TSTP Solution File: SWV637-1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWV637-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n022.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Wed Jul 20 16:27:20 EDT 2022
% Result : Timeout 300.03s 300.48s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWV637-1 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.13 % Command : bliksem %s
% 0.13/0.34 % Computer : n022.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % DateTime : Wed Jun 15 04:59:33 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.10/1.50 *** allocated 10000 integers for termspace/termends
% 1.10/1.50 *** allocated 10000 integers for clauses
% 1.10/1.50 *** allocated 10000 integers for justifications
% 1.10/1.50 *** allocated 15000 integers for termspace/termends
% 1.10/1.50 *** allocated 22500 integers for termspace/termends
% 1.10/1.50 *** allocated 33750 integers for termspace/termends
% 1.10/1.50 Bliksem 1.12
% 1.10/1.50
% 1.10/1.50
% 1.10/1.50 Automatic Strategy Selection
% 1.10/1.50
% 1.10/1.50 Clauses:
% 1.10/1.50 [
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.10/1.50 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ), ~(
% 1.10/1.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.10/1.50 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), Z, X ) ) ]
% 1.10/1.50 ,
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.50 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.10/1.50 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.10/1.50 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.10/1.50 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.10/1.50 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.10/1.50 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ), ~(
% 1.10/1.50 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.10/1.50 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.10/1.50 [ ~( 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'( X )
% 1.10/1.50 , 'c_Power_Opower_Opower'( 'c_HOL_Oone__class_Oone'( X ),
% 1.10/1.50 'c_HOL_Otimes__class_Otimes'( X ), X ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.10/1.50 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.10/1.50 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.50 X ), Y ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z )
% 1.10/1.50 ), X ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.10/1.50 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.50 ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ),
% 1.10/1.50 ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.10/1.50 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.50 ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.10/1.50 ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.10/1.50 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.10/1.50 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 1.10/1.50 'tc_nat' ) ) ],
% 1.10/1.50 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.10/1.50 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z,
% 1.10/1.50 'tc_nat' ) ) ],
% 1.10/1.50 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.10/1.50 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.10/1.50 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ) ],
% 1.10/1.50 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.10/1.50 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 1.10/1.50 'tc_nat' ) ) ],
% 1.10/1.50 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.10/1.50 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z,
% 1.10/1.50 'tc_nat' ) ) ],
% 1.10/1.50 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.10/1.50 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 1.10/1.50 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ), ~(
% 1.10/1.50 'c_lessequals'( Y, Z, X ) ), ~( 'c_lessequals'(
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ],
% 1.10/1.50 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.10/1.50 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 1.10/1.50 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ), ~(
% 1.10/1.50 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'(
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.10/1.50 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( hAPP( hAPP(
% 1.10/1.50 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), 'tc_nat' ) ],
% 1.10/1.50 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( hAPP( hAPP(
% 1.10/1.50 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ) ), 'tc_nat' ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.10/1.50 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~(
% 1.10/1.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.10/1.50 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z
% 1.10/1.50 ), X ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.10/1.50 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), T, X ), ~(
% 1.10/1.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.10/1.50 'c_lessequals'( Y, 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ]
% 1.10/1.50 ,
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.10/1.50 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.10/1.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.10/1.50 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ),
% 1.10/1.50 Z, X ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.10/1.50 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Y
% 1.10/1.50 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ), ~(
% 1.10/1.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 1.10/1.50 ,
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'( Y
% 1.10/1.50 , 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'(
% 1.10/1.50 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), Z, X ) ), ~(
% 1.10/1.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ]
% 1.10/1.50 ,
% 1.10/1.50 [ =( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ),
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X
% 1.10/1.50 , Y, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ),
% 1.10/1.50 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.50 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP(
% 1.10/1.50 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ),
% 1.10/1.50 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.50 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), hAPP( hAPP(
% 1.10/1.50 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.10/1.50 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.50 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP(
% 1.10/1.50 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.10/1.50 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.50 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), hAPP( hAPP(
% 1.10/1.50 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ) ],
% 1.10/1.50 [ =( 'c_List_Otake'( 'c_Suc'( X ), 'c_List_Olist_OCons'( Y, Z, T ), T )
% 1.10/1.50 , 'c_List_Olist_OCons'( Y, 'c_List_Otake'( X, Z, T ), T ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.10/1.50 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.10/1.50 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.10/1.50 'c_Power_Opower__class_Opower'( X ), Y ), T ) ), hAPP( hAPP(
% 1.10/1.50 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.10/1.50 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ) ) ],
% 1.10/1.50 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( =(
% 1.10/1.50 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( 'c_lessequals'(
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Y,
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.50 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( =(
% 1.10/1.50 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( 'c_lessequals'(
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Z,
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.10/1.50 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.10/1.50 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.10/1.50 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.10/1.50 ,
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.10/1.50 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.10/1.50 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.10/1.50 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.50 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.10/1.50 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.10/1.50 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.10/1.50 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.50 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.10/1.50 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.10/1.50 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.10/1.50 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.10/1.50 ,
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.10/1.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.10/1.50 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~(
% 1.10/1.50 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.10/1.50 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.10/1.50 ,
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.10/1.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.10/1.50 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~(
% 1.10/1.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.10/1.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.10/1.50 ,
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.10/1.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.10/1.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.10/1.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.10/1.50 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), X ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.10/1.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.10/1.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.10/1.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.10/1.50 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.10/1.50 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.50 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), T ), hAPP( hAPP(
% 1.10/1.50 'c_Power_Opower__class_Opower'( X ), Z ), T ), X ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 1.10/1.50 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.10/1.50 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 1.10/1.50 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.10/1.50 X ), X ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.10/1.50 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~(
% 1.10/1.50 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.10/1.50 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ),
% 1.10/1.50 Y, X ) ), ~( 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.50 X ), T ), Z ), X ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.10/1.50 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.10/1.50 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.10/1.50 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T
% 1.10/1.50 ), X ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.10/1.50 ), Y ), T ), Z, X ) ) ],
% 1.10/1.50 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.10/1.50 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.10/1.50 ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.50 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.10/1.50 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.10/1.50 ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.10/1.50 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.10/1.50 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.50 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.10/1.50 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.10/1.50 ), Y ), Z ), Y, X ), Z ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.50 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.10/1.50 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.10/1.50 ), Y ), Z ), Z, X ), Y ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.10/1.50 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.10/1.50 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( X ) ) ), hAPP( hAPP(
% 1.10/1.50 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( X ) ) ), 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.10/1.50 ],
% 1.10/1.50 [ =( 'c_Fact_Ofact__class_Ofact'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.10/1.50 'tc_nat' ) ), 'tc_nat' ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.10/1.50 ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.10/1.50 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.10/1.50 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.10/1.50 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.10/1.50 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.10/1.50 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.10/1.50 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.10/1.50 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.10/1.50 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.10/1.50 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.10/1.50 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.10/1.50 'c_HOL_Otimes__class_Otimes'( X ), Z ), hAPP( hAPP(
% 1.10/1.50 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.10/1.50 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.10/1.50 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.10/1.50 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.10/1.50 'c_HOL_Otimes__class_Otimes'( X ), T ), hAPP( hAPP(
% 1.10/1.50 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.10/1.50 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), U ) ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.10/1.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.10/1.50 'c_HOL_Oone__class_Oone'( X ), X ), ~( 'c_lessequals'( Y,
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.50 [ =( 'c_List_Oupt'( X, Y ), 'c_List_Olist_ONil'( 'tc_nat' ) ),
% 1.10/1.50 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.10/1.50 'class_Int_Onumber__ring'( X ) ), 'c_lessequals'(
% 1.10/1.50 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.10/1.50 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), ~( 'c_lessequals'( Y, Z
% 1.10/1.50 , 'tc_Int_Oint' ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.10/1.50 'class_Int_Onumber__ring'( X ) ), 'c_lessequals'( Y, Z, 'tc_Int_Oint' ),
% 1.10/1.50 ~( 'c_lessequals'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.10/1.50 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ) ],
% 1.10/1.50 [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), X ), ~(
% 1.10/1.50 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.10/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.10/1.50 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.50 X ), Y ), Z ), Z, X ), Y ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.10/1.50 ,
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.10/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( Y,
% 1.10/1.50 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.50 X ), Y ), Z ), Z, X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'(
% 1.10/1.50 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), Y, X ), Z ) ]
% 1.10/1.50 ,
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Oinverse__class_Odivide'(
% 1.10/1.50 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), Y, X ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.10/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.10/1.50 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.10/1.50 Z, X ) ), T ), 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.10/1.50 'c_Power_Opower__class_Opower'( X ), Y ), T ), hAPP( hAPP(
% 1.10/1.50 'c_Power_Opower__class_Opower'( X ), Z ), T ), X ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.10/1.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP(
% 1.10/1.50 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.10/1.50 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), X ), ~(
% 1.10/1.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.10/1.50 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Z, Y
% 1.10/1.50 , X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.10/1.50 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.10/1.50 , X ), 'c_HOL_Oord__class_Oless'( Z, Y, X ), =( Z, Y ) ],
% 1.10/1.50 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Z, Y
% 1.10/1.50 , X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.10/1.50 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.50 Y, X, 'tc_nat' ), =( Y, X ) ],
% 1.10/1.50 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), 'c_HOL_Oord__class_Oless'( Y, Z,
% 1.10/1.50 'tc_nat' ), =( Z, Y ), 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ],
% 1.10/1.50 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.50 Y, X, 'tc_nat' ), =( Y, X ) ],
% 1.10/1.50 [ =( X, Y ), ~( 'c_lessequals'( Y, X, 'tc_Int_Oint' ) ), ~(
% 1.10/1.50 'c_lessequals'( X, Y, 'tc_Int_Oint' ) ) ],
% 1.10/1.50 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Y, Z
% 1.10/1.50 , X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ],
% 1.10/1.50 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.10/1.50 , X ), =( Z, Y ), 'c_HOL_Oord__class_Oless'( Z, Y, X ) ],
% 1.10/1.50 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 1.10/1.50 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.10/1.50 ) ],
% 1.10/1.50 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 1.10/1.50 'c_HOL_Oord__class_Oless'( Z, Y, X ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.10/1.50 ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.10/1.50 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.10/1.50 ), =( Z, Y ) ],
% 1.10/1.50 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ), ~(
% 1.10/1.50 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), ~(
% 1.10/1.50 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 1.10/1.50 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ],
% 1.10/1.50 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ],
% 1.10/1.50 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 1.10/1.50 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.10/1.50 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~(
% 1.10/1.50 'c_lessequals'( Z, T, X ) ) ],
% 1.10/1.50 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 1.10/1.50 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.10/1.50 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~(
% 1.10/1.50 'c_lessequals'( Y, T, X ) ) ],
% 1.10/1.50 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.10/1.50 , 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.10/1.50 'c_HOL_Oplus__class_Oplus'( X ), T ), Y ), hAPP( hAPP(
% 1.10/1.50 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ) ) ],
% 1.10/1.50 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.10/1.50 , 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.10/1.50 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~(
% 1.10/1.50 'c_lessequals'( Z, T, X ) ) ],
% 1.10/1.50 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.10/1.50 , 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.10/1.50 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP(
% 1.10/1.50 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ],
% 1.10/1.50 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.10/1.50 , 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.10/1.50 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~(
% 1.10/1.50 'c_lessequals'( Y, T, X ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.10/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.10/1.50 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z
% 1.10/1.50 , X ) ), 'c_HOL_Oinverse__class_Odivide'( T, U, X ) ),
% 1.10/1.50 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.50 X ), Y ), T ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ), X
% 1.10/1.50 ) ) ],
% 1.10/1.50 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, Y ), T ) ), hAPP( hAPP( Z, Y ),
% 1.10/1.50 'c_Suc'( T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, Z, W, V0,
% 1.10/1.50 V1 ) ) ],
% 1.10/1.50 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), Z ), hAPP( hAPP( Y, Z ),
% 1.10/1.50 'c_Suc'( T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, Y, W, V0,
% 1.10/1.50 V1 ) ) ],
% 1.10/1.50 [ =( hAPP( hAPP( X, Y ), 'c_Suc'( Z ) ), hAPP( hAPP( T, Y ), hAPP( hAPP(
% 1.10/1.50 X, Y ), Z ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, T, X, W, V0, V1
% 1.10/1.50 ) ) ],
% 1.10/1.50 [ =( hAPP( hAPP( X, Y ), 'c_Suc'( Z ) ), hAPP( hAPP( T, Y ), hAPP( hAPP(
% 1.10/1.50 X, Y ), Z ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, T, X, W, V0, V1
% 1.10/1.50 ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.10/1.50 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.10/1.50 , Y ), 'c_HOL_Oone__class_Oone'( X ) ), X ) ],
% 1.10/1.50 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =( hAPP(
% 1.10/1.50 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.10/1.50 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.10/1.50 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.50 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.10/1.50 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.10/1.50 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~( 'c_lessequals'(
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.10/1.50 ), X ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.10/1.50 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ), ~(
% 1.10/1.50 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.10/1.50 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.50 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.10/1.50 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.10/1.50 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~( 'c_lessequals'(
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.10/1.50 ), X ) ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.10/1.50 , X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X )
% 1.10/1.50 ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.50 'class_Int_Onumber'( X ) ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.50 ), 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.10/1.50 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.10/1.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.10/1.50 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X ),
% 1.10/1.50 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.50 'class_Int_Onumber'( X ) ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.50 ), Y, X ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'(
% 1.10/1.50 Z, X ), 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.10/1.50 ), X ), ~( 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( T,
% 1.10/1.50 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.50 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.10/1.50 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.10/1.50 , X ), X ), T, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T
% 1.10/1.50 , X ) ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.10/1.50 , X ), 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.10/1.50 ), X ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.50 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.10/1.50 X ), X ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'(
% 1.10/1.50 Z, X ), 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.10/1.50 ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Oinverse__class_Odivide'( T,
% 1.10/1.50 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), X ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.50 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.10/1.50 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.10/1.50 , X ), X ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.10/1.50 ) ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.10/1.50 ), 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.10/1.50 ), X ) ],
% 1.10/1.50 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.10/1.50 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.10/1.50 ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ), hAPP( hAPP(
% 1.10/1.50 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z )
% 1.10/1.50 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.50 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.10/1.50 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.10/1.50 , Y ), Z ), Y, X ), 'c_Divides_Odiv__class_Omod'( Z, Y, X ) ) ],
% 1.10/1.50 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.10/1.50 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.10/1.50 , Y ), Z ), Z, X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.10/1.50 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.10/1.50 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 1.10/1.50 X ), X ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.10/1.50 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.10/1.50 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.10/1.50 X ), X ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.10/1.50 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.10/1.50 Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.10/1.50 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 1.10/1.50 X ), X ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.10/1.50 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 1.10/1.50 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.10/1.50 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.10/1.50 X ), X ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.10/1.50 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.10/1.50 , Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.10/1.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.10/1.50 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.10/1.50 ,
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.10/1.50 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.10/1.50 , Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.10/1.50 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.10/1.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.10/1.50 ,
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.10/1.50 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.10/1.50 , Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.10/1.50 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.10/1.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 1.10/1.50 ,
% 1.10/1.50 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.10/1.50 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.10/1.50 ), Z ) ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP(
% 1.10/1.50 hAPP( 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.50 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), Z ) ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.10/1.50 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.10/1.50 , Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 1.10/1.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 1.10/1.50 ,
% 1.10/1.50 [ =( 'c_List_Onth'( 'c_List_Olist_OCons'( X, Y, Z ), 'c_Suc'( T ), Z ),
% 1.10/1.50 'c_List_Onth'( Y, T, Z ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.10/1.50 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), =( Y
% 1.10/1.50 , 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.50 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.10/1.50 , X ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.10/1.50 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.10/1.50 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP(
% 1.10/1.50 hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), X ), ~(
% 1.10/1.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.10/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.10/1.50 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oinverse__class_Odivide'( Y, Z,
% 1.10/1.50 X ), X ), 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Omult__mono1'( X ) ), 'c_lessequals'( hAPP(
% 1.10/1.50 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.10/1.50 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~( 'c_lessequals'(
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Z, T, X ) )
% 1.10/1.50 ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ), 'c_lessequals'( hAPP(
% 1.10/1.50 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.10/1.50 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~( 'c_lessequals'(
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Z, T, X ) )
% 1.10/1.50 ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ), 'c_lessequals'( hAPP(
% 1.10/1.50 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.10/1.50 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ), ~( 'c_lessequals'(
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 1.10/1.50 ],
% 1.10/1.50 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( hAPP( hAPP(
% 1.10/1.50 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), 'tc_nat' ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.10/1.50 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.10/1.50 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.10/1.50 'c_Suc'( Y ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.50 [ =( 'c_Fact_Ofact__class_Ofact'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.10/1.50 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), 'tc_nat' ),
% 1.10/1.50 'c_Fact_Ofact__class_Ofact'( X, 'tc_nat' ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.10/1.50 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.10/1.50 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X )
% 1.10/1.50 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.10/1.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.10/1.50 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.10/1.50 T, X ) ) ],
% 1.10/1.50 [ ~( =( 'c_List_Oupt'( X, Y ), 'c_List_Olist_OCons'( Z, T, 'tc_nat' ) )
% 1.10/1.50 ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.10/1.50 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.10/1.50 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.10/1.50 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Oinverse'( Y
% 1.10/1.50 , X ), 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y
% 1.10/1.50 , X ) ) ],
% 1.10/1.50 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.10/1.50 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.10/1.50 ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ), T ), Z, X ),
% 1.10/1.50 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.10/1.50 ), Y ), T ), Z, X ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.50 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.50 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.10/1.50 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.10/1.50 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.10/1.50 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.10/1.50 , 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ),
% 1.10/1.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.50 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.10/1.50 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.10/1.50 , X ) ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.50 'c_HOL_Oinverse__class_Odivide'( T, Z, X ),
% 1.10/1.50 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.50 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.10/1.50 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.10/1.50 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.10/1.50 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.10/1.50 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ), ~(
% 1.10/1.50 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.10/1.50 , Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.50 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.50 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.10/1.50 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.50 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.10/1.50 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ), ~(
% 1.10/1.50 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.10/1.50 ), T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.50 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.50 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.10/1.50 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.10/1.50 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.10/1.50 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.10/1.50 , 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ), ~(
