 'c_Set_Oinsert'( Z, 'c_Orderings_Obot__class_Obot'(
% 1.42/1.82 'tc_fun'( Y, 'tc_bool' ) ), Y ) ) ), =( X, Z ) ],
% 1.42/1.82 [ ~( =( 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z
% 1.42/1.82 , 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' )
% 1.42/1.82 ) ) ), =( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) )
% 1.42/1.82 ) ],
% 1.42/1.82 [ ~( =( 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z
% 1.42/1.82 , 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' )
% 1.42/1.82 ) ) ), =( Y, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) )
% 1.42/1.82 ) ],
% 1.42/1.82 [ =( 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ), hAPP( 'c_Suc',
% 1.42/1.82 'c_HOL_Ominus__class_Ominus'( 'c_Int_Onumber__class_Onumber__of'( X,
% 1.42/1.82 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ) ), ~(
% 1.42/1.82 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.42/1.82 'tc_nat' ), 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' )
% 1.42/1.82 ) ) ) ],
% 1.42/1.82 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_lessequals'( hAPP( 'c_Suc', X ), 'tc_nat' ), hAPP( 'c_Suc', Y ) ) ) )
% 1.42/1.82 ],
% 1.42/1.82 [ hBOOL( hAPP( 'c_lessequals'( hAPP( 'c_Suc', X ), 'tc_nat' ), hAPP(
% 1.42/1.82 'c_Suc', Y ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ) )
% 1.42/1.82 ],
% 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 [ ~( hBOOL( hAPP( 'c_lessequals'( hAPP( 'c_Suc', X ), 'tc_nat' ), X ) )
% 1.42/1.82 ) ],
% 1.42/1.82 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_lessequals'( hAPP( 'c_Suc', X ), 'tc_nat' ), Y ) ) ) ],
% 1.42/1.82 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), hAPP( 'c_Suc', Y ) ) ),
% 1.42/1.82 ~( hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ) ) ],
% 1.42/1.82 [ =( X, Y ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y )
% 1.42/1.82 ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), hAPP(
% 1.42/1.82 'c_Suc', Y ) ) ) ) ],
% 1.42/1.82 [ =( X, Y ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, 'tc_nat' ),
% 1.42/1.82 hAPP( 'c_Suc', X ) ) ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y,
% 1.42/1.82 'tc_nat' ), X ) ) ],
% 1.42/1.82 [ =( X, Y ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ),
% 1.42/1.82 hAPP( 'c_Suc', Y ) ) ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X,
% 1.42/1.82 'tc_nat' ), Y ) ) ],
% 1.42/1.82 [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( 'c_Suc', X ), hAPP( 'c_Suc', Y
% 1.42/1.82 ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( 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 [ =( 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 [ =( 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_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( hAPP(
% 1.42/1.82 'c_Suc', X ), Y, 'tc_nat' ), hAPP( 'c_Suc', Z ), 'tc_nat' ),
% 1.42/1.82 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.42/1.82 'tc_nat' ), Z, 'tc_nat' ) ) ],
% 1.42/1.82 [ =( X, hAPP( 'c_Suc', Y ) ), hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' )
% 1.42/1.82 , Y ) ), ~( hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), hAPP( 'c_Suc', Y
% 1.42/1.82 ) ) ) ) ],
% 1.42/1.82 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), hAPP( 'c_Suc',
% 1.42/1.82 Y ) ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, 'tc_nat' ), X ) ) ]
% 1.42/1.82 ,
% 1.42/1.82 [ ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ) ), ~(
% 1.42/1.82 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, 'tc_nat' ), hAPP( 'c_Suc', X )
% 1.42/1.82 ) ) ) ],
% 1.42/1.82 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), X ) ), hBOOL(
% 1.42/1.82 hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), hAPP( 'c_Suc', X ) ) ) ]
% 1.42/1.82 ,
% 1.42/1.82 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ), ~( hBOOL(
% 1.42/1.82 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', X ), 'tc_nat' ), Y ) ) )
% 1.42/1.82 ],
% 1.42/1.82 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), hAPP( 'c_Suc',
% 1.42/1.82 Y ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) )
% 1.42/1.82 ) ],
% 1.42/1.82 [ =( hAPP( hAPP( X, Y ), hAPP( 'c_Suc', Z ) ), hAPP( hAPP( T, Y ), hAPP(
% 1.42/1.82 hAPP( X, Y ), Z ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, T, X, W,
% 1.42/1.82 V0, V1 ) ) ],
% 1.42/1.82 [ =( hAPP( hAPP( X, Y ), hAPP( 'c_Suc', Z ) ), hAPP( hAPP( T, Y ), hAPP(
% 1.42/1.82 hAPP( X, Y ), Z ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, T, X, W,
% 1.42/1.82 V0, V1 ) ) ],
% 1.42/1.82 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), Z ), hAPP( hAPP( Y, Z ),
% 1.42/1.82 hAPP( 'c_Suc', T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, Y, W
% 1.42/1.82 , V0, V1 ) ) ],
% 1.42/1.82 [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ), hBOOL( hAPP(
% 1.42/1.82 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.42/1.82 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ), ~(
% 1.42/1.82 hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) )
% 1.42/1.82 ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ), T ) ) ) ],
% 1.42/1.82 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP(
% 1.42/1.82 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.42/1.82 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ), ~(
% 1.42/1.82 hBOOL( hAPP( 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.42/1.82 ), ~( hBOOL( hAPP( 'c_lessequals'( T, X ), Z ) ) ) ],
% 1.42/1.82 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP(
% 1.42/1.82 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.42/1.82 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ), ~(
% 1.42/1.82 hBOOL( hAPP( 'c_lessequals'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.42/1.82 ), ~( hBOOL( hAPP( 'c_lessequals'( T, X ), Y ) ) ) ],
% 1.42/1.82 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.42/1.82 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.42/1.82 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ) ) ), =( T, U ), =( Z,
% 1.42/1.82 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.82 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =( hAPP(
% 1.42/1.82 hAPP( 'c_HOL_Oplus__class_Oplus'( 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 ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.42/1.82 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.82 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =( hAPP(
% 1.42/1.82 hAPP( 'c_HOL_Oplus__class_Oplus'( 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 ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.42/1.82 X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.82 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP(
% 1.42/1.82 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL(
% 1.42/1.82 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ) ]
% 1.42/1.82 ,
% 1.42/1.82 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP(
% 1.42/1.82 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_lessequals'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL(
% 1.42/1.82 hAPP( 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ]
% 1.42/1.82 ,
% 1.42/1.82 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP(
% 1.42/1.82 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_lessequals'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL(
% 1.42/1.82 hAPP( 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ]
% 1.42/1.82 ,
% 1.42/1.82 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.42/1.82 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ) ) ],
% 1.42/1.82 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.42/1.82 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL(
% 1.42/1.82 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ) ]
% 1.42/1.82 ,
% 1.42/1.82 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.42/1.82 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_lessequals'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL(
% 1.42/1.82 hAPP( 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ]
% 1.42/1.82 ,
% 1.42/1.82 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ), hBOOL(
% 1.42/1.82 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL(
% 1.42/1.82 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ) ]
% 1.42/1.82 ,
% 1.42/1.82 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.42/1.82 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP(
% 1.42/1.82 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ), ~( hBOOL(
% 1.42/1.82 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ) ) ],
% 1.42/1.82 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.42/1.82 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP(
% 1.42/1.82 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ), ~( hBOOL(
% 1.42/1.82 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ) ) ) ],
% 1.42/1.82 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.42/1.82 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP(
% 1.42/1.82 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ), ~( hBOOL(
% 1.42/1.82 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ) ) ],
% 1.42/1.82 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.42/1.82 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP(
% 1.42/1.82 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ), ~( hBOOL(
% 1.42/1.82 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ) ) ) ],
% 1.42/1.82 [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ), hBOOL( hAPP(
% 1.42/1.82 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.42/1.82 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) ), ~(
% 1.42/1.82 hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) )
% 1.42/1.82 ), ~( hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.42/1.82 , T ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Z, X ), U ) ) ), ~( hBOOL(
% 1.42/1.82 hAPP( 'c_lessequals'( Y, X ), T ) ) ) ],
% 1.42/1.82 [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ), hBOOL( hAPP(
% 1.42/1.82 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.42/1.82 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) ), ~(
% 1.42/1.82 hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) )
% 1.42/1.82 ), ~( hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.42/1.82 , Y ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Z, X ), U ) ) ), ~( hBOOL(
% 1.42/1.82 hAPP( 'c_lessequals'( Y, X ), T ) ) ) ],
% 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 ) ), hBOOL( hAPP(
% 1.42/1.82 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.42/1.82 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.42/1.82 X ), Y ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ) ],
% 1.42/1.82 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.42/1.82 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.42/1.82 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.42/1.82 X ), Y ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), X ), hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ) ) ) ) ],
% 1.42/1.82 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( hBOOL(
% 1.42/1.82 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.42/1.82 X ), Y ), Y ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.42/1.82 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.42/1.82 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.42/1.82 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.42/1.82 Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ) ],
% 1.42/1.82 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.42/1.82 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.42/1.82 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.42/1.82 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.42/1.82 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ), hBOOL(
% 1.42/1.82 hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y )
% 1.42/1.82 , Z ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_lessequals'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL(
% 1.42/1.82 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ) ]
% 1.42/1.82 ,
% 1.42/1.82 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ), hBOOL(
% 1.42/1.82 hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y )
% 1.42/1.82 , Z ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL(
% 1.42/1.82 hAPP( 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ]
% 1.42/1.82 ,
% 1.42/1.82 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ), hBOOL(
% 1.42/1.82 hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y )
% 1.42/1.82 , Z ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_lessequals'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL(
% 1.42/1.82 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ) ]
% 1.42/1.82 ,
% 1.42/1.82 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ), hBOOL(
% 1.42/1.82 hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y )
% 1.42/1.82 , Z ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL(
% 1.42/1.82 hAPP( 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ]
% 1.42/1.82 ,
% 1.42/1.82 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ), hBOOL(
% 1.42/1.82 hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y )
% 1.42/1.82 , Z ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL(
% 1.42/1.82 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ) ]
% 1.42/1.82 ,
% 1.42/1.82 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =( hAPP(
% 1.42/1.82 'c_HOL_Oinverse__class_Oinverse'( 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_Oinverse__class_Oinverse'(
% 1.42/1.82 X ), Z ) ), hAPP( 'c_HOL_Oinverse__class_Oinverse'( X ), Y ) ) ), =( Z,
% 1.42/1.82 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 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 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( hAPP(
% 1.42/1.82 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.42/1.82 ), Y ), Y, X ) ) ],
% 1.42/1.82 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.42/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( Y, hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z
% 1.42/1.82 , X ) ), Z ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 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_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z
% 1.42/1.82 , X ) ), Z ), 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_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 ) ), =( hAPP(
% 1.42/1.82 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.42/1.82 'c_HOL_Ozero__class_Ozero'( X ) ) ), hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.42/1.82 'c_HOL_Ozero__class_Ozero'( X ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.42/1.82 ,
% 1.42/1.82 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.42/1.82 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), hBOOL( hAPP(
% 1.42/1.82 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ),
% 1.42/1.82 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ), hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ) ) ) ) ],
% 1.42/1.82 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.42/1.82 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.42/1.82 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ), T ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.42/1.82 , Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.42/1.82 ) ) ) ],
% 1.42/1.82 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.42/1.82 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), hBOOL( hAPP(
% 1.42/1.82 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ),
% 1.42/1.82 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ), hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ) ],
% 1.42/1.82 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.42/1.82 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.42/1.82 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ), T ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.42/1.82 , Z ), Y ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y )
% 1.42/1.82 ) ) ) ],
% 1.42/1.82 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =(
% 1.42/1.82 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.42/1.82 'c_HOL_Oinverse__class_Odivide'( T, U, X ) ) ), =( U,
% 1.42/1.82 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.42/1.82 ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), U ), hAPP(
% 1.42/1.82 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ],
% 1.42/1.82 [ ~( 'class_Ring__and__Field_Ofield'( 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 ), T ), U ) ) ), =( Z,
% 1.42/1.82 'c_HOL_Ozero__class_Ozero'( X ) ), =( U, 'c_HOL_Ozero__class_Ozero'( X )
% 1.42/1.82 ), =( 'c_HOL_Oinverse__class_Odivide'( Y, U, X ),
% 1.42/1.82 'c_HOL_Oinverse__class_Odivide'( T, Z, X ) ) ],
% 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 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.42/1.82 X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ), Y, X ),
% 1.42/1.82 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.82 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), ~(
% 1.42/1.82 'class_RealVector_Ometric__space'( Y ) ), 'c_Lim_OLIM'( 'c_COMBB'( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( X ), Z ), T, X, X, Y ), U, hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( X ), Z ), W ), Y, X ), ~( 'c_Lim_OLIM'( T,
% 1.42/1.82 U, W, Y, X ) ) ],
% 1.42/1.82 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_Finite__Set_Osetsum'( Z, T, U
% 1.42/1.82 , X ) ), 'c_Finite__Set_Osetsum'( 'c_COMBB'( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z, X, X, U ), T, U, X ) ) ],
% 1.42/1.82 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), =( hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_Finite__Set_Osetsum'( Z, T, U
% 1.42/1.82 , X ) ), 'c_Finite__Set_Osetsum'( 'c_COMBB'( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z, X, X, U ), T, U, X ) ) ],
% 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'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.42/1.82 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( 'c_HOL_Ozero__class_Ozero'(
% 1.42/1.82 X ), 'c_HOL_Oinverse__class_Odivide'( Z,
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 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'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.42/1.82 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =(
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.42/1.82 'c_HOL_Oinverse__class_Odivide'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 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'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.42/1.82 X ), 'c_HOL_Oinverse__class_Odivide'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.42/1.82 , X ) ) ), =( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.42/1.82 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 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'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.42/1.82 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =(
% 1.42/1.82 'c_HOL_Oinverse__class_Odivide'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.42/1.82 , 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ],
% 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'( X ) ), ~( =( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.42/1.82 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.42/1.82 Z, X ) ) ), =( 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.42/1.82 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 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'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.42/1.82 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =(
% 1.42/1.82 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( Y
% 1.42/1.82 , X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.82 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.42/1.82 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.42/1.82 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.42/1.82 ), ~( =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.42/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.42/1.82 ) ) ],
% 1.42/1.82 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.42/1.82 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.42/1.82 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.42/1.82 ), =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ),
% 1.42/1.82 'c_HOL_Ozero__class_Ozero'( X ) ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.42/1.82 , =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.42/1.82 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.42/1.82 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.42/1.82 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y
% 1.42/1.82 ), 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.42/1.82 'tc_nat' ) ) ],
% 1.42/1.82 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), ~( 'class_Int_Onumber'(
% 1.42/1.82 X ) ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), hAPP( hAPP(
% 1.42/1.82 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), 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_Int_Onumber__class_Onumber__of'( Y, X ) ), Z ) ), hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.42/1.82 , X ) ), T ) ) ) ],
% 1.42/1.82 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( 'class_Int_Onumber'( X )
% 1.42/1.82 ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 1.42/1.82 'c_HOL_Ominus__class_Ominus'( Z, T, X ) ), 'c_HOL_Ominus__class_Ominus'(
% 1.42/1.82 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), Z ), hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.42/1.82 , X ) ), T ), X ) ) ],
% 1.42/1.82 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( 'class_Int_Onumber'( X )
% 1.42/1.82 ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.42/1.82 'c_HOL_Ominus__class_Ominus'( Y, Z, X ) ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( T, X ) ),
% 1.42/1.82 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.42/1.82 ), Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ) ],
% 1.42/1.82 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), ~( 'class_Int_Onumber'(
% 1.42/1.82 X ) ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.42/1.82 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( T, 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_Int_Onumber__class_Onumber__of'( T, X ) ) ), hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ) ) ],
% 1.42/1.82 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.42/1.82 'c_Finite__Set_Osetsum'( Y, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z,
% 1.42/1.82 'tc_bool' ) ), Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.82 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.42/1.82 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.42/1.82 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.42/1.82 hAPP( 'c_Suc', Y ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.82 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), 'c_Series_Osums'(
% 1.42/1.82 'c_COMBB'( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z, X, X,
% 1.42/1.82 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.42/1.82 , ~( 'c_Series_Osums'( Z, T, X ) ) ],
% 1.42/1.82 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), 'c_Series_Osums'(
% 1.42/1.82 'c_COMBB'( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z, X, X,
% 1.42/1.82 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.42/1.82 , ~( 'c_Series_Osums'( Z, T, X ) ) ],
% 1.42/1.82 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.42/1.82 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.42/1.82 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.42/1.82 ), ~( =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ),
% 1.42/1.82 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.42/1.82 ) ) ],
% 1.42/1.82 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( 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_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.42/1.82 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.42/1.82 [ ~( 'class_Power_Opower'( 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_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.42/1.82 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.42/1.82 [ ~( 'class_OrderedGroup_Omonoid__mult'( 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_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.42/1.82 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), Y ) ) ],
% 1.42/1.82 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( 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_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.42/1.82 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.42/1.82 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.42/1.82 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.42/1.82 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ) ) ],
% 1.42/1.82 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.42/1.82 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), Y ), hAPP( hAPP(
% 1.42/1.82 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ) ) ],
% 1.42/1.82 [ ~( 'class_Int_Oring__char__0'( X ) ), ~( 'class_Int_Onumber__ring'( X
% 1.42/1.82 ) ), ~( 'c_Int_Oiszero'( 'c_Int_Onumber__class_Onumber__of'(
% 1.42/1.82 'c_Int_OBit1'( Y ), X ), X ) ) ],
% 1.42/1.82 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.42/1.82 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_Int_Onumber__class_Onumber__of'(
% 1.42/1.82 'c_Int_OPls', X ) ), Y ) ],
% 1.42/1.82 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.42/1.82 'c_HOL_Oplus__class_Oplus'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.42/1.82 'c_Int_OPls', X ) ), Y ), Y ) ],
% 1.42/1.82 [ ~( 'class_Int_Onumber__ring'( X ) ), 'c_Int_Oiszero'(
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', X ), X ) ],
% 1.42/1.82 [ ~( 'class_Int_Oring__char__0'( X ) ), ~( 'class_Int_Onumber__ring'( X
% 1.42/1.82 ) ), 'c_Int_Oiszero'( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.42/1.82 Y ), X ), X ), ~( 'c_Int_Oiszero'( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.42/1.82 , X ), X ) ) ],
% 1.42/1.82 [ ~( 'class_Int_Oring__char__0'( X ) ), ~( 'class_Int_Onumber__ring'( X
% 1.42/1.82 ) ), 'c_Int_Oiszero'( 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.42/1.82 ~( 'c_Int_Oiszero'( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( Y
% 1.42/1.82 ), 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 ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.42/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.42/1.82 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ) ), Y ) ) ],
% 1.42/1.82 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.42/1.82 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 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 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.42/1.82 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 1.42/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, hAPP( 'c_Suc',
% 1.42/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.42/1.82 [ ~( =( hAPP( 'c_Suc', 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) )
% 1.42/1.82 , Y ) ), =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', X ), Y, 'tc_nat'
% 1.42/1.82 ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.42/1.82 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.42/1.82 'tc_nat' ), 'tc_nat' ), hAPP( 'c_Suc', X ) ) ) ],
% 1.42/1.82 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.42/1.82 'tc_nat' ), 'tc_nat' ), hAPP( 'c_Suc', X ) ) ) ],
% 1.42/1.82 [ =( X, hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X
% 1.42/1.82 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.42/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ) ) ],
% 1.42/1.82 [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), hAPP( 'c_Suc',
% 1.42/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ) ],
% 1.42/1.82 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( 'c_Suc',
% 1.42/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.42/1.82 'tc_nat' ) ), hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ]
% 1.42/1.82 ,
% 1.42/1.82 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.42/1.82 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 1.42/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 1.42/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.42/1.82 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.42/1.82 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, hAPP(
% 1.42/1.82 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, hAPP( 'c_Suc'
% 1.42/1.82 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.42/1.82 [ =( 'c_Divides_Odiv__class_Odiv'( X, hAPP( 'c_Suc',
% 1.42/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ), X ) ],
% 1.42/1.82 [ ~( =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP(
% 1.42/1.82 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( Y, 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 [ ~( =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP(
% 1.42/1.82 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( X,
% 1.42/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, hAPP( 'c_Suc',
% 1.42/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.42/1.82 [ =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.42/1.82 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 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_HOL_Oone__class_Oone'( 'tc_nat' ), hAPP( 'c_Suc',
% 1.42/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.42/1.82 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.42/1.82 'tc_nat' ), 'tc_nat' ), hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 1.42/1.82 'tc_nat' ) ) ) ) ],
% 1.42/1.82 [ ~( =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP(
% 1.42/1.82 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( X,
% 1.42/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 1.42/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.42/1.82 [ ~( =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP(
% 1.42/1.82 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( Y, hAPP(
% 1.42/1.82 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, hAPP( 'c_Suc'
% 1.42/1.82 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 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 [ =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.42/1.82 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( 'c_Suc',
% 1.42/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.42/1.82 'tc_nat' ) ) ) ],
% 1.42/1.82 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.42/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( 'c_Suc',
% 1.42/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), hAPP( 'c_Suc',
% 1.42/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.42/1.82 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, Y ), T ) ), hAPP( hAPP( Z, Y ),
% 1.42/1.82 hAPP( 'c_Suc', T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, Z, W
% 1.42/1.82 , V0, V1 ) ) ],
% 1.42/1.82 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), hAPP( 'c_Suc',
% 1.42/1.82 X ) ) ) ],
% 1.42/1.82 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), hAPP( 'c_Suc',
% 1.42/1.82 X ) ) ) ],
% 1.42/1.82 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', X ), 'tc_nat' )
% 1.42/1.82 , Y ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, 'tc_nat' ), Y ) )
% 1.42/1.82 ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Z ) ) ) ]
% 1.42/1.82 ,
% 1.42/1.82 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ),
% 1.42/1.82 hAPP( 'c_Suc', 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ) ), =(
% 1.42/1.82 hAPP( 'c_Suc', 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), Y ) ]
% 1.42/1.82 ,
% 1.42/1.82 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', X ), 'tc_nat' )
% 1.42/1.82 , Y ) ), =( hAPP( 'c_Suc', X ), Y ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ) ) ],
% 1.42/1.82 [ hBOOL( hAPP( 'c_lessequals'( hAPP( 'c_Suc', X ), 'tc_nat' ), Y ) ),
% 1.42/1.82 hBOOL( hAPP( 'c_lessequals'( Y, 'tc_nat' ), X ) ) ],
% 1.42/1.82 [ ~( hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_lessequals'( hAPP( 'c_Suc', Y ), 'tc_nat' ), X ) ) ) ],
% 1.42/1.82 [ hBOOL( hAPP( 'c_lessequals'( hAPP( 'c_Suc', X ), 'tc_nat' ), hAPP(
% 1.42/1.82 'c_Suc', X ) ) ) ],
% 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 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', X ), 'tc_nat' )
% 1.42/1.82 , hAPP( 'c_Suc', Y ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X,
% 1.42/1.82 'tc_nat' ), Y ) ) ) ],
% 1.42/1.82 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ), ~( hBOOL(
% 1.42/1.82 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', X ), 'tc_nat' ), hAPP(
% 1.42/1.82 'c_Suc', Y ) ) ) ) ],
% 1.42/1.82 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', X ), 'tc_nat' )
% 1.42/1.82 , hAPP( 'c_Suc', Y ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X,
% 1.42/1.82 'tc_nat' ), Y ) ) ) ],
% 1.42/1.82 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Int_Onumber__class_Onumber__of'( X
% 1.42/1.82 , 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ),
% 1.42/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.42/1.82 X, 'tc_Int_Oint' ), 'c_Int_OPls' ) ) ) ],
% 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 [ hBOOL( hAPP( 'c_lessequals'( 'c_Int_OBit1'( X ), 'tc_Int_Oint' ),
% 1.42/1.82 'c_Int_OBit1'( Y ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( X, 'tc_Int_Oint'
% 1.42/1.82 ), Y ) ) ) ],
% 1.42/1.82 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_Int_Oint' ), Y ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_lessequals'( 'c_Int_OBit1'( X ), 'tc_Int_Oint' ), 'c_Int_OBit1'( Y ) )
% 1.42/1.82 ) ) ],
% 1.42/1.82 [ hBOOL( hAPP( 'c_lessequals'( 'c_Int_OBit1'( X ), 'tc_Int_Oint' ),
% 1.42/1.82 'c_Int_OBit1'( Y ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( X, 'tc_Int_Oint'
% 1.42/1.82 ), Y ) ) ) ],
% 1.42/1.82 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_Int_Oint' ), Y ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_lessequals'( 'c_Int_OBit1'( X ), 'tc_Int_Oint' ), 'c_Int_OBit1'( Y ) )
% 1.42/1.82 ) ) ],
% 1.42/1.82 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ),
% 1.42/1.82 'tc_Int_Oint' ), 'c_Int_OBit1'( Y ) ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_HOL_Oord__class_Oless'( X, 'tc_Int_Oint' ), Y ) ) ) ],
% 1.42/1.82 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_Int_Oint' ), Y ) ), ~(
% 1.42/1.82 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'tc_Int_Oint'
% 1.42/1.82 ), 'c_Int_OBit1'( Y ) ) ) ) ],
% 1.42/1.82 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ),
% 1.42/1.82 'tc_Int_Oint' ), 'c_Int_OBit1'( Y ) ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_HOL_Oord__class_Oless'( X, 'tc_Int_Oint' ), Y ) ) ) ],
% 1.42/1.82 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_Int_Oint' ), Y ) ), ~(
% 1.42/1.82 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'tc_Int_Oint'
% 1.42/1.82 ), 'c_Int_OBit1'( Y ) ) ) ) ],
% 1.42/1.82 [ =( 'c_Int_OMin', 'c_Int_OBit1'( 'c_Int_OMin' ) ) ],
% 1.42/1.82 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', 'tc_Int_Oint' )
% 1.42/1.82 , 'c_Int_OBit1'( X ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( 'c_Int_OPls',
% 1.42/1.82 'tc_Int_Oint' ), X ) ) ) ],
% 1.42/1.82 [ hBOOL( hAPP( 'c_lessequals'( 'c_Int_OPls', 'tc_Int_Oint' ), X ) ), ~(
% 1.42/1.82 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', 'tc_Int_Oint' ),
% 1.42/1.82 'c_Int_OBit1'( X ) ) ) ) ],
% 1.42/1.82 [ hBOOL( hAPP( 'c_lessequals'( 'c_Int_OBit1'( X ), 'tc_Int_Oint' ),
% 1.42/1.82 'c_Int_OPls' ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X,
% 1.42/1.82 'tc_Int_Oint' ), 'c_Int_OPls' ) ) ) ],
% 1.42/1.82 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_Int_Oint' ),
% 1.42/1.82 'c_Int_OPls' ) ), ~( hBOOL( hAPP( 'c_lessequals'( 'c_Int_OBit1'( X ),
% 1.42/1.82 'tc_Int_Oint' ), 'c_Int_OPls' ) ) ) ],
% 1.42/1.82 [ ~( =( 'c_Int_OPls', 'c_Int_OMin' ) ) ],
% 1.42/1.82 [ ~( =( 'c_Int_OMin', 'c_Int_OPls' ) ) ],
% 1.42/1.82 [ ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', 'tc_Int_Oint'
% 1.42/1.82 ), 'c_Int_OPls' ) ) ) ],
% 1.42/1.82 [ hBOOL( hAPP( 'c_lessequals'( 'c_Int_OPls', 'tc_Int_Oint' ),
% 1.42/1.82 'c_Int_OPls' ) ) ],
% 1.42/1.82 [ hBOOL( hAPP( 'c_lessequals'( 'c_Int_OBit1'( X ), 'tc_Int_Oint' ),
% 1.42/1.82 'c_Int_OBit0'( Y ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X,
% 1.42/1.82 'tc_Int_Oint' ), Y ) ) ) ],
% 1.42/1.82 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_Int_Oint' ), Y ) ), ~(
% 1.42/1.82 hBOOL( hAPP( 'c_lessequals'( 'c_Int_OBit1'( X ), 'tc_Int_Oint' ),
% 1.42/1.82 'c_Int_OBit0'( Y ) ) ) ) ],
% 1.42/1.82 [ hBOOL( hAPP( 'c_lessequals'( 'c_Int_OBit1'( X ), 'tc_Int_Oint' ),
% 1.42/1.82 'c_Int_OBit0'( Y ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X,
% 1.42/1.82 'tc_Int_Oint' ), Y ) ) ) ],
% 1.42/1.82 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_Int_Oint' ), Y ) ), ~(
% 1.42/1.82 hBOOL( hAPP( 'c_lessequals'( 'c_Int_OBit1'( X ), 'tc_Int_Oint' ),
% 1.42/1.82 'c_Int_OBit0'( Y ) ) ) ) ],
% 1.42/1.82 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_Int_OBit0'( X ),
% 1.42/1.82 'tc_Int_Oint' ), 'c_Int_OBit1'( Y ) ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.42/1.82 X, 'tc_Int_Oint' ), Y ) ) ) ],
% 1.42/1.82 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_Int_Oint' ), Y ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_HOL_Oord__class_Oless'( 'c_Int_OBit0'( X ), 'tc_Int_Oint' ),
% 1.42/1.82 'c_Int_OBit1'( Y ) ) ) ) ],
% 1.42/1.82 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_Int_OBit0'( X ),
% 1.42/1.82 'tc_Int_Oint' ), 'c_Int_OBit1'( Y ) ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.42/1.82 X, 'tc_Int_Oint' ), Y ) ) ) ],
% 1.42/1.82 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_Int_Oint' ), Y ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_HOL_Oord__class_Oless'( 'c_Int_OBit0'( X ), 'tc_Int_Oint' ),
% 1.42/1.82 'c_Int_OBit1'( Y ) ) ) ) ],
% 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 [ hBOOL( hAPP( 'c_lessequals'( 'c_Int_OBit0'( X ), 'tc_Int_Oint' ),
% 1.42/1.82 'c_Int_OBit0'( Y ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( X, 'tc_Int_Oint'
% 1.42/1.82 ), Y ) ) ) ],
% 1.42/1.82 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_Int_Oint' ), Y ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_lessequals'( 'c_Int_OBit0'( X ), 'tc_Int_Oint' ), 'c_Int_OBit0'( Y ) )
% 1.42/1.82 ) ) ],
% 1.42/1.82 [ hBOOL( hAPP( 'c_lessequals'( 'c_Int_OBit0'( X ), 'tc_Int_Oint' ),
% 1.42/1.82 'c_Int_OBit0'( Y ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( X, 'tc_Int_Oint'
% 1.42/1.82 ), Y ) ) ) ],
% 1.42/1.82 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_Int_Oint' ), Y ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_lessequals'( 'c_Int_OBit0'( X ), 'tc_Int_Oint' ), 'c_Int_OBit0'( Y ) )
% 1.42/1.82 ) ) ],
% 1.42/1.82 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_Int_OBit0'( X ),
% 1.42/1.82 'tc_Int_Oint' ), 'c_Int_OBit0'( Y ) ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_HOL_Oord__class_Oless'( X, 'tc_Int_Oint' ), Y ) ) ) ],
% 1.42/1.82 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_Int_Oint' ), Y ) ), ~(
% 1.42/1.82 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_Int_OBit0'( X ), 'tc_Int_Oint'
% 1.42/1.82 ), 'c_Int_OBit0'( Y ) ) ) ) ],
% 1.42/1.82 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_Int_OBit0'( X ),
% 1.42/1.82 'tc_Int_Oint' ), 'c_Int_OBit0'( Y ) ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_HOL_Oord__class_Oless'( X, 'tc_Int_Oint' ), Y ) ) ) ],
% 1.42/1.82 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_Int_Oint' ), Y ) ), ~(
% 1.42/1.82 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_Int_OBit0'( X ), 'tc_Int_Oint'
% 1.42/1.82 ), 'c_Int_OBit0'( Y ) ) ) ) ],
% 1.42/1.82 [ =( X, 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_HOL_Oord__class_Oless'( Y, 'tc_nat' ), hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), hAPP( 'c_Suc', X ) ) ) ) )
% 1.42/1.82 , ~( hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), X ), 'tc_nat' ), Y ) ) ),
% 1.42/1.82 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.42/1.82 'tc_nat' ), 'tc_nat' ), Z ) ) ) ],
% 1.42/1.82 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.42/1.82 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'(
% 1.42/1.82 'tc_nat' ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.42/1.82 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ),
% 1.42/1.82 'c_Divides_Odiv__class_Odiv'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.42/1.82 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) )
% 1.42/1.82 , ~( 'c_Parity_Oeven__odd__class_Oeven'( 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 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.42/1.82 'tc_nat' ), 'tc_nat' ), X ) ) ) ],
% 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 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.42/1.82 'tc_nat' ), 'tc_nat' ), Y ) ) ) ],
% 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' ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.42/1.82 'tc_nat' ), X ) ) ) ],
% 1.42/1.82 [ hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.42/1.82 'tc_nat' ), X ), Y ), 'tc_nat' ), hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), hBOOL( hAPP(
% 1.42/1.82 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.42/1.82 'tc_nat' ), X ) ) ],
% 1.42/1.82 [ hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.42/1.82 'tc_nat' ), X ), Y ), 'tc_nat' ), hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ), hBOOL( hAPP(
% 1.42/1.82 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.42/1.82 'tc_nat' ), Y ) ) ],
% 1.42/1.82 [ hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.42/1.82 'tc_nat' ), X ), Y ), 'tc_nat' ), hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_lessequals'( Y, 'tc_nat' ), Z ) ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.42/1.82 'tc_nat' ), X ) ) ) ],
% 1.42/1.82 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z )
% 1.42/1.82 , X ), 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.42/1.82 Z ), Y ) ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), Z ) ) ) ],
% 1.42/1.82 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.42/1.82 'tc_nat' ), Z ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), X ), 'tc_nat' ), hAPP(
% 1.42/1.82 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ) ) ],
% 1.42/1.82 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.42/1.82 'tc_nat' ), Z ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ), 'tc_nat' ), hAPP(
% 1.42/1.82 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ) ) ) ],
% 1.42/1.82 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_HOL_Oord__class_Oless'( Y, 'tc_Int_Oint' ), 'c_Int_OPls' ) ) ), hBOOL(
% 1.42/1.82 hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_Int_Oint' ), 'c_Int_OPls' ) ) ]
% 1.42/1.82 ,
% 1.42/1.82 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Int_Onumber__class_Onumber__of'( X
% 1.42/1.82 , 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), 'tc_nat'
% 1.42/1.82 ), 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_HOL_Oord__class_Oless'( Y, 'tc_Int_Oint' ), 'c_Int_OPls' ) ) ) ],
% 1.42/1.82 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_HOL_Oord__class_Oless'( X, 'tc_Int_Oint' ), 'c_Int_OPls' ) ) ) ],
% 1.42/1.82 [ hBOOL( hAPP( 'c_lessequals'( 'c_Int_Onumber__class_Onumber__of'( X,
% 1.42/1.82 'tc_nat' ), 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' )
% 1.42/1.82 ) ), ~( hBOOL( hAPP( 'c_lessequals'( X, 'tc_Int_Oint' ), 'c_Int_OPls' )
% 1.42/1.82 ) ) ],
% 1.42/1.82 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_Int_Oint' ), 'c_Int_OPls' ) ),
% 1.42/1.82 hBOOL( hAPP( 'c_lessequals'( X, 'tc_Int_Oint' ), Y ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_lessequals'( 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ),
% 1.42/1.82 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ) ) ) ]
% 1.42/1.82 ,
% 1.42/1.82 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ), 'tc_nat' ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_HOL_Oord__class_Oless'( X, 'tc_Int_Oint' ), Y ) ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', 'tc_Int_Oint' ), Y ) ) ) ],
% 1.42/1.82 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', 'tc_Int_Oint' )
% 1.42/1.82 , X ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, 'tc_Int_Oint' ), X
% 1.42/1.82 ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), 'tc_nat' ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( X, '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 [ ~( 'class_Orderings_Oorder'( X ) ), =(
% 1.42/1.82 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.42/1.82 'c_SetInterval_Oord__class_OgreaterThanLessThan'( Y, Z, X ),
% 1.42/1.82 'c_SetInterval_Oord__class_OatLeast'( Z, X ), 'tc_fun'( X, 'tc_bool' ) )
% 1.42/1.82 , 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ) ],
% 1.42/1.82 [ ~( 'class_Orderings_Oorder'( X ) ), =(
% 1.42/1.82 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.42/1.82 'c_SetInterval_Oord__class_OlessThan'( Y, X ),
% 1.42/1.82 'c_SetInterval_Oord__class_OatLeastAtMost'( Y, Z, X ), 'tc_fun'( X,
% 1.42/1.82 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) )
% 1.42/1.82 ) ],
% 1.42/1.82 [ ~( 'class_Orderings_Oorder'( X ) ), =(
% 1.42/1.82 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.42/1.82 'c_SetInterval_Oord__class_OgreaterThanLessThan'( Y, Z, X ),
% 1.42/1.82 'c_SetInterval_Oord__class_OatLeastAtMost'( Z, T, X ), 'tc_fun'( X,
% 1.42/1.82 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) )
% 1.42/1.82 ) ],
% 1.42/1.82 [ ~( 'class_Orderings_Oorder'( X ) ), =(
% 1.42/1.82 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.42/1.82 'c_SetInterval_Oord__class_OatLeastAtMost'( Y, Z, X ),
% 1.42/1.82 'c_SetInterval_Oord__class_OgreaterThanLessThan'( Z, T, X ), 'tc_fun'( X
% 1.42/1.82 , 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' )
% 1.42/1.82 ) ) ],
% 1.42/1.82 [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 1.42/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.42/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), X ), Y ) ],
% 1.42/1.82 [ ~( 'class_OrderedGroup_Olordered__ab__group__add__meet'( X ) ), =(
% 1.42/1.82 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.42/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ) ), T ),
% 1.42/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( 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_Olordered__ab__group__add__meet'( X ) ), =(
% 1.42/1.82 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.42/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ) ),
% 1.42/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( 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 ), Y ), T ), X ) ) ],
% 1.42/1.82 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =( hAPP(
% 1.42/1.82 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.42/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ) ),
% 1.42/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( 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 ), Y ), T ), X ) ) ],
% 1.42/1.82 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =( hAPP(
% 1.42/1.82 hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.42/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ) ), T ),
% 1.42/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( 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_Lattices_Olower__semilattice'( X ) ), hBOOL( hAPP(
% 1.42/1.82 'c_lessequals'( Y, X ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ),
% 1.42/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( T, Z, X ) ) ) ) ],
% 1.42/1.82 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), hBOOL( hAPP(
% 1.42/1.82 'c_lessequals'( Y, X ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ),
% 1.42/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ) ) ) ) ],
% 1.42/1.82 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), hBOOL( hAPP(
% 1.42/1.82 'c_lessequals'( 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ),
% 1.42/1.82 X ), T ) ), ~( hBOOL( hAPP( 'c_lessequals'( Z, X ), T ) ) ) ],
% 1.42/1.82 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), hBOOL( hAPP(
% 1.42/1.82 'c_lessequals'( 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ),
% 1.42/1.82 X ), T ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ), T ) ) ) ],
% 1.42/1.82 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), hBOOL( hAPP(
% 1.42/1.82 'c_lessequals'( Y, X ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ),
% 1.42/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( T, Z, X ) ) ) ) ],
% 1.42/1.82 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), hBOOL( hAPP(
% 1.42/1.82 'c_lessequals'( Y, X ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ),
% 1.42/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ) ) ) ) ],
% 1.42/1.82 [ ~( 'class_Lattices_Odistrib__lattice'( X ) ), =(
% 1.42/1.82 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.42/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), T, X ),
% 1.42/1.82 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.42/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T, X ),
% 1.42/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ) ) ],
% 1.42/1.82 [ ~( 'class_Lattices_Odistrib__lattice'( X ) ), =(
% 1.42/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.42/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ),
% 1.42/1.82 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.42/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ),
% 1.42/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T, X ), X ) ) ],
% 1.42/1.82 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), hBOOL( hAPP(
% 1.42/1.82 'c_lessequals'( Y, X ), 'c_Lattices_Olower__semilattice__class_Oinf'( Z,
% 1.42/1.82 T, X ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ), T ) ) ), ~( hBOOL(
% 1.42/1.82 hAPP( 'c_lessequals'( Y, X ), Z ) ) ) ],
% 1.42/1.82 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), hBOOL( hAPP(
% 1.42/1.82 'c_lessequals'( Y, X ), 'c_Lattices_Olower__semilattice__class_Oinf'( Z,
% 1.42/1.82 T, X ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ), T ) ) ), ~( hBOOL(
% 1.42/1.82 hAPP( 'c_lessequals'( Y, X ), Z ) ) ) ],
% 1.42/1.82 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), hBOOL( hAPP(
% 1.42/1.82 'c_lessequals'( Y, X ), 'c_Lattices_Olower__semilattice__class_Oinf'( Z,
% 1.42/1.82 T, X ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ), T ) ) ), ~( hBOOL(
% 1.42/1.82 hAPP( 'c_lessequals'( Y, X ), Z ) ) ) ],
% 1.42/1.82 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), hBOOL( hAPP(
% 1.42/1.82 'c_lessequals'( 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ),
% 1.42/1.82 X ), Z ) ) ],
% 1.42/1.82 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), hBOOL( hAPP(
% 1.42/1.82 'c_lessequals'( 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ),
% 1.42/1.82 X ), Y ) ) ],
% 1.42/1.82 [ ~( 'class_Lattices_Olattice'( X ) ), hBOOL( hAPP( 'c_lessequals'(