% 1.10/1.50 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.10/1.50 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.10/1.50 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.10/1.50 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ), ~(
% 1.10/1.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.10/1.50 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ), ~( 'c_lessequals'( Y
% 1.10/1.50 , 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Z, T, X ) )
% 1.10/1.50 ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.10/1.50 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.10/1.50 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ), ~(
% 1.10/1.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.10/1.50 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ), ~( 'c_lessequals'(
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( T, Z, X ) )
% 1.10/1.50 ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.10/1.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.10/1.50 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ), ~(
% 1.10/1.50 'c_HOL_Oord__class_Oless'( U, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( X ), U, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 1.10/1.50 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) )
% 1.10/1.50 ],
% 1.10/1.50 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Suc'(
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.10/1.50 'tc_nat' ) ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.10/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.10/1.50 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), hAPP(
% 1.10/1.50 hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), hAPP( hAPP(
% 1.10/1.50 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.10/1.50 'c_HOL_Oone__class_Oone'( X ), Y, X ) ), Z ) ) ],
% 1.10/1.50 [ =( 'c_Suc'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.10/1.50 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), X ) ) ],
% 1.10/1.50 [ =( 'c_Suc'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X
% 1.10/1.50 ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.10/1.50 X ) ), =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.10/1.50 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.10/1.50 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.10/1.50 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.50 X ), Y ), T ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z )
% 1.10/1.50 ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.10/1.50 X ) ), =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.10/1.50 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.10/1.50 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.10/1.50 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.50 X ), Y ), T ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z )
% 1.10/1.50 ) ) ],
% 1.10/1.50 [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 1.10/1.50 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.10/1.50 'tc_nat' ) ), 'tc_nat' ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.50 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.10/1.50 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.10/1.50 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.50 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.50 ), X ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.10/1.50 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.10/1.50 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.50 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.50 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.10/1.50 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.50 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.50 ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.10/1.50 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.10/1.50 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.10/1.50 [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( X ), Y, 'tc_nat' ), 'c_Suc'(
% 1.10/1.50 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ) ), =( 'c_Suc'(
% 1.10/1.50 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), Y ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 1.10/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.10/1.50 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oinverse__class_Oinverse'( Y, X
% 1.10/1.50 ), X ), Y ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.50 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.10/1.50 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.10/1.50 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.50 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.50 ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP(
% 1.10/1.50 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.10/1.50 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ), ~(
% 1.10/1.50 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.10/1.50 , Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.50 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.50 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.10/1.50 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.50 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.50 ), X ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.10/1.50 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.10/1.50 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ), ~(
% 1.10/1.50 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.10/1.50 ), T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.10/1.50 'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( Z ) ), hAPP( hAPP(
% 1.10/1.50 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.10/1.50 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.10/1.50 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.10/1.50 'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( Z ) ), hAPP( hAPP(
% 1.10/1.50 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.10/1.50 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), Y ) ) ],
% 1.10/1.50 [ ~( 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.10/1.50 'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( Z ) ), hAPP( hAPP(
% 1.10/1.50 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.10/1.50 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.10/1.50 'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( Z ) ), hAPP( hAPP(
% 1.10/1.50 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.10/1.50 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.10/1.50 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.10/1.50 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.50 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), 'c_Suc'( Z ) ), hAPP( hAPP(
% 1.10/1.50 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.10/1.50 ), Z ) ) ) ],
% 1.10/1.50 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.10/1.50 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.50 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), 'c_Suc'( Z ) ), hAPP( hAPP(
% 1.10/1.50 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.10/1.50 ), Z ) ), Y ) ) ],
% 1.10/1.50 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~(
% 1.10/1.50 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.10/1.50 =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.10/1.50 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.10/1.50 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.10/1.50 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.10/1.50 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ) ],
% 1.10/1.50 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.10/1.50 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.10/1.50 , Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.10/1.50 'c_HOL_Oplus__class_Oplus'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X )
% 1.10/1.50 ), 'c_Divides_Odiv__class_Omod'( Z, T, X ) ), T, X ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.50 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.10/1.50 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.10/1.50 , X ) ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.10/1.50 'c_HOL_Oinverse__class_Odivide'( T, Z, X ),
% 1.10/1.50 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.50 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.10/1.50 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.10/1.50 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.10/1.50 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.10/1.50 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.10/1.50 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ),
% 1.10/1.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.10/1.50 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.10/1.50 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 1.10/1.50 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 1.10/1.50 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.10/1.50 , X ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~(
% 1.10/1.50 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.10/1.50 [ =( 'c_List_Onth'( 'c_List_Otake'( X, Y, Z ), T, Z ), 'c_List_Onth'( Y
% 1.10/1.50 , T, Z ) ), ~( 'c_HOL_Oord__class_Oless'( T, X, 'tc_nat' ) ) ],
% 1.10/1.50 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.10/1.50 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.10/1.50 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.10/1.50 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.10/1.50 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 1.10/1.50 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.10/1.50 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.10/1.50 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.10/1.50 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.10/1.50 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.10/1.50 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.10/1.50 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.10/1.50 X ), Y ), Z ) ), T ) ) ],
% 1.10/1.50 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.10/1.50 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.10/1.50 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.10/1.50 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.10/1.50 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 1.10/1.50 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.10/1.50 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.10/1.50 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.10/1.50 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ) ],
% 1.10/1.50 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.10/1.50 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.10/1.50 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), hAPP( hAPP(
% 1.10/1.50 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ) ],
% 1.10/1.50 [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =( hAPP( hAPP(
% 1.10/1.50 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.10/1.50 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.10/1.50 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.10/1.50 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.10/1.50 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.10/1.50 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.10/1.50 X ), Y ), Z ) ), T ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.10/1.50 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.10/1.50 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.10/1.50 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.10/1.50 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.10/1.50 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.10/1.50 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.10/1.50 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.10/1.50 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.10/1.50 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.10/1.50 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 1.10/1.50 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.10/1.50 'tc_nat' ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.10/1.50 'tc_nat' ), Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( hAPP(
% 1.10/1.50 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ],
% 1.10/1.50 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.10/1.50 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.10/1.50 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.10/1.50 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.10/1.50 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.10/1.50 'c_Power_Opower__class_Opower'( X ), Y ), T ) ) ) ],
% 1.10/1.50 [ =( 'c_List_Otake'( X, 'c_List_Odrop'( Y, Z, T ), T ), 'c_List_Odrop'(
% 1.10/1.50 Y, 'c_List_Otake'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X
% 1.10/1.50 ), Y ), Z, T ), T ) ) ],
% 1.10/1.50 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_lessequals'( Y, Z, X ) )
% 1.10/1.50 , ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.10/1.50 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.10/1.50 , X ), 'c_lessequals'( Z, Y, X ) ],
% 1.10/1.50 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'( Y, Y, X ) )
% 1.10/1.50 , ~( 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ],
% 1.10/1.50 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Y
% 1.10/1.50 , X ), 'c_lessequals'( Y, Y, X ) ],
% 1.10/1.50 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.10/1.50 , Z, X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ],
% 1.10/1.50 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 1.10/1.50 'c_HOL_Oord__class_Oless'( Z, Y, X ) ],
% 1.10/1.50 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.10/1.50 , X ), 'c_lessequals'( Z, Y, X ) ],
% 1.10/1.50 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'( Y, Z, X ) )
% 1.10/1.50 , ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.10/1.50 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.10/1.50 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.10/1.50 , Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.10/1.50 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_Divides_Odiv__class_Omod'( Z, T
% 1.10/1.50 , X ) ), T, X ) ) ],
% 1.10/1.50 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.10/1.50 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.10/1.50 , Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.10/1.50 'c_HOL_Oplus__class_Oplus'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X )
% 1.10/1.50 ), Z ), T, X ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Z, Y, X
% 1.10/1.50 ), X ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.10/1.50 ), X ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Z, Y, X
% 1.10/1.50 ), X ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.10/1.50 ), X ) ) ],
% 1.10/1.50 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.10/1.50 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ),
% 1.10/1.50 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.10/1.50 , Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 1.10/1.50 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.10/1.50 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.10/1.50 'c_Power_Opower__class_Opower'( X ), T ), Z ), X ), ~( 'c_lessequals'(
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 1.10/1.50 ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), ~( 'class_Int_Onumber'(
% 1.10/1.50 X ) ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.10/1.50 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), hAPP( hAPP(
% 1.10/1.50 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.10/1.50 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.50 X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), Z ) ), hAPP( hAPP(
% 1.10/1.50 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.10/1.50 , X ) ), T ) ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.10/1.50 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.10/1.50 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.10/1.50 ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_lessequals'( Y,
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.10/1.50 'c_Power_Opower__class_Opower'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 1.10/1.50 X ), X ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.10/1.50 'c_lessequals'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.10/1.50 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), hAPP( hAPP(
% 1.10/1.50 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.10/1.50 'c_lessequals'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.10/1.50 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP(
% 1.10/1.50 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.10/1.50 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.10/1.50 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~(
% 1.10/1.50 'c_lessequals'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.10/1.50 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.10/1.50 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP(
% 1.10/1.50 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ), ~(
% 1.10/1.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ]
% 1.10/1.50 ,
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.10/1.50 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.10/1.50 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~(
% 1.10/1.50 'c_lessequals'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.10/1.50 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.10/1.50 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), hAPP( hAPP(
% 1.10/1.50 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ), ~(
% 1.10/1.50 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.10/1.50 ,
% 1.10/1.50 [ =( X, 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X
% 1.10/1.50 , 'c_Suc'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat'
% 1.10/1.50 ) ) ],
% 1.10/1.50 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.10/1.50 'c_Suc'( X ), 'tc_nat' ) ],
% 1.10/1.50 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.10/1.50 'c_Suc'( X ), 'tc_nat' ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.10/1.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.10/1.50 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ),
% 1.10/1.50 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.10/1.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP(
% 1.10/1.50 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 1.10/1.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.10/1.50 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X )
% 1.10/1.50 , Y, X ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), =( hAPP( hAPP(
% 1.10/1.50 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.50 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.10/1.50 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ), U ) ), hAPP( hAPP(
% 1.10/1.50 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.50 X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ), U )
% 1.10/1.50 ) ],
% 1.10/1.50 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.10/1.50 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.10/1.50 ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.10/1.50 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.10/1.50 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.10/1.50 ,
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.10/1.50 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.10/1.50 ), Y ), Z ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), T ), Z ),
% 1.10/1.50 X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.10/1.50 , Z, 'tc_nat' ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y
% 1.10/1.50 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( Y,
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.10/1.50 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.50 X ), Z ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y )
% 1.10/1.50 ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( Y,
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.10/1.50 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.50 X ), Y ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z )
% 1.10/1.50 ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.10/1.50 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.10/1.50 , X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.10/1.50 ,
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.10/1.50 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.10/1.50 , X ) ) ],
% 1.10/1.50 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ), =( 'c_Suc'( X
% 1.10/1.50 ), Y ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.10/1.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ),
% 1.10/1.50 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.10/1.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.10/1.50 'c_HOL_Oone__class_Oone'( X ), X ) ) ],
% 1.10/1.50 [ ~( =( 'c_Suc'( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), Y ) )
% 1.10/1.50 , =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.50 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.10/1.50 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.10/1.50 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.10/1.50 X ), 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~(
% 1.10/1.50 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.10/1.50 , Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.50 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.10/1.50 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.10/1.50 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.10/1.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.50 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ), ~(
% 1.10/1.50 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( T,
% 1.10/1.50 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), X ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.10/1.50 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.10/1.50 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~( 'c_lessequals'( Y,
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( T, Z, X ) ) ]
% 1.10/1.50 ,
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.10/1.50 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.10/1.50 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ), ~( 'c_lessequals'( Z,
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( T, Y, X ) ) ]
% 1.10/1.50 ,
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.10/1.50 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.10/1.50 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.10/1.50 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.10/1.50 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ) ) ), =( T, U ), =( Z,
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =( hAPP(
% 1.10/1.50 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.10/1.50 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 1.10/1.50 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.10/1.50 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =( hAPP(
% 1.10/1.50 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.10/1.50 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 1.10/1.50 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.10/1.50 X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.50 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.10/1.50 'c_Fact_Ofact__class_Ofact'( X, 'tc_nat' ), 'tc_nat' ) ],
% 1.10/1.50 [ ~( =( X, 'c_Suc'( X ) ) ) ],
% 1.10/1.50 [ ~( =( 'c_Suc'( X ), X ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~( =( hAPP( hAPP(
% 1.10/1.50 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), 'c_HOL_Oone__class_Oone'( X
% 1.10/1.50 ) ) ), =( 'c_HOL_Oinverse__class_Oinverse'( Y, X ), Z ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.10/1.50 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.10/1.50 ), Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.50 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), Z, X ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.10/1.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.10/1.50 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z,
% 1.10/1.50 X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.10/1.50 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.10/1.50 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.10/1.50 , Y ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.50 Y, 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.10/1.50 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.10/1.50 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 1.10/1.50 X ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.10/1.50 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), Z, X ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.10/1.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.10/1.50 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.10/1.50 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ), ~(
% 1.10/1.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 1.10/1.50 ,
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.10/1.50 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.10/1.50 , X ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.10/1.50 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), Z, X ) ), ~(
% 1.10/1.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ]
% 1.10/1.50 ,
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.10/1.50 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.10/1.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.10/1.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.50 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.10/1.50 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.10/1.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.10/1.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.50 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), X ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.10/1.50 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.10/1.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.10/1.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.50 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.10/1.50 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.10/1.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.10/1.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.50 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), X ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.10/1.50 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.50 ), X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.10/1.50 , X ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.10/1.50 ,
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.10/1.50 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.50 ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z
% 1.10/1.50 , X ) ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.10/1.50 ,
% 1.10/1.50 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =( hAPP(
% 1.10/1.50 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ), Y ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.10/1.50 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.10/1.50 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X )
% 1.10/1.50 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.10/1.50 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.10/1.50 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.10/1.50 T, X ) ) ],
% 1.10/1.50 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ), ~(
% 1.10/1.50 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.10/1.50 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.10/1.50 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 1.10/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( =(
% 1.10/1.50 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.10/1.50 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ) ), =( Y, Z ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.50 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.10/1.50 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.10/1.50 , X ) ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.50 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.10/1.50 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.50 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.50 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.10/1.50 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.10/1.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.10/1.50 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.10/1.50 , 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.50 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.10/1.50 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.10/1.50 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.10/1.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.10/1.50 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.10/1.50 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.51 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.10/1.51 , X ) ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.10/1.51 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.51 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.10/1.51 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'(
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.51 ), X ) ), 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X )
% 1.10/1.51 , X ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.51 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.10/1.51 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'(
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.51 ), X ) ), ~( 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.51 X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.10/1.51 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.10/1.51 'c_Power_Opower__class_Opower'( X ), Y ), T ) ), hAPP( hAPP(
% 1.10/1.51 'c_Power_Opower__class_Opower'( X ), Z ), T ) ) ) ],
% 1.10/1.51 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =( hAPP( hAPP(
% 1.10/1.51 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.10/1.51 'c_Power_Opower__class_Opower'( X ), Y ), T ) ), hAPP( hAPP(
% 1.10/1.51 'c_Power_Opower__class_Opower'( X ), Z ), T ) ) ) ],
% 1.10/1.51 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.10/1.51 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.10/1.51 , Y ), 'c_Divides_Odiv__class_Omod'( Z, T, X ) ), T, X ),
% 1.10/1.51 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.10/1.51 , Y ), Z ), T, X ) ) ],
% 1.10/1.51 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.10/1.51 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.10/1.51 , 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ), T ), Z, X ),
% 1.10/1.51 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.10/1.51 , Y ), T ), Z, X ) ) ],
% 1.10/1.51 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.10/1.51 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.10/1.51 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.10/1.51 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_Suc'(
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.10/1.51 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( Y, hAPP( hAPP(
% 1.10/1.51 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.51 X ), 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ), Z ) ),
% 1.10/1.51 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ) ],
% 1.10/1.51 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 1.10/1.51 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.51 X ), 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ), Z ) ),
% 1.10/1.51 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ), Y ) ],
% 1.10/1.51 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 1.10/1.51 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.51 X ), Y ), 'c_Divides_Odiv__class_Odiv'( Z, Y, X ) ) ),
% 1.10/1.51 'c_Divides_Odiv__class_Omod'( Z, Y, X ) ), Z ) ],
% 1.10/1.51 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.10/1.51 ), =( Y, Z ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.10/1.51 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 1.10/1.51 ,