% 1.42/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), X ), Z ) ) ]
% 1.42/1.82 ,
% 1.42/1.82 [ ~( 'class_Lattices_Olattice'( X ) ), hBOOL( hAPP( 'c_lessequals'(
% 1.42/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), X ), Y ) ) ]
% 1.42/1.82 ,
% 1.42/1.82 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), hBOOL( hAPP(
% 1.42/1.82 'c_HOL_Oord__class_Oless'( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.42/1.82 Y, Z, X ), X ), T ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X )
% 1.42/1.82 , T ) ) ) ],
% 1.42/1.82 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), hBOOL( hAPP(
% 1.42/1.82 'c_HOL_Oord__class_Oless'( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.42/1.82 Y, Z, X ), X ), T ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X )
% 1.42/1.82 , T ) ) ) ],
% 1.42/1.82 [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 1.42/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.42/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), X ), Y ) ],
% 1.42/1.82 [ ~( 'class_Lattices_Odistrib__lattice'( X ) ), =(
% 1.42/1.82 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.42/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), T, X ),
% 1.42/1.82 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.42/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T, X ),
% 1.42/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ) ) ],
% 1.42/1.82 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.42/1.82 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 1.42/1.82 X ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.42/1.82 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.42/1.82 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.42/1.82 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.42/1.82 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), X ) ), Y ) ), Z ), X ) )
% 1.42/1.82 ],
% 1.42/1.82 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.42/1.82 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.42/1.82 'c_HOL_Oone__class_Oone'( X ) ), 'c_Int_Onumber__class_Onumber__of'(
% 1.42/1.82 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), X ) ) ],
% 1.42/1.82 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OMin', 'tc_nat' ),
% 1.42/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.42/1.82 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_Int_Oint' ),
% 1.42/1.82 'c_Int_OPls' ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.82 'c_Int_OBit1'( X ), 'tc_Int_Oint' ), 'c_Int_OPls' ) ) ) ],
% 1.42/1.82 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ),
% 1.42/1.82 'tc_Int_Oint' ), 'c_Int_OPls' ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_HOL_Oord__class_Oless'( X, 'tc_Int_Oint' ), 'c_Int_OPls' ) ) ) ],
% 1.42/1.82 [ hBOOL( hAPP( 'c_lessequals'( 'c_Int_OPls', 'tc_Int_Oint' ), X ) ), ~(
% 1.42/1.82 hBOOL( hAPP( 'c_lessequals'( 'c_Int_OPls', 'tc_Int_Oint' ), 'c_Int_OBit1'(
% 1.42/1.82 X ) ) ) ) ],
% 1.42/1.82 [ hBOOL( hAPP( 'c_lessequals'( 'c_Int_OPls', 'tc_Int_Oint' ),
% 1.42/1.82 'c_Int_OBit1'( X ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( 'c_Int_OPls',
% 1.42/1.82 'tc_Int_Oint' ), X ) ) ) ],
% 1.42/1.82 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_Int_Oint' ), Y ) ), ~(
% 1.42/1.82 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'tc_Int_Oint'
% 1.42/1.82 ), 'c_Int_OBit0'( Y ) ) ) ) ],
% 1.42/1.82 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ),
% 1.42/1.82 'tc_Int_Oint' ), 'c_Int_OBit0'( Y ) ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_HOL_Oord__class_Oless'( X, 'tc_Int_Oint' ), Y ) ) ) ],
% 1.42/1.82 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_Int_Oint' ), Y ) ), ~(
% 1.42/1.82 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'tc_Int_Oint'
% 1.42/1.82 ), 'c_Int_OBit0'( Y ) ) ) ) ],
% 1.42/1.82 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ),
% 1.42/1.82 'tc_Int_Oint' ), 'c_Int_OBit0'( Y ) ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_HOL_Oord__class_Oless'( X, 'tc_Int_Oint' ), Y ) ) ) ],
% 1.42/1.82 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_Int_Oint' ), Y ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_lessequals'( 'c_Int_OBit0'( X ), 'tc_Int_Oint' ), 'c_Int_OBit1'( Y ) )
% 1.42/1.82 ) ) ],
% 1.42/1.82 [ hBOOL( hAPP( 'c_lessequals'( 'c_Int_OBit0'( X ), 'tc_Int_Oint' ),
% 1.42/1.82 'c_Int_OBit1'( Y ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( X, 'tc_Int_Oint'
% 1.42/1.82 ), Y ) ) ) ],
% 1.42/1.82 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_Int_Oint' ), Y ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_lessequals'( 'c_Int_OBit0'( X ), 'tc_Int_Oint' ), 'c_Int_OBit1'( Y ) )
% 1.42/1.82 ) ) ],
% 1.42/1.82 [ hBOOL( hAPP( 'c_lessequals'( 'c_Int_OBit0'( X ), 'tc_Int_Oint' ),
% 1.42/1.82 'c_Int_OBit1'( Y ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( X, 'tc_Int_Oint'
% 1.42/1.82 ), Y ) ) ) ],
% 1.42/1.82 [ hBOOL( hAPP( 'c_lessequals'( 'c_Int_OPls', 'tc_Int_Oint' ), X ) ), ~(
% 1.42/1.82 hBOOL( hAPP( 'c_lessequals'( 'c_Int_OPls', 'tc_Int_Oint' ), 'c_Int_OBit0'(
% 1.42/1.82 X ) ) ) ) ],
% 1.42/1.82 [ hBOOL( hAPP( 'c_lessequals'( 'c_Int_OPls', 'tc_Int_Oint' ),
% 1.42/1.82 'c_Int_OBit0'( X ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( 'c_Int_OPls',
% 1.42/1.82 'tc_Int_Oint' ), X ) ) ) ],
% 1.42/1.82 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_Int_Oint' ),
% 1.42/1.82 'c_Int_OPls' ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.82 'c_Int_OBit0'( X ), 'tc_Int_Oint' ), 'c_Int_OPls' ) ) ) ],
% 1.42/1.82 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_Int_OBit0'( X ),
% 1.42/1.82 'tc_Int_Oint' ), 'c_Int_OPls' ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_HOL_Oord__class_Oless'( X, 'tc_Int_Oint' ), 'c_Int_OPls' ) ) ) ],
% 1.42/1.82 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', 'tc_Int_Oint' )
% 1.42/1.82 , X ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_Int_OPls',
% 1.42/1.82 'tc_Int_Oint' ), 'c_Int_OBit0'( X ) ) ) ) ],
% 1.42/1.82 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', 'tc_Int_Oint' )
% 1.42/1.82 , 'c_Int_OBit0'( X ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.82 'c_Int_OPls', 'tc_Int_Oint' ), X ) ) ) ],
% 1.42/1.82 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_Int_Oint' ), 'c_Int_OPls' ) ), ~(
% 1.42/1.82 hBOOL( hAPP( 'c_lessequals'( 'c_Int_OBit0'( X ), 'tc_Int_Oint' ),
% 1.42/1.82 'c_Int_OPls' ) ) ) ],
% 1.42/1.82 [ hBOOL( hAPP( 'c_lessequals'( 'c_Int_OBit0'( X ), 'tc_Int_Oint' ),
% 1.42/1.82 'c_Int_OPls' ) ), ~( hBOOL( hAPP( 'c_lessequals'( X, 'tc_Int_Oint' ),
% 1.42/1.82 'c_Int_OPls' ) ) ) ],
% 1.42/1.82 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP(
% 1.42/1.82 'c_Suc', X ) ) ), Y, 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.42/1.82 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.42/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), Y, 'tc_nat' ) ) ],
% 1.42/1.82 [ =( 'c_Divides_Odiv__class_Odiv'( X, hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP(
% 1.42/1.82 'c_Suc', Y ) ) ), 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( X, hAPP( hAPP(
% 1.42/1.82 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.42/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ), Y ), 'tc_nat' ) ) ],
% 1.42/1.82 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP(
% 1.42/1.82 'c_Suc', X ) ) ), Y, 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.42/1.82 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.42/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), Y, 'tc_nat' ) ) ],
% 1.42/1.82 [ =( 'c_Divides_Odiv__class_Omod'( X, hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP(
% 1.42/1.82 'c_Suc', Y ) ) ), 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X, hAPP( hAPP(
% 1.42/1.82 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.42/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ), Y ), 'tc_nat' ) ) ],
% 1.42/1.82 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP(
% 1.42/1.82 'c_Suc', X ) ) ), 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.42/1.82 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.42/1.82 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.42/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.42/1.82 Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.42/1.82 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP(
% 1.42/1.82 'c_Suc', X ) ) ), 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.42/1.82 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.42/1.82 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.42/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.42/1.82 Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.42/1.82 [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ),
% 1.42/1.82 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Ominus__class_Ominus'( Y,
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ),
% 1.42/1.82 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'(
% 1.42/1.82 'c_Int_OPls', 'tc_nat' ), 'tc_nat' ), Y ) ) ) ],
% 1.42/1.82 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.42/1.82 'c_Power_Opower__class_Opower'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.42/1.82 'c_Int_OMin', X ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' )
% 1.42/1.82 , 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ), Y ) ), 'c_HOL_Oone__class_Oone'( X ) ) ]
% 1.42/1.82 ,
% 1.42/1.82 [ ~( 'c_Ring__and__Field_Oordered__idom'( X, Y, Z, T, U, W, V0, V1, V2,
% 1.42/1.82 V3, V4 ) ), =( hAPP( hAPP( 'c_Power_Opower_Opower'( V1, V2, V4 ), Z ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ],
% 1.42/1.82 [ =( X, Y ), ~( hBOOL( hAPP( hAPP( Z, hAPP( hAPP( T, hAPP( hAPP(
% 1.42/1.82 'c_Power_Opower_Opower'( U, W, V0 ), X ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( U
% 1.42/1.82 , W, V0 ), V1 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.42/1.82 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), Y ) ) ), ~(
% 1.42/1.82 'c_Ring__and__Field_Oordered__idom'( V2, V3, Y, T, Z, V4, V5, U, W, V6,
% 1.42/1.82 V0 ) ) ],
% 1.42/1.82 [ =( X, Y ), ~( hBOOL( hAPP( hAPP( Z, hAPP( hAPP( T, hAPP( hAPP(
% 1.42/1.82 'c_Power_Opower_Opower'( U, W, V0 ), V1 ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( U
% 1.42/1.82 , W, V0 ), X ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.42/1.82 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), Y ) ) ), ~(
% 1.42/1.82 'c_Ring__and__Field_Oordered__idom'( V2, V3, Y, T, Z, V4, V5, U, W, V6,
% 1.42/1.82 V0 ) ) ],
% 1.42/1.82 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), hAPP( T, U ) ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y
% 1.42/1.82 , Z ), U ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.42/1.82 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ), ~(
% 1.42/1.82 'c_Ring__and__Field_Ocomm__ring__1'( X, Y, W, T, V0, V1, Z ) ) ],
% 1.42/1.82 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_Divides_Odiv__class_Omod'( X,
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit0'(
% 1.42/1.82 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' ), 'tc_nat' ), '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'( 'c_Divides_Odiv__class_Omod'( X,
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit0'(
% 1.42/1.82 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ) ]
% 1.42/1.82 ,
% 1.42/1.82 [ ~( 'c_Ring__and__Field_Oordered__idom'( X, Y, hAPP( hAPP( Z, hAPP(
% 1.42/1.82 hAPP( 'c_Power_Opower_Opower'( T, U, W ), V0 ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( T
% 1.42/1.82 , U, W ), V1 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.42/1.82 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ), Z, V2, V3, V4, T, U, V5
% 1.42/1.82 , W ) ), =( V0, hAPP( hAPP( Z, hAPP( hAPP( 'c_Power_Opower_Opower'( T, U
% 1.42/1.82 , W ), V0 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.42/1.82 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.42/1.82 'c_Power_Opower_Opower'( T, U, W ), V1 ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ],
% 1.42/1.82 [ ~( 'c_Ring__and__Field_Oordered__idom'( X, Y, hAPP( hAPP( Z, hAPP(
% 1.42/1.82 hAPP( 'c_Power_Opower_Opower'( T, U, W ), V0 ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( T
% 1.42/1.82 , U, W ), V1 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.42/1.82 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ), Z, V2, V3, V4, T, U, V5
% 1.42/1.82 , W ) ), =( V1, hAPP( hAPP( Z, hAPP( hAPP( 'c_Power_Opower_Opower'( T, U
% 1.42/1.82 , W ), V0 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.42/1.82 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.42/1.82 'c_Power_Opower_Opower'( T, U, W ), V1 ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ],
% 1.42/1.82 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, hAPP( hAPP(
% 1.42/1.82 'c_Power_Opower_Opower'( T, U, W ), V0 ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( T
% 1.42/1.82 , U, W ), V1 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.42/1.82 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ), ~(
% 1.42/1.82 'c_Ring__and__Field_Oordered__idom'( V2, V3, Y, Z, X, V4, V5, T, U, V6, W
% 1.42/1.82 ) ) ],
% 1.42/1.82 [ ~( 'c_Ring__and__Field_Oordered__idom'( X, Y, Z, T, U, W, V0, V1, V2,
% 1.42/1.82 V3, V4 ) ), hBOOL( hAPP( hAPP( U, hAPP( hAPP( T, hAPP( hAPP(
% 1.42/1.82 'c_Power_Opower_Opower'( V1, V2, V4 ), Z ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( V1
% 1.42/1.82 , V2, V4 ), Z ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.42/1.82 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), Z ) ) ],
% 1.42/1.82 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =( hAPP( hAPP(
% 1.42/1.82 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.42/1.82 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( 'c_Power_Opower_Opower'( Z, T,
% 1.42/1.82 U ), W ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.42/1.82 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), ~(
% 1.42/1.82 'c_Ring__and__Field_Oordered__idom'( V0, V1, Y, V2, X, V3, V4, Z, T, V5,
% 1.42/1.82 U ) ) ],
% 1.42/1.82 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( Y, T ), T ) ), ~(
% 1.42/1.82 'c_OrderedGroup_Omonoid__mult'( X, Y, Z ) ) ],
% 1.42/1.82 [ ~( 'c_Ring__and__Field_Oordered__idom'( X, Y, hAPP( hAPP(
% 1.42/1.82 'c_Power_Opower_Opower'( Z, T, U ), W ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ), V0, V1, V2, V3, Z, T, V4, U ) ), =( W,
% 1.42/1.82 hAPP( hAPP( 'c_Power_Opower_Opower'( Z, T, U ), W ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ],
% 1.42/1.82 [ =( hAPP( X, hAPP( hAPP( 'c_Power_Opower_Opower'( Y, Z, T ), U ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( Y
% 1.42/1.82 , Z, T ), U ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.42/1.82 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ), ~(
% 1.42/1.82 'c_Ring__and__Field_Oordered__idom'( W, V0, V1, V2, V3, V4, X, Y, Z, V5,
% 1.42/1.82 T ) ) ],
% 1.42/1.82 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), hAPP( T, U ) ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y
% 1.42/1.82 , Z ), U ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.42/1.82 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ), ~(
% 1.42/1.82 'c_Ring__and__Field_Oordered__idom'( W, V0, V1, V2, V3, V4, T, X, Y, V5,
% 1.42/1.82 Z ) ) ],
% 1.42/1.82 [ ~( 'c_Ring__and__Field_Oordered__idom'( X, Y, Z, T, U, W, V0, V1, V2,
% 1.42/1.82 V3, V4 ) ), =( hAPP( hAPP( T, hAPP( hAPP( 'c_Power_Opower_Opower'( V1, V2
% 1.42/1.82 , V4 ), Z ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.42/1.82 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.42/1.82 'c_Power_Opower_Opower'( V1, V2, V4 ), Z ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ) ), Z ) ],
% 1.42/1.82 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.42/1.82 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'(
% 1.42/1.82 'tc_nat' ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.42/1.82 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ],
% 1.42/1.82 [ ~( hBOOL( hAPP( hAPP( X, hAPP( hAPP( 'c_Power_Opower_Opower'( Y, Z, T
% 1.42/1.82 ), U ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ) ), W ) ) ), ~(
% 1.42/1.82 'c_Ring__and__Field_Oordered__idom'( V0, V1, W, V2, V3, X, V4, Y, Z, V5,
% 1.42/1.82 T ) ) ],
% 1.42/1.82 [ ~( hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( 'c_Power_Opower_Opower'( Z,
% 1.42/1.82 T, U ), Y ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.42/1.82 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ), ~(
% 1.42/1.82 'c_Ring__and__Field_Oordered__idom'( W, V0, Y, V1, V2, X, V3, Z, T, V4, U
% 1.42/1.82 ) ) ],
% 1.42/1.82 [ ~( hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, hAPP( hAPP(
% 1.42/1.82 'c_Power_Opower_Opower'( Z, T, U ), W ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( Z
% 1.42/1.82 , T, U ), V0 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.42/1.82 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), V1 ) ) ), ~(
% 1.42/1.82 'c_Ring__and__Field_Oordered__idom'( V2, V3, V1, Y, V4, X, V5, Z, T, V6,
% 1.42/1.82 U ) ) ],
% 1.42/1.82 [ ~( hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, hAPP( hAPP(
% 1.42/1.82 'c_Power_Opower_Opower'( T, U, W ), Y ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( T
% 1.42/1.82 , U, W ), Y ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.42/1.82 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ) ), ~(
% 1.42/1.82 'c_Ring__and__Field_Oordered__idom'( V0, V1, Y, Z, V2, X, V3, T, U, V4, W
% 1.42/1.82 ) ) ],
% 1.42/1.82 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.42/1.82 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), X ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.82 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), X ) ],
% 1.42/1.82 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, hAPP( hAPP(
% 1.42/1.82 'c_Power_Opower_Opower'( T, U, W ), V0 ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( T
% 1.42/1.82 , U, W ), V1 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.42/1.82 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ), =( V0, Y ), ~(
% 1.42/1.82 'c_Ring__and__Field_Oordered__idom'( V2, V3, Y, Z, V4, X, V5, T, U, V6, W
% 1.42/1.82 ) ) ],
% 1.42/1.82 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, hAPP( hAPP(
% 1.42/1.82 'c_Power_Opower_Opower'( T, U, W ), V0 ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( T
% 1.42/1.82 , U, W ), V1 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.42/1.82 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ), =( V1, Y ), ~(
% 1.42/1.82 'c_Ring__and__Field_Oordered__idom'( V2, V3, Y, Z, V4, X, V5, T, U, V6, W
% 1.42/1.82 ) ) ],
% 1.42/1.82 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( 'c_Power_Opower_Opower'( Z, T,
% 1.42/1.82 U ), W ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.42/1.82 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), =( W, Y ), ~(
% 1.42/1.82 'c_Ring__and__Field_Oordered__idom'( V0, V1, Y, V2, V3, X, V4, Z, T, V5,
% 1.42/1.82 U ) ) ],
% 1.42/1.82 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), 'tc_nat' ), hAPP(
% 1.42/1.82 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ), ~( hBOOL(
% 1.42/1.82 hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Z ) ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.42/1.82 'tc_nat' ), Y ) ) ) ],
% 1.42/1.82 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), 'tc_nat' ), hAPP(
% 1.42/1.82 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), ~( hBOOL(
% 1.42/1.82 hAPP( 'c_HOL_Oord__class_Oless'( Y, 'tc_nat' ), Z ) ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.42/1.82 'tc_nat' ), X ) ) ) ],
% 1.42/1.82 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), 'tc_nat' ), hAPP(
% 1.42/1.82 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), ~( hBOOL(
% 1.42/1.82 hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.42/1.82 'tc_nat' ), X ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y,
% 1.42/1.82 'tc_nat' ), Z ) ) ) ],
% 1.42/1.82 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), 'tc_nat' ), hAPP(
% 1.42/1.82 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ), ~( hBOOL(
% 1.42/1.82 hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.42/1.82 'tc_nat' ), Y ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X,
% 1.42/1.82 'tc_nat' ), Z ) ) ) ],
% 1.42/1.82 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ), ~( hBOOL(
% 1.42/1.82 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.42/1.82 'tc_nat' ), Z ), X ), 'tc_nat' ), hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.42/1.82 'tc_nat' ), Z ) ) ) ],
% 1.42/1.82 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), 'tc_nat' ), hAPP(
% 1.42/1.82 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), ~( hBOOL(
% 1.42/1.82 hAPP( 'c_HOL_Oord__class_Oless'( Y, 'tc_nat' ), Z ) ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.42/1.82 'tc_nat' ), X ) ) ) ],
% 1.42/1.82 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.42/1.82 'tc_nat' ), 'tc_nat' ), X ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X ) ) ) ) ],
% 1.42/1.82 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.42/1.82 'tc_nat' ), 'tc_nat' ), X ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ) ) ],
% 1.42/1.82 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.42/1.82 'tc_nat' ), 'tc_nat' ), X ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.82 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X ), 'tc_nat'
% 1.42/1.82 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), X ) ) ) )
% 1.42/1.82 ],
% 1.42/1.82 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.42/1.82 'tc_nat' ), 'tc_nat' ), X ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.82 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), 'tc_nat'
% 1.42/1.82 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ) )
% 1.42/1.82 ],
% 1.42/1.82 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.42/1.82 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), ~(
% 1.42/1.82 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.42/1.82 'tc_nat' ), 'tc_nat' ), X ) ) ), =( Y, Z ) ],
% 1.42/1.82 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.42/1.82 'tc_nat' ), 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.42/1.82 'tc_nat' ), X ), Y ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), Y ) ) ), ~( hBOOL(
% 1.42/1.82 hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.42/1.82 'tc_nat' ), X ) ) ) ],
% 1.42/1.82 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.42/1.82 'tc_nat' ) ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.42/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y ), 'tc_nat' ),
% 1.42/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.42/1.82 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP(
% 1.42/1.82 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.42/1.82 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), T ) ) ) ), =( Z, T ), =( Y
% 1.42/1.82 , 'c_HOL_Ozero__class_Ozero'( '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' ) ), =( X,
% 1.42/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.42/1.82 [ ~( =( X, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y
% 1.42/1.82 ) ) ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 1.42/1.82 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.42/1.82 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), X, 'tc_nat' ),
% 1.42/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.42/1.82 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.42/1.82 'c_Finite__Set_Osetsum'( Y, 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.42/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit0'(
% 1.42/1.82 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat', X )
% 1.42/1.82 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 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( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), hAPP( Y,
% 1.42/1.82 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ) ), hAPP( Y,
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), hAPP( Y,
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.42/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ],
% 1.42/1.82 [ hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.42/1.82 'tc_nat' ), hAPP( 'c_Suc', X ) ), Y ), 'tc_nat' ), hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc', X ) ), Z ) ) ),
% 1.42/1.82 ~( hBOOL( hAPP( 'c_lessequals'( Y, 'tc_nat' ), Z ) ) ) ],
% 1.42/1.82 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.42/1.82 hAPP( 'c_Suc', Z ) ), X ), 'tc_nat' ), hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc', Z ) ), Y ) ) ) )
% 1.42/1.82 ],
% 1.42/1.82 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc', X ) ), Y ),
% 1.42/1.82 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP(
% 1.42/1.82 'c_Suc', X ) ), Z ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y,
% 1.42/1.82 'tc_nat' ), Z ) ) ) ],
% 1.42/1.82 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ), ~( hBOOL(
% 1.42/1.82 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.42/1.82 'tc_nat' ), hAPP( 'c_Suc', Z ) ), X ), 'tc_nat' ), hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc', Z ) ), Y ) ) ) )
% 1.42/1.82 ],
% 1.42/1.82 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc'
% 1.42/1.82 , X ) ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ),
% 1.42/1.82 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.42/1.82 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), hAPP(
% 1.42/1.82 'c_Suc', Y ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.42/1.82 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.42/1.82 [ ~( 'class_Orderings_Oorder'( X ) ), ~( =(
% 1.42/1.82 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ),
% 1.42/1.82 'c_SetInterval_Oord__class_OatLeastLessThan'( Y, Z, X ) ) ), ~( hBOOL(
% 1.42/1.82 hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ) ) ],
% 1.42/1.82 [ ~( 'class_Orderings_Oorder'( X ) ), =( 'c_Orderings_Obot__class_Obot'(
% 1.42/1.82 'tc_fun'( X, 'tc_bool' ) ), 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.42/1.82 Y, Z, X ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ) ],
% 1.42/1.82 [ ~( 'class_Orderings_Oorder'( X ) ), =(
% 1.42/1.82 'c_SetInterval_Oord__class_OatLeastLessThan'( Y, Z, X ),
% 1.42/1.82 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ), ~( hBOOL(
% 1.42/1.82 hAPP( 'c_lessequals'( Z, X ), Y ) ) ) ],
% 1.42/1.82 [ ~( 'class_Orderings_Oorder'( X ) ), ~( =(
% 1.42/1.82 'c_SetInterval_Oord__class_OatLeastLessThan'( Y, Z, X ),
% 1.42/1.82 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ) ), ~( hBOOL(
% 1.42/1.82 hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ) ) ],
% 1.42/1.82 [ ~( 'class_Orderings_Oorder'( X ) ), =(
% 1.42/1.82 'c_SetInterval_Oord__class_OatLeastLessThan'( Y, Z, X ),
% 1.42/1.82 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ), hBOOL( hAPP(
% 1.42/1.82 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ) ],
% 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__ring'( X ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.82 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.42/1.82 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'(
% 1.42/1.82 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), X ), 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__ring'( X ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.82 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oinverse__class_Odivide'( Y
% 1.42/1.82 , 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.82 'c_Int_OPls' ) ), X ), X ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.82 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ) ],
% 1.42/1.82 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP(
% 1.42/1.82 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP(
% 1.42/1.82 hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.42/1.82 ) ],
% 1.42/1.82 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =( hAPP( hAPP(
% 1.42/1.82 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP(
% 1.42/1.82 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), =( Y, Z ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL(
% 1.42/1.82 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ) ]
% 1.42/1.82 ,
% 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 ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.42/1.82 ), Y ), Y ) ) ],
% 1.42/1.82 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP(
% 1.42/1.82 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.42/1.82 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ],
% 1.42/1.82 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =( hAPP( hAPP(
% 1.42/1.82 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.42/1.82 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.42/1.82 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.42/1.82 =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.82 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =( hAPP( hAPP(
% 1.42/1.82 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.42/1.82 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.42/1.82 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.42/1.82 =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.82 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.42/1.82 'c_lessequals'( Y, X ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.42/1.82 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_lessequals'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), hAPP( hAPP(
% 1.42/1.82 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ) ],
% 1.42/1.82 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP(
% 1.42/1.82 hAPP( 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.42/1.82 ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ) ],
% 1.42/1.82 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.42/1.82 ), Y ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.42/1.82 ) ],
% 1.42/1.82 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP( hAPP(
% 1.42/1.82 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.42/1.82 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.42/1.82 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.42/1.82 ,
% 1.42/1.82 [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.42/1.82 'c_Int_OBit0'( 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat'
% 1.42/1.82 ), 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'(
% 1.42/1.82 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), =(
% 1.42/1.82 'c_Divides_Odiv__class_Omod'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.42/1.82 'c_Int_OBit0'( 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat'
% 1.42/1.82 ), 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.42/1.82 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), =(
% 1.42/1.82 'c_Divides_Odiv__class_Omod'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.42/1.82 'c_Int_OBit0'( 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat'
% 1.42/1.82 ), 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), =(
% 1.42/1.82 'c_Divides_Odiv__class_Omod'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.42/1.82 'c_Int_OBit0'( 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat'
% 1.42/1.82 ), 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.42/1.82 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ), hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ), U ) ), hAPP( hAPP(
% 1.42/1.82 'c_Power_Opower_Opower'( X, Y, Z ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.42/1.82 X, Y, Z ), T ), U ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.42/1.82 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ), ~(
% 1.42/1.82 'c_OrderedGroup_Omonoid__mult'( X, Y, Z ) ) ],
% 1.42/1.82 [ ~( 'class_Lattices_Odistrib__lattice'( X ) ), =(
% 1.42/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.42/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ),
% 1.42/1.82 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.42/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ),
% 1.42/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T, X ), X ) ) ],
% 1.42/1.82 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 1.42/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), Z ), ~( hBOOL(
% 1.42/1.82 hAPP( 'c_lessequals'( Z, X ), Y ) ) ) ],
% 1.42/1.82 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), ~( =(
% 1.42/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), Y ) ), hBOOL(
% 1.42/1.82 hAPP( 'c_lessequals'( Y, X ), Z ) ) ],
% 1.42/1.82 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 1.42/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), Y ), ~( hBOOL(
% 1.42/1.82 hAPP( 'c_lessequals'( Y, X ), Z ) ) ) ],
% 1.42/1.82 [ ~( =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ), =( X,
% 1.42/1.82 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.42/1.82 [ ~( =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ), =( Y,
% 1.42/1.82 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 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_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.42/1.82 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.42/1.82 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), T ) ) ],
% 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 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 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' ), 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' ), X ), T ) ), hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ) ), =( Y, T ), =( X
% 1.42/1.82 , Z ) ],
% 1.42/1.82 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 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' ), 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' ), X ), T ) ), hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ) ), =( Y, T ), =( X
% 1.42/1.82 , Z ) ],
% 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 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), X ) ) ) ) ],
% 1.42/1.82 [ hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.42/1.82 'tc_nat' ), X ), Y ), 'tc_nat' ), hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_lessequals'( Y, 'tc_nat' ), T ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( X
% 1.42/1.82 , 'tc_nat' ), Z ) ) ) ],
% 1.42/1.82 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.42/1.82 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), Z ), 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 ) ), hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ) ) ],
% 1.42/1.82 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), hAPP(
% 1.42/1.82 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ), 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 ) ), hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ) ],
% 1.42/1.82 [ hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.42/1.82 'tc_nat' ), X ), Y ), 'tc_nat' ), hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_lessequals'( X, 'tc_nat' ), Z ) ) ) ],
% 1.42/1.82 [ hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.42/1.82 'tc_nat' ), X ), Y ), 'tc_nat' ), hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_lessequals'( Y, 'tc_nat' ), Z ) ) ) ],
% 1.42/1.82 [ hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.42/1.82 'tc_nat' ), X ), Y ), 'tc_nat' ), hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_lessequals'( Y, 'tc_nat' ), Z ) ) ) ],
% 1.42/1.82 [ hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.42/1.82 'tc_nat' ), X ), Y ), 'tc_nat' ), hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_lessequals'( X, 'tc_nat' ), Z ) ) ) ],
% 1.42/1.82 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ), ~( hBOOL(
% 1.42/1.82 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.42/1.82 'tc_nat' ), Z ), X ), 'tc_nat' ), hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ) ) ],
% 1.42/1.82 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ), ~( hBOOL(
% 1.42/1.82 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.42/1.82 'tc_nat' ), X ), Z ), 'tc_nat' ), hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ) ) ) ],
% 1.42/1.82 [ =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_HOL_Oone__class_Oone'(
% 1.42/1.82 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ) ],
% 1.42/1.82 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.42/1.82 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), X ), X ) ],
% 1.42/1.82 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.42/1.82 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), X ) ],
% 1.42/1.82 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 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 ) ), 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 ) ), hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.42/1.82 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 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 ) ), 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 ) ), hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.42/1.82 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.42/1.82 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.42/1.82 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.42/1.82 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ) ) ],
% 1.42/1.82 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.42/1.82 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), =( X, 'c_HOL_Oone__class_Oone'(
% 1.42/1.82 'tc_nat' ) ) ],
% 1.42/1.82 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.42/1.82 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), =( Y, 'c_HOL_Oone__class_Oone'(
% 1.42/1.82 'tc_nat' ) ) ],
% 1.42/1.82 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), 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 ), Y ) ), 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' ), hAPP( hAPP(
% 1.42/1.82 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ), Y ) ), T ) ) ],
% 1.42/1.82 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.42/1.82 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ), Z ),
% 1.42/1.82 'c_HOL_Ominus__class_Ominus'( 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_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ),
% 1.42/1.82 'c_HOL_Ominus__class_Ominus'( 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 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), X ) ) ) ],
% 1.42/1.82 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.42/1.82 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'(
% 1.42/1.82 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( '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 [ =( 'c_SetInterval_Oord__class_OatLeastLessThan'( X, hAPP( 'c_Suc', Y )
% 1.42/1.82 , 'tc_nat' ), 'c_Set_Oinsert'( Y,
% 1.42/1.82 'c_SetInterval_Oord__class_OatLeastLessThan'( X, Y, 'tc_nat' ), 'tc_nat'
% 1.42/1.82 ) ), ~( hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ) ) ],
% 1.42/1.82 [ =( 'c_Set_Oimage'( X, 'c_Lattices_Oupper__semilattice__class_Osup'( Y
% 1.42/1.82 , Z, 'tc_fun'( T, 'tc_bool' ) ), T, U ),
% 1.42/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( 'c_Set_Oimage'( X, Y, T, U
% 1.42/1.82 ), 'c_Set_Oimage'( X, Z, T, U ), 'tc_fun'( U, 'tc_bool' ) ) ) ],
% 1.42/1.82 [ =( 'c_Set_Oimage'( X, 'c_Set_Oinsert'( Y, Z, T ), T, U ),
% 1.42/1.82 'c_Set_Oinsert'( hAPP( X, Y ), 'c_Set_Oimage'( X, Z, T, U ), U ) ) ],
% 1.42/1.82 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( 'c_Set_Oinsert'( X, Y
% 1.42/1.82 , Z ), 'c_Set_Oinsert'( X, T, Z ), 'tc_fun'( Z, 'tc_bool' ) ),
% 1.42/1.82 'c_Set_Oinsert'( X, 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T,
% 1.42/1.82 'tc_fun'( Z, 'tc_bool' ) ), Z ) ) ],
% 1.42/1.82 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X,
% 1.42/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, 'tc_fun'( T,
% 1.42/1.82 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ),
% 1.42/1.82 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.42/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( T,
% 1.42/1.82 'tc_bool' ) ), 'c_Lattices_Oupper__semilattice__class_Osup'( X, Z,
% 1.42/1.82 'tc_fun'( T, 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 1.42/1.82 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.42/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 1.42/1.82 'tc_bool' ) ), T, 'tc_fun'( Z, 'tc_bool' ) ),
% 1.42/1.82 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.42/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( X, T, 'tc_fun'( Z,
% 1.42/1.82 'tc_bool' ) ), 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T,
% 1.42/1.82 'tc_fun'( Z, 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.42/1.82 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 1.42/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, 'tc_fun'( T,
% 1.42/1.82 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ),
% 1.42/1.82 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.42/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( T,
% 1.42/1.82 'tc_bool' ) ), 'c_Lattices_Olower__semilattice__class_Oinf'( X, Z,
% 1.42/1.82 'tc_fun'( T, 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 1.42/1.82 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.42/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 1.42/1.82 'tc_bool' ) ), T, 'tc_fun'( Z, 'tc_bool' ) ),
% 1.42/1.82 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.42/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( X, T, 'tc_fun'( Z,
% 1.42/1.82 'tc_bool' ) ), 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T,
% 1.42/1.82 'tc_fun'( Z, 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.42/1.82 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.42/1.82 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.42/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 1.42/1.82 'tc_bool' ) ), 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T,
% 1.42/1.82 'tc_fun'( Z, 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ),
% 1.42/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( T, X, 'tc_fun'( Z,
% 1.42/1.82 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ),
% 1.42/1.82 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.42/1.82 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.42/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 1.42/1.82 'tc_bool' ) ), 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T,
% 1.42/1.82 'tc_fun'( Z, 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ),
% 1.42/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( T, X, 'tc_fun'( Z,
% 1.42/1.82 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.42/1.82 [ =( 'c_HOL_Oord__class_Oless'( 'v_n', 'tc_nat' ), 'c_lessequals'( hAPP(
% 1.42/1.82 'c_Suc', 'v_n' ), 'tc_nat' ) ) ],
% 1.42/1.82 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.42/1.82 'tc_nat' ), 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.42/1.82 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'(
% 1.42/1.82 'tc_nat' ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.42/1.82 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) ) ), ~( hBOOL(
% 1.42/1.82 hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.42/1.82 'tc_nat' ), X ) ) ) ],
% 1.42/1.82 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.42/1.82 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'(
% 1.42/1.82 'tc_nat' ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.42/1.82 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), hAPP( 'c_Suc',
% 1.42/1.82 'c_Divides_Odiv__class_Odiv'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.42/1.82 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) )
% 1.42/1.82 ), 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 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 ) ), hBOOL( hAPP( 'c_lessequals'( Y, X ),
% 1.42/1.82 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.42/1.82 , X ), X ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ),
% 1.42/1.82 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Z
% 1.42/1.82 , X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ) ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), Z ) ) ) ],
% 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 ) ), hBOOL( hAPP( 'c_lessequals'(
% 1.42/1.82 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.42/1.82 , X ), X ), X ), T ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.42/1.82 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ), Y ) ) ), ~( hBOOL(
% 1.42/1.82 hAPP( 'c_lessequals'( Y, X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.42/1.82 ), T ), 'c_Int_Onumber__class_Onumber__of'( 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 ) ), hBOOL( hAPP( 'c_lessequals'(
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.42/1.82 'c_HOL_Oinverse__class_Odivide'( Z, T, X ) ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_lessequals'( 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.42/1.82 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Z
% 1.42/1.82 , X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ) ) ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ), Z ) ) ) ],
% 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 ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.42/1.82 'c_HOL_Oinverse__class_Odivide'( Z, T, X ) ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_HOL_Oord__class_Oless'( T, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.42/1.82 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ), hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.42/1.82 , X ) ), T ) ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.42/1.82 , X ) ), T ), X ), Z ) ) ) ],
% 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 ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.42/1.82 'c_HOL_Oinverse__class_Odivide'( Z, T, X ) ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_HOL_Oord__class_Oless'( T, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.42/1.82 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ), hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.42/1.82 , X ) ), T ) ) ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.82 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ],
% 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 ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X
% 1.42/1.82 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T ) ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_HOL_Oord__class_Oless'( T, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.42/1.82 , hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X )
% 1.42/1.82 , X ), T ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ),
% 1.42/1.82 'c_HOL_Oinverse__class_Odivide'( 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 ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.42/1.82 'c_HOL_Oinverse__class_Odivide'( Z, T, X ) ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ), X
% 1.42/1.82 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_HOL_Oord__class_Oless'( Z, X ), hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.42/1.82 , X ) ), T ) ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.42/1.82 , X ) ), T ), X ), Z ) ) ) ],
% 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 ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.42/1.82 'c_HOL_Oinverse__class_Odivide'( Z, T, X ) ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ), X
% 1.42/1.82 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), hBOOL( hAPP(
% 1.42/1.82 'c_HOL_Oord__class_Oless'( T, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.42/1.82 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.42/1.82 , X ) ), T ), X ), Z ) ) ) ],
% 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 ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.42/1.82 'c_HOL_Oinverse__class_Odivide'( Z, T, X ) ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ), X
% 1.42/1.82 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_HOL_Oord__class_Oless'( Z, X ), hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.42/1.82 , X ) ), T ) ) ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.82 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ],
% 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 ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.82 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.42/1.82 , 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ), Y ) ) ), ~(
% 1.42/1.82 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( T
% 1.42/1.82 , X ) ), Z ) ) ) ) ],
% 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 ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X
% 1.42/1.82 ), 'c_HOL_Oinverse__class_Odivide'( Z,
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.42/1.82 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ), hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ) ) ), hBOOL( hAPP(
% 1.42/1.82 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 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 ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.82 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.42/1.82 , X ), X ), X ), T ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.82 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.42/1.82 , T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ), Y ) ) ), hBOOL(
% 1.42/1.82 hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 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 ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.82 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ) ), hBOOL( hAPP(
% 1.42/1.82 'c_HOL_Oord__class_Oless'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.42/1.82 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( T
% 1.42/1.82 , X ) ), Z ) ) ) ) ],
% 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 ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.82 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.42/1.82 , 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ), Y ) ) ), hBOOL(
% 1.42/1.82 hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z
% 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 ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X
% 1.42/1.82 ), 'c_HOL_Oinverse__class_Odivide'( Z,
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X ), X
% 1.42/1.82 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_HOL_Oord__class_Oless'( Z, X ), hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ) ) ), hBOOL( hAPP(
% 1.42/1.82 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 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 ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X
% 1.42/1.82 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X ), X
% 1.42/1.82 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), hBOOL( hAPP(
% 1.42/1.82 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_HOL_Oord__class_Oless'( Z, X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( T, X ), 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 ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.82 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.42/1.82 , X ), X ), X ), T ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ),