% 1.10/1.51 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.10/1.51 ), =( Y, Z ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.10/1.51 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.10/1.51 ), ~( 'c_lessequals'( Y, Z, X ) ), =( Y, Z ) ],
% 1.10/1.51 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Y
% 1.10/1.51 , Z, X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ) ],
% 1.10/1.51 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 1.10/1.51 ,
% 1.10/1.51 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.10/1.51 ), ~( 'c_lessequals'( Y, Z, X ) ), =( Z, Y ) ],
% 1.10/1.51 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.10/1.51 ), =( Z, Y ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.10/1.51 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.10/1.51 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), ~( 'c_lessequals'(
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 1.10/1.51 ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.10/1.51 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.10/1.51 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), ~( 'c_lessequals'( Z,
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( T, Y, X ) ) ]
% 1.10/1.51 ,
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.10/1.51 'c_HOL_Oinverse__class_Oinverse'( hAPP( hAPP(
% 1.10/1.51 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), hAPP( hAPP(
% 1.10/1.51 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y
% 1.10/1.51 , X ) ), Z ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.51 X ), Y ), Z ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z
% 1.10/1.51 , X ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.10/1.51 ,
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.51 X ), Y ), Z ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.10/1.51 , X ) ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.10/1.51 ,
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.51 X ), Y ), Z ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.10/1.51 , X ) ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.10/1.51 ,
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.10/1.51 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ), X ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.10/1.51 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.10/1.51 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~( 'c_lessequals'( Z,
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.10/1.51 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.51 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.10/1.51 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.10/1.51 , X ), X ), T, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T
% 1.10/1.51 , X ) ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.10/1.51 , X ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y, hAPP(
% 1.10/1.51 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.51 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.10/1.51 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.10/1.51 , X ), X ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.10/1.51 ) ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.10/1.51 ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.10/1.51 [ ~( 'class_OrderedGroup_Oab__semigroup__mult'( X ) ), =( hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), Z ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), Z ), hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.10/1.51 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.10/1.51 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.10/1.51 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.10/1.51 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.10/1.51 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.51 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.10/1.51 ) ) ],
% 1.10/1.51 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.10/1.51 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.10/1.51 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.51 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.10/1.51 ) ) ],
% 1.10/1.51 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.10/1.51 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.10/1.51 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.10/1.51 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.10/1.51 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.10/1.51 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.10/1.51 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.10/1.51 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.51 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.10/1.51 ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Ocomm__semiring'( X ) ), =( hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.10/1.51 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.10/1.51 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.10/1.51 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ), ~( 'c_lessequals'( U, Z
% 1.10/1.51 , X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), U
% 1.10/1.51 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_lessequals'(
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.10/1.51 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.10/1.51 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' )
% 1.10/1.51 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y
% 1.10/1.51 , 'tc_nat' ) ) ],
% 1.10/1.51 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.10/1.51 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' )
% 1.10/1.51 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X
% 1.10/1.51 , 'tc_nat' ) ) ],
% 1.10/1.51 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.10/1.51 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ) ) ],
% 1.10/1.51 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.10/1.51 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.10/1.51 ,
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.51 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.10/1.51 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.10/1.51 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.51 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Z
% 1.10/1.51 , X ) ), T ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'(
% 1.10/1.51 'c_HOL_Oinverse__class_Odivide'( Y, T, X ),
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.10/1.51 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.10/1.51 X ), ~( 'c_lessequals'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.10/1.51 ,
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.10/1.51 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.51 X ), Y ), Z ), X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.10/1.51 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.51 X ), Z ), Y ), X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.10/1.51 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.51 X ), Y ), Z ), X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.10/1.51 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.51 X ), Z ), Y ), X ) ) ],
% 1.10/1.51 [ =( 'c_Divides_Odiv__class_Odiv'( X, 'c_Suc'(
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ), X ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.10/1.51 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.51 X ), 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.10/1.51 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), X
% 1.10/1.51 ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.10/1.51 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.51 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.10/1.51 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.10/1.51 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ), 'c_lessequals'(
% 1.10/1.51 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X ), ~( 'c_lessequals'(
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( Z, U, X ) )
% 1.10/1.51 , ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ), 'c_lessequals'(
% 1.10/1.51 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X ), ~( 'c_lessequals'(
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Z, U, X ) )
% 1.10/1.51 , ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.10/1.51 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.10/1.51 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.10/1.51 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X
% 1.10/1.51 ), 'c_Divides_Odiv__class_Odiv'( Z, T, X ) ), =( Y,
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.51 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.10/1.51 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.10/1.51 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X
% 1.10/1.51 ), 'c_Divides_Odiv__class_Odiv'( Y, T, X ) ), =( Z,
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =( hAPP( hAPP(
% 1.10/1.51 'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( Z ) ), hAPP( hAPP(
% 1.10/1.51 'c_Power_Opower__class_Opower'( X ), T ), 'c_Suc'( Z ) ) ) ), =( Y, T ),
% 1.10/1.51 ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.10/1.51 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.10/1.51 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.10/1.51 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), Z, 'tc_nat' ), hAPP(
% 1.10/1.51 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.10/1.51 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( X,
% 1.10/1.51 Z, 'tc_nat' ) ), 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ) ),
% 1.10/1.51 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.10/1.51 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X, Z, 'tc_nat' ) ),
% 1.10/1.51 'c_Divides_Odiv__class_Omod'( Y, Z, 'tc_nat' ) ), Z, 'tc_nat' ) ) ) ]
% 1.10/1.51 ,
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), Y
% 1.10/1.51 , X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.10/1.51 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 1.10/1.51 X ) ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.10/1.51 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ]
% 1.10/1.51 ,
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.10/1.51 , X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.51 X ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), Y, X ) ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.10/1.51 ), T ), Z ), X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.10/1.51 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 1.10/1.51 X ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), Y, X ) ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.10/1.51 ), T ), Z ), X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( T, Z, X )
% 1.10/1.51 , X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.51 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.51 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.10/1.51 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.10/1.51 ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.51 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), Z, X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.51 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.10/1.51 ,
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.51 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.10/1.51 ,
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.51 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.10/1.51 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.10/1.51 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.10/1.51 ), Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_Divides_Odiv__class_Omod'( Z,
% 1.10/1.51 T, X ) ), T, X ) ) ],
% 1.10/1.51 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.10/1.51 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.10/1.51 ), Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X
% 1.10/1.51 ) ), Z ), T, X ) ) ],
% 1.10/1.51 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.10/1.51 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, 'c_Suc'(
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.10/1.51 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.10/1.51 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.10/1.51 [ =( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ),
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X
% 1.10/1.51 , Y, 'tc_nat' ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.10/1.51 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.51 X ), Y ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z )
% 1.10/1.51 ), X ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.10/1.51 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.51 X ), Y ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z )
% 1.10/1.51 ), X ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ),
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ),
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =( hAPP( hAPP(
% 1.10/1.51 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.10/1.51 'c_Power_Opower__class_Opower'( X ), T ), Z ) ) ), =( Y, T ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.10/1.51 'tc_nat' ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X )
% 1.10/1.51 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.10/1.51 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.51 X ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X
% 1.10/1.51 ), 'c_HOL_Oinverse__class_Odivide'( Y, T, X ) ), =( Z,
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.10/1.51 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.51 X ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X
% 1.10/1.51 ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ) ), =( Y,
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.51 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.10/1.51 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.10/1.51 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.10/1.51 X ), 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~( 'c_lessequals'(
% 1.10/1.51 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.51 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ), ~( 'c_lessequals'( Y,
% 1.10/1.51 'c_HOL_Oinverse__class_Odivide'( T, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.10/1.51 , X ), X ), X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.51 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.10/1.51 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.10/1.51 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.10/1.51 ), X ) ), ~( 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.51 X ), T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.51 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~( 'c_lessequals'(
% 1.10/1.51 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( T
% 1.10/1.51 , X ), X ), Z, X ) ) ],
% 1.10/1.51 [ =( 'c_Fact_Ofact__class_Ofact'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.10/1.51 , 'tc_nat' ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z
% 1.10/1.51 , X ) ), T ), 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), Z, X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.10/1.51 'c_Groebner__Basis_Ogb__semiring'( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), 'c_Power_Opower__class_Opower'( X ),
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ), X ) ]
% 1.10/1.51 ,
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__comm__semiring__strict'( X ) ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.10/1.51 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.10/1.51 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) )
% 1.10/1.51 , ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.10/1.51 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X )
% 1.10/1.51 , ~( 'c_HOL_Oord__class_Oless'( T, Y, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.51 Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.10/1.51 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X )
% 1.10/1.51 , ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.10/1.51 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X )
% 1.10/1.51 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) )
% 1.10/1.51 , ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.10/1.51 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X )
% 1.10/1.51 , ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.10/1.51 , ~( 'c_HOL_Oord__class_Oless'( T, Y, X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.10/1.51 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.10/1.51 , ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.51 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.10/1.51 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.10/1.51 , ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.10/1.51 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.10/1.51 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) )
% 1.10/1.51 , ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.10/1.51 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.10/1.51 , ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.10/1.51 , ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.10/1.51 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.10/1.51 , ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.10/1.51 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ]
% 1.10/1.51 ,
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.10/1.51 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.10/1.51 , ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.51 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.10/1.51 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.10/1.51 ,
% 1.10/1.51 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.10/1.51 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.10/1.51 , Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), Z, X )
% 1.10/1.51 , 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 1.10/1.51 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.10/1.51 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.10/1.51 , Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), T, X )
% 1.10/1.51 , 'c_Divides_Odiv__class_Omod'( Y, T, X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.10/1.51 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'( Y,
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Z, hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ), ~( 'c_lessequals'(
% 1.10/1.51 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), Z, X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.10/1.51 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'( Y,
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( T,
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'( Z,
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'( Y,
% 1.10/1.51 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.10/1.51 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'(
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), Y, X ) ), ~( 'c_lessequals'(
% 1.10/1.51 Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.10/1.51 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'(
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 'c_HOL_Oord__class_Oless'( Z,
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Oord__class_Oless'( Z,
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.10/1.51 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), Y, X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.10/1.51 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.10/1.51 X ), Y ), Z ), T, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.10/1.51 'c_HOL_Oinverse__class_Odivide'( Y, T, X ) ),
% 1.10/1.51 'c_HOL_Oinverse__class_Odivide'( Z, T, X ) ) ) ],
% 1.10/1.51 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 1.10/1.51 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.10/1.51 X ), Y ), Z ), T, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.10/1.51 'c_HOL_Oinverse__class_Odivide'( Y, T, X ) ),
% 1.10/1.51 'c_HOL_Oinverse__class_Odivide'( Z, T, X ) ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Z, X ) ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.10/1.51 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.10/1.51 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 1.10/1.51 'c_lessequals'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ]
% 1.10/1.51 ,
% 1.10/1.51 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.10/1.51 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ]
% 1.10/1.51 ,
% 1.10/1.51 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.10/1.51 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ) ) ]
% 1.10/1.51 ,
% 1.10/1.51 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.10/1.51 [ =( 'c_List_Oupt'( 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ),
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ), 'c_List_Olist_OCons'(
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ), 'c_List_Oupt'( 'c_Suc'(
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ),
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ), 'tc_nat' ) ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( X,
% 1.10/1.51 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), 'tc_nat' )
% 1.10/1.51 ) ],
% 1.10/1.51 [ ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), =( 'c_List_Oupt'( X
% 1.10/1.51 , Y ), 'c_List_Olist_OCons'( X, 'c_List_Oupt'( hAPP( hAPP(
% 1.10/1.51 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'(
% 1.10/1.51 'tc_nat' ) ), Y ), 'tc_nat' ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), 'c_Int_Oiszero'(
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~( =(
% 1.10/1.51 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.10/1.51 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( =(
% 1.10/1.51 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.10/1.51 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =( Y,
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_Int_Oiszero'( Y, X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =( hAPP(
% 1.10/1.51 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.10/1.51 X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =( hAPP(
% 1.10/1.51 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.10/1.51 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =( hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.10/1.51 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =( hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.10/1.51 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.10/1.51 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.51 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.10/1.51 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.51 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.10/1.51 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.51 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.10/1.51 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.51 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.10/1.51 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.10/1.51 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.10/1.51 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.51 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.10/1.51 'c_Divides_Odiv__class_Omod'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.10/1.51 ) ],
% 1.10/1.51 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.10/1.51 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 1.10/1.51 ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 1.10/1.51 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oinverse__class_Oinverse'( Y, X
% 1.10/1.51 ), X ), Y ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.10/1.51 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.10/1.51 ,
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.10/1.51 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.10/1.51 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~( =(
% 1.10/1.51 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.10/1.51 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ) ), =( Y, Z ), =( Z,
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.10/1.51 ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oring__1__no__zero__divisors'( X ) ), ~(
% 1.10/1.51 =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ),
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.51 ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.10/1.51 ), ~( =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ),
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.51 ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), ~( =(
% 1.10/1.51 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.51 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =( hAPP(
% 1.10/1.51 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.51 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =( hAPP(
% 1.10/1.51 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.51 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.51 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.10/1.51 'c_Divides_Odiv__class_Odiv'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.51 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.10/1.51 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.51 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), ~( =( hAPP(
% 1.10/1.51 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.51 ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.10/1.51 X ) ), ~( =( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) )
% 1.10/1.51 , =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.51 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.10/1.51 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.51 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =( hAPP(
% 1.10/1.51 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.10/1.51 , 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.10/1.51 ,
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.10/1.51 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.10/1.51 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.10/1.51 'c_HOL_Oinverse__class_Odivide'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.10/1.51 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.10/1.51 'c_HOL_Oinverse__class_Odivide'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.10/1.51 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.51 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 1.10/1.51 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.10/1.51 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.51 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 1.10/1.51 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.10/1.51 Y ) ],
% 1.10/1.51 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 1.10/1.51 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.10/1.51 Y ) ],
% 1.10/1.51 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.10/1.51 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.10/1.51 Y ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.10/1.51 X ) ), =( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.10/1.51 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.10/1.51 Y ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.10/1.51 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.51 X ) ), 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.10/1.51 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ]
% 1.10/1.51 ,
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.10/1.51 , X ), ~( 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.51 X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.10/1.51 , Y ), T ), Z, X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.10/1.51 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.51 X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.10/1.51 , Y ), T ), Z, X ) ) ],
% 1.10/1.51 [ 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.51 X, 'c_Suc'( X ), 'tc_nat' ) ],
% 1.10/1.51 [ ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( Y, 'c_Suc'( X ), 'tc_nat' ) ) ],
% 1.10/1.51 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.10/1.51 , Y ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP(
% 1.10/1.51 hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.10/1.51 ,
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.10/1.51 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.10/1.51 ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.10/1.51 ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.10/1.51 , Z ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X )
% 1.10/1.51 ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.10/1.51 ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.51 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.10/1.51 ,
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.51 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.10/1.51 ,
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.51 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.10/1.51 ,
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.51 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.10/1.51 ,
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.10/1.51 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.10/1.51 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X )
% 1.10/1.51 ), 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ), hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.10/1.51 X ), Y ), Z ) ), 'c_HOL_Oinverse__class_Oinverse'( Y, X ) ) ),
% 1.10/1.51 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ) ), =( Z,
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.10/1.51 ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =( hAPP( hAPP(
% 1.10/1.51 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X )
% 1.10/1.51 ), 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ), hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X
% 1.10/1.51 ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) ),
% 1.10/1.51 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ) ), =( Z,
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.10/1.51 ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.10/1.51 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.10/1.51 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.10/1.51 'c_HOL_Oone__class_Oone'( X ) ), X ), Z, X ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.10/1.51 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.10/1.51 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.10/1.51 'c_HOL_Oone__class_Oone'( X ) ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.51 Y, Z, X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.10/1.51 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.10/1.51 ) ), T ), 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.10/1.51 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ), Z, X ) ), =( Z,
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.10/1.51 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Oinverse__class_Odivide'( Z
% 1.10/1.51 , T, X ) ), 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.10/1.51 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), T, X ) ), =( T,
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.10/1.51 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.10/1.51 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) )
% 1.10/1.51 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.10/1.51 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), hAPP( hAPP(
% 1.10/1.51 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.10/1.51 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.10/1.51 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( T, Y, X ) ) ],
% 1.10/1.51 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), hAPP( hAPP( Y, U ), T ) )
% 1.10/1.51 , hAPP( hAPP( Y, hAPP( hAPP( X, Z ), U ) ), T ) ), ~(
% 1.10/1.51 'c_Groebner__Basis_Ogb__semiring'( X, Y, W, V0, V1, V2 ) ) ],
% 1.10/1.51 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), T ), hAPP( hAPP( Y, hAPP(
% 1.10/1.51 hAPP( X, Z ), U ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, Y, W
% 1.10/1.51 , V0, U, V1 ) ) ],
% 1.10/1.51 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), Y ) ), hAPP( hAPP( Z, hAPP(
% 1.10/1.51 hAPP( X, T ), U ) ), Y ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, Z, W