% 1.42/1.82 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.42/1.82 , T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ), Y ) ) ), hBOOL(
% 1.42/1.82 hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 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 ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.42/1.82 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ), T ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ), X
% 1.42/1.82 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), hBOOL( hAPP(
% 1.42/1.82 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( T,
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), 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 ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.82 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) )
% 1.42/1.82 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( T
% 1.42/1.82 , X ) ), Z ) ) ) ) ],
% 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 ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X
% 1.42/1.82 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T ) ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) )
% 1.42/1.82 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.82 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 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 ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.42/1.82 'c_HOL_Oinverse__class_Odivide'( Z, T, X ) ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) )
% 1.42/1.82 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.42/1.82 , X ) ), T ), X ), Z ) ) ) ],
% 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 ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.42/1.82 hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), Z ), X ), T ) ), ~( hBOOL(
% 1.42/1.82 hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z
% 1.42/1.82 ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.42/1.82 'c_HOL_Oinverse__class_Odivide'( 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 ) ), hBOOL( hAPP( 'c_lessequals'(
% 1.42/1.82 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ), Y ) ) ), ~( hBOOL(
% 1.42/1.82 hAPP( 'c_lessequals'( Y, X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.42/1.82 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ) ) ) ) ],
% 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 ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.82 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_HOL_Oord__class_Oless'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.42/1.82 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( T
% 1.42/1.82 , X ) ), Z ), X ), Y ) ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.82 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ],
% 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 ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.42/1.82 hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), Z ), X ), T ) ), ~( hBOOL(
% 1.42/1.82 hAPP( 'c_HOL_Oord__class_Oless'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.42/1.82 ) ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.82 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X
% 1.42/1.82 ), 'c_Int_Onumber__class_Onumber__of'( 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 ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X
% 1.42/1.82 ), 'c_HOL_Oinverse__class_Odivide'( Z,
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.42/1.82 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ), hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ) ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.42/1.82 , Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), Z ) ) ) ],
% 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 ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.82 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.42/1.82 , X ), X ), X ), T ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.82 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.42/1.82 , T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ), Y ) ) ), ~(
% 1.42/1.82 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 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 ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.82 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_HOL_Oord__class_Oless'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.42/1.82 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( T
% 1.42/1.82 , X ) ), Z ), X ), Y ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y
% 1.42/1.82 , X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ) ) ) ) ],
% 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 ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X
% 1.42/1.82 ), 'c_HOL_Oinverse__class_Odivide'( Z,
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.42/1.82 , hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( T, X ), X ),
% 1.42/1.82 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.42/1.82 , Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), Z ) ) ) ],
% 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 ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.82 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.42/1.82 , X ), X ), X ), T ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.82 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ), hBOOL( hAPP(
% 1.42/1.82 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ), X
% 1.42/1.82 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_HOL_Oord__class_Oless'( Y, X ), hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 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 ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X
% 1.42/1.82 ), 'c_HOL_Oinverse__class_Odivide'( Z,
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X ), X
% 1.42/1.82 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_HOL_Oord__class_Oless'( Z, X ), hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ) ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.42/1.82 , Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), Z ) ) ) ],
% 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 ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.82 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.42/1.82 , X ), X ), X ), T ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ),
% 1.42/1.82 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.42/1.82 , T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ), Y ) ) ), ~(
% 1.42/1.82 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 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 ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X
% 1.42/1.82 ), 'c_HOL_Oinverse__class_Odivide'( Z,
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.42/1.82 , Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), Z ) ) ) ],
% 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 ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.42/1.82 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ), T ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Oinverse__class_Odivide'( T,
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( Z, X ), 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 ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.82 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.42/1.82 , X ), X ), X ), T ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.82 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.42/1.82 Z, X ) ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), hAPP(
% 1.42/1.82 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 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 ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X
% 1.42/1.82 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), X ), Z ) ) ) ],
% 1.42/1.82 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.42/1.82 'class_Int_Onumber__ring'( X ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.42/1.82 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_HOL_Oord__class_Oless'( Y, 'tc_Int_Oint' ), 'c_Int_OPls' ) ) ) ],
% 1.42/1.82 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.42/1.82 'class_Int_Onumber__ring'( X ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.82 Y, 'tc_Int_Oint' ), 'c_Int_OPls' ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ), X
% 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 'class_Int_Onumber__ring'( X ) ), hBOOL( hAPP( 'c_lessequals'(
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.42/1.82 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y,
% 1.42/1.82 'tc_Int_Oint' ), 'c_Int_OPls' ) ) ) ],
% 1.42/1.82 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.42/1.82 'class_Int_Onumber__ring'( X ) ), hBOOL( hAPP( 'c_lessequals'( Y,
% 1.42/1.82 'tc_Int_Oint' ), 'c_Int_OPls' ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 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 'class_Int_Onumber__ring'( X ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.82 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.42/1.82 Y, X ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_Int_OPls',
% 1.42/1.82 'tc_Int_Oint' ), Y ) ) ) ],
% 1.42/1.82 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.42/1.82 'class_Int_Onumber__ring'( X ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.42/1.82 'c_Int_OPls', 'tc_Int_Oint' ), Y ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ) ) ],
% 1.42/1.82 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.42/1.82 'class_Int_Onumber__ring'( X ) ), hBOOL( hAPP( 'c_lessequals'(
% 1.42/1.82 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.42/1.82 Y, X ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( 'c_Int_OPls', 'tc_Int_Oint' )
% 1.42/1.82 , Y ) ) ) ],
% 1.42/1.82 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.42/1.82 'class_Int_Onumber__ring'( X ) ), hBOOL( hAPP( 'c_lessequals'(
% 1.42/1.82 'c_Int_OPls', 'tc_Int_Oint' ), Y ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.42/1.82 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.42/1.82 Y, X ) ) ) ) ],
% 1.42/1.82 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.42/1.82 X ), 'c_HOL_Oone__class_Oone'( X ) ), 'c_HOL_Oone__class_Oone'( X ) ) ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( Y ), X ) ) ],
% 1.42/1.82 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.42/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP(
% 1.42/1.82 hAPP( 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.42/1.82 ) ), 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ) ) ) ), hBOOL(
% 1.42/1.82 hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 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_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.42/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), hBOOL( hAPP(
% 1.42/1.82 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP(
% 1.42/1.82 hAPP( 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ) ) ) ],
% 1.42/1.82 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.42/1.82 'class_Power_Opower'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.42/1.82 , 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( hAPP( hAPP(
% 1.42/1.82 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.42/1.82 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.42/1.82 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =(
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.42/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_lessequals'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ), X ),
% 1.42/1.82 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.42/1.82 [ =( X, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ),
% 1.42/1.82 'c_Parity_Osko__Parity__Xeven__mult__two__ex__1__1'( X ) ) ), ~(
% 1.42/1.82 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.42/1.82 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( 'c_Power_Opower_Opower'( Z, T,
% 1.42/1.82 U ), W ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ), V0 ) ) ) ), ~(
% 1.42/1.82 'c_Ring__and__Field_Oordered__idom'( V1, V2, Y, V3, X, V4, V5, Z, T, V6,
% 1.42/1.82 U ) ) ],
% 1.42/1.82 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), hAPP( T, U ) ),
% 1.42/1.82 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ), W ) ), hAPP( hAPP(
% 1.42/1.82 'c_Power_Opower_Opower'( X, Y, Z ), U ), hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ), W ) ) ), ~(
% 1.42/1.82 'c_Ring__and__Field_Ocomm__ring__1'( X, Y, V0, T, V1, V2, Z ) ) ],
% 1.42/1.82 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), hAPP( T, X ) ),
% 1.42/1.82 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ), U ) ), X ), ~(
% 1.42/1.82 'c_Ring__and__Field_Ocomm__ring__1'( X, Y, W, T, V0, V1, Z ) ) ],
% 1.42/1.82 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), ~(
% 1.42/1.82 'class_RealVector_Ometric__space'( Y ) ), 'c_Lim_OLIM'( 'c_COMBB'( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( X ), Z ), T, X, X, Y ), U,
% 1.42/1.82 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_Lim_OLIM'( T, U,
% 1.42/1.82 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.42/1.82 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), ~(
% 1.42/1.82 'class_RealVector_Ometric__space'( Y ) ), 'c_Lim_OLIM'( 'c_COMBB'( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( X ), Z ), T, X, X, Y ), U,
% 1.42/1.82 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_Lim_OLIM'( T, U,
% 1.42/1.82 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 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'( X ) ), =( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.42/1.82 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.42/1.82 X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 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'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( hAPP(
% 1.42/1.82 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( Z, X ) ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y ), =(
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 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'( X ) ), =( Y, 'c_HOL_Oinverse__class_Odivide'( hAPP(
% 1.42/1.82 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( Z, X ) ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ), =(
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 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'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.42/1.82 X ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ) ) ), =( hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.42/1.82 , X ) ), T ), Z ), =( T, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 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'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.42/1.82 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =(
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.42/1.82 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.42/1.82 X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), Z ), Z, X ) ) ],
% 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'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.42/1.82 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =(
% 1.42/1.82 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.42/1.82 X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), Z ), Z, X ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ],
% 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'( X ) ), =( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.42/1.82 , 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.42/1.82 , X ) ), Z ), Z, X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 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'( X ) ), =( Y, hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ), =(
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 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'( X ) ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.42/1.82 X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y ), =(
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 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'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( hAPP(
% 1.42/1.82 hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), Z ), Z, X ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), =( Z,
% 1.42/1.82 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 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'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( hAPP(
% 1.42/1.82 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.42/1.82 ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.42/1.82 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 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'( X ) ), ~( =( 'c_HOL_Oinverse__class_Odivide'( Y, Z,
% 1.42/1.82 X ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ), =( Y, hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( T
% 1.42/1.82 , X ) ), Z ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 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 ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', X ), X ),
% 1.42/1.82 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.82 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( Y ), 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 ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ) ],
% 1.42/1.82 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.42/1.82 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.42/1.82 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.42/1.82 ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.42/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( =( hAPP( hAPP(
% 1.42/1.82 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.42/1.82 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.42/1.82 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.42/1.82 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.42/1.82 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.42/1.82 'c_HOL_Ozero__class_Ozero'( X ) ), =( 'c_Int_Onumber__class_Onumber__of'(
% 1.42/1.82 Y, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.42/1.82 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.42/1.82 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.42/1.82 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.42/1.82 ), =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ),
% 1.42/1.82 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.42/1.82 , 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ), =(
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.42/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.42/1.82 [ ~( 'class_Int_Onumber__ring'( X ) ), ~( 'c_Int_Oiszero'(
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ), X
% 1.42/1.82 ) ) ],
% 1.42/1.82 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oone__class_Oone'( X )
% 1.42/1.82 , 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X )
% 1.42/1.82 ) ],
% 1.42/1.82 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ),
% 1.42/1.82 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.42/1.82 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.42/1.82 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ), X
% 1.42/1.82 ), Y ) ],
% 1.42/1.82 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.42/1.82 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ), X
% 1.42/1.82 ), Y ) ],
% 1.42/1.82 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.42/1.82 'class_Int_Onumber__ring'( X ) ), =( hAPP(
% 1.42/1.82 'c_HOL_Oinverse__class_Oinverse'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.42/1.82 'c_Int_OBit1'( 'c_Int_OPls' ), X ) ), 'c_Int_Onumber__class_Onumber__of'(
% 1.42/1.82 'c_Int_OBit1'( 'c_Int_OPls' ), X ) ) ],
% 1.42/1.82 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.42/1.82 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.42/1.82 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.42/1.82 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.42/1.82 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.42/1.82 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.42/1.82 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), X ) ), Y ) ), Z ) ) ) ]
% 1.42/1.82 ,
% 1.42/1.82 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.42/1.82 'c_HOL_Ozero__class_Ozero'( X ) ), ~( hBOOL( hAPP( 'c_lessequals'( hAPP(
% 1.42/1.82 hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.42/1.82 ) ) ) ) ],
% 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( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), 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( '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 ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.42/1.82 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ],
% 1.42/1.82 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP(
% 1.42/1.82 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.42/1.82 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ) ) ],
% 1.42/1.82 [ =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_lessequals'( X, 'tc_Int_Oint' ), 'c_Int_OPls' ) ) ) ],
% 1.42/1.82 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ) ), hBOOL( hAPP(
% 1.42/1.82 'c_lessequals'( X, 'tc_Int_Oint' ), 'c_Int_OPls' ) ) ],
% 1.42/1.82 [ =( 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ),
% 1.42/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.42/1.82 X, 'tc_Int_Oint' ), 'c_Int_OPls' ) ) ) ],
% 1.42/1.82 [ ~( =( 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ),
% 1.42/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), hBOOL( hAPP( 'c_lessequals'(
% 1.42/1.82 X, 'tc_Int_Oint' ), 'c_Int_OPls' ) ) ],
% 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_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 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc',
% 1.42/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ), hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 1.42/1.82 'tc_nat' ) ), 'tc_nat' ), X ) ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 1.42/1.82 'tc_nat' ) ), 'tc_nat' ), Y ) ) ) ],
% 1.42/1.82 [ hBOOL( hAPP( 'c_lessequals'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 1.42/1.82 'tc_nat' ) ), 'tc_nat' ), X ) ), ~( hBOOL( hAPP( 'c_lessequals'( hAPP(
% 1.42/1.82 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ), hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X ) ) ) ) ],
% 1.42/1.82 [ hBOOL( hAPP( 'c_lessequals'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 1.42/1.82 'tc_nat' ) ), 'tc_nat' ), X ) ), ~( hBOOL( hAPP( 'c_lessequals'( hAPP(
% 1.42/1.82 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ), hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ) ) ],
% 1.42/1.82 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 1.42/1.82 'tc_nat' ) ), 'tc_nat' ), Y ) ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 1.42/1.82 'tc_nat' ) ), 'tc_nat' ), X ) ) ) ],
% 1.42/1.82 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X ) ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 1.42/1.82 'tc_nat' ) ), 'tc_nat' ), Y ) ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 1.42/1.82 'tc_nat' ) ), 'tc_nat' ), X ) ) ) ],
% 1.42/1.82 [ hBOOL( hAPP( 'c_lessequals'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 1.42/1.82 'tc_nat' ) ), 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.42/1.82 'tc_nat' ), X ), Y ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( hAPP( 'c_Suc',
% 1.42/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ), Y ) ) ), ~( hBOOL(
% 1.42/1.82 hAPP( 'c_lessequals'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.42/1.82 ) ), 'tc_nat' ), X ) ) ) ],
% 1.42/1.82 [ =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ),
% 1.42/1.82 'tc_nat' ) ) ],
% 1.42/1.82 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ),
% 1.42/1.82 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.42/1.82 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), hAPP( T, X ) ),
% 1.42/1.82 hAPP( 'c_Suc', hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ), U ) ) ), hAPP( T, X ) ), ~(
% 1.42/1.82 'c_Ring__and__Field_Ocomm__ring__1'( X, Y, W, T, V0, V1, Z ) ) ],
% 1.42/1.82 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ), hAPP( 'c_Suc'
% 1.42/1.82 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ), U ) ) ), hAPP( hAPP( Y, T ), hAPP( hAPP(
% 1.42/1.82 'c_Power_Opower_Opower'( X, Y, Z ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.42/1.82 X, Y, Z ), T ), U ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.42/1.82 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), ~(
% 1.42/1.82 'c_OrderedGroup_Omonoid__mult'( X, Y, Z ) ) ],
% 1.42/1.82 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( 'c_Power_Opower_Opower'( Y, Z, T ),
% 1.42/1.82 U ), hAPP( 'c_Suc', hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' )
% 1.42/1.82 , 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ), W ) ) ) ), V0 ) ), ~( hBOOL( hAPP( hAPP(
% 1.42/1.82 X, U ), V0 ) ) ), ~( 'c_Ring__and__Field_Oordered__idom'( V1, V2, V0, V3
% 1.42/1.82 , V4, X, V5, Y, Z, V6, T ) ) ],
% 1.42/1.82 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( X, Y ), hAPP(
% 1.42/1.82 hAPP( 'c_Power_Opower_Opower'( T, U, W ), Z ), hAPP( 'c_Suc', hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ), V0 ) ) ) ) ) ), ~(
% 1.42/1.82 'c_Ring__and__Field_Oordered__idom'( V1, V2, Y, V3, X, V4, V5, T, U, V6,
% 1.42/1.82 W ) ) ],
% 1.42/1.82 [ =( X, hAPP( 'c_Suc', hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.42/1.82 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.42/1.82 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ),
% 1.42/1.82 'c_Parity_Osko__Parity__Xodd__Suc__mult__two__ex__1__1'( X ) ) ) ),
% 1.42/1.82 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.42/1.82 [ ~( 'class_Orderings_Oorder'( X ) ), =(
% 1.42/1.82 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.42/1.82 'c_SetInterval_Oord__class_OatLeastLessThan'( Y, Z, X ),
% 1.42/1.82 'c_SetInterval_Oord__class_OatLeast'( Z, X ), 'tc_fun'( X, 'tc_bool' ) )
% 1.42/1.82 , 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ) ],
% 1.42/1.82 [ ~( 'class_Orderings_Oorder'( X ) ), =(
% 1.42/1.82 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.42/1.82 'c_SetInterval_Oord__class_OgreaterThanLessThan'( Y, Z, X ),
% 1.42/1.82 'c_SetInterval_Oord__class_OatLeastLessThan'( Z, T, X ), 'tc_fun'( X,
% 1.42/1.82 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) )
% 1.42/1.82 ) ],
% 1.42/1.82 [ ~( 'class_Orderings_Oorder'( X ) ), =(
% 1.42/1.82 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.42/1.82 'c_SetInterval_Oord__class_OatLeastLessThan'( Y, Z, X ),
% 1.42/1.82 'c_SetInterval_Oord__class_OatLeastAtMost'( Z, T, X ), 'tc_fun'( X,
% 1.42/1.82 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) )
% 1.42/1.82 ) ],
% 1.42/1.82 [ ~( 'class_Orderings_Oorder'( X ) ), =(
% 1.42/1.82 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.42/1.82 'c_SetInterval_Oord__class_OlessThan'( Y, X ),
% 1.42/1.82 'c_SetInterval_Oord__class_OatLeastLessThan'( Y, Z, X ), 'tc_fun'( X,
% 1.42/1.82 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) )
% 1.42/1.82 ) ],
% 1.42/1.82 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.42/1.82 'c_Finite__Set_Osetsum'( Y, 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.42/1.82 hAPP( 'c_Suc', Z ), hAPP( 'c_Suc', T ), 'tc_nat' ), 'tc_nat', X ),
% 1.42/1.82 'c_Finite__Set_Osetsum'( 'c_COMBB'( Y, 'c_Suc', 'tc_nat', X, 'tc_nat' ),
% 1.42/1.82 'c_SetInterval_Oord__class_OatLeastLessThan'( Z, T, 'tc_nat' ), 'tc_nat'
% 1.42/1.82 , X ) ) ],
% 1.42/1.82 [ =( 'c_SetInterval_Oord__class_OatLeastLessThan'( X, hAPP( 'c_Suc', Y )
% 1.42/1.82 , 'tc_nat' ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_nat',
% 1.42/1.82 'tc_bool' ) ) ), hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ) ],
% 1.42/1.82 [ =( 'c_SetInterval_Oord__class_OatLeastLessThan'( X, hAPP( 'c_Suc', X )
% 1.42/1.82 , 'tc_nat' ), 'c_Set_Oinsert'( X, 'c_Orderings_Obot__class_Obot'(
% 1.42/1.82 'tc_fun'( 'tc_nat', 'tc_bool' ) ), 'tc_nat' ) ) ],
% 1.42/1.82 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP(
% 1.42/1.82 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ), ~( hBOOL(
% 1.42/1.82 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.42/1.82 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ) ) ) ) ],
% 1.42/1.82 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP(
% 1.42/1.82 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.42/1.82 ), Y ), hAPP( 'c_Suc', hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.42/1.82 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.42/1.82 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ), X ),
% 1.42/1.82 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.42/1.82 ],
% 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', hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ), hAPP( hAPP(
% 1.42/1.82 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.42/1.82 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ),
% 1.42/1.82 hAPP( 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 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ],
% 1.42/1.82 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.42/1.82 'c_Power_Opower__class_Opower'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.42/1.82 'c_Int_OMin', X ) ), hAPP( 'c_Suc', hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ), Y ) ) ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OMin', X ) ) ],
% 1.42/1.82 [ =( hAPP( 'c_Suc', 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), 'c_HOL_Oone__class_Oone'( 'tc_nat' )
% 1.42/1.82 , 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ), =( X, 'c_HOL_Ozero__class_Ozero'(
% 1.42/1.82 'tc_nat' ) ) ],
% 1.42/1.82 [ =( 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.42/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit0'(
% 1.42/1.82 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' ), 'tc_nat' ),
% 1.42/1.82 'c_Set_Oinsert'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Set_Oinsert'(
% 1.42/1.82 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'c_Set_Oinsert'(
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.82 'c_Int_OPls' ) ), 'tc_nat' ), 'c_Set_Oinsert'(
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.42/1.82 'c_Int_OPls' ) ), 'tc_nat' ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'(
% 1.42/1.82 'tc_nat', 'tc_bool' ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) )
% 1.42/1.82 ],
% 1.42/1.82 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.42/1.82 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.42/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.42/1.82 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), Y ) ) ]
% 1.42/1.82 ,
% 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 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( 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_Finite__Set_Osetsum'( Y,
% 1.42/1.82 'c_SetInterval_Oord__class_OatLeastLessThan'( hAPP( 'c_Suc',
% 1.42/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Z, 'tc_nat' ), 'tc_nat', X ),
% 1.42/1.82 'c_Finite__Set_Osetsum'( Y, 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.42/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_nat' ), 'tc_nat', X ) ) ]
% 1.42/1.82 ,
% 1.42/1.82 [ =( hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP( 'c_Suc', X ) ) ), hAPP( hAPP(
% 1.42/1.82 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.42/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ) ],
% 1.42/1.82 [ =( hAPP( hAPP( X, Y ), Y ), hAPP( hAPP( Z, Y ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( T
% 1.42/1.82 , X, Z, U, W, V0 ) ) ],
% 1.42/1.82 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ), hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ), Z ) ),
% 1.42/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_HOL_Oord__class_Oless'( X, 'tc_Int_Oint' ), 'c_Int_OPls' ) ) ) ],
% 1.42/1.82 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.42/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_HOL_Oord__class_Oless'( X, 'tc_Int_Oint' ), 'c_Int_OPls' ) ) ) ],
% 1.42/1.82 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.82 'c_Int_OPls' ) ), X ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y )
% 1.42/1.82 , Y ) ) ],
% 1.42/1.82 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.42/1.82 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), X ) ), Y ), hAPP( hAPP(
% 1.42/1.82 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ) ) ],
% 1.42/1.82 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =( hAPP( hAPP(
% 1.42/1.82 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y
% 1.42/1.82 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.82 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =( hAPP( hAPP(
% 1.42/1.82 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.82 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP( hAPP(
% 1.42/1.82 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.82 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.42/1.82 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.42/1.82 X ), Y ), Y ) ) ],
% 1.42/1.82 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ), hAPP( hAPP(
% 1.42/1.82 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ],
% 1.42/1.82 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.42/1.82 'tc_nat' ), 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.42/1.82 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ],
% 1.42/1.82 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', hAPP( 'c_Suc', X ) ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.82 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X
% 1.42/1.82 , 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.82 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) ) ],
% 1.42/1.82 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( 'c_Suc', hAPP( 'c_Suc', X ) ) ) ]
% 1.42/1.82 ,
% 1.42/1.82 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), hAPP( 'c_Suc', hAPP( 'c_Suc', X ) )
% 1.42/1.82 ) ],
% 1.42/1.82 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( 'c_Suc', hAPP( 'c_Suc', X ) ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.82 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), hAPP( 'c_Suc',
% 1.42/1.82 'c_Divides_Odiv__class_Odiv'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.42/1.82 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) )
% 1.42/1.82 ) ],
% 1.42/1.82 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), hAPP( hAPP(
% 1.42/1.82 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), X ) ) ],
% 1.42/1.82 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.42/1.82 'tc_nat' ), X ), X ) ) ],
% 1.42/1.82 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), 'tc_nat' ) ],
% 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_Otimes__class_Otimes'( 'tc_nat' ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), hAPP( hAPP(
% 1.42/1.82 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.42/1.82 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ],
% 1.42/1.82 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.42/1.82 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.42/1.82 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), hAPP( hAPP( T, hAPP(
% 1.42/1.82 hAPP( X, Y ), Z ) ), hAPP( hAPP( X, Y ), Z ) ) ), ~(
% 1.42/1.82 'c_Groebner__Basis_Ogb__semiring'( U, T, X, W, V0, V1 ) ) ],
% 1.42/1.82 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), ~( 'class_Int_Onumber'(
% 1.42/1.82 X ) ), =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.42/1.82 X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ) ],
% 1.42/1.82 [ =( X, hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X
% 1.42/1.82 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ],
% 1.42/1.82 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.42/1.82 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.42/1.82 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.42/1.82 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.42/1.82 [ =( hAPP( hAPP( X, Y ), hAPP( 'c_Suc', hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ), hAPP( hAPP( T, Y ), hAPP( hAPP(
% 1.42/1.82 T, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, Y ), Z ) ) ) ), ~(
% 1.42/1.82 'c_Groebner__Basis_Ogb__semiring'( U, T, X, W, V0, V1 ) ) ],
% 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' ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ), 'tc_nat' ) ) ],
% 1.42/1.82 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.42/1.82 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ), hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.42/1.82 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.42/1.82 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ],
% 1.42/1.82 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.42/1.82 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ), hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.42/1.82 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.42/1.82 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ) ],
% 1.42/1.82 [ =( hAPP( 'c_Suc', hAPP( 'c_Suc', 'c_HOL_Ominus__class_Ominus'( hAPP(
% 1.42/1.82 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit0'(
% 1.42/1.82 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' ) ), X ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.82 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit0'(
% 1.42/1.82 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' ) ), X ) ), =( X,
% 1.42/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.42/1.82 [ =( hAPP( 'c_Suc', hAPP( 'c_Suc', 'c_HOL_Ominus__class_Ominus'( hAPP(
% 1.42/1.82 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.42/1.82 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) )
% 1.42/1.82 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ), =( X, 'c_HOL_Ozero__class_Ozero'(
% 1.42/1.82 'tc_nat' ) ) ],
% 1.42/1.82 [ =( 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.42/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), 'tc_nat' ),
% 1.42/1.82 'c_Lattices_Oupper__semilattice__class_Osup'( 'c_Set_Oimage'( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ),
% 1.42/1.82 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.42/1.82 'tc_nat' ), X, 'tc_nat' ), 'tc_nat', 'tc_nat' ), 'c_Set_Oimage'(
% 1.42/1.82 'c_COMBB'( 'c_Suc', hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ), 'tc_nat', 'tc_nat', 'tc_nat' ),
% 1.42/1.82 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.42/1.82 'tc_nat' ), X, 'tc_nat' ), 'tc_nat', 'tc_nat' ), 'tc_fun'( 'tc_nat',
% 1.42/1.82 'tc_bool' ) ) ) ],
% 1.42/1.82 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Ozero__class_Ozero'( X
% 1.42/1.82 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', X ) ) ],
% 1.42/1.82 [ =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', 'tc_nat' ) ) ],
% 1.42/1.82 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.82 'c_Int_OPls' ) ), 'tc_nat' ), hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.42/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.42/1.82 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 1.42/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Y, X ), Y ) ],
% 1.42/1.82 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X, X, 'tc_fun'( Y,
% 1.42/1.82 'tc_bool' ) ), X ) ],
% 1.42/1.82 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 1.42/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.42/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), X ),
% 1.42/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ) ) ],
% 1.42/1.82 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 1.42/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 1.42/1.82 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ),
% 1.42/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 1.42/1.82 'tc_bool' ) ) ) ],
% 1.42/1.82 [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 1.42/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.42/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), X ),
% 1.42/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ) ) ],
% 1.42/1.82 [ =( 'c_Set_Oimage'( X, 'c_Set_Oimage'( Y, Z, T, U ), U, W ),
% 1.42/1.82 'c_Set_Oimage'( 'c_COMBB'( X, Y, U, W, T ), Z, T, W ) ) ],
% 1.42/1.82 [ =( 'c_SetInterval_Oord__class_OatLeastLessThan'( X,
% 1.42/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ),
% 1.42/1.82 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_nat', 'tc_bool' ) ) ) ]
% 1.42/1.82 ,
% 1.42/1.82 [ =( 'c_Int_OBit0'( 'c_Int_OPls' ), 'c_Int_OPls' ) ],
% 1.42/1.82 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ),
% 1.42/1.82 'tc_nat' ), hAPP( 'c_Suc', '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 [ ~( =( hAPP( 'c_Suc', X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ]
% 1.42/1.82 ,
% 1.42/1.82 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', 'tc_nat' ),
% 1.42/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.42/1.82 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.42/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', X ),
% 1.42/1.82 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.82 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =( hAPP(
% 1.42/1.82 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.42/1.82 X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.82 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =( hAPP(
% 1.42/1.82 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.42/1.82 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.82 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =( hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.42/1.82 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.82 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =( hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.42/1.82 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.82 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.42/1.82 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.82 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.42/1.82 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.82 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.42/1.82 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.82 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.42/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), 'c_HOL_Ozero__class_Ozero'(
% 1.42/1.82 'tc_nat' ) ) ],
% 1.42/1.82 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.42/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.42/1.82 'tc_nat' ) ) ],
% 1.42/1.82 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.42/1.82 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.82 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.42/1.82 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.82 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.42/1.82 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.82 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.42/1.82 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.82 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc'
% 1.42/1.82 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), hAPP( 'c_Suc',
% 1.42/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), hAPP( 'c_Suc',
% 1.42/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 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 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.42/1.82 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), =( Y
% 1.42/1.82 , Z ), =( X, '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 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), =( X
% 1.42/1.82 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y, Z ) ],
% 1.42/1.82 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.42/1.82 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ), =( Y
% 1.42/1.82 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, Z ) ],
% 1.42/1.82 [ ~( =( 'c_Int_OPls', 'c_Int_OBit1'( X ) ) ) ],
% 1.42/1.82 [ ~( =( 'c_Int_OBit1'( X ), 'c_Int_OPls' ) ) ],
% 1.42/1.82 [ ~( 'class_Orderings_Oorder'( X ) ), =(
% 1.42/1.82 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.42/1.82 'c_SetInterval_Oord__class_OatLeastLessThan'( Y, Z, X ),
% 1.42/1.82 'c_SetInterval_Oord__class_OatLeastLessThan'( Z, T, X ), 'tc_fun'( X,
% 1.42/1.82 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) )
% 1.42/1.82 ) ],
% 1.42/1.82 [ ~( =( 'c_Int_OBit0'( X ), 'c_Int_OPls' ) ), =( X, 'c_Int_OPls' ) ]
% 1.42/1.82 ,
% 1.42/1.82 [ ~( =( 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ) ) ), =( X, Y ) ],
% 1.42/1.82 [ ~( =( 'c_Int_OBit1'( X ), 'c_Int_OBit0'( Y ) ) ) ],
% 1.42/1.82 [ =( 'c_Int_OPls', 'c_Int_OBit0'( 'c_Int_OPls' ) ) ],
% 1.42/1.82 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( X, Z, 'tc_fun'( T,
% 1.42/1.82 'tc_bool' ) ), Y ) ) ) ],
% 1.42/1.82 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP(
% 1.42/1.82 'c_Lattices_Olower__semilattice__class_Oinf'( Z, X, 'tc_fun'( T,
% 1.42/1.82 'tc_bool' ) ), Y ) ) ) ],
% 1.42/1.82 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), 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 ), hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ) ) ],
% 1.42/1.82 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ) ) ],
% 1.42/1.82 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), 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 ), Z ), hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ],
% 1.42/1.82 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), 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 ), hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ) ) ],
% 1.42/1.82 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.42/1.82 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), Z ) ) ],
% 1.42/1.82 [ ~( 'class_OrderedGroup_Oab__semigroup__mult'( X ) ), =( hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.42/1.82 [ hBOOL( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y,
% 1.42/1.82 'tc_fun'( Z, 'tc_bool' ) ), T ) ), ~( hBOOL( hAPP( Y, T ) ) ), ~( hBOOL(
% 1.42/1.82 hAPP( X, T ) ) ) ],
% 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_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.42/1.82 'c_Int_OPls' ) ), 'tc_nat' ), hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP( 'c_Suc'
% 1.42/1.82 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ) ],
% 1.42/1.82 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =( hAPP(
% 1.42/1.82 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ), Y ) ],
% 1.42/1.82 [ ~( =( 'c_Set_Oimage'( X, Y, Z, T ), 'c_Orderings_Obot__class_Obot'(
% 1.42/1.82 'tc_fun'( T, 'tc_bool' ) ) ) ), =( Y, 'c_Orderings_Obot__class_Obot'(
% 1.42/1.82 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.42/1.82 [ ~( =( hAPP( 'c_Suc', X ), X ) ) ],
% 1.42/1.82 [ ~( =( X, hAPP( 'c_Suc', X ) ) ) ],
% 1.42/1.82 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.42/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.42/1.82 'tc_nat' ) ), Y ) ) ],
% 1.42/1.82 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 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 ), 'c_HOL_Ozero__class_Ozero'(
% 1.42/1.82 'tc_nat' ) ) ) ],
% 1.42/1.82 [ =( 'c_Set_Oimage'( 'c_Suc',
% 1.42/1.82 'c_SetInterval_Oord__class_OatLeastLessThan'( X, Y, 'tc_nat' ), 'tc_nat'
% 1.42/1.82 , 'tc_nat' ), 'c_SetInterval_Oord__class_OatLeastLessThan'( hAPP( 'c_Suc'
% 1.42/1.82 , X ), hAPP( 'c_Suc', Y ), 'tc_nat' ) ) ],
% 1.42/1.82 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =( hAPP(
% 1.42/1.82 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), 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 ), Z ) ) ],
% 1.42/1.82 [ ~( hBOOL( hAPP( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool'
% 1.42/1.82 ) ), Y ) ) ) ],
% 1.42/1.82 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.42/1.82 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.42/1.83 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.42/1.83 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.42/1.83 'c_HOL_Otimes__class_Otimes'( X ), T ), hAPP( hAPP(
% 1.42/1.83 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.42/1.83 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), U ) ) ) ],
% 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_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.42/1.83 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), 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 ), Z ), hAPP( hAPP(
% 1.42/1.83 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) ) ) ],
% 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_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.42/1.83 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.42/1.83 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.42/1.83 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.42/1.83 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ) ) ],
% 1.42/1.83 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 1.42/1.83 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.42/1.83 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ),
% 1.42/1.83 'c_Lattices_Olower__semilattice__class_Oinf'( Z,
% 1.42/1.83 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T, X ), X ) ) ],
% 1.42/1.83 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 1.42/1.83 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.42/1.83 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), T, X ),
% 1.42/1.83 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.42/1.83 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ) ) ],
% 1.42/1.83 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.42/1.83 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 1.42/1.83 'tc_bool' ) ), T, 'tc_fun'( Z, 'tc_bool' ) ),
% 1.42/1.83 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 1.42/1.83 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T, 'tc_fun'( Z,
% 1.42/1.83 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.42/1.83 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 1.42/1.83 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, 'tc_fun'( T,
% 1.42/1.83 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ),
% 1.42/1.83 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.42/1.83 'c_Lattices_Olower__semilattice__class_Oinf'( X, Z, 'tc_fun'( T,
% 1.42/1.83 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 1.42/1.83 [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 1.42/1.83 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.42/1.83 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ),
% 1.42/1.83 'c_Lattices_Olower__semilattice__class_Oinf'( Z,
% 1.42/1.83 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T, X ), X ) ) ],
% 1.42/1.83 [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 1.42/1.83 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.42/1.83 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), T, X ),
% 1.42/1.83 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.42/1.83 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ) ) ],
% 1.42/1.83 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), ~( =(