% 1.10/1.51 , V0, U, V1 ) ) ],
% 1.10/1.51 [ =( hAPP( hAPP( X, Y ), Y ), hAPP( hAPP( Z, hAPP( hAPP( X, T ), T ) ),
% 1.10/1.51 Y ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, Z, U, W, T, V0 ) ) ],
% 1.10/1.51 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.10/1.51 X, T, U, Y, W, V0 ) ) ],
% 1.10/1.51 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.10/1.51 X, T, U, Z, W, V0 ) ) ],
% 1.10/1.51 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 1.10/1.51 'c_Groebner__Basis_Ogb__semiring'( T, X, U, W, V0, V1 ) ) ],
% 1.10/1.51 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), U ), hAPP( hAPP( Y, hAPP(
% 1.10/1.51 hAPP( X, Z ), U ) ), hAPP( hAPP( X, T ), U ) ) ), ~(
% 1.10/1.51 'c_Groebner__Basis_Ogb__semiring'( Y, X, W, V0, V1, V2 ) ) ],
% 1.10/1.51 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.10/1.51 T, X, U, Y, W, V0 ) ) ],
% 1.10/1.51 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.10/1.51 T, X, U, Z, W, V0 ) ) ],
% 1.10/1.51 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.10/1.51 T, X, U, W, Y, V0 ) ) ],
% 1.10/1.51 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.10/1.51 T, X, U, W, Z, V0 ) ) ],
% 1.10/1.51 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 1.10/1.51 , hAPP( hAPP( X, hAPP( hAPP( X, Y ), T ) ), hAPP( hAPP( X, Z ), U ) ) ),
% 1.10/1.51 ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, V0, V1, V2, V3 ) ) ],
% 1.10/1.51 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 1.10/1.51 , hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), hAPP( hAPP( X, T ), U ) ) ) ),
% 1.10/1.51 ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, V0, V1, V2, V3 ) ) ],
% 1.10/1.51 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 1.10/1.51 , hAPP( hAPP( X, T ), hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), U ) ) ),
% 1.10/1.51 ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, V0, V1, V2, V3 ) ) ],
% 1.10/1.51 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, hAPP(
% 1.10/1.51 hAPP( X, Y ), T ) ), Z ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, W
% 1.10/1.51 , V0, V1, V2 ) ) ],
% 1.10/1.51 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, Y ),
% 1.10/1.51 hAPP( hAPP( X, Z ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X,
% 1.10/1.51 W, V0, V1, V2 ) ) ],
% 1.10/1.51 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 1.10/1.51 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, W
% 1.10/1.51 , V0, V1, V2 ) ) ],
% 1.10/1.51 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, Z ),
% 1.10/1.51 hAPP( hAPP( X, Y ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X,
% 1.10/1.51 W, V0, V1, V2 ) ) ],
% 1.10/1.51 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 1.10/1.51 , hAPP( hAPP( X, hAPP( hAPP( X, Y ), T ) ), hAPP( hAPP( X, Z ), U ) ) ),
% 1.10/1.51 ~( 'c_Groebner__Basis_Ogb__semiring'( X, W, V0, V1, V2, V3 ) ) ],
% 1.10/1.51 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, Y ),
% 1.10/1.51 hAPP( hAPP( X, Z ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U,
% 1.10/1.51 W, V0, V1, V2 ) ) ],
% 1.10/1.51 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, Z ),
% 1.10/1.51 hAPP( hAPP( X, Y ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U,
% 1.10/1.51 W, V0, V1, V2 ) ) ],
% 1.10/1.51 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, hAPP(
% 1.10/1.51 hAPP( X, Y ), T ) ), Z ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U, W
% 1.10/1.51 , V0, V1, V2 ) ) ],
% 1.10/1.51 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 1.10/1.51 'c_Groebner__Basis_Ogb__semiring'( X, T, U, W, V0, V1 ) ) ],
% 1.10/1.51 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 1.10/1.51 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U, W
% 1.10/1.51 , V0, V1, V2 ) ) ],
% 1.10/1.51 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.10/1.51 X, T, U, Y, W, V0 ) ) ],
% 1.10/1.51 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 1.10/1.51 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U, W
% 1.10/1.51 , V0, V1, V2 ) ) ],
% 1.10/1.51 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 1.10/1.51 'c_Groebner__Basis_Ogb__semiring'( X, T, U, W, V0, V1 ) ) ],
% 1.10/1.51 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.10/1.51 T, X, U, Y, W, V0 ) ) ],
% 1.10/1.51 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.10/1.51 T, X, U, W, Y, V0 ) ) ],
% 1.10/1.51 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 1.10/1.51 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, W
% 1.10/1.51 , V0, V1, V2 ) ) ],
% 1.10/1.51 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 1.10/1.51 'c_Groebner__Basis_Ogb__semiring'( T, X, U, W, V0, V1 ) ) ],
% 1.10/1.51 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), U ) ), hAPP( hAPP( Z, hAPP(
% 1.10/1.51 hAPP( X, Y ), T ) ), hAPP( hAPP( X, Y ), U ) ) ), ~(
% 1.10/1.51 'c_Groebner__Basis_Ogb__semiring'( Z, X, W, V0, V1, V2 ) ) ],
% 1.10/1.51 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), U ), hAPP( hAPP( Y, hAPP(
% 1.10/1.51 hAPP( X, Z ), U ) ), hAPP( hAPP( X, T ), U ) ) ), ~(
% 1.10/1.51 'c_Groebner__Basis_Ogb__semiring'( W, Y, X, V0, V1, V2 ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.10/1.51 ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z
% 1.10/1.51 , X ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.10/1.51 ,
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.10/1.51 ), X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.10/1.51 , X ) ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.10/1.51 ,
% 1.10/1.51 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.10/1.51 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ) ) ), =( X, Z
% 1.10/1.51 ) ],
% 1.10/1.51 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.10/1.51 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ), =( Y, Z
% 1.10/1.51 ) ],
% 1.10/1.51 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.10/1.51 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ), =( Y, Z
% 1.10/1.51 ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.10/1.51 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP(
% 1.10/1.51 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 1.10/1.51 [ ~( 'class_OrderedGroup_Ocancel__ab__semigroup__add'( X ) ), ~( =( hAPP(
% 1.10/1.51 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.10/1.51 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 1.10/1.51 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =( hAPP(
% 1.10/1.51 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.10/1.51 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 1.10/1.51 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =( hAPP(
% 1.10/1.51 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.10/1.51 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ), =( Y, T ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.10/1.51 , Y ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.10/1.51 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.10/1.51 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.10/1.51 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.10/1.51 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.10/1.51 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.10/1.51 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.10/1.51 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.10/1.51 'c_HOL_Oinverse__class_Oinverse'( hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X
% 1.10/1.51 ) ), 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 1.10/1.51 'c_HOL_Oinverse__class_Oinverse'( hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Oinverse'( Z, X
% 1.10/1.51 ) ), 'c_HOL_Oinverse__class_Oinverse'( Y, X ) ) ), =( Z,
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.10/1.51 ) ],
% 1.10/1.51 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.10/1.51 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.10/1.51 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.10/1.51 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.10/1.51 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.51 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Z
% 1.10/1.51 , X ) ), T ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.51 'c_HOL_Oinverse__class_Odivide'( Y, T, X ),
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.51 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.51 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.10/1.51 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.51 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.10/1.51 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.10/1.51 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.51 ), X ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.10/1.51 ), T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ), ~(
% 1.10/1.51 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.51 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.10/1.51 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.10/1.51 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.51 ), X ) ), ~( 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.51 X ), Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ), ~(
% 1.10/1.51 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.10/1.51 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'(
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), Y, X ) ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.10/1.51 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'(
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 'c_HOL_Oord__class_Oless'( Z,
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y, hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.10/1.51 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'( Y,
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Z, hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.10/1.51 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'( Y,
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( T,
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), Z, X ) ) ],
% 1.10/1.51 [ =( 'c_List_Odrop'( 'c_Suc'( X ), 'c_List_Olist_OCons'( Y, Z, T ), T )
% 1.10/1.51 , 'c_List_Odrop'( X, Z, T ) ) ],
% 1.10/1.51 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Suc'( X ) )
% 1.10/1.51 , Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), 'c_Suc'(
% 1.10/1.51 Y ) ) ) ],
% 1.10/1.51 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.10/1.51 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( Y, 'c_Suc'(
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.10/1.51 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.10/1.51 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( X,
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, 'c_Suc'(
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.10/1.51 [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.10/1.51 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.10/1.51 'tc_nat' ) ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ]
% 1.10/1.51 ,
% 1.10/1.51 [ 'c_HOL_Oord__class_Oless'( 'c_Divides_Odiv__class_Omod'( X, Y,
% 1.10/1.51 'tc_nat' ), Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.51 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.10/1.51 ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( T
% 1.10/1.51 , 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.51 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.51 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.10/1.51 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.51 ), X ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.51 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X ),
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.10/1.51 ), X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Oinverse__class_Odivide'(
% 1.10/1.51 Y, 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.51 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.10/1.51 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.10/1.51 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.51 ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), =( Y
% 1.10/1.51 , 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X )
% 1.10/1.51 , X ) ) ],
% 1.10/1.51 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =( hAPP( hAPP(
% 1.10/1.51 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.10/1.51 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.10/1.51 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) ) ), =( hAPP( hAPP(
% 1.10/1.51 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), U ) ],
% 1.10/1.51 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.10/1.51 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.10/1.51 Y ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.10/1.51 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.10/1.51 Y ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.10/1.51 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.10/1.51 Y ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.51 'class_Int_Onumber'( X ) ), ~( =( 'c_HOL_Oinverse__class_Odivide'( Y, Z,
% 1.10/1.51 X ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ), =( Y, hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( T
% 1.10/1.51 , X ) ), Z ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.51 'class_Int_Onumber'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( hAPP(
% 1.10/1.51 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.10/1.51 ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.51 'class_Int_Onumber'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( hAPP(
% 1.10/1.51 hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), Z ), Z, X ),
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), =( Z,
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.51 'class_Int_Onumber'( X ) ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.51 X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ),
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y ), =(
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.51 ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.51 'class_Int_Onumber'( X ) ), =( Y, hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ),
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ), =(
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.51 ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.51 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.10/1.51 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( T,
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.51 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.51 ), X ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.10/1.51 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ),
% 1.10/1.51 ~( 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.10/1.51 , 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.51 'class_Int_Onumber'( X ) ), =( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.10/1.51 , 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.10/1.51 , X ) ), Z ), Z, X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.51 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.51 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.51 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X
% 1.10/1.51 ), X ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.10/1.51 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ),
% 1.10/1.51 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X )
% 1.10/1.51 , 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.51 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.10/1.51 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.10/1.51 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.51 ), X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.51 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.51 ), X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( T,
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.51 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.51 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.10/1.51 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.51 ), X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.51 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.51 ), X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( T,
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.51 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.10/1.51 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =(
% 1.10/1.51 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.51 X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), Z ), Z, X ),
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.51 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.10/1.51 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =(
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.10/1.51 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.51 X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), Z ), Z, X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.51 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.10/1.51 X ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ) ) ), =( hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.10/1.51 , X ) ), T ), Z ), =( T, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.51 'class_Int_Onumber'( X ) ), =( Y, 'c_HOL_Oinverse__class_Odivide'( hAPP(
% 1.10/1.51 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( Z, X ) ),
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ), =(
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.51 ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.51 'class_Int_Onumber'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( hAPP(
% 1.10/1.51 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( Z, X ) ),
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y ), =(
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.51 ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.51 'class_Int_Onumber'( X ) ), =( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.51 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.51 X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.51 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), X
% 1.10/1.51 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.10/1.51 ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.51 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), X
% 1.10/1.51 ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.10/1.51 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.10/1.51 ,
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'(
% 1.10/1.51 'c_HOL_Oone__class_Oone'( X ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.10/1.51 ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.10/1.51 ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'(
% 1.10/1.51 'c_HOL_Oone__class_Oone'( X ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.10/1.51 ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.10/1.51 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), Y, X ), ~(
% 1.10/1.51 'c_lessequals'( Z, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.10/1.51 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.10/1.51 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.10/1.51 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), Z, X ), ~(
% 1.10/1.51 'c_lessequals'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.10/1.51 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.10/1.51 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =( hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Oinverse__class_Oinverse'(
% 1.10/1.51 Y, X ) ), 'c_HOL_Oone__class_Oone'( X ) ), =( Y,
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =( hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X
% 1.10/1.51 ) ), Y ), 'c_HOL_Oone__class_Oone'( X ) ), =( Y,
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X
% 1.10/1.51 ) ), Y ), 'c_HOL_Oone__class_Oone'( X ) ), =( Y,
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.10/1.51 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.10/1.51 'c_HOL_Oone__class_Oone'( X ) ), X ) ],
% 1.10/1.51 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.10/1.51 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.10/1.51 , Y ), Z ), Z, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.10/1.51 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ), 'c_HOL_Oone__class_Oone'( X )
% 1.10/1.51 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.51 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.10/1.51 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.10/1.51 , Y ), Z ), Y, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.10/1.51 'c_Divides_Odiv__class_Odiv'( Z, Y, X ) ), 'c_HOL_Oone__class_Oone'( X )
% 1.10/1.51 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.10/1.51 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.10/1.51 'c_HOL_Oone__class_Oone'( X ), Y, X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.10/1.51 X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.10/1.51 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.10/1.51 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ),
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.10/1.51 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ),
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.10/1.51 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oone__class_Oone'( X ),
% 1.10/1.51 X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.10/1.51 'c_HOL_Oone__class_Oone'( X ), Y, X ), X ), ~( 'c_lessequals'(
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.10/1.51 'c_HOL_Oone__class_Oone'( X ), Y, X ), X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.10/1.51 'c_HOL_Oone__class_Oone'( X ), Y, X ), 'c_lessequals'( Y,
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.10/1.51 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oone__class_Oone'( X ),
% 1.10/1.51 X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( 'c_lessequals'(
% 1.10/1.51 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.10/1.51 , X ) ) ],
% 1.10/1.51 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.10/1.51 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.51 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.10/1.51 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.10/1.51 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.10/1.51 'tc_nat' ) ), X ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.10/1.51 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y
% 1.10/1.51 ), X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( 'class_Int_Onumber'( X )
% 1.10/1.51 ), =( 'c_HOL_Oinverse__class_Oinverse'(
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.10/1.51 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ),
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_lessequals'( Y,
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.10/1.51 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ),
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.10/1.51 ), Y ), 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ),
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), ~( 'c_Int_Oiszero'(
% 1.10/1.51 'c_HOL_Oone__class_Oone'( X ), X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 1.10/1.51 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oone__class_Oone'( X ), X ),
% 1.10/1.51 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.10/1.51 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oone__class_Oone'( X ), X ),
% 1.10/1.51 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.10/1.51 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.10/1.51 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y )
% 1.10/1.51 , 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.10/1.51 'c_HOL_Oinverse__class_Odivide'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y
% 1.10/1.51 ) ],
% 1.10/1.51 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.10/1.51 Y ) ],
% 1.10/1.51 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 1.10/1.51 Y ) ],
% 1.10/1.51 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =( hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 1.10/1.51 Y ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 1.10/1.51 Y ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.10/1.51 Y ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 1.10/1.51 Y ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( =(
% 1.10/1.51 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oone__class_Oone'( X ) )
% 1.10/1.51 ), =( Y, 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.10/1.51 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.10/1.51 'c_Divides_Odiv__class_Odiv'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y )
% 1.10/1.51 ],
% 1.10/1.51 [ ~( hBOOL( hAPP( X, 'c_Divides_Odiv__class_Omod'( Y,
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ) ), hBOOL( hAPP( X
% 1.10/1.51 , Y ) ) ],
% 1.10/1.51 [ ~( hBOOL( hAPP( X, Y ) ) ), hBOOL( hAPP( X,
% 1.10/1.51 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.10/1.51 'tc_nat' ) ) ) ],
% 1.10/1.51 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ),
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ],
% 1.10/1.51 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 1.10/1.51 [ ~( hBOOL( hAPP( X, 'c_Divides_Odiv__class_Odiv'( Y,
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ) ), hBOOL( hAPP( X
% 1.10/1.51 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.10/1.51 [ ~( hBOOL( hAPP( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), hBOOL(
% 1.10/1.51 hAPP( X, 'c_Divides_Odiv__class_Odiv'( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.10/1.51 'tc_nat' ), 'tc_nat' ) ) ) ],
% 1.10/1.51 [ hBOOL( hAPP( X, 'c_Divides_Odiv__class_Odiv'( Y,
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ), ~( hBOOL( hAPP( X
% 1.10/1.51 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.10/1.51 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.10/1.51 'tc_nat' ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.10/1.51 [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.10/1.51 [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.10/1.51 [ ~( 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.10/1.51 ), 'tc_nat' ) ) ],
% 1.10/1.51 [ ~( 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.10/1.51 ), 'tc_nat' ) ) ],
% 1.10/1.51 [ ~( =( 'c_Fact_Ofact__class_Ofact'( X, 'tc_nat' ),
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.10/1.51 [ =( hAPP( hAPP( X, Y ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Z ),
% 1.10/1.51 ~( 'c_Groebner__Basis_Ogb__semiring'( T, U, X, W, Z, V0 ) ) ],
% 1.10/1.51 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.10/1.51 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.10/1.51 [ ~( =( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y )
% 1.10/1.51 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.10/1.51 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), X
% 1.10/1.51 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.10/1.51 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( X ) ) ) ],
% 1.10/1.51 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( X ) ) ) ],
% 1.10/1.51 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.10/1.51 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.10/1.51 [ =( 'c_List_Odrop'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, Y ), X )
% 1.10/1.51 ],
% 1.10/1.51 [ =( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.10/1.51 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ],
% 1.10/1.51 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), X ) ],
% 1.10/1.51 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.10/1.51 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.51 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), 'c_HOL_Oone__class_Oone'(
% 1.10/1.51 'tc_nat' ) ), Y ) ],
% 1.10/1.51 [ 'c_lessequals'( 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ), 'tc_Int_Oint'
% 1.10/1.51 ), ~( 'c_lessequals'( X, Y, 'tc_Int_Oint' ) ) ],
% 1.10/1.51 [ 'c_lessequals'( X, Y, 'tc_Int_Oint' ), ~( 'c_lessequals'(
% 1.10/1.51 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ), 'tc_Int_Oint' ) ) ],
% 1.10/1.51 [ 'c_lessequals'( 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ), 'tc_Int_Oint'
% 1.10/1.51 ), ~( 'c_lessequals'( X, Y, 'tc_Int_Oint' ) ) ],
% 1.10/1.51 [ 'c_lessequals'( X, Y, 'tc_Int_Oint' ), ~( 'c_lessequals'(
% 1.10/1.51 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ), 'tc_Int_Oint' ) ) ],
% 1.10/1.51 [ 'c_lessequals'( 'c_Int_OPls', 'c_Int_OPls', 'tc_Int_Oint' ) ],
% 1.10/1.51 [ 'c_lessequals'( 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ), 'tc_Int_Oint'
% 1.10/1.51 ), ~( 'c_lessequals'( X, Y, 'tc_Int_Oint' ) ) ],
% 1.10/1.51 [ 'c_lessequals'( X, Y, 'tc_Int_Oint' ), ~( 'c_lessequals'(
% 1.10/1.51 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ), 'tc_Int_Oint' ) ) ],
% 1.10/1.51 [ 'c_lessequals'( 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ), 'tc_Int_Oint'
% 1.10/1.51 ), ~( 'c_lessequals'( X, Y, 'tc_Int_Oint' ) ) ],
% 1.10/1.51 [ 'c_lessequals'( X, Y, 'tc_Int_Oint' ), ~( 'c_lessequals'(
% 1.10/1.51 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ), 'tc_Int_Oint' ) ) ],
% 1.10/1.51 [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( 'c_Suc'( 'c_Suc'( X ) ) ),
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), 'tc_nat' ),
% 1.10/1.51 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.10/1.51 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'(
% 1.10/1.51 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), X ),
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.10/1.51 ), Y ), 'c_Suc'( Z ) ), 'c_HOL_Oone__class_Oone'( X ), X ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.10/1.51 ,
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.51 'c_HOL_Oinverse__class_Oinverse'( Z, X ),
% 1.10/1.51 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.10/1.51 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.51 'c_HOL_Oinverse__class_Oinverse'( Z, X ),
% 1.10/1.51 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.10/1.51 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.10/1.51 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.10/1.51 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.10/1.51 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.10/1.51 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.10/1.51 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.51 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), hAPP( hAPP(
% 1.10/1.51 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.10/1.51 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.10/1.51 ), Z ) ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.10/1.51 ), T ) ) ) ],
% 1.10/1.51 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.10/1.51 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.51 'c_HOL_Oplus__class_Oplus'( X ), X ), hAPP( hAPP(
% 1.10/1.51 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.10/1.51 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.10/1.51 ), T ) ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Z
% 1.10/1.51 ), T ) ) ) ],
% 1.10/1.51 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 1.10/1.51 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.10/1.51 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 1.10/1.51 'c_lessequals'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.10/1.51 [ =( 'c_List_Oupt'( X, Y ), 'c_List_Olist_OCons'( X, 'c_List_Oupt'(
% 1.10/1.51 'c_Suc'( X ), Y ), 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 1.10/1.51 'tc_nat' ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X )
% 1.10/1.51 , X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X )
% 1.10/1.51 , X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.10/1.51 ,
% 1.10/1.51 [ =( 'c_Divides_Odiv__class_Odiv'( 'c_Suc'( X ), Y, 'tc_nat' ), hAPP(
% 1.10/1.51 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.10/1.51 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( X,
% 1.10/1.51 Y, 'tc_nat' ) ), 'c_Divides_Odiv__class_Odiv'( 'c_Suc'(
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ) ),
% 1.10/1.51 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.10/1.51 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ),
% 1.10/1.51 'c_Divides_Odiv__class_Omod'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.10/1.51 'tc_nat' ) ), Y, 'tc_nat' ) ), Y, 'tc_nat' ) ) ) ],