% 1.42/1.83 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.42/1.83 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 1.42/1.83 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.83 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =( hAPP(
% 1.42/1.83 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.42/1.83 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 1.42/1.83 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.83 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =( hAPP(
% 1.42/1.83 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.42/1.83 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.42/1.83 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.42/1.83 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.42/1.83 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.42/1.83 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X,
% 1.42/1.83 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.42/1.83 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.42/1.83 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.42/1.83 'c_Int_OBit1'( 'c_Int_OPls' ), X ) ), Y ), Y ) ],
% 1.42/1.83 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.42/1.83 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.42/1.83 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ) )
% 1.42/1.83 , Y ) ],
% 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 [ ~( =( 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 [ ~( 'class_Lattices_Obounded__lattice'( X ) ), =(
% 1.42/1.83 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.42/1.83 'c_Orderings_Obot__class_Obot'( X ), X ), 'c_Orderings_Obot__class_Obot'(
% 1.42/1.83 X ) ) ],
% 1.42/1.83 [ ~( 'class_Lattices_Obounded__lattice'( X ) ), =(
% 1.42/1.83 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.42/1.83 'c_Orderings_Obot__class_Obot'( X ), Y, X ),
% 1.42/1.83 'c_Orderings_Obot__class_Obot'( X ) ) ],
% 1.42/1.83 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.42/1.83 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ), Y, 'tc_fun'(
% 1.42/1.83 X, 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool'
% 1.42/1.83 ) ) ) ],
% 1.42/1.83 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 1.42/1.83 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ), 'tc_fun'( Y,
% 1.42/1.83 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) )
% 1.42/1.83 ) ],
% 1.42/1.83 [ ~( =( 'c_Int_OPls', 'c_Int_OBit0'( X ) ) ), =( 'c_Int_OPls', X ) ]
% 1.42/1.83 ,
% 1.42/1.83 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( 'c_Suc', X ) ) ) ]
% 1.42/1.83 ,
% 1.42/1.83 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( 'c_Suc', X ) ) ) ]
% 1.42/1.83 ,
% 1.42/1.83 [ ~( =( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ),
% 1.42/1.83 'c_Set_Oimage'( Y, Z, T, X ) ) ), =( Z, 'c_Orderings_Obot__class_Obot'(
% 1.42/1.83 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 1.42/1.83 [ ~( =( 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ) ) ), =( X, Y ) ],
% 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 ), Z ), hAPP( hAPP(
% 1.42/1.83 'c_HOL_Otimes__class_Otimes'( X ), Z ), 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' ), 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 ), Y ), Z ), hAPP( hAPP(
% 1.42/1.83 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ) ],
% 1.42/1.83 [ =( hAPP( 'c_COMBB'( X, Y, Z, T, U ), W ), hAPP( X, hAPP( Y, W ) ) ) ]
% 1.42/1.83 ,
% 1.42/1.83 [ =( hAPP( 'c_Suc', hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.42/1.83 ) ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.83 'c_Int_OPls' ) ), 'tc_nat' ) ) ],
% 1.42/1.83 [ =( 'c_Set_Oimage'( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y,
% 1.42/1.83 'tc_bool' ) ), Y, Z ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z,
% 1.42/1.83 'tc_bool' ) ) ) ],
% 1.42/1.83 [ ~( 'class_Int_Oring__char__0'( X ) ), ~( 'class_Int_Onumber__ring'( X
% 1.42/1.83 ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.42/1.83 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ), =( Y, Z ) ],
% 1.42/1.83 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 1.42/1.83 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ),
% 1.42/1.83 'c_Lattices_Olower__semilattice__class_Oinf'( Z, Y, X ) ) ],
% 1.42/1.83 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 1.42/1.83 'tc_bool' ) ), 'c_Lattices_Olower__semilattice__class_Oinf'( Y, X,
% 1.42/1.83 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.42/1.83 [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 1.42/1.83 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ),
% 1.42/1.83 'c_Lattices_Olower__semilattice__class_Oinf'( Z, Y, X ) ) ],
% 1.42/1.83 [ ~( =( 'c_Int_OBit0'( X ), 'c_Int_OBit1'( Y ) ) ) ],
% 1.42/1.83 [ =( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ),
% 1.42/1.83 'c_Set_Oimage'( Y, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool'
% 1.42/1.83 ) ), Z, X ) ) ],
% 1.42/1.83 [ ~( =( 'c_Lattices_Olower__semilattice__class_Oinf'( 'c_Set_Oimage'(
% 1.42/1.83 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.42/1.83 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.83 'c_Int_OPls' ) ), 'tc_nat' ) ),
% 1.42/1.83 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.42/1.83 'tc_nat' ), 'v_n', 'tc_nat' ), 'tc_nat', 'tc_nat' ), 'c_Set_Oimage'(
% 1.42/1.83 'c_COMBB'( 'c_Suc', hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.42/1.83 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.42/1.83 'c_Int_OPls' ) ), 'tc_nat' ) ), 'tc_nat', 'tc_nat', 'tc_nat' ),
% 1.42/1.83 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.42/1.83 'tc_nat' ), 'v_n', 'tc_nat' ), 'tc_nat', 'tc_nat' ), 'tc_fun'( 'tc_nat',
% 1.42/1.83 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_nat',
% 1.42/1.83 'tc_bool' ) ) ) ) ],
% 1.42/1.83 [ 'class_Lattices_Oupper__semilattice'( 'tc_fun'( X, Y ) ), ~(
% 1.42/1.83 'class_Lattices_Olattice'( Y ) ) ],
% 1.42/1.83 [ 'class_Lattices_Olower__semilattice'( 'tc_fun'( X, Y ) ), ~(
% 1.42/1.83 'class_Lattices_Olattice'( Y ) ) ],
% 1.42/1.83 [ 'class_Lattices_Odistrib__lattice'( 'tc_fun'( X, Y ) ), ~(
% 1.42/1.83 'class_Lattices_Odistrib__lattice'( Y ) ) ],
% 1.42/1.83 [ 'class_Lattices_Obounded__lattice'( 'tc_fun'( X, Y ) ), ~(
% 1.42/1.83 'class_Lattices_Obounded__lattice'( Y ) ) ],
% 1.42/1.83 [ 'class_Orderings_Opreorder'( 'tc_fun'( X, Y ) ), ~(
% 1.42/1.83 'class_Orderings_Opreorder'( Y ) ) ],
% 1.42/1.83 [ 'class_Lattices_Olattice'( 'tc_fun'( X, Y ) ), ~(
% 1.42/1.83 'class_Lattices_Olattice'( Y ) ) ],
% 1.42/1.83 [ 'class_Orderings_Oorder'( 'tc_fun'( X, Y ) ), ~(
% 1.42/1.83 'class_Orderings_Oorder'( Y ) ) ],
% 1.42/1.83 [ 'class_Orderings_Obot'( 'tc_fun'( X, Y ) ), ~( 'class_Orderings_Obot'(
% 1.42/1.83 Y ) ) ],
% 1.42/1.83 [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( 'tc_nat' )
% 1.42/1.83 ],
% 1.42/1.83 [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( 'tc_nat'
% 1.42/1.83 ) ],
% 1.42/1.83 [ 'class_Ring__and__Field_Oordered__comm__semiring__strict'( 'tc_nat' )
% 1.42/1.83 ],
% 1.42/1.83 [ 'class_Ring__and__Field_Opordered__cancel__semiring'( 'tc_nat' ) ]
% 1.42/1.83 ,
% 1.42/1.83 [ 'class_Ring__and__Field_Oordered__semiring__strict'( 'tc_nat' ) ],
% 1.42/1.83 [ 'class_OrderedGroup_Opordered__ab__semigroup__add'( 'tc_nat' ) ],
% 1.42/1.83 [ 'class_OrderedGroup_Opordered__comm__monoid__add'( 'tc_nat' ) ],
% 1.42/1.83 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'( 'tc_nat' ) ],
% 1.42/1.83 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_nat' ) ],
% 1.42/1.83 [ 'class_Ring__and__Field_Opordered__semiring'( 'tc_nat' ) ],
% 1.42/1.83 [ 'class_Ring__and__Field_Oordered__semiring'( 'tc_nat' ) ],
% 1.42/1.83 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_nat' ) ],
% 1.42/1.83 [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_nat' ) ],
% 1.42/1.83 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_nat' ) ],
% 1.42/1.83 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_nat' ) ],
% 1.42/1.83 [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_nat' ) ],
% 1.42/1.83 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_nat' ) ],
% 1.42/1.83 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_nat' ) ],
% 1.42/1.83 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_nat' ) ],
% 1.42/1.83 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_nat' ) ],
% 1.42/1.83 [ 'class_Lattices_Oupper__semilattice'( 'tc_nat' ) ],
% 1.42/1.83 [ 'class_Lattices_Olower__semilattice'( 'tc_nat' ) ],
% 1.42/1.83 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_nat' ) ],
% 1.42/1.83 [ 'class_Ring__and__Field_Osemiring__0'( 'tc_nat' ) ],
% 1.42/1.83 [ 'class_Ring__and__Field_Omult__mono1'( 'tc_nat' ) ],
% 1.42/1.83 [ 'class_Ring__and__Field_Omult__zero'( 'tc_nat' ) ],
% 1.42/1.83 [ 'class_Ring__and__Field_Omult__mono'( 'tc_nat' ) ],
% 1.42/1.83 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_nat' ) ],
% 1.42/1.83 [ 'class_Lattices_Odistrib__lattice'( 'tc_nat' ) ],
% 1.42/1.83 [ 'class_Ring__and__Field_Osemiring'( 'tc_nat' ) ],
% 1.42/1.83 [ 'class_OrderedGroup_Omonoid__add'( 'tc_nat' ) ],
% 1.42/1.83 [ 'class_Divides_Osemiring__div'( 'tc_nat' ) ],
% 1.42/1.83 [ 'class_Orderings_Opreorder'( 'tc_nat' ) ],
% 1.42/1.83 [ 'class_Orderings_Olinorder'( 'tc_nat' ) ],
% 1.42/1.83 [ 'class_Lattices_Olattice'( 'tc_nat' ) ],
% 1.42/1.83 [ 'class_Orderings_Oorder'( 'tc_nat' ) ],
% 1.42/1.83 [ 'class_Orderings_Obot'( 'tc_nat' ) ],
% 1.42/1.83 [ 'class_Power_Opower'( 'tc_nat' ) ],
% 1.42/1.83 [ 'class_Int_Onumber'( 'tc_nat' ) ],
% 1.42/1.83 [ 'class_Lattices_Oupper__semilattice'( 'tc_bool' ) ],
% 1.42/1.83 [ 'class_Lattices_Olower__semilattice'( 'tc_bool' ) ],
% 1.42/1.83 [ 'class_Lattices_Odistrib__lattice'( 'tc_bool' ) ],
% 1.42/1.83 [ 'class_Lattices_Obounded__lattice'( 'tc_bool' ) ],
% 1.42/1.83 [ 'class_Orderings_Opreorder'( 'tc_bool' ) ],
% 1.42/1.83 [ 'class_Lattices_Olattice'( 'tc_bool' ) ],
% 1.42/1.83 [ 'class_Orderings_Oorder'( 'tc_bool' ) ],
% 1.42/1.83 [ 'class_Orderings_Obot'( 'tc_bool' ) ],
% 1.42/1.83 [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'(
% 1.42/1.83 'tc_Int_Oint' ) ],
% 1.42/1.83 [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'(
% 1.42/1.83 'tc_Int_Oint' ) ],
% 1.42/1.83 [ 'class_Ring__and__Field_Oordered__comm__semiring__strict'(
% 1.42/1.83 'tc_Int_Oint' ) ],
% 1.42/1.83 [ 'class_Ring__and__Field_Opordered__cancel__semiring'( 'tc_Int_Oint' )
% 1.42/1.83 ],
% 1.42/1.83 [ 'class_OrderedGroup_Olordered__ab__group__add__meet'( 'tc_Int_Oint' )
% 1.42/1.83 ],
% 1.42/1.83 [ 'class_OrderedGroup_Olordered__ab__group__add__join'( 'tc_Int_Oint' )
% 1.42/1.83 ],
% 1.42/1.83 [ 'class_Ring__and__Field_Oring__1__no__zero__divisors'( 'tc_Int_Oint' )
% 1.42/1.83 ],
% 1.42/1.83 [ 'class_Ring__and__Field_Oordered__semiring__strict'( 'tc_Int_Oint' ) ]
% 1.42/1.83 ,
% 1.42/1.83 [ 'class_OrderedGroup_Opordered__ab__semigroup__add'( 'tc_Int_Oint' ) ]
% 1.42/1.83 ,
% 1.42/1.83 [ 'class_OrderedGroup_Opordered__comm__monoid__add'( 'tc_Int_Oint' ) ]
% 1.42/1.83 ,
% 1.42/1.83 [ 'class_Ring__and__Field_Oring__no__zero__divisors'( 'tc_Int_Oint' ) ]
% 1.42/1.83 ,
% 1.42/1.83 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'( 'tc_Int_Oint' ) ]
% 1.42/1.83 ,
% 1.42/1.83 [ 'class_Ring__and__Field_Oordered__ring__strict'( 'tc_Int_Oint' ) ]
% 1.42/1.83 ,
% 1.42/1.83 [ 'class_OrderedGroup_Opordered__ab__group__add'( 'tc_Int_Oint' ) ],
% 1.42/1.83 [ 'class_OrderedGroup_Olordered__ab__group__add'( 'tc_Int_Oint' ) ],
% 1.42/1.83 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_Int_Oint' ) ],
% 1.42/1.83 [ 'class_Ring__and__Field_Opordered__semiring'( 'tc_Int_Oint' ) ],
% 1.42/1.83 [ 'class_Ring__and__Field_Oordered__semiring'( 'tc_Int_Oint' ) ],
% 1.42/1.83 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_Int_Oint' ) ],
% 1.42/1.83 [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_Int_Oint' ) ],
% 1.42/1.83 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_Int_Oint' ) ],
% 1.42/1.83 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_Int_Oint' ) ],
% 1.42/1.83 [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_Int_Oint' ) ],
% 1.42/1.83 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_Int_Oint' ) ],
% 1.42/1.83 [ 'class_Ring__and__Field_Opordered__ring'( 'tc_Int_Oint' ) ],
% 1.42/1.83 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_Int_Oint' ) ],
% 1.42/1.83 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_Int_Oint' ) ],
% 1.42/1.83 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_Int_Oint' ) ],
% 1.42/1.83 [ 'class_Ring__and__Field_Oordered__idom'( 'tc_Int_Oint' ) ],
% 1.42/1.83 [ 'class_Lattices_Oupper__semilattice'( 'tc_Int_Oint' ) ],
% 1.42/1.83 [ 'class_Lattices_Olower__semilattice'( 'tc_Int_Oint' ) ],
% 1.42/1.83 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_Int_Oint' ) ],
% 1.42/1.83 [ 'class_Ring__and__Field_Osemiring__0'( 'tc_Int_Oint' ) ],
% 1.42/1.83 [ 'class_Ring__and__Field_Omult__mono1'( 'tc_Int_Oint' ) ],
% 1.42/1.83 [ 'class_OrderedGroup_Oab__group__add'( 'tc_Int_Oint' ) ],
% 1.42/1.83 [ 'class_Ring__and__Field_Omult__zero'( 'tc_Int_Oint' ) ],
% 1.42/1.83 [ 'class_Ring__and__Field_Omult__mono'( 'tc_Int_Oint' ) ],
% 1.42/1.83 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_Int_Oint' ) ],
% 1.42/1.83 [ 'class_Lattices_Odistrib__lattice'( 'tc_Int_Oint' ) ],
% 1.42/1.83 [ 'class_Ring__and__Field_Osemiring'( 'tc_Int_Oint' ) ],
% 1.42/1.83 [ 'class_OrderedGroup_Omonoid__add'( 'tc_Int_Oint' ) ],
% 1.42/1.83 [ 'class_OrderedGroup_Ogroup__add'( 'tc_Int_Oint' ) ],
% 1.42/1.83 [ 'class_Divides_Osemiring__div'( 'tc_Int_Oint' ) ],
% 1.42/1.83 [ 'class_Ring__and__Field_Oring'( 'tc_Int_Oint' ) ],
% 1.42/1.83 [ 'class_Ring__and__Field_Oidom'( 'tc_Int_Oint' ) ],
% 1.42/1.83 [ 'class_Orderings_Opreorder'( 'tc_Int_Oint' ) ],
% 1.42/1.83 [ 'class_Orderings_Olinorder'( 'tc_Int_Oint' ) ],
% 1.42/1.83 [ 'class_Lattices_Olattice'( 'tc_Int_Oint' ) ],
% 1.42/1.83 [ 'class_Divides_Oring__div'( 'tc_Int_Oint' ) ],
% 1.42/1.83 [ 'class_Orderings_Oorder'( 'tc_Int_Oint' ) ],
% 1.42/1.83 [ 'class_Int_Oring__char__0'( 'tc_Int_Oint' ) ],
% 1.42/1.83 [ 'class_Int_Onumber__ring'( 'tc_Int_Oint' ) ],
% 1.42/1.83 [ 'class_Power_Opower'( 'tc_Int_Oint' ) ],
% 1.42/1.83 [ 'class_Int_Onumber'( 'tc_Int_Oint' ) ],
% 1.42/1.83 [ =( 'c_COMBC'( X, Y, Z, T, U, W ), hAPP( hAPP( X, Z ), Y ) ) ],
% 1.42/1.83 [ =( hAPP( 'c_COMBB'( X, Y, Z, T, U ), W ), hAPP( X, hAPP( Y, W ) ) ) ]
% 1.42/1.83 ,
% 1.42/1.83 [ 'c_fequal'( X, X, Y ) ],
% 1.42/1.83 [ =( X, Y ), ~( 'c_fequal'( X, Y, Z ) ) ]
% 1.42/1.83 ] .
% 1.42/1.83
% 1.42/1.83
% 1.42/1.83 percentage equality = 0.235869, percentage horn = 0.846057
% 1.42/1.83 This is a problem with some equality
% 1.42/1.83
% 1.42/1.83
% 1.42/1.83
% 1.42/1.83 Options Used:
% 1.42/1.83
% 1.42/1.83 useres = 1
% 1.42/1.83 useparamod = 1
% 1.42/1.83 useeqrefl = 1
% 1.42/1.83 useeqfact = 1
% 1.42/1.83 usefactor = 1
% 1.42/1.83 usesimpsplitting = 0
% 1.42/1.83 usesimpdemod = 5
% 1.42/1.83 usesimpres = 3
% 1.42/1.83
% 1.42/1.83 resimpinuse = 1000
% 1.42/1.83 resimpclauses = 20000
% 1.42/1.83 substype = eqrewr
% 1.42/1.83 backwardsubs = 1
% 1.42/1.83 selectoldest = 5
% 1.42/1.83
% 1.42/1.83 litorderings [0] = split
% 1.42/1.83 litorderings [1] = extend the termordering, first sorting on arguments
% 1.42/1.83
% 1.42/1.83 termordering = kbo
% 1.42/1.83
% 1.42/1.83 litapriori = 0
% 1.42/1.83 termapriori = 1
% 1.42/1.83 litaposteriori = 0
% 1.42/1.83 termaposteriori = 0
% 1.42/1.83 demodaposteriori = 0
% 1.42/1.83 ordereqreflfact = 0
% 1.42/1.83
% 1.42/1.83 litselect = negord
% 1.42/1.83
% 1.42/1.83 maxweight = 15
% 1.42/1.83 maxdepth = 30000
% 1.42/1.83 maxlength = 115
% 1.42/1.83 maxnrvars = 195
% 1.42/1.83 excuselevel = 1
% 1.42/1.83 increasemaxweight = 1
% 1.42/1.83
% 1.42/1.83 maxselected = 10000000
% 1.42/1.83 maxnrclauses = 10000000
% 1.42/1.83
% 1.42/1.83 showgenerated = 0
% 1.42/1.83 showkept = 0
% 1.42/1.83 showselected = 0
% 1.42/1.83 showdeleted = 0
% 1.42/1.83 showresimp = 1
% 1.42/1.83 showstatus = 2000
% 1.42/1.83
% 1.42/1.83 prologoutput = 1
% 1.42/1.83 nrgoals = 5000000
% 1.42/1.83 totalproof = 1
% 1.42/1.83
% 1.42/1.83 Symbols occurring in the translation:
% 1.42/1.83
% 1.42/1.83 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 1.42/1.83 . [1, 2] (w:1, o:172, a:1, s:1, b:0),
% 1.42/1.83 ! [4, 1] (w:0, o:87, a:1, s:1, b:0),
% 1.42/1.84 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.42/1.84 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.42/1.84 'class_Ring__and__Field_Oordered__field' [40, 1] (w:1, o:96, a:1, s:1
% 1.42/1.84 , b:0),
% 1.42/1.84 'class_Ring__and__Field_Odivision__by__zero' [41, 1] (w:1, o:99, a:1
% 1.42/1.84 , s:1, b:0),
% 1.42/1.84 'c_HOL_Ozero__class_Ozero' [42, 1] (w:1, o:100, a:1, s:1, b:0),
% 1.42/1.84 'c_HOL_Oord__class_Oless' [43, 2] (w:1, o:197, a:1, s:1, b:0),
% 1.42/1.84 hAPP [45, 2] (w:1, o:198, a:1, s:1, b:0),
% 1.42/1.84 hBOOL [46, 1] (w:1, o:101, a:1, s:1, b:0),
% 1.42/1.84 'c_HOL_Oone__class_Oone' [47, 1] (w:1, o:102, a:1, s:1, b:0),
% 1.42/1.84 'c_HOL_Oinverse__class_Oinverse' [48, 1] (w:1, o:103, a:1, s:1, b:0)
% 1.42/1.84 ,
% 1.42/1.84 'class_Power_Opower' [49, 1] (w:1, o:127, a:1, s:1, b:0),
% 1.42/1.84 'c_Power_Opower__class_Opower' [50, 1] (w:1, o:129, a:1, s:1, b:0),
% 1.42/1.84 'tc_nat' [52, 0] (w:1, o:15, a:1, s:1, b:0),
% 1.42/1.84 'class_Ring__and__Field_Ocomm__semiring__1' [53, 1] (w:1, o:97, a:1
% 1.42/1.84 , s:1, b:0),
% 1.42/1.84 'class_Int_Onumber' [54, 1] (w:1, o:130, a:1, s:1, b:0),
% 1.42/1.84 'c_lessequals' [55, 2] (w:1, o:199, a:1, s:1, b:0),
% 1.42/1.84 'c_Int_Onumber__class_Onumber__of' [57, 2] (w:1, o:200, a:1, s:1, b:0
% 1.42/1.84 ),
% 1.42/1.84 'c_HOL_Oinverse__class_Odivide' [59, 3] (w:1, o:206, a:1, s:1, b:0),
% 1.42/1.84
% 1.42/1.84 'c_Power_Opower_Opower' [62, 3] (w:1, o:208, a:1, s:1, b:0),
% 1.42/1.84 'c_HOL_Otimes__class_Otimes' [63, 1] (w:1, o:131, a:1, s:1, b:0),
% 1.42/1.84 'c_OrderedGroup_Omonoid__mult' [66, 3] (w:1, o:207, a:1, s:1, b:0),
% 1.42/1.84 'class_Divides_Osemiring__div' [67, 1] (w:1, o:133, a:1, s:1, b:0),
% 1.42/1.84 'c_HOL_Oplus__class_Oplus' [68, 1] (w:1, o:134, a:1, s:1, b:0),
% 1.42/1.84 'c_Divides_Odiv__class_Omod' [69, 3] (w:1, o:209, a:1, s:1, b:0),
% 1.42/1.84 'class_OrderedGroup_Ocomm__monoid__add' [70, 1] (w:1, o:104, a:1, s:1
% 1.42/1.84 , b:0),
% 1.42/1.84 'c_Ring__and__Field_Oordered__idom' [79, 11] (w:1, o:227, a:1, s:1
% 1.42/1.84 , b:0),
% 1.42/1.84 'class_Ring__and__Field_Oordered__semidom' [80, 1] (w:1, o:136, a:1
% 1.42/1.84 , s:1, b:0),
% 1.42/1.84 'c_Divides_Odiv__class_Odiv' [82, 3] (w:1, o:210, a:1, s:1, b:0),
% 1.42/1.84 'class_Ring__and__Field_Ofield' [83, 1] (w:1, o:137, a:1, s:1, b:0),
% 1.42/1.84
% 1.42/1.84 'c_HOL_Ominus__class_Ominus' [86, 3] (w:1, o:211, a:1, s:1, b:0),
% 1.42/1.84 'c_Suc' [87, 0] (w:1, o:58, a:1, s:1, b:0),
% 1.42/1.84 'class_Ring__and__Field_Odivision__ring' [88, 1] (w:1, o:138, a:1, s:
% 1.42/1.84 1, b:0),
% 1.42/1.84 'class_Ring__and__Field_Oordered__idom' [89, 1] (w:1, o:139, a:1, s:1
% 1.42/1.84 , b:0),
% 1.42/1.84 'c_Parity_Oeven__odd__class_Oeven' [90, 2] (w:1, o:201, a:1, s:1, b:0
% 1.42/1.84 ),
% 1.42/1.84 'class_Lattices_Oupper__semilattice' [91, 1] (w:1, o:140, a:1, s:1
% 1.42/1.84 , b:0),
% 1.42/1.84 'c_Lattices_Oupper__semilattice__class_Osup' [92, 3] (w:1, o:212, a:1
% 1.42/1.84 , s:1, b:0),
% 1.42/1.84 'c_Int_OMin' [95, 0] (w:1, o:60, a:1, s:1, b:0),
% 1.42/1.84 'tc_Int_Oint' [96, 0] (w:1, o:61, a:1, s:1, b:0),
% 1.42/1.84 'class_Orderings_Oorder' [97, 1] (w:1, o:105, a:1, s:1, b:0),
% 1.42/1.84 'c_SetInterval_Oord__class_OatLeastAtMost' [98, 3] (w:1, o:213, a:1
% 1.42/1.84 , s:1, b:0),
% 1.42/1.84 'tc_bool' [99, 0] (w:1, o:62, a:1, s:1, b:0),
% 1.42/1.84 'tc_fun' [100, 2] (w:1, o:202, a:1, s:1, b:0),
% 1.42/1.84 'c_Orderings_Obot__class_Obot' [101, 1] (w:1, o:128, a:1, s:1, b:0),
% 1.42/1.84
% 1.42/1.84 'c_SetInterval_Oord__class_OatLeastLessThan' [103, 3] (w:1, o:214, a:
% 1.42/1.84 1, s:1, b:0),
% 1.42/1.84 'c_Finite__Set_Osetsum' [104, 4] (w:1, o:220, a:1, s:1, b:0),
% 1.42/1.84 'class_OrderedGroup_Omonoid__mult' [106, 1] (w:1, o:109, a:1, s:1, b:
% 1.42/1.84 0),
% 1.42/1.84 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le' [107, 1]
% 1.42/1.84 (w:1, o:110, a:1, s:1, b:0),
% 1.42/1.84 'class_OrderedGroup_Opordered__ab__semigroup__add' [108, 1] (w:1, o:
% 1.42/1.84 111, a:1, s:1, b:0),
% 1.42/1.84 'class_Orderings_Olinorder' [112, 1] (w:1, o:112, a:1, s:1, b:0),
% 1.42/1.84 'c_Set_Oinsert' [114, 3] (w:1, o:215, a:1, s:1, b:0),
% 1.42/1.84 'c_SetInterval_Oord__class_OgreaterThanLessThan' [116, 3] (w:1, o:216
% 1.42/1.84 , a:1, s:1, b:0),
% 1.42/1.84 'class_RealVector_Ometric__space' [118, 1] (w:1, o:141, a:1, s:1, b:0
% 1.42/1.84 ),
% 1.42/1.84 'class_RealVector_Oreal__normed__algebra__1' [119, 1] (w:1, o:142, a:
% 1.42/1.84 1, s:1, b:0),
% 1.42/1.84 'c_Lim_OLIM' [122, 5] (w:1, o:222, a:1, s:1, b:0),
% 1.42/1.84 'class_Lattices_Olattice' [124, 1] (w:1, o:143, a:1, s:1, b:0),
% 1.42/1.84 'c_Lattices_Olower__semilattice__class_Oinf' [125, 3] (w:1, o:217, a:
% 1.42/1.84 1, s:1, b:0),
% 1.42/1.84 'class_Int_Onumber__ring' [128, 1] (w:1, o:144, a:1, s:1, b:0),
% 1.42/1.84 'class_OrderedGroup_Opordered__comm__monoid__add' [129, 1] (w:1, o:
% 1.42/1.84 113, a:1, s:1, b:0),
% 1.42/1.84 'class_OrderedGroup_Olordered__ab__group__add' [132, 1] (w:1, o:106
% 1.42/1.84 , a:1, s:1, b:0),
% 1.42/1.84 'class_RealVector_Oreal__normed__field' [133, 1] (w:1, o:145, a:1, s:
% 1.42/1.84 1, b:0),
% 1.42/1.84 'class_OrderedGroup_Oab__group__add' [135, 1] (w:1, o:114, a:1, s:1
% 1.42/1.84 , b:0),
% 1.42/1.84 'class_Ring__and__Field_Opordered__ring' [136, 1] (w:1, o:149, a:1
% 1.42/1.84 , s:1, b:0),
% 1.42/1.84 'class_OrderedGroup_Opordered__ab__group__add' [139, 1] (w:1, o:115
% 1.42/1.84 , a:1, s:1, b:0),
% 1.42/1.84 'c_Int_OPls' [142, 0] (w:1, o:76, a:1, s:1, b:0),
% 1.42/1.84 'c_Int_OBit1' [143, 1] (w:1, o:151, a:1, s:1, b:0),
% 1.42/1.84 'c_Groebner__Basis_Ogb__semiring' [149, 6] (w:1, o:224, a:1, s:1, b:0
% 1.42/1.84 ),
% 1.42/1.84 'c_Int_OBit0' [150, 1] (w:1, o:150, a:1, s:1, b:0),
% 1.42/1.84 'class_Ring__and__Field_Oring' [151, 1] (w:1, o:152, a:1, s:1, b:0),
% 7.35/7.75
% 7.35/7.75 'class_OrderedGroup_Ogroup__add' [152, 1] (w:1, o:116, a:1, s:1, b:0)
% 7.35/7.75 ,
% 7.35/7.75 'class_OrderedGroup_Olordered__ab__group__add__join' [153, 1] (w:1
% 7.35/7.75 , o:107, a:1, s:1, b:0),
% 7.35/7.75 'class_Orderings_Opreorder' [154, 1] (w:1, o:117, a:1, s:1, b:0),
% 7.35/7.75 'class_OrderedGroup_Oab__semigroup__add' [155, 1] (w:1, o:118, a:1
% 7.35/7.75 , s:1, b:0),
% 7.35/7.75 'class_Divides_Oring__div' [160, 1] (w:1, o:132, a:1, s:1, b:0),
% 7.35/7.75 'class_Ring__and__Field_Oidom' [161, 1] (w:1, o:153, a:1, s:1, b:0),
% 7.35/7.75
% 7.35/7.75 'class_OrderedGroup_Ocancel__ab__semigroup__add' [162, 1] (w:1, o:119
% 7.35/7.75 , a:1, s:1, b:0),
% 7.35/7.75 'class_OrderedGroup_Ocancel__semigroup__add' [163, 1] (w:1, o:120, a:
% 7.35/7.75 1, s:1, b:0),
% 7.35/7.75 'class_RealVector_Oreal__field' [165, 1] (w:1, o:154, a:1, s:1, b:0)
% 7.35/7.75 ,
% 7.35/7.75 'class_RealVector_Oreal__normed__algebra' [169, 1] (w:1, o:155, a:1
% 7.35/7.75 , s:1, b:0),
% 7.35/7.75 'class_Ring__and__Field_Oordered__ring__strict' [170, 1] (w:1, o:135
% 7.35/7.75 , a:1, s:1, b:0),
% 7.35/7.75 'c_SetInterval_Oord__class_OlessThan' [171, 2] (w:1, o:203, a:1, s:1
% 7.35/7.75 , b:0),
% 7.35/7.75 'c_Int_Oiszero' [172, 2] (w:1, o:204, a:1, s:1, b:0),
% 7.35/7.75 'class_RealVector_Oreal__normed__div__algebra' [173, 1] (w:1, o:156
% 7.35/7.75 , a:1, s:1, b:0),
% 7.35/7.75 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add' [176, 1]
% 7.35/7.75 (w:1, o:121, a:1, s:1, b:0),
% 7.35/7.75 'class_Ring__and__Field_Osemiring__1' [177, 1] (w:1, o:160, a:1, s:1
% 7.35/7.75 , b:0),
% 7.35/7.75 'class_Ring__and__Field_Ozero__neq__one' [178, 1] (w:1, o:161, a:1
% 7.35/7.75 , s:1, b:0),
% 7.35/7.75 'class_Ring__and__Field_Oring__1__no__zero__divisors' [179, 1] (w:1
% 7.35/7.75 , o:157, a:1, s:1, b:0),
% 7.35/7.75 'class_Ring__and__Field_Ono__zero__divisors' [180, 1] (w:1, o:95, a:1
% 7.35/7.75 , s:1, b:0),
% 7.35/7.75 'class_Ring__and__Field_Omult__zero' [181, 1] (w:1, o:92, a:1, s:1
% 7.35/7.75 , b:0),
% 7.35/7.75 'class_OrderedGroup_Omonoid__add' [182, 1] (w:1, o:122, a:1, s:1, b:0
% 7.35/7.75 ),
% 7.35/7.75 'class_RealVector_Oreal__normed__vector' [183, 1] (w:1, o:162, a:1
% 7.35/7.75 , s:1, b:0),
% 7.35/7.75 'c_COMBB' [184, 5] (w:1, o:223, a:1, s:1, b:0),
% 7.35/7.75 'class_Ring__and__Field_Oordered__semiring__strict' [185, 1] (w:1, o:
% 7.35/7.75 146, a:1, s:1, b:0),
% 7.35/7.75 'c_SetInterval_Oord__class_OatLeast' [186, 2] (w:1, o:205, a:1, s:1
% 7.35/7.75 , b:0),
% 7.35/7.75 'class_Ring__and__Field_Oordered__semiring' [188, 1] (w:1, o:147, a:1
% 7.35/7.75 , s:1, b:0),
% 7.35/7.75 'class_Ring__and__Field_Ocomm__semiring' [191, 1] (w:1, o:98, a:1, s:
% 7.35/7.75 1, b:0),
% 7.35/7.75 'class_OrderedGroup_Ocomm__monoid__mult' [192, 1] (w:1, o:123, a:1
% 7.35/7.75 , s:1, b:0),
% 7.35/7.75 'class_Ring__and__Field_Osemiring' [193, 1] (w:1, o:163, a:1, s:1, b:
% 7.35/7.75 0),
% 7.35/7.75 'class_Ring__and__Field_Osemiring__0' [194, 1] (w:1, o:159, a:1, s:1
% 7.35/7.75 , b:0),
% 7.35/7.75 'c_Series_Osums' [195, 3] (w:1, o:218, a:1, s:1, b:0),
% 7.35/7.75 'class_Ring__and__Field_Oordered__comm__semiring__strict' [196, 1]
% 7.35/7.75 (w:1, o:148, a:1, s:1, b:0),
% 7.35/7.75 'class_Ring__and__Field_Omult__mono1' [197, 1] (w:1, o:93, a:1, s:1
% 7.35/7.75 , b:0),
% 7.35/7.75 'class_Ring__and__Field_Omult__mono' [198, 1] (w:1, o:94, a:1, s:1
% 7.35/7.75 , b:0),
% 7.35/7.75 'class_Lattices_Obounded__lattice' [199, 1] (w:1, o:164, a:1, s:1, b:
% 7.35/7.75 0),
% 7.35/7.75 'class_Orderings_Obot' [200, 1] (w:1, o:124, a:1, s:1, b:0),
% 7.35/7.75 'class_Ring__and__Field_Opordered__cancel__semiring' [201, 1] (w:1
% 7.35/7.75 , o:165, a:1, s:1, b:0),