% 1.10/1.51 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.10/1.51 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.10/1.51 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.10/1.51 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ) ) ],
% 1.10/1.51 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.10/1.51 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.10/1.51 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ), ~( 'c_lessequals'(
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.10/1.51 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.10/1.51 'c_Divides_Odiv__class_Omod'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), Z
% 1.10/1.51 , X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 1.10/1.51 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.10/1.51 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.10/1.51 , Z ), T ), X ), ~( 'c_lessequals'( Y, T, X ) ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 1.10/1.51 ,
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.10/1.51 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.10/1.51 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.51 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.10/1.51 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.10/1.51 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ), ~(
% 1.10/1.51 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.10/1.51 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'(
% 1.10/1.51 X ), Y ), Z ), X ), ~( 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), Y,
% 1.10/1.51 X ) ) ],
% 1.10/1.51 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Suc'( X ) )
% 1.10/1.51 , Y ), 'c_Suc'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.10/1.51 Y ) ) ) ],
% 1.10/1.51 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), 'c_Suc'( Y
% 1.10/1.51 ) ), 'c_Suc'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y
% 1.10/1.51 ) ) ) ],
% 1.10/1.51 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 1.10/1.51 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.10/1.51 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.10/1.51 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ), Z ) ),
% 1.10/1.51 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ), T ), hAPP( hAPP(
% 1.10/1.51 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ],
% 1.10/1.51 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 1.10/1.51 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.10/1.51 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.10/1.51 'c_Divides_Odiv__class_Odiv'( Z, Y, X ) ) ), 'c_Divides_Odiv__class_Omod'(
% 1.10/1.51 Z, Y, X ) ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T )
% 1.10/1.51 ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.51 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.10/1.51 ), X ), ~( 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( T,
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.51 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.10/1.51 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.10/1.51 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.51 ), X ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.10/1.51 ), T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.51 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X ),
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.10/1.51 ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.51 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.10/1.51 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.10/1.51 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.51 ), X ) ), ~( 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.51 X ), Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.10/1.51 ), Y ), Z ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), T ),
% 1.10/1.51 X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X )
% 1.10/1.51 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.10/1.51 ), ~( 'c_HOL_Oord__class_Oless'( T, Z, 'tc_nat' ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.51 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.51 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.10/1.51 , 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.51 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.51 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.10/1.51 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.51 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.51 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.10/1.51 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.51 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.51 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.10/1.51 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.10/1.51 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.10/1.51 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.51 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.51 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.10/1.51 , 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.10/1.51 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.10/1.51 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.10/1.51 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 1.10/1.51 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.10/1.51 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ) ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.51 X, T, 'tc_nat' ) ],
% 1.10/1.51 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), hAPP(
% 1.10/1.51 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.10/1.51 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.10/1.51 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 1.10/1.51 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.10/1.51 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.10/1.51 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.10/1.51 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.51 ), X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.10/1.51 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.51 ), X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'( Z,
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.10/1.51 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.51 ), X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'( Y,
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.10/1.51 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.51 ), X ) ) ],
% 1.10/1.51 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ), 'c_Suc'( U ) )
% 1.10/1.51 , hAPP( hAPP( Y, T ), hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T )
% 1.10/1.51 , U ) ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'( Y
% 1.10/1.51 , Z, X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.51 Z, X ) ), ~( 'c_lessequals'( 'c_HOL_Oinverse__class_Oinverse'( Z, X ),
% 1.10/1.51 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.10/1.51 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.10/1.51 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.10/1.51 'c_lessequals'( Z, Y, X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'( Y
% 1.10/1.51 , Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.51 ), X ) ), ~( 'c_lessequals'( 'c_HOL_Oinverse__class_Oinverse'( Z, X ),
% 1.10/1.51 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.10/1.51 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.10/1.51 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.10/1.51 'c_lessequals'( Z, Y, X ) ) ],
% 1.10/1.51 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.10/1.51 'c_Divides_Odiv__class_Odiv'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), Z
% 1.10/1.51 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.51 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.10/1.51 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.10/1.51 ), Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X
% 1.10/1.51 ) ), 'c_Divides_Odiv__class_Omod'( Z, T, X ) ), T, X ) ) ],
% 1.10/1.51 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.10/1.51 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), Y ), hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.10/1.51 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.10/1.51 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), hAPP( hAPP( Y, Z ), U ) )
% 1.10/1.51 , hAPP( hAPP( Y, Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.10/1.51 , T ), U ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, Y, V0, V1, V2
% 1.10/1.51 ) ) ],
% 1.10/1.51 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.10/1.51 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.10/1.51 , Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), T, X )
% 1.10/1.51 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ),
% 1.10/1.51 'c_Divides_Odiv__class_Odiv'( Y, T, X ) ) ), =( T,
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.51 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.10/1.51 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.10/1.51 , Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), Z, X )
% 1.10/1.51 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ),
% 1.10/1.51 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ) ), =( Z,
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.10/1.51 , Y ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.51 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), Y, X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.10/1.51 , X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.51 X ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), Y, X ) ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.10/1.51 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 1.10/1.51 X ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), Y, X ) ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.10/1.51 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 1.10/1.51 X ) ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.10/1.51 , ~( 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.10/1.51 ), Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( T,
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'( Z
% 1.10/1.51 , 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.10/1.51 , X ), ~( 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.51 X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.10/1.51 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.51 X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.10/1.51 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.51 X ) ), 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.10/1.51 , ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.51 X ), Y ), T ), Z, X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.10/1.51 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oone__class_Oone'( X ),
% 1.10/1.51 X ), ~( 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.10/1.51 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.10/1.51 X ), 'c_HOL_Oone__class_Oone'( X ) ), 'c_HOL_Oone__class_Oone'( X ) ) ),
% 1.10/1.51 Y ) ) ],
% 1.10/1.51 [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ],
% 1.10/1.51 [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.51 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.10/1.51 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.10/1.51 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.51 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.10/1.51 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( T,
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.10/1.51 hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.51 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.10/1.51 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.10/1.51 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.10/1.51 , 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( hAPP(
% 1.10/1.51 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.10/1.51 ), Y ), Y, X ) ) ],
% 1.10/1.51 [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 1.10/1.51 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.10/1.51 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 1.10/1.51 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 1.10/1.51 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.10/1.51 , U ), Y ), Z, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.10/1.51 'c_HOL_Oplus__class_Oplus'( X ), W ), T ), Z, X ) ) ],
% 1.10/1.51 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.10/1.51 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ],
% 1.10/1.51 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.10/1.51 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( X,
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.10/1.51 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.10/1.51 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( Y, 'c_Suc'(
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_Suc'(
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.10/1.51 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.10/1.51 ,
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.10/1.51 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.10/1.51 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.51 X ), Y ), U ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.10/1.51 ) ) ), =( Z, U ), =( Y, T ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.10/1.51 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.10/1.51 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.51 X ), Y ), U ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.10/1.51 ) ) ), =( Z, U ), =( Y, T ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 1.10/1.51 'c_HOL_Oinverse__class_Oinverse'( hAPP( hAPP(
% 1.10/1.51 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), hAPP( hAPP(
% 1.10/1.51 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y
% 1.10/1.51 , X ) ), Z ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.51 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Z
% 1.10/1.51 , X ) ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( T,
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.10/1.51 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.51 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.10/1.51 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.10/1.51 ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.10/1.51 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) )
% 1.10/1.51 , 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ],
% 1.10/1.51 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_Suc'( X ), 'tc_nat' ) )
% 1.10/1.51 , 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ],
% 1.10/1.51 [ =( X, Y ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ],
% 1.10/1.51 [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 1.10/1.51 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.10/1.51 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 1.10/1.51 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 1.10/1.51 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.10/1.51 ), U ), Y ), Z, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), W ), T ), Z, X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.51 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.10/1.51 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.10/1.51 ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.10/1.51 , 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.51 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.10/1.51 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.10/1.51 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.51 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Z
% 1.10/1.51 , X ) ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( T,
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_lessequals'(
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.10/1.51 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.10/1.51 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.10/1.51 ) ), 'c_HOL_Oinverse__class_Odivide'( T, U, X ) ),
% 1.10/1.51 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.10/1.51 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), U ) ), hAPP(
% 1.10/1.51 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ), hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ), X ) ), =( U,
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.10/1.51 ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( Y, hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z
% 1.10/1.51 , X ) ), Z ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z
% 1.10/1.51 , X ) ), Z ), Y ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.10/1.51 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.51 X ), Y ), Z ) ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP(
% 1.10/1.51 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Oone__class_Oone'( X )
% 1.10/1.51 ) ), Z ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.10/1.51 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ), hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.10/1.51 X ), Z ), 'c_HOL_Oone__class_Oone'( X ) ) ), Y ) ) ],
% 1.10/1.51 [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Suc'(
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ),
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.10/1.51 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.10/1.51 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.51 'c_HOL_Oplus__class_Oplus'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.10/1.51 Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), ~( 'class_Int_Onumber'(
% 1.10/1.51 X ) ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.10/1.51 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ),
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( T, X ) ), hAPP( hAPP(
% 1.10/1.51 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.51 X ), Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ), hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.10/1.51 'c_HOL_Oone__class_Oone'( X ), X ), ~( 'c_lessequals'(
% 1.10/1.51 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.10/1.51 X ) ) ],
% 1.10/1.51 [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.10/1.51 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Suc'(
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.10/1.51 'tc_nat' ) ) ) ],
% 1.10/1.51 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Y
% 1.10/1.51 , X ) ) ],
% 1.10/1.51 [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ],
% 1.10/1.51 [ =( 'c_Divides_Odiv__class_Odiv'( 'c_Suc'( 'c_Suc'( 'c_Suc'( X ) ) ),
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), 'tc_nat' ),
% 1.10/1.51 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.10/1.51 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'(
% 1.10/1.51 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), X ),
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.10/1.51 [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Suc'( 'c_Suc'( 'c_Suc'( Y ) ) )
% 1.10/1.51 , 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X, hAPP( hAPP(
% 1.10/1.51 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.10/1.51 'c_Int_OPls' ) ), 'tc_nat' ) ), Y ), 'tc_nat' ) ) ],
% 1.10/1.51 [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( 'c_Suc'( 'c_Suc'( X ) ) ), Y
% 1.10/1.51 , 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.10/1.51 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.10/1.51 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), Y, 'tc_nat' ) ) ],
% 1.10/1.51 [ =( 'c_Divides_Odiv__class_Odiv'( X, 'c_Suc'( 'c_Suc'( 'c_Suc'( Y ) ) )
% 1.10/1.51 , 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( X, hAPP( hAPP(
% 1.10/1.51 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.10/1.51 'c_Int_OPls' ) ), 'tc_nat' ) ), Y ), 'tc_nat' ) ) ],
% 1.10/1.51 [ =( 'c_Divides_Odiv__class_Odiv'( 'c_Suc'( 'c_Suc'( 'c_Suc'( X ) ) ), Y
% 1.10/1.51 , 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.10/1.51 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.10/1.51 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), Y, 'tc_nat' ) ) ],
% 1.10/1.51 [ 'c_HOL_Oord__class_Oless'( 'c_Divides_Odiv__class_Odiv'( X, Y,
% 1.10/1.51 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), Y,
% 1.10/1.51 'tc_nat' ) ) ],
% 1.10/1.51 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =(
% 1.10/1.51 'c_Fact_Ofact__class_Ofact'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.10/1.51 'tc_nat' ), X ), Y ), 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) )
% 1.10/1.51 ],
% 1.10/1.51 [ =( 'c_List_Otake'( X, 'c_List_Olist_ONil'( Y ), Y ),
% 1.10/1.51 'c_List_Olist_ONil'( Y ) ) ],
% 1.10/1.51 [ =( 'c_List_Odrop'( X, 'c_List_Olist_ONil'( Y ), Y ),
% 1.10/1.51 'c_List_Olist_ONil'( Y ) ) ],
% 1.10/1.51 [ ~( =( 'c_List_Olist_OCons'( X, Y, Z ), 'c_List_Omap'( T, U, W, Z ) ) )
% 1.10/1.51 , =( U, 'c_List_Olist_OCons'(
% 1.10/1.51 'c_List_Osko__List__XCons__eq__map__conv__1__1'( T, X, Y, U, W, Z ),
% 1.10/1.51 'c_List_Osko__List__XCons__eq__map__conv__1__2'( T, X, Y, U, W, Z ), W )
% 1.10/1.51 ) ],
% 1.10/1.51 [ ~( =( 'c_List_Olist_OCons'( X, Y, Z ), 'c_List_Omap'( T, U, W, Z ) ) )
% 1.10/1.51 , =( U, 'c_List_Olist_OCons'(
% 1.10/1.51 'c_List_Osko__List__XCons__eq__map__D__1__1'( T, X, Y, U, W, Z ),
% 1.10/1.51 'c_List_Osko__List__XCons__eq__map__D__1__2'( T, X, Y, U, W, Z ), W ) ) ]
% 1.10/1.51 ,
% 1.10/1.51 [ ~( =( 'c_List_Omap'( X, Y, Z, T ), 'c_List_Olist_OCons'( U, W, T ) ) )
% 1.10/1.51 , =( Y, 'c_List_Olist_OCons'(
% 1.10/1.51 'c_List_Osko__List__Xmap__eq__Cons__conv__1__1'( X, Y, U, W, Z, T ),
% 1.10/1.51 'c_List_Osko__List__Xmap__eq__Cons__conv__1__2'( X, Y, U, W, Z, T ), Z )
% 1.10/1.51 ) ],
% 1.10/1.51 [ ~( =( 'c_List_Omap'( X, Y, Z, T ), 'c_List_Olist_OCons'( U, W, T ) ) )
% 1.10/1.51 , =( Y, 'c_List_Olist_OCons'(
% 1.10/1.51 'c_List_Osko__List__Xmap__eq__Cons__D__1__1'( X, Y, U, W, Z, T ),
% 1.10/1.51 'c_List_Osko__List__Xmap__eq__Cons__D__1__2'( X, Y, U, W, Z, T ), Z ) ) ]
% 1.10/1.51 ,
% 1.10/1.51 [ =( hAPP( hAPP( X, Y ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), Y ),
% 1.10/1.51 ~( 'c_Groebner__Basis_Ogb__semiring'( Z, T, X, U, W, V0 ) ) ],
% 1.10/1.51 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.10/1.51 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Oone__class_Oone'(
% 1.10/1.51 'tc_nat' ) ), Y ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.10/1.51 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Oone__class_Oone'(
% 1.10/1.51 'tc_nat' ) ), Y ) ],
% 1.10/1.51 [ =( 'c_Fact_Ofact__class_Ofact'( 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 1.10/1.51 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.10/1.51 [ =( 'c_List_Odrop'( X, 'c_List_Omap'( Y, Z, T, U ), U ), 'c_List_Omap'(
% 1.10/1.51 Y, 'c_List_Odrop'( X, Z, T ), T, U ) ) ],
% 1.10/1.51 [ =( 'c_List_Otake'( X, 'c_List_Omap'( Y, Z, T, U ), U ), 'c_List_Omap'(
% 1.10/1.51 Y, 'c_List_Otake'( X, Z, T ), T, U ) ) ],
% 1.10/1.51 [ =( 'c_List_Oupt'( 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ),
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ), 'c_List_Olist_ONil'(
% 1.10/1.51 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ),
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), 'tc_nat' ) ],
% 1.10/1.51 [ ~( =( 'c_List_Oupt'( X, Y ), 'c_List_Olist_OCons'( Z, T, 'tc_nat' ) )
% 1.10/1.51 ), =( 'c_List_Oupt'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.10/1.51 , X ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), Y ), T ) ],
% 1.10/1.51 [ ~( =( 'c_List_Oupt'( X, Y ), 'c_List_Olist_OCons'( Z, T, 'tc_nat' ) )
% 1.10/1.51 ), =( X, Z ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.10/1.51 'class_Int_Onumber__ring'( X ) ), 'c_lessequals'(
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.51 ), X ), ~( 'c_lessequals'( Y, 'c_Int_OPls', 'tc_Int_Oint' ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.10/1.51 'class_Int_Onumber__ring'( X ) ), 'c_lessequals'( Y, 'c_Int_OPls',
% 1.10/1.51 'tc_Int_Oint' ), ~( 'c_lessequals'( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.10/1.51 , X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.10/1.51 'class_Int_Onumber__ring'( X ) ), 'c_lessequals'(
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X
% 1.10/1.51 ), X ), ~( 'c_lessequals'( 'c_Int_OPls', Y, 'tc_Int_Oint' ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.10/1.51 'class_Int_Onumber__ring'( X ) ), 'c_lessequals'( 'c_Int_OPls', Y,
% 1.10/1.51 'tc_Int_Oint' ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.10/1.51 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ), X ) ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =(
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.10/1.51 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ), X ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =(
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.10/1.51 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.51 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.10/1.51 X ), 'c_HOL_Oone__class_Oone'( X ) ), 'c_HOL_Oone__class_Oone'( X ) ) ),
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( Y ), X ) ) ],
% 1.10/1.51 [ =( 'c_Suc'( 'c_Suc'( 'c_Suc'( X ) ) ), hAPP( hAPP(
% 1.10/1.51 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.10/1.51 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ) ],
% 1.10/1.51 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.10/1.51 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.10/1.51 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.51 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), Y ) ) ]
% 1.10/1.51 ,
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.51 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.10/1.51 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP(
% 1.10/1.51 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.10/1.51 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.10/1.51 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.10/1.51 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.10/1.51 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.10/1.51 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.10/1.51 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.10/1.51 ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.10/1.51 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.10/1.51 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.10/1.51 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.10/1.51 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.10/1.51 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.10/1.51 ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.10/1.51 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.10/1.51 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.10/1.51 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.10/1.51 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.10/1.51 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ]
% 1.10/1.51 ,
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.10/1.51 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.10/1.51 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.10/1.51 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.10/1.51 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.10/1.51 'c_Int_OPls' ) ), 'tc_nat' ) ) ), X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.10/1.51 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.10/1.51 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.10/1.51 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.10/1.51 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.10/1.51 'c_Int_OPls' ) ), 'tc_nat' ) ) ), X ), =( Z, 'c_HOL_Ozero__class_Ozero'(
% 1.10/1.51 X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.10/1.51 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.10/1.51 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.10/1.51 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.10/1.51 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.10/1.51 'c_Int_OPls' ) ), 'tc_nat' ) ) ), X ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.10/1.51 X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.10/1.51 X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.10/1.51 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.10/1.51 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.10/1.51 'c_Int_OPls' ) ), 'tc_nat' ) ) ), X ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.10/1.51 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.10/1.51 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.10/1.51 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.10/1.51 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.10/1.51 ],
% 1.10/1.51 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.10/1.51 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.10/1.51 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ),
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.10/1.51 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.10/1.51 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.10/1.51 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.10/1.51 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.10/1.51 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.10/1.51 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.10/1.51 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), X ) ), Y ) ), Z ) ) ) ]
% 1.10/1.51 ,
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.51 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.10/1.51 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =(
% 1.10/1.51 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( Y
% 1.10/1.51 , X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.51 'class_Int_Onumber'( X ) ), ~( =( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.10/1.51 Z, X ) ) ), =( 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.51 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.10/1.51 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =(
% 1.10/1.51 'c_HOL_Oinverse__class_Odivide'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.10/1.51 , 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.51 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.10/1.51 X ), 'c_HOL_Oinverse__class_Odivide'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.10/1.51 , X ) ) ), =( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.51 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.10/1.51 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =(
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.10/1.51 'c_HOL_Oinverse__class_Odivide'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.10/1.51 ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.51 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.10/1.51 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( 'c_HOL_Ozero__class_Ozero'(
% 1.10/1.51 X ), 'c_HOL_Oinverse__class_Odivide'( Z,
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.51 'c_HOL_Oone__class_Oone'( X ), X ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 1.10/1.51 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'(
% 1.10/1.51 X ), X ) ) ],
% 1.10/1.51 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.10/1.51 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Oone__class_Oone'( X ), X ),
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ), X ) ]
% 1.10/1.51 ,
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.51 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.10/1.51 'c_Divides_Odiv__class_Odiv'( Y, Y, X ), 'c_HOL_Oone__class_Oone'( X ) )
% 1.10/1.51 , =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =(
% 1.10/1.51 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Oone__class_Oone'( X )
% 1.10/1.51 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, Z ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y
% 1.10/1.51 , Y, X ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.10/1.51 'c_HOL_Oinverse__class_Odivide'( Y, Y, X ), 'c_HOL_Oone__class_Oone'( X )
% 1.10/1.51 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.10/1.51 'c_HOL_Oinverse__class_Odivide'( Y, Y, X ), 'c_HOL_Oone__class_Oone'( X )
% 1.10/1.51 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.10/1.51 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.10/1.51 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y
% 1.10/1.51 ), 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.10/1.51 'tc_nat' ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.10/1.51 ), =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ),