% 7.35/7.75 'class_Ring__and__Field_Opordered__semiring' [202, 1] (w:1, o:166, a:
% 7.35/7.75 1, s:1, b:0),
% 7.35/7.75 'class_Int_Oring__char__0' [204, 1] (w:1, o:167, a:1, s:1, b:0),
% 7.35/7.75 'class_OrderedGroup_Olordered__ab__group__add__meet' [207, 1] (w:1
% 7.35/7.75 , o:108, a:1, s:1, b:0),
% 7.35/7.75 'class_Lattices_Olower__semilattice' [208, 1] (w:1, o:168, a:1, s:1
% 7.35/7.75 , b:0),
% 7.35/7.75 'class_Lattices_Odistrib__lattice' [209, 1] (w:1, o:169, a:1, s:1, b:
% 7.35/7.75 0),
% 7.35/7.75 'c_Ring__and__Field_Ocomm__ring__1' [210, 7] (w:1, o:226, a:1, s:1
% 7.35/7.75 , b:0),
% 7.35/7.75 'c_Set_Oimage' [211, 4] (w:1, o:221, a:1, s:1, b:0),
% 7.35/7.75 'v_n' [212, 0] (w:1, o:81, a:1, s:1, b:0),
% 7.35/7.75 'c_Parity_Osko__Parity__Xeven__mult__two__ex__1__1' [213, 1] (w:1, o:
% 7.35/7.75 170, a:1, s:1, b:0),
% 7.35/7.75 'c_Parity_Osko__Parity__Xodd__Suc__mult__two__ex__1__1' [214, 1] (w:1
% 7.35/7.75 , o:171, a:1, s:1, b:0),
% 7.35/7.75 'class_Ring__and__Field_Oring__no__zero__divisors' [217, 1] (w:1, o:
% 24.31/24.71 158, a:1, s:1, b:0),
% 24.31/24.71 'class_OrderedGroup_Oab__semigroup__mult' [219, 1] (w:1, o:125, a:1
% 24.31/24.71 , s:1, b:0),
% 24.31/24.71 'class_OrderedGroup_Oab__semigroup__idem__mult' [220, 1] (w:1, o:126
% 24.31/24.71 , a:1, s:1, b:0),
% 24.31/24.71 'c_COMBC' [225, 6] (w:1, o:225, a:1, s:1, b:0),
% 24.31/24.71 'c_fequal' [226, 3] (w:1, o:219, a:1, s:1, b:0).
% 24.31/24.71
% 24.31/24.71
% 24.31/24.71 Starting Search:
% 24.31/24.71
% 24.31/24.71 Resimplifying inuse:
% 24.31/24.71 Done
% 24.31/24.71
% 24.31/24.71
% 24.31/24.71 Intermediate Status:
% 24.31/24.71 Generated: 3125
% 24.31/24.71 Kept: 2007
% 24.31/24.71 Inuse: 100
% 24.31/24.71 Deleted: 6
% 24.31/24.71 Deletedinuse: 0
% 24.31/24.71
% 24.31/24.71 Resimplifying inuse:
% 24.31/24.71 Done
% 24.31/24.71
% 24.31/24.71 Resimplifying inuse:
% 24.31/24.71 Done
% 24.31/24.71
% 24.31/24.71
% 24.31/24.71 Intermediate Status:
% 24.31/24.71 Generated: 9862
% 24.31/24.71 Kept: 4232
% 24.31/24.71 Inuse: 275
% 24.31/24.71 Deleted: 12
% 24.31/24.71 Deletedinuse: 1
% 24.31/24.71
% 24.31/24.71 Resimplifying inuse:
% 24.31/24.71 Done
% 24.31/24.71
% 24.31/24.71
% 24.31/24.71 Intermediate Status:
% 24.31/24.71 Generated: 21281
% 24.31/24.71 Kept: 6633
% 24.31/24.71 Inuse: 300
% 24.31/24.71 Deleted: 12
% 24.31/24.71 Deletedinuse: 1
% 24.31/24.71
% 24.31/24.71 Resimplifying inuse:
% 24.31/24.71 Done
% 24.31/24.71
% 24.31/24.71 Resimplifying inuse:
% 24.31/24.71 Done
% 24.31/24.71
% 24.31/24.71
% 24.31/24.71 Intermediate Status:
% 24.31/24.71 Generated: 32320
% 24.31/24.71 Kept: 10109
% 24.31/24.71 Inuse: 341
% 24.31/24.71 Deleted: 12
% 24.31/24.71 Deletedinuse: 1
% 24.31/24.71
% 24.31/24.71 Resimplifying inuse:
% 24.31/24.71 Done
% 24.31/24.71
% 24.31/24.71 Resimplifying inuse:
% 24.31/24.71 Done
% 24.31/24.71
% 24.31/24.71
% 24.31/24.71 Intermediate Status:
% 24.31/24.71 Generated: 42893
% 24.31/24.71 Kept: 12761
% 24.31/24.71 Inuse: 410
% 24.31/24.71 Deleted: 12
% 24.31/24.71 Deletedinuse: 1
% 24.31/24.71
% 24.31/24.71 Resimplifying inuse:
% 24.31/24.71 Done
% 24.31/24.71
% 24.31/24.71 Resimplifying inuse:
% 24.31/24.71 Done
% 24.31/24.71
% 24.31/24.71
% 24.31/24.71 Intermediate Status:
% 24.31/24.71 Generated: 47807
% 24.31/24.71 Kept: 14925
% 24.31/24.71 Inuse: 460
% 24.31/24.71 Deleted: 12
% 24.31/24.71 Deletedinuse: 1
% 24.31/24.71
% 24.31/24.71 Resimplifying inuse:
% 24.31/24.71 Done
% 24.31/24.71
% 24.31/24.71 Resimplifying inuse:
% 24.31/24.71 Done
% 24.31/24.71
% 24.31/24.71
% 24.31/24.71 Intermediate Status:
% 24.31/24.71 Generated: 52781
% 24.31/24.71 Kept: 16946
% 24.31/24.71 Inuse: 495
% 24.31/24.71 Deleted: 12
% 24.31/24.71 Deletedinuse: 1
% 24.31/24.71
% 24.31/24.71 Resimplifying inuse:
% 24.31/24.71 Done
% 24.31/24.71
% 24.31/24.71
% 24.31/24.71 Intermediate Status:
% 24.31/24.71 Generated: 61513
% 24.31/24.71 Kept: 19470
% 24.31/24.71 Inuse: 525
% 24.31/24.71 Deleted: 12
% 24.31/24.71 Deletedinuse: 1
% 24.31/24.71
% 24.31/24.71 Resimplifying inuse:
% 24.31/24.71 Done
% 24.31/24.71
% 24.31/24.71 Resimplifying clauses:
% 24.31/24.71 Done
% 24.31/24.71
% 24.31/24.71 Resimplifying inuse:
% 24.31/24.71 Done
% 24.31/24.71
% 24.31/24.71
% 24.31/24.71 Intermediate Status:
% 24.31/24.71 Generated: 69381
% 24.31/24.71 Kept: 21573
% 24.31/24.71 Inuse: 550
% 24.31/24.71 Deleted: 511
% 24.31/24.71 Deletedinuse: 1
% 24.31/24.71
% 24.31/24.71 Resimplifying inuse:
% 24.31/24.71 Done
% 24.31/24.71
% 24.31/24.71 Resimplifying inuse:
% 24.31/24.71 Done
% 24.31/24.71
% 24.31/24.71
% 24.31/24.71 Intermediate Status:
% 24.31/24.71 Generated: 75143
% 24.31/24.71 Kept: 23617
% 24.31/24.71 Inuse: 595
% 24.31/24.71 Deleted: 511
% 24.31/24.71 Deletedinuse: 1
% 24.31/24.71
% 24.31/24.71 Resimplifying inuse:
% 24.31/24.71 Done
% 24.31/24.71
% 24.31/24.71 Resimplifying inuse:
% 24.31/24.71 Done
% 24.31/24.71
% 24.31/24.71
% 24.31/24.71 Intermediate Status:
% 24.31/24.71 Generated: 81666
% 24.31/24.71 Kept: 25797
% 24.31/24.71 Inuse: 625
% 24.31/24.71 Deleted: 511
% 24.31/24.71 Deletedinuse: 1
% 24.31/24.71
% 24.31/24.71 Resimplifying inuse:
% 24.31/24.71 Done
% 24.31/24.71
% 24.31/24.71
% 24.31/24.71 Intermediate Status:
% 24.31/24.71 Generated: 93168
% 24.31/24.71 Kept: 28848
% 24.31/24.71 Inuse: 655
% 24.31/24.71 Deleted: 511
% 24.31/24.71 Deletedinuse: 1
% 24.31/24.71
% 24.31/24.71 Resimplifying inuse:
% 24.31/24.71 Done
% 24.31/24.71
% 24.31/24.71 Resimplifying inuse:
% 24.31/24.71 Done
% 24.31/24.71
% 24.31/24.71
% 24.31/24.71 Intermediate Status:
% 24.31/24.71 Generated: 105328
% 24.31/24.71 Kept: 32720
% 24.31/24.71 Inuse: 695
% 24.31/24.71 Deleted: 512
% 24.31/24.71 Deletedinuse: 2
% 24.31/24.71
% 24.31/24.71 Resimplifying inuse:
% 24.31/24.71 Done
% 24.31/24.71
% 24.31/24.71 Resimplifying inuse:
% 24.31/24.71 Done
% 24.31/24.71
% 24.31/24.71
% 24.31/24.71 Intermediate Status:
% 24.31/24.71 Generated: 113527
% 24.31/24.71 Kept: 36630
% 24.31/24.71 Inuse: 700
% 24.31/24.71 Deleted: 512
% 24.31/24.71 Deletedinuse: 2
% 24.31/24.71
% 24.31/24.71 Resimplifying inuse:
% 24.31/24.71 Done
% 24.31/24.71
% 24.31/24.71
% 24.31/24.71 Intermediate Status:
% 24.31/24.71 Generated: 119451
% 24.31/24.71 Kept: 38958
% 24.31/24.71 Inuse: 705
% 24.31/24.71 Deleted: 512
% 24.31/24.71 Deletedinuse: 2
% 24.31/24.71
% 24.31/24.71 Resimplifying inuse:
% 24.31/24.71 Done
% 24.31/24.71
% 24.31/24.71
% 24.31/24.71 Intermediate Status:
% 24.31/24.71 Generated: 125588
% 24.31/24.71 Kept: 41313
% 24.31/24.71 Inuse: 710
% 24.31/24.71 Deleted: 512
% 24.31/24.71 Deletedinuse: 2
% 24.31/24.71
% 24.31/24.71 Resimplifying inuse:
% 24.31/24.71 Done
% 24.31/24.71
% 24.31/24.71 Resimplifying clauses:
% 24.31/24.71 Done
% 24.31/24.71
% 24.31/24.71 Resimplifying inuse:
% 24.31/24.71 Done
% 24.31/24.71
% 24.31/24.71
% 24.31/24.71 Intermediate Status:
% 24.31/24.71 Generated: 141560
% 24.31/24.71 Kept: 45833
% 24.31/24.71 Inuse: 730
% 24.31/24.71 Deleted: 593
% 24.31/24.71 Deletedinuse: 2
% 24.31/24.71
% 24.31/24.71 Resimplifying inuse:
% 24.31/24.71 Done
% 24.31/24.71
% 24.31/24.71 Resimplifying inuse:
% 24.31/24.71 Done
% 24.31/24.71
% 24.31/24.71
% 24.31/24.71 Intermediate Status:
% 24.31/24.71 Generated: 148763
% 24.31/24.71 Kept: 47839
% 24.31/24.71 Inuse: 741
% 24.31/24.71 Deleted: 594
% 24.31/24.71 Deletedinuse: 3
% 24.31/24.71
% 24.31/24.71 Resimplifying inuse:
% 24.31/24.71 Done
% 24.31/24.71
% 24.31/24.71
% 24.31/24.71 Intermediate Status:
% 24.31/24.71 Generated: 159371
% 24.31/24.71 Kept: 50934
% 24.31/24.71 Inuse: 765
% 24.31/24.71 Deleted: 594
% 24.31/24.71 Deletedinuse: 3
% 24.31/24.71
% 24.31/24.71 Resimplifying inuse:
% 24.31/24.71 Done
% 24.31/24.71
% 24.31/24.71 Resimplifying inuse:
% 24.31/24.71 Done
% 24.31/24.71
% 24.31/24.71
% 24.31/24.71 Intermediate Status:
% 24.31/24.71 Generated: 165486
% 24.31/24.71 Kept: 52944
% 24.31/24.71 Inuse: 785
% 24.31/24.71 Deleted: 594
% 24.31/24.71 Deletedinuse: 3
% 24.31/24.71
% 24.31/24.71 Resimplifying inuse:
% 24.31/24.71 Done
% 24.31/24.71
% 24.31/24.71
% 24.31/24.71 Intermediate Status:
% 24.31/24.71 Generated: 175606
% 24.31/24.71 Kept: 56164
% 24.31/24.71 Inuse: 795
% 24.31/24.71 Deleted: 594
% 24.31/24.71 Deletedinuse: 3
% 24.31/24.71
% 24.31/24.71 Resimplifying inuse:
% 24.31/24.71 Done
% 24.31/24.71
% 24.31/24.71 Resimplifying inuse:
% 24.31/24.71 Done
% 24.31/24.71
% 24.31/24.71
% 24.31/24.71 Intermediate Status:
% 24.31/24.71 Generated: 184328
% 24.31/24.71 Kept: 58433
% 24.31/24.71 Inuse: 820
% 24.31/24.71 Deleted: 594
% 24.31/24.71 Deletedinuse: 3
% 24.31/24.71
% 24.31/24.71 Resimplifying inuse:
% 24.31/24.71 Done
% 24.31/24.71
% 24.31/24.71 Resimplifying inuse:
% 24.31/24.71 Done
% 24.31/24.71
% 24.31/24.71
% 24.31/24.71 Intermediate Status:
% 24.31/24.71 Generated: 195851
% 24.31/24.71 Kept: 60614
% 24.31/24.71 Inuse: 850
% 24.31/24.71 Deleted: 594
% 24.31/24.71 Deletedinuse: 3
% 24.31/24.71
% 24.31/24.71 Resimplifying inuse:
% 73.53/73.88 Done
% 73.53/73.88
% 73.53/73.88 Resimplifying clauses:
% 73.53/73.88 Done
% 73.53/73.88
% 73.53/73.88 Resimplifying inuse:
% 73.53/73.88 Done
% 73.53/73.88
% 73.53/73.88
% 73.53/73.88 Intermediate Status:
% 73.53/73.88 Generated: 205637
% 73.53/73.88 Kept: 62855
% 73.53/73.88 Inuse: 880
% 73.53/73.88 Deleted: 674
% 73.53/73.88 Deletedinuse: 3
% 73.53/73.88
% 73.53/73.88 Resimplifying inuse:
% 73.53/73.88 Done
% 73.53/73.88
% 73.53/73.88 Resimplifying inuse:
% 73.53/73.88 Done
% 73.53/73.88
% 73.53/73.88
% 73.53/73.88 Intermediate Status:
% 73.53/73.88 Generated: 214341
% 73.53/73.88 Kept: 65122
% 73.53/73.88 Inuse: 910
% 73.53/73.88 Deleted: 674
% 73.53/73.88 Deletedinuse: 3
% 73.53/73.88
% 73.53/73.88 Resimplifying inuse:
% 73.53/73.88 Done
% 73.53/73.88
% 73.53/73.88 Resimplifying inuse:
% 73.53/73.88 Done
% 73.53/73.88
% 73.53/73.88
% 73.53/73.88 Intermediate Status:
% 73.53/73.88 Generated: 222656
% 73.53/73.88 Kept: 67214
% 73.53/73.88 Inuse: 935
% 73.53/73.88 Deleted: 674
% 73.53/73.88 Deletedinuse: 3
% 73.53/73.88
% 73.53/73.88 Resimplifying inuse:
% 73.53/73.88 Done
% 73.53/73.88
% 73.53/73.88 Resimplifying inuse:
% 73.53/73.88 Done
% 73.53/73.88
% 73.53/73.88
% 73.53/73.88 Intermediate Status:
% 73.53/73.88 Generated: 228197
% 73.53/73.88 Kept: 69436
% 73.53/73.88 Inuse: 950
% 73.53/73.88 Deleted: 674
% 73.53/73.88 Deletedinuse: 3
% 73.53/73.88
% 73.53/73.88 Resimplifying inuse:
% 73.53/73.88 Done
% 73.53/73.88
% 73.53/73.88 Resimplifying inuse:
% 73.53/73.88 Done
% 73.53/73.88
% 73.53/73.88
% 73.53/73.88 Intermediate Status:
% 73.53/73.88 Generated: 236714
% 73.53/73.88 Kept: 72120
% 73.53/73.88 Inuse: 975
% 73.53/73.88 Deleted: 674
% 73.53/73.88 Deletedinuse: 3
% 73.53/73.88
% 73.53/73.88 Resimplifying inuse:
% 73.53/73.88 Done
% 73.53/73.88
% 73.53/73.88 Resimplifying inuse:
% 73.53/73.88 Done
% 73.53/73.88
% 73.53/73.88
% 73.53/73.88 Intermediate Status:
% 73.53/73.88 Generated: 246465
% 73.53/73.88 Kept: 74374
% 73.53/73.88 Inuse: 1005
% 73.53/73.88 Deleted: 674
% 73.53/73.88 Deletedinuse: 3
% 73.53/73.88
% 73.53/73.88 Resimplifying inuse:
% 73.53/73.88 Done
% 73.53/73.88
% 73.53/73.88 Resimplifying inuse:
% 73.53/73.88 Done
% 73.53/73.88
% 73.53/73.88
% 73.53/73.88 Intermediate Status:
% 73.53/73.88 Generated: 255010
% 73.53/73.88 Kept: 76416
% 73.53/73.88 Inuse: 1030
% 73.53/73.88 Deleted: 678
% 73.53/73.88 Deletedinuse: 7
% 73.53/73.88
% 73.53/73.88 Resimplifying inuse:
% 73.53/73.88 Done
% 73.53/73.88
% 73.53/73.88 Resimplifying inuse:
% 73.53/73.88 Done
% 73.53/73.88
% 73.53/73.88
% 73.53/73.88 Intermediate Status:
% 73.53/73.88 Generated: 263838
% 73.53/73.88 Kept: 78685
% 73.53/73.88 Inuse: 1055
% 73.53/73.88 Deleted: 678
% 73.53/73.88 Deletedinuse: 7
% 73.53/73.88
% 73.53/73.88 Resimplifying inuse:
% 73.53/73.88 Done
% 73.53/73.88
% 73.53/73.88
% 73.53/73.88 Intermediate Status:
% 73.53/73.88 Generated: 272581
% 73.53/73.88 Kept: 81056
% 73.53/73.88 Inuse: 1080
% 73.53/73.88 Deleted: 678
% 73.53/73.88 Deletedinuse: 7
% 73.53/73.88
% 73.53/73.88 Resimplifying inuse:
% 73.53/73.88 Done
% 73.53/73.88
% 73.53/73.88 Resimplifying inuse:
% 73.53/73.88 Done
% 73.53/73.88
% 73.53/73.88 Resimplifying clauses:
% 73.53/73.88 Done
% 73.53/73.88
% 73.53/73.88
% 73.53/73.88 Intermediate Status:
% 73.53/73.88 Generated: 279380
% 73.53/73.88 Kept: 83148
% 73.53/73.88 Inuse: 1090
% 73.53/73.88 Deleted: 1077
% 73.53/73.88 Deletedinuse: 7
% 73.53/73.88
% 73.53/73.88 Resimplifying inuse:
% 73.53/73.88 Done
% 73.53/73.88
% 73.53/73.88 Resimplifying inuse:
% 73.53/73.88 Done
% 73.53/73.88
% 73.53/73.88
% 73.53/73.88 Intermediate Status:
% 73.53/73.88 Generated: 287240
% 73.53/73.88 Kept: 86497
% 73.53/73.88 Inuse: 1096
% 73.53/73.88 Deleted: 1077
% 73.53/73.88 Deletedinuse: 7
% 73.53/73.88
% 73.53/73.88 Resimplifying inuse:
% 73.53/73.88 Done
% 73.53/73.88
% 73.53/73.88 Resimplifying inuse:
% 73.53/73.88 Done
% 73.53/73.88
% 73.53/73.88
% 73.53/73.88 Intermediate Status:
% 73.53/73.88 Generated: 294576
% 73.53/73.88 Kept: 88649
% 73.53/73.88 Inuse: 1120
% 73.53/73.88 Deleted: 1077
% 73.53/73.88 Deletedinuse: 7
% 73.53/73.88
% 73.53/73.88 Resimplifying inuse:
% 73.53/73.88 Done
% 73.53/73.88
% 73.53/73.88 Resimplifying inuse:
% 73.53/73.88 Done
% 73.53/73.88
% 73.53/73.88
% 73.53/73.88 Intermediate Status:
% 73.53/73.88 Generated: 305530
% 73.53/73.88 Kept: 91279
% 73.53/73.88 Inuse: 1145
% 73.53/73.88 Deleted: 1077
% 73.53/73.88 Deletedinuse: 7
% 73.53/73.88
% 73.53/73.88 Resimplifying inuse:
% 73.53/73.88 Done
% 73.53/73.88
% 73.53/73.88 Resimplifying inuse:
% 73.53/73.88 Done
% 73.53/73.88
% 73.53/73.88
% 73.53/73.88 Intermediate Status:
% 73.53/73.88 Generated: 315255
% 73.53/73.88 Kept: 93531
% 73.53/73.88 Inuse: 1190
% 73.53/73.88 Deleted: 1077
% 73.53/73.88 Deletedinuse: 7
% 73.53/73.88
% 73.53/73.88 Resimplifying inuse:
% 73.53/73.88 Done
% 73.53/73.88
% 73.53/73.88 Resimplifying inuse:
% 73.53/73.88 Done
% 73.53/73.88
% 73.53/73.88
% 73.53/73.88 Intermediate Status:
% 73.53/73.88 Generated: 323716
% 73.53/73.88 Kept: 95562
% 73.53/73.88 Inuse: 1225
% 73.53/73.88 Deleted: 1077
% 73.53/73.88 Deletedinuse: 7
% 73.53/73.88
% 73.53/73.88 Resimplifying inuse:
% 73.53/73.88 Done
% 73.53/73.88
% 73.53/73.88 Resimplifying inuse:
% 73.53/73.88 Done
% 73.53/73.88
% 73.53/73.88
% 73.53/73.88 Intermediate Status:
% 73.53/73.88 Generated: 335221
% 73.53/73.88 Kept: 97797
% 73.53/73.88 Inuse: 1260
% 73.53/73.88 Deleted: 1079
% 73.53/73.88 Deletedinuse: 9
% 73.53/73.88
% 73.53/73.88 Resimplifying inuse:
% 73.53/73.88 Done
% 73.53/73.88
% 73.53/73.88 Resimplifying inuse:
% 73.53/73.88 Done
% 73.53/73.88
% 73.53/73.88
% 73.53/73.88 Intermediate Status:
% 73.53/73.88 Generated: 346051
% 73.53/73.88 Kept: 99920
% 73.53/73.88 Inuse: 1290
% 73.53/73.88 Deleted: 1080
% 73.53/73.88 Deletedinuse: 10
% 73.53/73.88
% 73.53/73.88 Resimplifying inuse:
% 73.53/73.88 Done
% 73.53/73.88
% 73.53/73.88 Resimplifying inuse:
% 73.53/73.88 Done
% 73.53/73.88
% 73.53/73.88
% 73.53/73.88 Intermediate Status:
% 73.53/73.88 Generated: 359662
% 73.53/73.88 Kept: 103700
% 73.53/73.88 Inuse: 1320
% 73.53/73.88 Deleted: 1080
% 73.53/73.88 Deletedinuse: 10
% 73.53/73.88
% 73.53/73.88 Resimplifying inuse:
% 73.53/73.88 Done
% 73.53/73.88
% 73.53/73.88 Resimplifying clauses:
% 73.53/73.88 Done
% 73.53/73.88
% 73.53/73.88 Resimplifying inuse:
% 73.53/73.88 Done
% 73.53/73.88
% 73.53/73.88
% 73.53/73.88 Intermediate Status:
% 73.53/73.88 Generated: 368911
% 73.53/73.88 Kept: 105845
% 73.53/73.88 Inuse: 1345
% 73.53/73.88 Deleted: 1644
% 73.53/73.88 Deletedinuse: 10
% 73.53/73.88
% 73.53/73.88 Resimplifying inuse:
% 73.53/73.88 Done
% 73.53/73.88
% 73.53/73.88 Resimplifying inuse:
% 73.53/73.88 Done
% 73.53/73.88
% 73.53/73.88
% 73.53/73.88 Intermediate Status:
% 73.53/73.88 Generated: 377208
% 73.53/73.88 Kept: 107846
% 73.53/73.88 Inuse: 1366
% 73.53/73.88 Deleted: 1644
% 73.53/73.88 Deletedinuse: 10
% 73.53/73.88
% 73.53/73.88 Resimplifying inuse:
% 73.53/73.88 Done
% 73.53/73.88
% 73.53/73.88 Resimplifying inuse:
% 73.53/73.88 Done
% 73.53/73.88
% 73.53/73.88
% 73.53/73.88 Intermediate Status:
% 73.53/73.88 Generated: 385995
% 73.53/73.88 Kept: 110121
% 73.53/73.88 Inuse: 1385
% 73.53/73.88 Deleted: 1644
% 73.53/73.88 Deletedinuse: 10
% 73.53/73.88
% 73.53/73.88 Resimplifying inuse:
% 73.53/73.88 Done
% 73.53/73.88
% 73.53/73.88
% 73.53/73.88 Intermediate Status:
% 73.53/73.88 Generated: 395499
% 73.53/73.88 Kept: 112281
% 73.53/73.88 Inuse: 1405
% 73.53/73.88 Deleted: 1644
% 73.53/73.88 Deletedinuse: 10
% 73.53/73.88
% 73.53/73.88 Resimplifying inuse:
% 73.53/73.88 Done
% 73.53/73.88
% 73.53/73.88 Resimplifying inuse:
% 73.53/73.88 Done
% 73.53/73.88
% 73.53/73.88
% 73.53/73.88 Intermediate Status:
% 73.53/73.88 Generated: 417482
% 73.53/73.88 Kept: 116358
% 73.53/73.88 Inuse: 1430
% 73.53/73.88 Deleted: 1644
% 73.53/73.88 Deletedinuse: 10
% 73.53/73.88
% 73.53/73.88 Resimplifying inuse:
% 73.53/73.88 Done
% 73.53/73.88
% 73.53/73.88
% 73.53/73.88 Intermediate Status:
% 73.53/73.88 Generated: 432624
% 73.53/73.88 Kept: 118567
% 73.53/73.88 Inuse: 1435
% 73.53/73.88 Deleted: 1644
% 153.74/154.14 Deletedinuse: 10
% 153.74/154.14
% 153.74/154.14 Resimplifying inuse:
% 153.74/154.14 Done
% 153.74/154.14
% 153.74/154.14
% 153.74/154.14 Intermediate Status:
% 153.74/154.14 Generated: 447851
% 153.74/154.14 Kept: 120758
% 153.74/154.14 Inuse: 1440
% 153.74/154.14 Deleted: 1644
% 153.74/154.14 Deletedinuse: 10
% 153.74/154.14
% 153.74/154.14 Resimplifying inuse:
% 153.74/154.14 Done
% 153.74/154.14
% 153.74/154.14
% 153.74/154.14 Intermediate Status:
% 153.74/154.14 Generated: 463150
% 153.74/154.14 Kept: 122959
% 153.74/154.14 Inuse: 1445
% 153.74/154.14 Deleted: 1644
% 153.74/154.14 Deletedinuse: 10
% 153.74/154.14
% 153.74/154.14 Resimplifying inuse:
% 153.74/154.14 Done
% 153.74/154.14
% 153.74/154.14
% 153.74/154.14 Intermediate Status:
% 153.74/154.14 Generated: 478564
% 153.74/154.14 Kept: 125166
% 153.74/154.14 Inuse: 1450
% 153.74/154.14 Deleted: 1644
% 153.74/154.14 Deletedinuse: 10
% 153.74/154.14
% 153.74/154.14 Resimplifying inuse:
% 153.74/154.14 Done
% 153.74/154.14
% 153.74/154.14 Resimplifying clauses:
% 153.74/154.14 Done
% 153.74/154.14
% 153.74/154.14
% 153.74/154.14 Intermediate Status:
% 153.74/154.14 Generated: 494020
% 153.74/154.14 Kept: 127382
% 153.74/154.14 Inuse: 1455
% 153.74/154.14 Deleted: 2141
% 153.74/154.14 Deletedinuse: 10
% 153.74/154.14
% 153.74/154.14 Resimplifying inuse:
% 153.74/154.14 Done
% 153.74/154.14
% 153.74/154.14 Resimplifying inuse:
% 153.74/154.14 Done
% 153.74/154.14
% 153.74/154.14
% 153.74/154.14 Intermediate Status:
% 153.74/154.14 Generated: 508956
% 153.74/154.14 Kept: 131531
% 153.74/154.14 Inuse: 1475
% 153.74/154.14 Deleted: 2141
% 153.74/154.14 Deletedinuse: 10
% 153.74/154.14
% 153.74/154.14 Resimplifying inuse:
% 153.74/154.14 Done
% 153.74/154.14
% 153.74/154.14 Resimplifying inuse:
% 153.74/154.14 Done
% 153.74/154.14
% 153.74/154.14
% 153.74/154.14 Intermediate Status:
% 153.74/154.14 Generated: 531423
% 153.74/154.14 Kept: 137952
% 153.74/154.14 Inuse: 1505
% 153.74/154.14 Deleted: 2141
% 153.74/154.14 Deletedinuse: 10
% 153.74/154.14
% 153.74/154.14 Resimplifying inuse:
% 153.74/154.14 Done
% 153.74/154.15
% 153.74/154.15 Resimplifying inuse:
% 153.74/154.15 Done
% 153.74/154.15
% 153.74/154.15
% 153.74/154.15 Intermediate Status:
% 153.74/154.15 Generated: 539959
% 153.74/154.15 Kept: 140705
% 153.74/154.15 Inuse: 1520
% 153.74/154.15 Deleted: 2141
% 153.74/154.15 Deletedinuse: 10
% 153.74/154.15
% 153.74/154.15 Resimplifying inuse:
% 153.74/154.15 Done
% 153.74/154.15
% 153.74/154.15 Resimplifying inuse:
% 153.74/154.15 Done
% 153.74/154.15
% 153.74/154.15
% 153.74/154.15 Intermediate Status:
% 153.74/154.15 Generated: 548291
% 153.74/154.15 Kept: 142835
% 153.74/154.15 Inuse: 1535
% 153.74/154.15 Deleted: 2141
% 153.74/154.15 Deletedinuse: 10
% 153.74/154.15
% 153.74/154.15
% 153.74/154.15 Intermediate Status:
% 153.74/154.15 Generated: 559279
% 153.74/154.15 Kept: 145812
% 153.74/154.15 Inuse: 1545
% 153.74/154.15 Deleted: 2141
% 153.74/154.15 Deletedinuse: 10
% 153.74/154.15
% 153.74/154.15 Resimplifying inuse:
% 153.74/154.15 Done
% 153.74/154.15
% 153.74/154.15 Resimplifying clauses:
% 153.74/154.15 Done
% 153.74/154.15
% 153.74/154.15 Resimplifying inuse:
% 153.74/154.15 Done
% 153.74/154.15
% 153.74/154.15
% 153.74/154.15 Intermediate Status:
% 153.74/154.15 Generated: 573149
% 153.74/154.15 Kept: 149750
% 153.74/154.15 Inuse: 1560
% 153.74/154.15 Deleted: 2274
% 153.74/154.15 Deletedinuse: 11
% 153.74/154.15
% 153.74/154.15 Resimplifying inuse:
% 153.74/154.15 Done
% 153.74/154.15
% 153.74/154.15 Resimplifying inuse:
% 153.74/154.15 Done
% 153.74/154.15
% 153.74/154.15
% 153.74/154.15 Intermediate Status:
% 153.74/154.15 Generated: 581500
% 153.74/154.15 Kept: 152073
% 153.74/154.15 Inuse: 1575
% 153.74/154.15 Deleted: 2274
% 153.74/154.15 Deletedinuse: 11
% 153.74/154.15
% 153.74/154.15 Resimplifying inuse:
% 153.74/154.15 Done
% 153.74/154.15
% 153.74/154.15
% 153.74/154.15 Intermediate Status:
% 153.74/154.15 Generated: 590005
% 153.74/154.15 Kept: 154082
% 153.74/154.15 Inuse: 1590
% 153.74/154.15 Deleted: 2274
% 153.74/154.15 Deletedinuse: 11
% 153.74/154.15
% 153.74/154.15 Resimplifying inuse:
% 153.74/154.15 Done
% 153.74/154.15
% 153.74/154.15 Resimplifying inuse:
% 153.74/154.15 Done
% 153.74/154.15
% 153.74/154.15
% 153.74/154.15 Intermediate Status:
% 153.74/154.15 Generated: 598889
% 153.74/154.15 Kept: 156367
% 153.74/154.15 Inuse: 1610
% 153.74/154.15 Deleted: 2274
% 153.74/154.15 Deletedinuse: 11
% 153.74/154.15
% 153.74/154.15 Resimplifying inuse:
% 153.74/154.15 Done
% 153.74/154.15
% 153.74/154.15 Resimplifying inuse:
% 153.74/154.15 Done
% 153.74/154.15
% 153.74/154.15
% 153.74/154.15 Intermediate Status:
% 153.74/154.15 Generated: 608366
% 153.74/154.15 Kept: 158641
% 153.74/154.15 Inuse: 1625
% 153.74/154.15 Deleted: 2274
% 153.74/154.15 Deletedinuse: 11
% 153.74/154.15
% 153.74/154.15 Resimplifying inuse:
% 153.74/154.15 Done
% 153.74/154.15
% 153.74/154.15 Resimplifying inuse:
% 153.74/154.15 Done
% 153.74/154.15
% 153.74/154.15
% 153.74/154.15 Intermediate Status:
% 153.74/154.15 Generated: 617036
% 153.74/154.15 Kept: 160804
% 153.74/154.15 Inuse: 1645
% 153.74/154.15 Deleted: 2274
% 153.74/154.15 Deletedinuse: 11
% 153.74/154.15
% 153.74/154.15 Resimplifying inuse:
% 153.74/154.15 Done
% 153.74/154.15
% 153.74/154.15 Resimplifying inuse:
% 153.74/154.15 Done
% 153.74/154.15
% 153.74/154.15
% 153.74/154.15 Intermediate Status:
% 153.74/154.15 Generated: 625747
% 153.74/154.15 Kept: 163233
% 153.74/154.15 Inuse: 1665
% 153.74/154.15 Deleted: 2274
% 153.74/154.15 Deletedinuse: 11
% 153.74/154.15
% 153.74/154.15 Resimplifying inuse:
% 153.74/154.15 Done
% 153.74/154.15
% 153.74/154.15
% 153.74/154.15 Intermediate Status:
% 153.74/154.15 Generated: 636056
% 153.74/154.15 Kept: 166084
% 153.74/154.15 Inuse: 1675
% 153.74/154.15 Deleted: 2274
% 153.74/154.15 Deletedinuse: 11
% 153.74/154.15
% 153.74/154.15 Resimplifying inuse:
% 153.74/154.15 Done
% 153.74/154.15
% 153.74/154.15 Resimplifying clauses:
% 153.74/154.15 Done
% 153.74/154.15
% 153.74/154.15 Resimplifying inuse:
% 153.74/154.15 Done
% 153.74/154.15
% 153.74/154.15
% 153.74/154.15 Intermediate Status:
% 153.74/154.15 Generated: 646527
% 153.74/154.15 Kept: 168494
% 153.74/154.15 Inuse: 1700
% 153.74/154.15 Deleted: 4595
% 153.74/154.15 Deletedinuse: 12
% 153.74/154.15
% 153.74/154.15 Resimplifying inuse:
% 153.74/154.15 Done
% 153.74/154.15
% 153.74/154.15 Resimplifying inuse:
% 153.74/154.15 Done
% 153.74/154.15
% 153.74/154.15
% 153.74/154.15 Intermediate Status:
% 153.74/154.15 Generated: 655313
% 153.74/154.15 Kept: 170580
% 153.74/154.15 Inuse: 1715
% 153.74/154.15 Deleted: 4595
% 153.74/154.15 Deletedinuse: 12
% 153.74/154.15
% 153.74/154.15 Resimplifying inuse:
% 153.74/154.15 Done
% 153.74/154.15
% 153.74/154.15 Resimplifying inuse:
% 153.74/154.15 Done
% 153.74/154.15
% 153.74/154.15
% 153.74/154.15 Intermediate Status:
% 153.74/154.15 Generated: 687308
% 153.74/154.15 Kept: 175182
% 153.74/154.15 Inuse: 1735
% 153.74/154.15 Deleted: 4595
% 153.74/154.15 Deletedinuse: 12
% 153.74/154.15
% 153.74/154.15 Resimplifying inuse:
% 153.74/154.15 Done
% 153.74/154.15
% 153.74/154.15 Resimplifying inuse:
% 153.74/154.15 Done
% 153.74/154.15
% 153.74/154.15
% 153.74/154.15 Intermediate Status:
% 153.74/154.15 Generated: 702993
% 153.74/154.15 Kept: 179755
% 153.74/154.15 Inuse: 1750
% 153.74/154.15 Deleted: 4595
% 153.74/154.15 Deletedinuse: 12
% 153.74/154.15
% 153.74/154.15 Resimplifying inuse:
% 153.74/154.15 Done
% 153.74/154.15
% 153.74/154.15 Resimplifying inuse:
% 153.74/154.15 Done
% 153.74/154.15
% 153.74/154.15
% 153.74/154.15 Intermediate Status:
% 153.74/154.15 Generated: 717443
% 153.74/154.15 Kept: 181952
% 153.74/154.15 Inuse: 1790
% 153.74/154.15 Deleted: 4595
% 153.74/154.15 Deletedinuse: 12
% 153.74/154.15
% 153.74/154.15 Resimplifying inuse:
% 153.74/154.15 Done
% 153.74/154.15
% 153.74/154.15
% 153.74/154.15 Intermediate Status:
% 153.74/154.15 Generated: 740442
% 153.74/154.15 Kept: 186808
% 153.74/154.15 Inuse: 1800
% 153.74/154.15 Deleted: 4595
% 153.74/154.15 Deletedinuse: 12
% 153.74/154.15
% 153.74/154.15 Resimplifying inuse:
% 153.74/154.15 Done
% 153.74/154.15
% 153.74/154.15 Resimplifying clauses:
% 153.74/154.15 Done
% 153.74/154.15
% 153.74/154.15 Resimplifying inuse:
% 153.74/154.15 Done
% 153.74/154.15
% 153.74/154.15
% 153.74/154.15 Intermediate Status:
% 153.74/154.15 Generated: 750411
% 153.74/154.15 Kept: 189036
% 153.74/154.15 Inuse: 1820
% 153.74/154.15 Deleted: 4836
% 153.74/154.15 Deletedinuse: 13
% 153.74/154.15
% 153.74/154.15 ResimplifyiCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------