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ) ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.10/1.51 , =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.10/1.51 ), ~( =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.10/1.51 ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.10/1.51 ), ~( =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ),
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.51 ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.10/1.51 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.10/1.51 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.10/1.51 [ ~( 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.10/1.51 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.10/1.51 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.10/1.51 [ ~( 'class_Int_Oring__char__0'( X ) ), ~( 'class_Int_Onumber__ring'( X
% 1.10/1.51 ) ), ~( 'c_Int_Oiszero'( 'c_Int_Onumber__class_Onumber__of'(
% 1.10/1.51 'c_Int_OBit1'( Y ), X ), X ) ) ],
% 1.10/1.51 [ ~( 'class_Int_Onumber__ring'( X ) ), 'c_Int_Oiszero'(
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', X ), X ) ],
% 1.10/1.51 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.10/1.51 'c_HOL_Oplus__class_Oplus'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.10/1.51 'c_Int_OPls', X ) ), Y ), Y ) ],
% 1.10/1.51 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.10/1.51 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_Int_Onumber__class_Onumber__of'(
% 1.10/1.51 'c_Int_OPls', X ) ), Y ) ],
% 1.10/1.51 [ ~( 'class_Int_Oring__char__0'( X ) ), ~( 'class_Int_Onumber__ring'( X
% 1.10/1.51 ) ), 'c_Int_Oiszero'( 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.10/1.51 ~( 'c_Int_Oiszero'( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( Y
% 1.10/1.51 ), X ), X ) ) ],
% 1.10/1.51 [ ~( 'class_Int_Oring__char__0'( X ) ), ~( 'class_Int_Onumber__ring'( X
% 1.10/1.51 ) ), 'c_Int_Oiszero'( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.10/1.51 Y ), X ), X ), ~( 'c_Int_Oiszero'( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.10/1.51 , X ), X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.10/1.51 'class_Int_Onumber__ring'( X ) ), 'c_lessequals'(
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Oone__class_Oone'( X )
% 1.10/1.51 , X ), ~( 'c_lessequals'( Y, 'c_Int_OBit1'( 'c_Int_OPls' ), 'tc_Int_Oint'
% 1.10/1.51 ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.10/1.51 'class_Int_Onumber__ring'( X ) ), 'c_lessequals'( Y, 'c_Int_OBit1'(
% 1.10/1.51 'c_Int_OPls' ), 'tc_Int_Oint' ), ~( 'c_lessequals'(
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Oone__class_Oone'( X )
% 1.10/1.51 , X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.10/1.51 'class_Int_Onumber__ring'( X ) ), 'c_lessequals'(
% 1.10/1.51 'c_HOL_Oone__class_Oone'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.10/1.51 , X ), ~( 'c_lessequals'( 'c_Int_OBit1'( 'c_Int_OPls' ), Y, 'tc_Int_Oint'
% 1.10/1.51 ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.10/1.51 'class_Int_Onumber__ring'( X ) ), 'c_lessequals'( 'c_Int_OBit1'(
% 1.10/1.51 'c_Int_OPls' ), Y, 'tc_Int_Oint' ), ~( 'c_lessequals'(
% 1.10/1.51 'c_HOL_Oone__class_Oone'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.10/1.51 , X ) ) ],
% 1.10/1.51 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.10/1.51 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.51 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ),
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.10/1.51 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.10/1.51 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ) ), Y ) ) ],
% 1.10/1.51 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.10/1.51 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), X ) ), Y ), hAPP( hAPP(
% 1.10/1.51 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ) ) ],
% 1.10/1.51 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.10/1.51 'c_Int_OPls' ) ), X ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y )
% 1.10/1.51 , Y ) ) ],
% 1.10/1.51 [ =( 'c_List_Odrop'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.10/1.51 'c_List_Olist_OCons'( X, Y, Z ), Z ), 'c_List_Olist_OCons'( X, Y, Z ) ) ]
% 1.10/1.51 ,
% 1.10/1.51 [ =( 'c_List_Onth'( 'c_List_Olist_OCons'( X, Y, Z ),
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z ), X ) ],
% 1.10/1.51 [ 'c_lessequals'( 'c_Int_OPls', 'c_Int_OBit1'( X ), 'tc_Int_Oint' ), ~(
% 1.10/1.51 'c_lessequals'( 'c_Int_OPls', X, 'tc_Int_Oint' ) ) ],
% 1.10/1.51 [ 'c_lessequals'( 'c_Int_OPls', X, 'tc_Int_Oint' ), ~( 'c_lessequals'(
% 1.10/1.51 'c_Int_OPls', 'c_Int_OBit1'( X ), 'tc_Int_Oint' ) ) ],
% 1.10/1.51 [ 'c_lessequals'( 'c_Int_OBit0'( X ), 'c_Int_OBit1'( Y ), 'tc_Int_Oint'
% 1.10/1.51 ), ~( 'c_lessequals'( X, Y, 'tc_Int_Oint' ) ) ],
% 1.10/1.51 [ 'c_lessequals'( X, Y, 'tc_Int_Oint' ), ~( 'c_lessequals'(
% 1.10/1.51 'c_Int_OBit0'( X ), 'c_Int_OBit1'( Y ), 'tc_Int_Oint' ) ) ],
% 1.10/1.51 [ 'c_lessequals'( 'c_Int_OBit0'( X ), 'c_Int_OBit1'( Y ), 'tc_Int_Oint'
% 1.10/1.51 ), ~( 'c_lessequals'( X, Y, 'tc_Int_Oint' ) ) ],
% 1.10/1.51 [ 'c_lessequals'( X, Y, 'tc_Int_Oint' ), ~( 'c_lessequals'(
% 1.10/1.51 'c_Int_OBit0'( X ), 'c_Int_OBit1'( Y ), 'tc_Int_Oint' ) ) ],
% 1.10/1.51 [ 'c_lessequals'( 'c_Int_OBit0'( X ), 'c_Int_OPls', 'tc_Int_Oint' ), ~(
% 1.10/1.51 'c_lessequals'( X, 'c_Int_OPls', 'tc_Int_Oint' ) ) ],
% 1.10/1.51 [ 'c_lessequals'( X, 'c_Int_OPls', 'tc_Int_Oint' ), ~( 'c_lessequals'(
% 1.10/1.51 'c_Int_OBit0'( X ), 'c_Int_OPls', 'tc_Int_Oint' ) ) ],
% 1.10/1.51 [ 'c_lessequals'( 'c_Int_OPls', 'c_Int_OBit0'( X ), 'tc_Int_Oint' ), ~(
% 1.10/1.51 'c_lessequals'( 'c_Int_OPls', X, 'tc_Int_Oint' ) ) ],
% 1.10/1.51 [ 'c_lessequals'( 'c_Int_OPls', X, 'tc_Int_Oint' ), ~( 'c_lessequals'(
% 1.10/1.51 'c_Int_OPls', 'c_Int_OBit0'( X ), 'tc_Int_Oint' ) ) ],
% 1.10/1.51 [ =( 'c_List_Otake'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, Y ),
% 1.10/1.51 'c_List_Olist_ONil'( Y ) ) ],
% 1.10/1.51 [ ~( =( 'c_List_Otake'( X, Y, Z ), 'c_List_Olist_ONil'( Z ) ) ), =( Y,
% 1.10/1.51 'c_List_Olist_ONil'( Z ) ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.10/1.51 ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ), hAPP( hAPP(
% 1.10/1.51 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.10/1.51 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ],
% 1.10/1.51 [ =( 'c_Divides_Odiv__class_Odiv'( 'c_Suc'( 'c_Suc'( X ) ),
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.10/1.51 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'c_Suc'(
% 1.10/1.51 'c_Divides_Odiv__class_Odiv'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.10/1.51 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) )
% 1.10/1.51 ) ],
% 1.10/1.51 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.10/1.51 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), X ),
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.10/1.51 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), X ) ],
% 1.10/1.51 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.10/1.51 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), 'c_Suc'( 'c_Suc'( X ) ) ) ],
% 1.10/1.51 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.10/1.51 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_Suc'( 'c_Suc'( X ) ) ) ],
% 1.10/1.51 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.10/1.51 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.10/1.51 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.51 X ), Y ), Y ) ) ],
% 1.10/1.51 [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( 'c_Suc'( X ) ),
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.10/1.51 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X
% 1.10/1.51 , 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.10/1.51 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) ) ],
% 1.10/1.51 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.10/1.51 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.10/1.51 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ),
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.10/1.51 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.10/1.51 'tc_nat' ) ) ],
% 1.10/1.51 [ =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'c_Suc'(
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.10/1.51 [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ],
% 1.10/1.51 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.10/1.51 , Y, X ) ) ],
% 1.10/1.51 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.10/1.51 , Y, X ) ) ],
% 1.10/1.51 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.10/1.51 , X ), 'c_lessequals'( Z, Y, X ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.10/1.51 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.10/1.51 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.10/1.51 ,
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.51 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.10/1.51 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.10/1.51 , Z ), T ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, T, 'tc_nat' ) )
% 1.10/1.51 , ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 1.10/1.51 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.10/1.51 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.10/1.51 T, X ) ) ],
% 1.10/1.51 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.10/1.51 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.10/1.51 ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ),
% 1.10/1.51 ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.10/1.51 ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.10/1.51 ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.10/1.51 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.10/1.51 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ), ~( 'c_lessequals'( U, Z
% 1.10/1.51 , X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), U
% 1.10/1.51 , X ) ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'(
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP(
% 1.10/1.51 'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( Z ) ), X ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.10/1.51 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.10/1.51 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.10/1.51 [ =( 'c_List_Odrop'( X, 'c_List_Odrop'( Y, Z, T ), T ), 'c_List_Odrop'(
% 1.10/1.51 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), Z, T ) ) ]
% 1.10/1.51 ,
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.10/1.51 Y, Z, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ),
% 1.10/1.51 ~( 'c_lessequals'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.10/1.51 'c_Suc'( T ) ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.10/1.51 'c_Suc'( T ) ), X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.10/1.51 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X )
% 1.10/1.51 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ]
% 1.10/1.51 ,
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.10/1.51 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X )
% 1.10/1.51 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) )
% 1.10/1.51 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.10/1.51 'c_lessequals'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ]
% 1.10/1.51 ,
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =( hAPP( hAPP(
% 1.10/1.51 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.10/1.51 'c_Power_Opower__class_Opower'( X ), Y ), T ) ) ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ), =( Z
% 1.10/1.51 , T ) ],
% 1.10/1.51 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'class_Int_Onumber'( X ) ),
% 1.10/1.51 ~( 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.10/1.51 , 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ), ~( 'c_lessequals'(
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.10/1.51 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'class_Int_Onumber'( X ) ),
% 1.10/1.51 'c_lessequals'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.10/1.51 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.10/1.51 'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( Z ) ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.10/1.51 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), Y ), hAPP( hAPP(
% 1.10/1.51 'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( Z ) ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.10/1.51 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), hAPP( hAPP(
% 1.10/1.51 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Oinverse__class_Oinverse'(
% 1.10/1.51 Z, X ) ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.10/1.51 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.10/1.51 Z, X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.10/1.51 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ) ) ],
% 1.10/1.51 [ 'c_HOL_Oord__class_Oless'( 'c_Fact_Ofact__class_Ofact'( X, 'tc_nat' )
% 1.10/1.51 , 'c_Fact_Ofact__class_Ofact'( Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.10/1.51 'tc_nat' ) ) ],
% 1.10/1.51 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.10/1.51 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.10/1.51 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.51 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.10/1.51 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.51 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), T ), Y ), hAPP( hAPP(
% 1.10/1.51 'c_Power_Opower__class_Opower'( X ), T ), Z ), X ) ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), T, X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.10/1.51 ), Y ), Z ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), T ),
% 1.10/1.51 X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X )
% 1.10/1.51 ), ~( 'c_HOL_Oord__class_Oless'( Z, T, 'tc_nat' ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.51 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), T ), Y ), hAPP( hAPP(
% 1.10/1.51 'c_Power_Opower__class_Opower'( X ), T ), Z ), X ) ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), T, X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.10/1.51 ), Y ), Z ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), T ),
% 1.10/1.51 X ), ~( 'c_HOL_Oord__class_Oless'( Z, T, 'tc_nat' ) ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.51 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.10/1.51 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'(
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.51 ), X ) ), ~( 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.51 X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ), ~(
% 1.10/1.51 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.51 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.10/1.51 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'(
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.51 ), X ) ), 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X )
% 1.10/1.51 , X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X )
% 1.10/1.51 ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.51 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.10/1.51 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.51 ), X ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.10/1.51 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ),
% 1.10/1.51 ~( 'c_lessequals'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.10/1.51 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ],
% 1.10/1.51 [ ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.10/1.51 'tc_nat' ), X ), Y ), Y, 'tc_nat' ) ) ],
% 1.10/1.51 [ ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.10/1.51 'tc_nat' ), X ), Y ), X, 'tc_nat' ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.10/1.51 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.10/1.51 Z, X ) ), T ), 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.10/1.51 'c_Power_Opower__class_Opower'( X ), Y ), T ), hAPP( hAPP(
% 1.10/1.51 'c_Power_Opower__class_Opower'( X ), Z ), T ), X ) ), =( Z,
% 1.10/1.51 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.10/1.51 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), T, X ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.10/1.51 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), Y, X ) ) ]
% 1.10/1.51 ,
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.10/1.51 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.10/1.51 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ),
% 1.10/1.51 Y, X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z,
% 1.10/1.51 X ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.10/1.51 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.10/1.51 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~(
% 1.10/1.51 'c_lessequals'( Z, 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ) ) ]
% 1.10/1.51 ,
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.10/1.51 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.10/1.51 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.10/1.51 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T
% 1.10/1.51 ), X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T
% 1.10/1.51 , X ) ],
% 1.10/1.51 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.51 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.51 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.10/1.51 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.10/1.52 , X ), X ), T, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T
% 1.10/1.52 , X ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.10/1.52 , T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ),
% 1.10/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.52 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.10/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.52 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.10/1.52 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.10/1.52 , X ), X ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.10/1.52 ) ), ~( 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.10/1.52 , Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ),
% 1.10/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.52 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.10/1.52 [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 1.10/1.52 'c_Divides_Odiv__class_Omod'( 'c_Suc'( 'c_Divides_Odiv__class_Omod'( X, Y
% 1.10/1.52 , 'tc_nat' ) ), Y, 'tc_nat' ) ) ],
% 1.10/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.10/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.10/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.52 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.52 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.10/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.10/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.10/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.52 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.10/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.10/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.10/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.10/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.52 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.10/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.10/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.10/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.52 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.52 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.52 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.10/1.52 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.10/1.52 , Z ), Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) )
% 1.10/1.52 ],
% 1.10/1.52 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.10/1.52 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.10/1.52 'tc_nat' ), Z ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.10/1.52 , Z ), Y ), 'tc_nat' ) ) ],
% 1.10/1.52 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.10/1.52 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.10/1.52 , X ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) )
% 1.10/1.52 ],
% 1.10/1.52 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.10/1.52 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.52 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Y ), hAPP( hAPP(
% 1.10/1.52 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ) ) ],
% 1.10/1.52 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.10/1.52 , 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.10/1.52 , Y ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ),
% 1.10/1.52 ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.10/1.52 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.10/1.52 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.10/1.52 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~(
% 1.10/1.52 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.10/1.52 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.10/1.52 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.52 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP(
% 1.10/1.52 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ],
% 1.10/1.52 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.10/1.52 , 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.10/1.52 , Y ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ),
% 1.10/1.52 ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.10/1.52 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.10/1.52 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.10/1.52 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~(
% 1.10/1.52 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.10/1.52 [ ~( =( 'c_List_Odrop'( X, Y, Z ), 'c_List_Olist_OCons'( T, U, Z ) ) ),
% 1.10/1.52 =( 'c_List_Onth'( Y, X, Z ), T ) ],
% 1.10/1.52 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Y, X ) ]
% 1.10/1.52 ,
% 1.10/1.52 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Y, X ) ],
% 1.10/1.52 [ 'c_lessequals'( X, Y, 'tc_Int_Oint' ), ~( 'c_lessequals'( Z, Y,
% 1.10/1.52 'tc_Int_Oint' ) ), ~( 'c_lessequals'( X, Z, 'tc_Int_Oint' ) ) ],
% 1.10/1.52 [ 'c_lessequals'( X, X, 'tc_Int_Oint' ) ],
% 1.10/1.52 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.10/1.52 , X ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_lessequals'( Y, T
% 1.10/1.52 , X ) ) ],
% 1.10/1.52 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.10/1.52 , X ), ~( 'c_lessequals'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T
% 1.10/1.52 , X ) ) ],
% 1.10/1.52 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.10/1.52 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T )
% 1.10/1.52 , X ), ~( 'c_lessequals'( U, T, X ) ), ~( 'c_lessequals'( Y, hAPP( hAPP(
% 1.10/1.52 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ), X ) ) ],
% 1.10/1.52 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.10/1.52 'c_lessequals'( T, Z, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.10/1.52 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.10/1.52 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.10/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.10/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 1.10/1.52 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.52 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.10/1.52 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_lessequals'( T, Z, X
% 1.10/1.52 ) ) ],
% 1.10/1.52 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.10/1.52 ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X
% 1.10/1.52 ) ) ],
% 1.10/1.52 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.10/1.52 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( T, Z, X ) ) ],
% 1.10/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.10/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.10/1.52 'c_HOL_Oone__class_Oone'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.52 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.10/1.52 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.10/1.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_Suc'(
% 1.10/1.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_Suc'(
% 1.10/1.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.10/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.52 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.10/1.52 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.10/1.52 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~( 'c_lessequals'(
% 1.10/1.52 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.10/1.52 ), X ) ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.10/1.52 , X ), ~( 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.10/1.52 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.10/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.52 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.10/1.52 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.10/1.52 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~( 'c_lessequals'(
% 1.10/1.52 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.10/1.52 ), X ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.10/1.52 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ),
% 1.10/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.10/1.52 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.10/1.52 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.10/1.52 ), Y ), Z ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.52 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.10/1.52 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.10/1.52 ), Y ), Z ), Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.52 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.10/1.52 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.10/1.52 , X ), X ), T, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T
% 1.10/1.52 , X ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.10/1.52 , T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ), ~(
% 1.10/1.52 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.10/1.52 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.10/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.52 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.10/1.52 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.10/1.52 , X ), X ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.10/1.52 ) ), ~( 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.10/1.52 , Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ), ~(
% 1.10/1.52 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.10/1.52 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.10/1.52 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 1.10/1.52 'c_HOL_Oplus__class_Oplus'( X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X )
% 1.10/1.52 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.10/1.52 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ), Z ) ), Y ) ],
% 1.10/1.52 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( hAPP(
% 1.10/1.52 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.10/1.52 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.10/1.52 'c_HOL_Ozero__class_Ozero'( X ) ) ), hAPP( hAPP(
% 1.10/1.52 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.10/1.52 'c_HOL_Ozero__class_Ozero'( X ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.10/1.52 ,
% 1.10/1.52 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.10/1.52 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.52 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.52 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), hAPP( hAPP(
% 1.10/1.52 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ) ],
% 1.10/1.52 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.10/1.52 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.10/1.52 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.10/1.52 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.10/1.52 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ) ],
% 1.10/1.52 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.10/1.52 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.52 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.52 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), hAPP( hAPP(
% 1.10/1.52 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ) ],
% 1.10/1.52 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.10/1.52 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.10/1.52 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.10/1.52 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), hAPP( hAPP(
% 1.10/1.52 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ) ],
% 1.10/1.52 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =(
% 1.10/1.52 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.10/1.52 'c_HOL_Oinverse__class_Odivide'( T, U, X ) ) ), =( U,
% 1.10/1.52 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.10/1.52 ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), U ), hAPP(
% 1.10/1.52 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ],
% 1.10/1.52 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =( hAPP( hAPP(
% 1.10/1.52 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.10/1.52 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) ), =( Z,
% 1.10/1.52 'c_HOL_Ozero__class_Ozero'( X ) ), =( U, 'c_HOL_Ozero__class_Ozero'( X )
% 1.10/1.52 ), =( 'c_HOL_Oinverse__class_Odivide'( Y, U, X ),
% 1.10/1.52 'c_HOL_Oinverse__class_Odivide'( T, Z, X ) ) ],
% 1.10/1.52 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.10/1.52 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.10/1.52 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X
% 1.10/1.52 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.10/1.52 'c_Divides_Odiv__class_Omod'( Z, T, X ) ) ) ],
% 1.10/1.52 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.10/1.52 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.10/1.52 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X
% 1.10/1.52 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.10/1.52 'c_Divides_Odiv__class_Omod'( Y, T, X ) ), Z ) ) ],
% 1.10/1.52 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.10/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.10/1.52 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.52 X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ), Y, X ),
% 1.10/1.52 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.52 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.10/1.52 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.10/1.52 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 1.10/1.52 'c_lessequals'( Z, Y, X ) ],
% 1.10/1.52 [ 'c_lessequals'( X, Y, 'tc_Int_Oint' ), 'c_lessequals'( Y, X,
% 1.10/1.52 'tc_Int_Oint' ) ],
% 1.10/1.52 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.10/1.52 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.10/1.52 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.10/1.52 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.10/1.52 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Z
% 1.10/1.52 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.10/1.52 [ =( 'c_Fact_Ofact__class_Ofact'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.10/1.52 , 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.10/1.52 [ =( 'c_List_Odrop'( 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 1.10/1.52 'c_List_Olist_OCons'( X, Y, Z ), Z ), Y ) ],
% 1.10/1.52 [ ~( =( 'c_List_Omap'( X, Y, Z, T ), 'c_List_Olist_OCons'( U, W, T ) ) )
% 1.10/1.52 , =( 'c_List_Omap'( X, 'c_List_Osko__List__Xmap__eq__Cons__D__1__2'( X, Y
% 1.10/1.52 , U, W, Z, T ), Z, T ), W ) ],
% 1.10/1.52 [ ~( =( 'c_List_Omap'( X, Y, Z, T ), 'c_List_Olist_OCons'( U, W, T ) ) )
% 1.10/1.52 , =( hAPP( X, 'c_List_Osko__List__Xmap__eq__Cons__D__1__1'( X, Y, U, W, Z
% 1.10/1.52 , T ) ), U ) ],
% 1.10/1.52 [ ~( =( 'c_List_Omap'( X, Y, Z, T ), 'c_List_Olist_OCons'( U, W, T ) ) )
% 1.10/1.52 , =( hAPP( X, 'c_List_Osko__List__Xmap__eq__Cons__conv__1__1'( X, Y, U, W
% 1.10/1.52 , Z, T ) ), U ) ],
% 1.10/1.52 [ ~( =( 'c_List_Olist_OCons'( X, Y, Z ), 'c_List_Omap'( T, U, W, Z ) ) )
% 1.10/1.52 , =( X, hAPP( T, 'c_List_Osko__List__XCons__eq__map__conv__1__1'( T, X, Y
% 1.10/1.52 , U, W, Z ) ) ) ],
% 1.10/1.52 [ ~( =( 'c_List_Olist_OCons'( X, Y, Z ), 'c_List_Omap'( T, U, W, Z ) ) )
% 1.10/1.52 , =( Y, 'c_List_Omap'( T, 'c_List_Osko__List__XCons__eq__map__conv__1__2'(
% 1.10/1.52 T, X, Y, U, W, Z ), W, Z ) ) ],
% 1.10/1.52 [ ~( =( 'c_List_Omap'( X, Y, Z, T ), 'c_List_Olist_OCons'( U, W, T ) ) )
% 1.10/1.52 , =( 'c_List_Omap'( X, 'c_List_Osko__List__Xmap__eq__Cons__conv__1__2'( X
% 1.10/1.52 , Y, U, W, Z, T ), Z, T ), W ) ],
% 1.10/1.52 [ ~( =( 'c_List_Olist_OCons'( X, Y, Z ), 'c_List_Omap'( T, U, W, Z ) ) )
% 1.10/1.52 , =( X, hAPP( T, 'c_List_Osko__List__XCons__eq__map__D__1__1'( T, X, Y, U
% 1.10/1.52 , W, Z ) ) ) ],
% 1.10/1.52 [ ~( =( 'c_List_Olist_OCons'( X, Y, Z ), 'c_List_Omap'( T, U, W, Z ) ) )
% 1.10/1.52 , =( Y, 'c_List_Omap'( T, 'c_List_Osko__List__XCons__eq__map__D__1__2'( T
% 1.10/1.52 , X, Y, U, W, Z ), W, Z ) ) ],
% 1.10/1.52 [ =( 'c_List_Oupt'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 1.10/1.52 'c_List_Olist_ONil'( 'tc_nat' ) ) ],
% 1.10/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.52 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.52 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.10/1.52 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.10/1.52 'c_Int_OPls' ) ), X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.52 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.10/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.52 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.52 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.52 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.10/1.52 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.10/1.52 'c_Int_OPls' ) ), X ), X ), X ) ) ],
% 1.10/1.52 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP( hAPP(
% 1.10/1.52 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.10/1.52 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.10/1.52 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.10/1.52 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.10/1.52 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.10/1.52 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.10/1.52 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.10/1.52 ,
% 1.10/1.52 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.10/1.52 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.10/1.52 ), Y ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.10/1.52 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.10/1.52 ,
% 1.10/1.52 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.10/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.10/1.52 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.10/1.52 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.10/1.52 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ) ],
% 1.10/1.52 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.10/1.52 Y, Z, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ),
% 1.10/1.52 ~( 'c_lessequals'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.10/1.52 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.10/1.52 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP(
% 1.10/1.52 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.10/1.52 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.10/1.52 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ) ],
% 1.10/1.52 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =( hAPP( hAPP(
% 1.10/1.52 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.10/1.52 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.10/1.52 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.10/1.52 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.10/1.52 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.10/1.52 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.10/1.52 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.10/1.52 =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.52 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =( hAPP( hAPP(
% 1.10/1.52 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.10/1.52 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.10/1.52 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.10/1.52 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.10/1.52 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.10/1.52 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.10/1.52 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.10/1.52 =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.52 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.10/1.52 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.10/1.52 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.10/1.52 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.10/1.52 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ],
% 1.10/1.52 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.10/1.52 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.52 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ),
% 1.10/1.52 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.10/1.52 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.10/1.52 ), Y ), Y ) ) ],
% 1.10/1.52 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =( hAPP( hAPP(
% 1.10/1.52 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.10/1.52 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.10/1.52 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP(
% 1.10/1.52 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.10/1.52 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.10/1.52 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), =( Y, Z ), ~( 'c_lessequals'(
% 1.10/1.52 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.10/1.52 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.10/1.52 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.10/1.52 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.10/1.52 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.10/1.52 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.10/1.52 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.52 ) ) ],
% 1.10/1.52 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), ~( 'class_Int_Onumber'(
% 1.10/1.52 X ) ), =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ),
% 1.10/1.52 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 1.10/1.52 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.10/1.52 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.52 X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 1.10/1.52 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ) ],
% 1.10/1.52 [ =( X, 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 1.10/1.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X
% 1.10/1.52 , 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.10/1.52 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) ) ],
% 1.10/1.52 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.10/1.52 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.10/1.52 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.10/1.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( X ) )
% 1.10/1.52 ],
% 1.10/1.52 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.10/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.52 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.10/1.52 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', X ), X ),
% 1.10/1.52 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.52 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.10/1.52 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( Y ), X ), hAPP( hAPP(
% 1.10/1.52 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.10/1.52 X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.10/1.52 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ),
% 1.10/1.52 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ) ],
% 1.10/1.52 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.10/1.52 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.10/1.52 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.10/1.52 ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.10/1.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( =( hAPP( hAPP(
% 1.10/1.52 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.10/1.52 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.10/1.52 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.10/1.52 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.10/1.52 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.10/1.52 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.10/1.52 ), =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ),
% 1.10/1.52 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.10/1.52 , 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ), =(
% 1.10/1.52 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.10/1.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.10/1.52 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.10/1.52 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.10/1.52 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.10/1.52 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.10/1.52 'c_HOL_Ozero__class_Ozero'( X ) ), =( 'c_Int_Onumber__class_Onumber__of'(
% 1.10/1.52 Y, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.10/1.52 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.52 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.52 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.52 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.10/1.52 'c_HOL_Oone__class_Oone'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.10/1.52 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), X ), X ), X ) ],
% 1.10/1.52 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.10/1.52 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( Y ), X ), hAPP( hAPP(
% 1.10/1.52 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.10/1.52 X ), 'c_HOL_Oone__class_Oone'( X ) ), 'c_Int_Onumber__class_Onumber__of'(
% 1.10/1.52 Y, X ) ) ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ) ],
% 1.10/1.52 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.10/1.52 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Oinverse'(
% 1.10/1.52 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ), X
% 1.10/1.52 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X
% 1.10/1.52 ) ) ],
% 1.10/1.52 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.10/1.52 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.10/1.52 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ), X
% 1.10/1.52 ), Y ) ],
% 1.10/1.52 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.10/1.52 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.10/1.52 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ), X
% 1.10/1.52 ), Y ) ],
% 1.10/1.52 [ ~( 'class_Int_Onumber__ring'( X ) ), ~( 'c_Int_Oiszero'(
% 1.10/1.52 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ), X
% 1.10/1.52 ) ) ],
% 1.10/1.52 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.10/1.52 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.10/1.52 'c_Int_OBit1'( 'c_Int_OPls' ), X ) ), Y ), Y ) ],
% 1.10/1.52 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.10/1.52 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.10/1.52 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ) )
% 1.10/1.52 , Y ) ],
% 1.10/1.52 [ ~( =( 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ),
% 1.10/1.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_lessequals'( X,
% 1.10/1.52 'c_Int_OPls', 'tc_Int_Oint' ) ],
% 1.10/1.52 [ =( 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ),
% 1.10/1.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_lessequals'( X,
% 1.10/1.52 'c_Int_OPls', 'tc_Int_Oint' ) ) ],
% 1.10/1.52 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.10/1.52 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ) ), 'c_lessequals'( X
% 1.10/1.52 , 'c_Int_OPls', 'tc_Int_Oint' ) ],
% 1.10/1.52 [ =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.10/1.52 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ), ~( 'c_lessequals'( X
% 1.10/1.52 , 'c_Int_OPls', 'tc_Int_Oint' ) ) ],
% 1.10/1.52 [ ~( =( 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ),
% 1.10/1.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( 'c_List_Onth'(
% 1.10/1.52 'c_List_Olist_OCons'( Y, Z, T ), 'c_Int_Onumber__class_Onumber__of'( X,
% 1.10/1.52 'tc_nat' ), T ), Y ) ],
% 1.10/1.52 [ ~( =( 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ),
% 1.10/1.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( 'c_List_Odrop'(
% 1.10/1.52 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ), 'c_List_Olist_OCons'(
% 1.10/1.52 Y, Z, T ), T ), 'c_List_Olist_OCons'( Y, Z, T ) ) ],
% 1.10/1.52 [ =( 'c_List_Otake'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.10/1.52 'c_List_Olist_OCons'( X, Y, Z ), Z ), 'c_List_Olist_ONil'( Z ) ) ],
% 1.10/1.52 [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.10/1.52 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ),
% 1.10/1.52 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X,
% 1.10/1.52 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.10/1.52 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ) ],
% 1.10/1.52 [ ~( =( 'c_Divides_Odiv__class_Omod'( X,
% 1.10/1.52 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.10/1.52 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oone__class_Oone'(
% 1.10/1.52 'tc_nat' ) ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.10/1.52 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X,
% 1.10/1.52 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.10/1.52 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ],
% 1.10/1.52 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.10/1.52 'c_Divides_Odiv__class_Odiv'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.10/1.52 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ),
% 1.10/1.52 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'(
% 1.10/1.52 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.10/1.52 [ =( 'c_List_Otake'( 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 1.10/1.52 'c_List_Olist_OCons'( X, Y, Z ), Z ), 'c_List_Olist_OCons'( X,
% 1.10/1.52 'c_List_Olist_ONil'( Z ), Z ) ) ],
% 1.10/1.52 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.10/1.52 'class_Power_Opower'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.10/1.52 , 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( hAPP( hAPP(
% 1.10/1.52 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.10/1.52 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.10/1.52 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.10/1.52 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ),
% 1.10/1.52 'tc_nat' ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.10/1.52 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.10/1.52 'c_Int_OPls' ) ), 'tc_nat' ), 'c_Suc'( 'c_Suc'( 'c_Suc'(
% 1.10/1.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ) ],
% 1.10/1.52 [ =( hAPP( hAPP( X, Y ), Y ), hAPP( hAPP( Z, Y ),
% 1.10/1.52 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.10/1.52 'c_Int_OPls' ) ), 'tc_nat' ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( T
% 1.10/1.52 , X, Z, U, W, V0 ) ) ],
% 1.10/1.52 [ ~( =( 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ),
% 1.10/1.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( 'c_List_Otake'(
% 1.10/1.52 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ), 'c_List_Olist_OCons'(
% 1.10/1.52 Y, Z, T ), T ), 'c_List_Olist_ONil'( T ) ) ],
% 1.10/1.52 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.10/1.52 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.10/1.52 'c_HOL_Oone__class_Oone'( X ) ), 'c_Int_Onumber__class_Onumber__of'(
% 1.10/1.52 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), X ) ) ],
% 1.10/1.52 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP( hAPP(
% 1.10/1.52 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.10/1.52 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.10/1.52 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.52 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =( hAPP( hAPP(
% 1.10/1.52 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.10/1.52 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.10/1.52 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.52 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =( hAPP( hAPP(
% 1.10/1.52 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.10/1.52 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.10/1.52 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y
% 1.10/1.52 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.52 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =( hAPP( hAPP(
% 1.10/1.52 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.10/1.52 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.10/1.52 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.10/1.52 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.10/1.52 'c_Int_OPls' ) ), 'tc_nat' ), 'c_Suc'( 'c_Suc'(
% 1.10/1.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.10/1.52 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.10/1.52 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.10/1.52 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) ],
% 1.10/1.52 [ =( 'c_Suc'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ),
% 1.10/1.52 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.10/1.52 'c_Int_OPls' ) ), 'tc_nat' ) ) ],
% 1.10/1.52 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.10/1.52 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'(
% 1.10/1.52 'tc_nat' ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.10/1.52 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ],
% 1.10/1.52 [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.10/1.52 'c_Int_OBit0'( 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat'
% 1.10/1.52 ), 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'(
% 1.10/1.52 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), =(
% 1.10/1.52 'c_Divides_Odiv__class_Omod'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.10/1.52 'c_Int_OBit0'( 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat'
% 1.10/1.52 ), 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.10/1.52 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), =(
% 1.10/1.52 'c_Divides_Odiv__class_Omod'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.10/1.52 'c_Int_OBit0'( 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat'
% 1.10/1.52 ), 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), =(
% 1.10/1.52 'c_Divides_Odiv__class_Omod'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.10/1.52 'c_Int_OBit0'( 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat'
% 1.10/1.52 ), 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.10/1.52 [ ~( =( 'c_List_Omap'( X, Y, Z, T ), 'c_List_Olist_ONil'( T ) ) ), =( Y
% 1.10/1.52 , 'c_List_Olist_ONil'( Z ) ) ],
% 1.10/1.52 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.52 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', X ) ) ],
% 1.10/1.52 [ =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.10/1.52 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', 'tc_nat' ) ) ],
% 1.10/1.52 [ =( 'c_Int_OBit0'( 'c_Int_OPls' ), 'c_Int_OPls' ) ],
% 1.10/1.52 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', 'tc_nat' ),
% 1.10/1.52 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.10/1.52 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.10/1.52 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', X ),
% 1.10/1.52 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.52 [ ~( =( 'c_Int_OPls', 'c_Int_OBit1'( X ) ) ) ],
% 1.10/1.52 [ ~( =( 'c_Int_OBit1'( X ), 'c_Int_OPls' ) ) ],
% 1.10/1.52 [ ~( =( 'c_Int_OBit0'( X ), 'c_Int_OPls' ) ), =( X, 'c_Int_OPls' ) ]
% 1.10/1.52 ,
% 1.10/1.52 [ ~( =( 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ) ) ), =( X, Y ) ],
% 1.10/1.52 [ =( 'c_List_Omap'( X, 'c_List_Olist_ONil'( Y ), Y, Z ),
% 1.10/1.52 'c_List_Olist_ONil'( Z ) ) ],
% 1.10/1.52 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =(
% 1.10/1.52 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ) ) ) ],
% 1.10/1.52 [ ~( =( 'c_List_Olist_OCons'( X, Y, Z ), 'c_List_Olist_ONil'( Z ) ) ) ]
% 1.10/1.52 ,
% 1.10/1.52 [ ~( =( 'c_List_Olist_OCons'( X, Y, Z ), 'c_List_Olist_ONil'( Z ) ) ) ]
% 1.10/1.52 ,
% 1.10/1.52 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ),
% 1.10/1.52 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.10/1.52 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.10/1.52 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ),
% 1.10/1.52 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.10/1.52 [ ~( =( X, 'c_List_Olist_OCons'( Y, X, Z ) ) ) ],
% 1.10/1.52 [ ~( =( 'c_List_Olist_OCons'( X, Y, Z ), Y ) ) ],
% 1.10/1.52 [ ~( =( 'c_Int_OBit1'( X ), 'c_Int_OBit0'( Y ) ) ) ],
% 1.10/1.52 [ =( 'c_Int_OPls', 'c_Int_OBit0'( 'c_Int_OPls' ) ) ],
% 1.10/1.52 [ =( 'c_List_Olist_ONil'( X ), 'c_List_Omap'( Y, 'c_List_Olist_ONil'( Z
% 1.10/1.52 ), Z, X ) ) ],
% 1.10/1.52 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oone__class_Oone'( X )
% 1.10/1.52 , 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X )
% 1.10/1.52 ) ],
% 1.10/1.52 [ =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 1.10/1.52 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ),
% 1.10/1.52 'tc_nat' ) ) ],
% 1.10/1.52 [ ~( =( 'c_List_Olist_OCons'( X, Y, Z ), 'c_List_Olist_OCons'( T, U, Z )
% 1.10/1.52 ) ), =( X, T ) ],
% 1.10/1.52 [ ~( =( 'c_List_Olist_OCons'( X, Y, Z ), 'c_List_Olist_OCons'( T, U, Z )
% 1.10/1.52 ) ), =( Y, U ) ],
% 1.10/1.52 [ ~( =( 'c_List_Olist_ONil'( X ), 'c_List_Olist_OCons'( Y, Z, X ) ) ) ]
% 1.10/1.52 ,
% 1.10/1.52 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =(
% 1.10/1.52 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.10/1.52 [ ~( =( 'c_List_Olist_ONil'( X ), 'c_List_Omap'( Y, Z, T, X ) ) ), =( Z
% 1.10/1.52 , 'c_List_Olist_ONil'( T ) ) ],
% 1.10/1.52 [ ~( =( 'c_Int_OPls', 'c_Int_OBit0'( X ) ) ), =( 'c_Int_OPls', X ) ]
% 1.10/1.52 ,
% 1.10/1.52 [ ~( =( 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ) ) ), =( X, Y ) ],
% 1.10/1.52 [ ~( 'class_Int_Oring__char__0'( X ) ), ~( 'class_Int_Onumber__ring'( X
% 1.10/1.52 ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.10/1.52 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ), =( Y, Z ) ],
% 1.10/1.52 [ =( 'c_List_Omap'( X, 'c_List_Olist_OCons'( Y, Z, T ), T, U ),
% 1.10/1.52 'c_List_Olist_OCons'( hAPP( X, Y ), 'c_List_Omap'( X, Z, T, U ), U ) ) ]
% 1.10/1.52 ,
% 1.10/1.52 [ =( 'c_List_Olist_OCons'( hAPP( X, Y ), 'c_List_Omap'( X, Z, T, U ), U
% 1.10/1.52 ), 'c_List_Omap'( X, 'c_List_Olist_OCons'( Y, Z, T ), T, U ) ) ],
% 1.10/1.52 [ =( 'c_List_Omap'( X, 'c_List_Olist_OCons'( Y, Z, T ), T, U ),
% 1.10/1.52 'c_List_Olist_OCons'( hAPP( X, Y ), 'c_List_Omap'( X, Z, T, U ), U ) ) ]
% 1.10/1.52 ,
% 1.10/1.52 [ ~( =( 'c_Int_OBit0'( X ), 'c_Int_OBit1'( Y ) ) ) ],
% 1.10/1.52 [ ~( =( 'c_List_Omap'( 'c_FFT__Mirabelle_ODFT'(
% 1.10/1.52 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit0'(
% 1.10/1.52 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' ), 'v_a' ),
% 1.10/1.52 'c_List_Olist_OCons'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.10/1.52 'c_List_Olist_OCons'( 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 1.10/1.52 'c_List_Olist_OCons'( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.10/1.52 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'c_List_Olist_OCons'(
% 1.10/1.52 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.10/1.52 'c_Int_OPls' ) ), 'tc_nat' ), 'c_List_Olist_ONil'( 'tc_nat' ), 'tc_nat' )
% 1.10/1.52 , 'tc_nat' ), 'tc_nat' ), 'tc_nat' ), 'tc_nat', 'tc_Complex_Ocomplex' ),
% 1.10/1.52 'v_x' ) ) ],
% 1.10/1.52 [ 'class_Orderings_Opreorder'( 'tc_fun'( X, Y ) ), ~(
% 1.10/1.52 'class_Orderings_Opreorder'( Y ) ) ],
% 1.10/1.52 [ 'class_Orderings_Oorder'( 'tc_fun'( X, Y ) ), ~(
% 1.10/1.52 'class_Orderings_Oorder'( Y ) ) ],
% 1.10/1.52 [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( 'tc_nat' )
% 1.10/1.52 ],
% 1.10/1.52 [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( 'tc_nat'
% 1.10/1.52 ) ],
% 1.10/1.52 [ 'class_Ring__and__Field_Oordered__comm__semiring__strict'( 'tc_nat' )
% 1.10/1.52 ],
% 1.10/1.52 [ 'class_Ring__and__Field_Opordered__cancel__semiring'( 'tc_nat' ) ]
% 1.10/1.52 ,
% 1.10/1.52 [ 'class_Ring__and__Field_Oordered__semiring__strict'( 'tc_nat' ) ],
% 1.10/1.52 [ 'class_OrderedGroup_Opordered__ab__semigroup__add'( 'tc_nat' ) ],
% 1.10/1.52 [ 'class_OrderedGroup_Opordered__comm__monoid__add'( 'tc_nat' ) ],
% 1.10/1.52 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'( 'tc_nat' ) ],
% 1.10/1.52 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_nat' ) ],
% 1.10/1.52 [ 'class_Ring__and__Field_Opordered__semiring'( 'tc_nat' ) ],
% 1.10/1.52 [ 'class_Ring__and__Field_Oordered__semiring'( 'tc_nat' ) ],
% 1.10/1.52 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_nat' ) ],
% 1.10/1.52 [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_nat' ) ],
% 1.10/1.52 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_nat' ) ],
% 1.10/1.52 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_nat' ) ],
% 1.10/1.52 [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_nat' ) ],
% 1.10/1.52 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_nat' ) ],
% 1.10/1.52 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_nat' ) ],
% 1.10/1.52 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_nat' ) ],
% 1.10/1.52 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_nat' ) ],
% 1.10/1.52 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_nat' ) ],
% 1.10/1.52 [ 'class_Ring__and__Field_Osemiring__0'( 'tc_nat' ) ],
% 1.10/1.52 [ 'class_Ring__and__Field_Omult__mono1'( 'tc_nat' ) ],
% 1.10/1.52 [ 'class_Ring__and__Field_Omult__zero'( 'tc_nat' ) ],
% 1.10/1.52 [ 'class_Ring__and__Field_Omult__mono'( 'tc_nat' ) ],
% 1.10/1.52 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_nat' ) ],
% 1.10/1.52 [ 'class_Ring__and__Field_Osemiring'( 'tc_nat' ) ],
% 1.10/1.52 [ 'class_OrderedGroup_Omonoid__add'( 'tc_nat' ) ],
% 1.10/1.52 [ 'class_Divides_Osemiring__div'( 'tc_nat' ) ],
% 1.10/1.52 [ 'class_Orderings_Opreorder'( 'tc_nat' ) ],
% 1.10/1.52 [ 'class_Orderings_Olinorder'( 'tc_nat' ) ],
% 1.10/1.52 [ 'class_Orderings_Oorder'( 'tc_nat' ) ],
% 1.10/1.52 [ 'class_Power_Opower'( 'tc_nat' ) ],
% 1.10/1.52 [ 'class_Int_Onumber'( 'tc_nat' ) ],
% 1.10/1.52 [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'(
% 1.10/1.52 'tc_Int_Oint' ) ],
% 1.10/1.52 [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'(
% 1.10/1.52 'tc_Int_Oint' ) ],
% 1.10/1.52 [ 'class_Ring__and__Field_Oordered__comm__semiring__strict'(
% 1.10/1.52 'tc_Int_Oint' ) ],
% 1.10/1.52 [ 'class_Ring__and__Field_Opordered__cancel__semiring'( 'tc_Int_Oint' )
% 1.10/1.52 ],
% 1.10/1.52 [ 'class_Ring__and__Field_Oring__1__no__zero__divisors'( 'tc_Int_Oint' )
% 1.10/1.52 ],
% 1.10/1.52 [ 'class_Ring__and__Field_Oordered__semiring__strict'( 'tc_Int_Oint' ) ]
% 1.10/1.52 ,
% 1.10/1.52 [ 'class_OrderedGroup_Opordered__ab__semigroup__add'( 'tc_Int_Oint' ) ]
% 1.10/1.52 ,
% 1.10/1.52 [ 'class_OrderedGroup_Opordered__comm__monoid__add'( 'tc_Int_Oint' ) ]
% 1.10/1.52 ,
% 1.10/1.52 [ 'class_Ring__and__Field_Oring__no__zero__divisors'( 'tc_Int_Oint' ) ]
% 1.10/1.52 ,
% 1.10/1.52 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'( 'tc_Int_Oint' ) ]
% 1.10/1.52 ,
% 1.10/1.52 [ 'class_Ring__and__Field_Oordered__ring__strict'( 'tc_Int_Oint' ) ]
% 1.10/1.52 ,
% 1.10/1.52 [ 'class_OrderedGroup_Opordered__ab__group__add'( 'tc_Int_Oint' ) ],
% 1.10/1.52 [ 'class_OrderedGroup_Olordered__ab__group__add'( 'tc_Int_Oint' ) ],
% 1.10/1.52 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_Int_Oint' ) ],
% 1.10/1.52 [ 'class_Ring__and__Field_Opordered__semiring'( 'tc_Int_Oint' ) ],
% 1.10/1.52 [ 'class_Ring__and__Field_Oordered__semiring'( 'tc_Int_Oint' ) ],
% 1.10/1.52 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_Int_Oint' ) ],
% 1.10/1.52 [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_Int_Oint' ) ],
% 1.10/1.52 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_Int_Oint' ) ],
% 1.10/1.52 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_Int_Oint' ) ],
% 1.10/1.52 [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_Int_Oint' ) ],
% 1.10/1.52 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_Int_Oint' ) ],
% 1.10/1.52 [ 'class_Ring__and__Field_Opordered__ring'( 'tc_Int_Oint' ) ],
% 1.10/1.52 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_Int_Oint' ) ],
% 1.10/1.52 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_Int_Oint' ) ],
% 1.10/1.52 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_Int_Oint' ) ],
% 1.10/1.52 [ 'class_Ring__and__Field_Oordered__idom'( 'tc_Int_Oint' ) ],
% 1.10/1.52 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_Int_Oint' ) ],
% 1.10/1.52 [ 'class_Ring__and__Field_Osemiring__0'( 'tc_Int_Oint' ) ],
% 1.10/1.52 [ 'class_Ring__and__Field_Omult__mono1'( 'tc_Int_Oint' ) ],
% 1.10/1.52 [ 'class_OrderedGroup_Oab__group__add'( 'tc_Int_Oint' ) ],
% 1.10/1.52 [ 'class_Ring__and__Field_Omult__zero'( 'tc_Int_Oint' ) ],
% 1.10/1.52 [ 'class_Ring__and__Field_Omult__mono'( 'tc_Int_Oint' ) ],
% 1.10/1.52 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_Int_Oint' ) ],
% 1.10/1.52 [ 'class_Ring__and__Field_Osemiring'( 'tc_Int_Oint' ) ],
% 1.10/1.52 [ 'class_OrderedGroup_Omonoid__add'( 'tc_Int_Oint' ) ],
% 1.10/1.52 [ 'class_Divides_Osemiring__div'( 'tc_Int_Oint' ) ],
% 1.10/1.52 [ 'class_Ring__and__Field_Oidom'( 'tc_Int_Oint' ) ],
% 1.10/1.52 [ 'class_Orderings_Opreorder'( 'tc_Int_Oint' ) ],
% 1.10/1.52 [ 'class_Orderings_Olinorder'( 'tc_Int_Oint' ) ],
% 1.10/1.52 [ 'class_Orderings_Oorder'( 'tc_Int_Oint' ) ],
% 1.10/1.52 [ 'class_Int_Oring__char__0'( 'tc_Int_Oint' ) ],
% 1.10/1.52 [ 'class_Int_Onumber__ring'( 'tc_Int_Oint' ) ],
% 1.10/1.52 [ 'class_Power_Opower'( 'tc_Int_Oint' ) ],
% 1.10/1.52 [ 'class_Int_Onumber'( 'tc_Int_Oint' ) ],
% 1.10/1.52 [ 'class_Ring__and__Field_Oring__1__no__zero__divisors'(
% 1.10/1.52 'tc_Complex_Ocomplex' ) ],
% 1.10/1.52 [ 'class_Ring__and__Field_Oring__no__zero__divisors'(
% 1.10/1.52 'tc_Complex_Ocomplex' ) ],
% 1.10/1.52 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'(
% 1.10/1.52 'tc_Complex_Ocomplex' ) ],
% 1.10/1.52 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_Complex_Ocomplex' )
% 1.10/1.52 ],
% 1.10/1.52 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_Complex_Ocomplex' )
% 1.10/1.52 ],
% 1.10/1.52 [ 'class_Ring__and__Field_Odivision__by__zero'( 'tc_Complex_Ocomplex' )
% 1.10/1.52 ],
% 1.10/1.52 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_Complex_Ocomplex' ) ]
% 1.10/1.52 ,
% 1.10/1.52 [ 'class_RealVector_Oreal__normed__algebra'( 'tc_Complex_Ocomplex' ) ]
% 1.10/1.52 ,
% 1.10/1.52 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_Complex_Ocomplex' ) ]
% 1.10/1.52 ,
% 1.10/1.52 [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_Complex_Ocomplex' ) ]
% 1.10/1.52 ,
% 1.10/1.52 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_Complex_Ocomplex' ) ]
% 1.10/1.52 ,
% 1.10/1.52 [ 'class_Ring__and__Field_Odivision__ring'( 'tc_Complex_Ocomplex' ) ]
% 1.10/1.52 ,
% 1.10/1.52 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_Complex_Ocomplex' ) ]
% 1.10/1.52 ,
% 1.10/1.52 [ 'class_RealVector_Oreal__normed__field'( 'tc_Complex_Ocomplex' ) ]
% 1.10/1.52 ,
% 1.10/1.52 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_Complex_Ocomplex' ) ]
% 1.10/1.52 ,
% 1.10/1.52 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_Complex_Ocomplex' ) ]
% 1.10/1.52 ,
% 1.10/1.52 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_Complex_Ocomplex' ) ],
% 1.10/1.52 [ 'class_Ring__and__Field_Osemiring__0'( 'tc_Complex_Ocomplex' ) ],
% 1.10/1.52 [ 'class_OrderedGroup_Oab__group__add'( 'tc_Complex_Ocomplex' ) ],
% 1.10/1.52 [ 'class_Ring__and__Field_Omult__zero'( 'tc_Complex_Ocomplex' ) ],
% 1.10/1.52 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_Complex_Ocomplex' ) ],
% 1.10/1.52 [ 'class_Ring__and__Field_Osemiring'( 'tc_Complex_Ocomplex' ) ],
% 1.10/1.52 [ 'class_OrderedGroup_Omonoid__add'( 'tc_Complex_Ocomplex' ) ],
% 1.10/1.52 [ 'class_Ring__and__Field_Ofield'( 'tc_Complex_Ocomplex' ) ],
% 1.10/1.52 [ 'class_Ring__and__Field_Oidom'( 'tc_Complex_Ocomplex' ) ],
% 1.10/1.52 [ 'class_Int_Oring__char__0'( 'tc_Complex_Ocomplex' ) ],
% 1.10/1.52 [ 'class_Int_Onumber__ring'( 'tc_Complex_Ocomplex' ) ],
% 1.10/1.52 [ 'class_Power_Opower'( 'tc_Complex_Ocomplex' ) ],
% 1.10/1.52 [ 'class_Int_Onumber'( 'tc_Complex_Ocomplex' ) ],
% 1.10/1.52 [ 'c_fequal'( X, X, Y ) ],
% 1.10/1.52 [ =( X, Y ), ~( 'c_fequal'( X, Y, Z ) ) ]
% 1.10/1.52 ] .
% 1.10/1.52
% 1.10/1.52
% 1.10/1.52 percentage equality = 0.219323, percentage horn = 0.824615
% 1.10/1.52 This is a problem with some equality
% 1.10/1.52
% 1.10/1.52
% 1.10/1.52
% 1.10/1.52 Options Used:
% 1.10/1.52
% 1.10/1.52 useres = 1
% 1.10/1.52 useparamod = 1
% 1.10/1.52 useeqrefl = 1
% 1.10/1.52 useeqfact = 1
% 1.10/1.52 usefactor = 1
% 1.10/1.52 usesimpsplitting = 0
% 1.10/1.52 usesimpdemod = 5
% 1.10/1.52 usesimpres = 3
% 1.10/1.52
% 1.10/1.52 resimpinuse = 1000
% 1.10/1.52 resimpclauses = 20000
% 1.10/1.52 substype = eqrewr
% 1.10/1.52 backwardsubs = 1
% 1.10/1.52 selectoldest = 5
% 1.10/1.52
% 1.10/1.52 litorderings [0] = split
% 1.10/1.52 litorderings [1] = extend the termordering, first sorting on arguments
% 1.10/1.52
% 1.10/1.52 termordering = kbo
% 1.10/1.52
% 1.10/1.52 litapriori = 0
% 1.10/1.52 termapriori = 1
% 1.10/1.52 litaposteriori = 0
% 1.10/1.52 termaposteriori = 0
% 1.10/1.52 demodaposteriori = 0
% 1.10/1.52 ordereqreflfact = 0
% 1.10/1.52
% 1.10/1.52 litselect = negord
% 1.10/1.52
% 1.10/1.52 maxweight = 15
% 1.10/1.52 maxdepth = 30000
% 1.10/1.52 maxlength = 115
% 1.10/1.52 maxnrvars = 195
% 1.10/1.52 excuselevel = 1
% 1.10/1.52 increasemaxweight = 1
% 1.10/1.52
% 1.10/1.52 maxselected = 10000000
% 1.10/1.52 maxnrclauses = 10000000
% 1.10/1.52
% 1.10/1.52 showgenerated = 0
% 1.10/1.52 showkept = 0
% 1.10/1.52 showselected = 0
% 1.10/1.52 showdeleted = 0
% 1.10/1.52 showresimp = 1
% 1.10/1.52 showstatus = 2000
% 1.10/1.52
% 1.10/1.52 prologoutput = 1
% 1.10/1.52 nrgoals = 5000000
% 1.10/1.52 totalproof = 1
% 1.10/1.52
% 1.10/1.52 Symbols occurring in the translation:
% 1.10/1.52
% 1.10/1.52 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 1.10/1.52 . [1, 2] (w:1, o:136, a:1, s:1, b:0),
% 1.10/1.52 ! [4, 1] (w:0, o:69, a:1, s:1, b:0),
% 1.10/1.52 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.10/1.52 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.10/1.52 'class_Ring__and__Field_Oordered__field' [40, 1] (w:1, o:75, a:1, s:1
% 1.10/1.52 , b:0),
% 1.10/1.52 'class_Ring__and__Field_Odivision__by__zero' [41, 1] (w:1, o:78, a:1
% 1.10/1.52 , s:1, b:0),
% 1.10/1.52 'c_HOL_Otimes__class_Otimes' [43, 1] (w:1, o:79, a:1, s:1, b:0),
% 1.10/1.52 hAPP [45, 2] (w:1, o:161, a:1, s:1, b:0),
% 1.10/1.52 'c_lessequals' [47, 3] (w:1, o:169, a:1, s:1, b:0),
% 1.10/1.52 'c_HOL_Ozero__class_Ozero' [48, 1] (w:1, o:80, a:1, s:1, b:0),
% 1.10/1.52 'c_HOL_Oord__class_Oless' [49, 3] (w:1, o:170, a:1, s:1, b:0),
% 1.10/1.52 'c_HOL_Oinverse__class_Odivide' [50, 3] (w:1, o:171, a:1, s:1, b:0),
% 1.10/1.52
% 1.10/1.52 'class_Int_Onumber' [51, 1] (w:1, o:81, a:1, s:1, b:0),
% 1.10/1.52 'c_Int_Onumber__class_Onumber__of' [53, 2] (w:1, o:163, a:1, s:1, b:0
% 1.10/1.52 ),
% 1.10/1.52 'class_Power_Opower' [54, 1] (w:1, o:101, a:1, s:1, b:0),
% 1.10/1.52 'c_Power_Opower__class_Opower' [55, 1] (w:1, o:102, a:1, s:1, b:0),
% 1.10/1.52 'c_HOL_Oone__class_Oone' [56, 1] (w:1, o:103, a:1, s:1, b:0),
% 1.10/1.52 'c_Power_Opower_Opower' [57, 3] (w:1, o:172, a:1, s:1, b:0),
% 1.10/1.52 'class_Ring__and__Field_Oordered__ring__strict' [58, 1] (w:1, o:104
% 1.10/1.52 , a:1, s:1, b:0),
% 1.10/1.52 'c_HOL_Oplus__class_Oplus' [59, 1] (w:1, o:105, a:1, s:1, b:0),
% 1.10/1.52 'tc_nat' [62, 0] (w:1, o:26, a:1, s:1, b:0),
% 1.10/1.52 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le' [68, 1]
% 1.10/1.52 (w:1, o:82, a:1, s:1, b:0),
% 1.10/1.52 'class_OrderedGroup_Ocomm__monoid__add' [69, 1] (w:1, o:83, a:1, s:1
% 1.10/1.52 , b:0),
% 1.10/1.52 'c_Suc' [70, 1] (w:1, o:106, a:1, s:1, b:0),
% 1.10/1.52 'c_Divides_Odiv__class_Odiv' [72, 3] (w:1, o:173, a:1, s:1, b:0),
% 1.10/1.52 'class_Ring__and__Field_Oordered__semiring' [73, 1] (w:1, o:107, a:1
% 1.10/1.52 , s:1, b:0),
% 1.10/1.52 'class_Ring__and__Field_Oordered__semiring__strict' [74, 1] (w:1, o:
% 1.10/1.52 108, a:1, s:1, b:0),
% 1.10/1.52 'c_List_Olist_OCons' [76, 3] (w:1, o:174, a:1, s:1, b:0),
% 1.10/1.52 'c_List_Otake' [77, 3] (w:1, o:175, a:1, s:1, b:0),
% 1.10/1.52 'class_Ring__and__Field_Ocomm__semiring__1' [78, 1] (w:1, o:76, a:1
% 1.10/1.52 , s:1, b:0),
% 1.10/1.52 'class_OrderedGroup_Opordered__comm__monoid__add' [81, 1] (w:1, o:84
% 1.10/1.52 , a:1, s:1, b:0),
% 1.10/1.52 'class_Ring__and__Field_Oordered__idom' [82, 1] (w:1, o:109, a:1, s:1
% 1.10/1.52 , b:0),
% 1.10/1.52 'class_OrderedGroup_Olordered__ab__group__add' [83, 1] (w:1, o:85, a:
% 1.10/1.52 1, s:1, b:0),
% 1.10/1.52 'class_Ring__and__Field_Oordered__semidom' [84, 1] (w:1, o:110, a:1
% 1.10/1.52 , s:1, b:0),
% 1.10/1.52 'class_Divides_Osemiring__div' [85, 1] (w:1, o:111, a:1, s:1, b:0),
% 1.10/1.52 'c_Fact_Ofact__class_Ofact' [86, 2] (w:1, o:164, a:1, s:1, b:0),
% 1.10/1.52 'c_HOL_Oinverse__class_Oinverse' [91, 2] (w:1, o:162, a:1, s:1, b:0)
% 1.10/1.52 ,
% 1.10/1.52 'c_List_Oupt' [92, 2] (w:1, o:165, a:1, s:1, b:0),
% 1.10/1.52 'c_List_Olist_ONil' [93, 1] (w:1, o:112, a:1, s:1, b:0),
% 1.10/1.52 'class_Int_Onumber__ring' [94, 1] (w:1, o:113, a:1, s:1, b:0),
% 1.10/1.52 'tc_Int_Oint' [95, 0] (w:1, o:51, a:1, s:1, b:0),
% 1.10/1.52 'c_Divides_Odiv__class_Omod' [96, 3] (w:1, o:176, a:1, s:1, b:0),
% 1.10/1.52 'class_Ring__and__Field_Ofield' [97, 1] (w:1, o:114, a:1, s:1, b:0),
% 1.10/1.52
% 1.10/1.52 'class_Orderings_Oorder' [98, 1] (w:1, o:86, a:1, s:1, b:0),
% 5.13/5.51 'class_Orderings_Olinorder' [99, 1] (w:1, o:87, a:1, s:1, b:0),
% 5.13/5.51 hBOOL [101, 1] (w:1, o:115, a:1, s:1, b:0),
% 5.13/5.51 'class_OrderedGroup_Opordered__ab__semigroup__add' [102, 1] (w:1, o:
% 5.13/5.51 88, a:1, s:1, b:0),
% 5.13/5.51 'c_Groebner__Basis_Ogb__semiring' [108, 6] (w:1, o:181, a:1, s:1, b:0
% 5.13/5.51 ),
% 5.13/5.51 'class_OrderedGroup_Oab__semigroup__idem__mult' [109, 1] (w:1, o:89
% 5.13/5.51 , a:1, s:1, b:0),
% 5.13/5.51 'c_List_Onth' [110, 3] (w:1, o:177, a:1, s:1, b:0),
% 5.13/5.51 'class_Ring__and__Field_Omult__mono1' [111, 1] (w:1, o:116, a:1, s:1
% 5.13/5.51 , b:0),
% 5.13/5.51 'class_Ring__and__Field_Omult__mono' [112, 1] (w:1, o:117, a:1, s:1
% 5.13/5.51 , b:0),
% 5.13/5.51 'class_Ring__and__Field_Osemiring__0' [113, 1] (w:1, o:120, a:1, s:1
% 5.13/5.51 , b:0),
% 5.13/5.51 'class_Ring__and__Field_Oidom' [115, 1] (w:1, o:121, a:1, s:1, b:0),
% 5.13/5.51
% 5.13/5.51 'class_Ring__and__Field_Odivision__ring' [116, 1] (w:1, o:122, a:1
% 5.13/5.51 , s:1, b:0),
% 5.13/5.51 'class_OrderedGroup_Omonoid__mult' [117, 1] (w:1, o:90, a:1, s:1, b:0
% 5.13/5.51 ),
% 5.13/5.51 'class_Orderings_Opreorder' [118, 1] (w:1, o:91, a:1, s:1, b:0),
% 5.13/5.51 'class_OrderedGroup_Oab__group__add' [119, 1] (w:1, o:92, a:1, s:1
% 5.13/5.51 , b:0),
% 5.13/5.51 'class_OrderedGroup_Oab__semigroup__add' [120, 1] (w:1, o:93, a:1, s:
% 5.13/5.51 1, b:0),
% 5.13/5.51 'c_List_Odrop' [121, 3] (w:1, o:178, a:1, s:1, b:0),
% 5.13/5.51 'class_Ring__and__Field_Osemiring' [122, 1] (w:1, o:123, a:1, s:1, b:
% 5.13/5.51 0),
% 5.13/5.51 'class_Ring__and__Field_Opordered__ring' [125, 1] (w:1, o:125, a:1
% 5.13/5.51 , s:1, b:0),
% 5.13/5.51 'class_OrderedGroup_Ocomm__monoid__mult' [127, 1] (w:1, o:94, a:1, s:
% 5.13/5.51 1, b:0),
% 5.13/5.51 'class_Ring__and__Field_Opordered__cancel__semiring' [128, 1] (w:1
% 5.13/5.51 , o:126, a:1, s:1, b:0),
% 5.13/5.51 'class_OrderedGroup_Oab__semigroup__mult' [129, 1] (w:1, o:95, a:1
% 5.13/5.51 , s:1, b:0),
% 5.13/5.51 'class_RealVector_Oreal__normed__algebra' [130, 1] (w:1, o:127, a:1
% 5.13/5.51 , s:1, b:0),
% 5.13/5.51 'class_Ring__and__Field_Ocomm__semiring' [135, 1] (w:1, o:77, a:1, s:
% 5.13/5.51 1, b:0),
% 5.13/5.51 'class_Ring__and__Field_Opordered__semiring' [136, 1] (w:1, o:128, a:
% 5.13/5.51 1, s:1, b:0),
% 5.13/5.51 'class_Ring__and__Field_Oordered__comm__semiring__strict' [137, 1]
% 5.13/5.51 (w:1, o:124, a:1, s:1, b:0),
% 5.13/5.51 'class_RealVector_Oreal__normed__field' [138, 1] (w:1, o:129, a:1, s:
% 5.13/5.51 1, b:0),
% 5.13/5.51 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add' [139, 1]
% 5.13/5.51 (w:1, o:96, a:1, s:1, b:0),
% 5.13/5.51 'class_Ring__and__Field_Osemiring__1' [140, 1] (w:1, o:130, a:1, s:1
% 5.13/5.51 , b:0),
% 5.13/5.51 'c_Int_Oiszero' [141, 2] (w:1, o:166, a:1, s:1, b:0),
% 5.13/5.51 'class_Ring__and__Field_Oring__no__zero__divisors' [142, 1] (w:1, o:
% 5.13/5.51 118, a:1, s:1, b:0),
% 5.13/5.51 'class_Ring__and__Field_Omult__zero' [143, 1] (w:1, o:131, a:1, s:1
% 5.13/5.51 , b:0),
% 5.13/5.51 'class_Ring__and__Field_Oring__1__no__zero__divisors' [144, 1] (w:1
% 5.13/5.51 , o:119, a:1, s:1, b:0),
% 5.13/5.51 'class_Ring__and__Field_Ozero__neq__one' [145, 1] (w:1, o:132, a:1
% 5.13/5.51 , s:1, b:0),
% 5.13/5.51 'class_Ring__and__Field_Ono__zero__divisors' [146, 1] (w:1, o:74, a:1
% 5.13/5.51 , s:1, b:0),
% 5.13/5.51 'class_OrderedGroup_Omonoid__add' [147, 1] (w:1, o:97, a:1, s:1, b:0)
% 5.13/5.51 ,
% 5.13/5.51 'class_OrderedGroup_Ocancel__ab__semigroup__add' [148, 1] (w:1, o:98
% 5.13/5.51 , a:1, s:1, b:0),
% 5.13/5.51 'class_OrderedGroup_Ocancel__semigroup__add' [149, 1] (w:1, o:99, a:1
% 5.13/5.51 , s:1, b:0),
% 5.13/5.51 'c_Int_OBit1' [155, 1] (w:1, o:134, a:1, s:1, b:0),
% 5.13/5.51 'c_Int_OPls' [158, 0] (w:1, o:58, a:1, s:1, b:0),
% 5.13/5.51 'c_Int_OBit0' [159, 1] (w:1, o:133, a:1, s:1, b:0),
% 5.13/5.51 'c_List_Omap' [165, 4] (w:1, o:180, a:1, s:1, b:0),
% 5.13/5.51 'c_List_Osko__List__XCons__eq__map__conv__1__1' [166, 6] (w:1, o:182
% 5.13/5.51 , a:1, s:1, b:0),
% 5.13/5.51 'c_List_Osko__List__XCons__eq__map__conv__1__2' [167, 6] (w:1, o:183
% 5.13/5.51 , a:1, s:1, b:0),
% 5.13/5.51 'c_List_Osko__List__XCons__eq__map__D__1__1' [168, 6] (w:1, o:184, a:
% 5.13/5.51 1, s:1, b:0),
% 5.13/5.51 'c_List_Osko__List__XCons__eq__map__D__1__2' [169, 6] (w:1, o:185, a:
% 5.13/5.51 1, s:1, b:0),
% 5.13/5.51 'c_List_Osko__List__Xmap__eq__Cons__conv__1__1' [170, 6] (w:1, o:186
% 5.13/5.51 , a:1, s:1, b:0),
% 5.13/5.51 'c_List_Osko__List__Xmap__eq__Cons__conv__1__2' [171, 6] (w:1, o:187
% 5.13/5.51 , a:1, s:1, b:0),
% 5.13/5.51 'c_List_Osko__List__Xmap__eq__Cons__D__1__1' [172, 6] (w:1, o:188, a:
% 24.02/24.39 1, s:1, b:0),
% 24.02/24.39 'c_List_Osko__List__Xmap__eq__Cons__D__1__2' [173, 6] (w:1, o:189, a:
% 24.02/24.39 1, s:1, b:0),
% 24.02/24.39 'class_Int_Oring__char__0' [174, 1] (w:1, o:135, a:1, s:1, b:0),
% 24.02/24.39 'class_OrderedGroup_Opordered__ab__group__add' [175, 1] (w:1, o:100
% 24.02/24.39 , a:1, s:1, b:0),
% 24.02/24.39 'v_a' [180, 0] (w:1, o:62, a:1, s:1, b:0),
% 24.02/24.39 'c_FFT__Mirabelle_ODFT' [181, 2] (w:1, o:167, a:1, s:1, b:0),
% 24.02/24.39 'tc_Complex_Ocomplex' [182, 0] (w:1, o:63, a:1, s:1, b:0),
% 24.02/24.39 'v_x' [183, 0] (w:1, o:64, a:1, s:1, b:0),
% 24.02/24.39 'tc_fun' [186, 2] (w:1, o:168, a:1, s:1, b:0),
% 24.02/24.39 'c_fequal' [187, 3] (w:1, o:179, a:1, s:1, b:0).
% 24.02/24.39
% 24.02/24.39
% 24.02/24.39 Starting Search:
% 24.02/24.39
% 24.02/24.39 Resimplifying inuse:
% 24.02/24.39 Done
% 24.02/24.39
% 24.02/24.39
% 24.02/24.39 Intermediate Status:
% 24.02/24.39 Generated: 4057
% 24.02/24.39 Kept: 2004
% 24.02/24.39 Inuse: 160
% 24.02/24.39 Deleted: 6
% 24.02/24.39 Deletedinuse: 0
% 24.02/24.39
% 24.02/24.39 Resimplifying inuse:
% 24.02/24.39 Done
% 24.02/24.39
% 24.02/24.39 Resimplifying inuse:
% 24.02/24.39 Done
% 24.02/24.39
% 24.02/24.39
% 24.02/24.39 Intermediate Status:
% 24.02/24.39 Generated: 8157
% 24.02/24.39 Kept: 4033
% 24.02/24.39 Inuse: 245
% 24.02/24.39 Deleted: 11
% 24.02/24.39 Deletedinuse: 0
% 24.02/24.39
% 24.02/24.39 Resimplifying inuse:
% 24.02/24.39 Done
% 24.02/24.39
% 24.02/24.39 Resimplifying inuse:
% 24.02/24.39 Done
% 24.02/24.39
% 24.02/24.39
% 24.02/24.39 Intermediate Status:
% 24.02/24.39 Generated: 16833
% 24.02/24.39 Kept: 6456
% 24.02/24.39 Inuse: 294
% 24.02/24.39 Deleted: 12
% 24.02/24.39 Deletedinuse: 0
% 24.02/24.39
% 24.02/24.39 Resimplifying inuse:
% 24.02/24.39 Done
% 24.02/24.39
% 24.02/24.39 Resimplifying inuse:
% 24.02/24.39 Done
% 24.02/24.39
% 24.02/24.39
% 24.02/24.39 Intermediate Status:
% 24.02/24.39 Generated: 23970
% 24.02/24.39 Kept: 8491
% 24.02/24.39 Inuse: 411
% 24.02/24.39 Deleted: 20
% 24.02/24.39 Deletedinuse: 0
% 24.02/24.39
% 24.02/24.39 Resimplifying inuse:
% 24.02/24.39 Done
% 24.02/24.39
% 24.02/24.39 Resimplifying inuse:
% 24.02/24.39 Done
% 24.02/24.39
% 24.02/24.39
% 24.02/24.39 Intermediate Status:
% 24.02/24.39 Generated: 31776
% 24.02/24.39 Kept: 11271
% 24.02/24.39 Inuse: 477
% 24.02/24.39 Deleted: 21
% 24.02/24.39 Deletedinuse: 0
% 24.02/24.39
% 24.02/24.39 Resimplifying inuse:
% 24.02/24.39 Done
% 24.02/24.39
% 24.02/24.39 Resimplifying inuse:
% 24.02/24.39 Done
% 24.02/24.39
% 24.02/24.39
% 24.02/24.39 Intermediate Status:
% 24.02/24.39 Generated: 39337
% 24.02/24.39 Kept: 13282
% 24.02/24.39 Inuse: 540
% 24.02/24.39 Deleted: 28
% 24.02/24.39 Deletedinuse: 0
% 24.02/24.39
% 24.02/24.39 Resimplifying inuse:
% 24.02/24.39 Done
% 24.02/24.39
% 24.02/24.39 Resimplifying inuse:
% 24.02/24.39 Done
% 24.02/24.39
% 24.02/24.39
% 24.02/24.39 Intermediate Status:
% 24.02/24.39 Generated: 46793
% 24.02/24.39 Kept: 15291
% 24.02/24.39 Inuse: 617
% 24.02/24.39 Deleted: 34
% 24.02/24.39 Deletedinuse: 0
% 24.02/24.39
% 24.02/24.39 Resimplifying inuse:
% 24.02/24.39 Done
% 24.02/24.39
% 24.02/24.39 Resimplifying inuse:
% 24.02/24.39 Done
% 24.02/24.39
% 24.02/24.39
% 24.02/24.39 Intermediate Status:
% 24.02/24.39 Generated: 57755
% 24.02/24.39 Kept: 17300
% 24.02/24.39 Inuse: 706
% 24.02/24.39 Deleted: 38
% 24.02/24.39 Deletedinuse: 0
% 24.02/24.39
% 24.02/24.39 Resimplifying inuse:
% 24.02/24.39 Done
% 24.02/24.39
% 24.02/24.39 Resimplifying inuse:
% 24.02/24.39 Done
% 24.02/24.39
% 24.02/24.39
% 24.02/24.39 Intermediate Status:
% 24.02/24.39 Generated: 65868
% 24.02/24.39 Kept: 19346
% 24.02/24.39 Inuse: 772
% 24.02/24.39 Deleted: 40
% 24.02/24.39 Deletedinuse: 1
% 24.02/24.39
% 24.02/24.39 Resimplifying inuse:
% 24.02/24.39 Done
% 24.02/24.39
% 24.02/24.39 Resimplifying clauses:
% 24.02/24.39 Done
% 24.02/24.39
% 24.02/24.39 Resimplifying inuse:
% 24.02/24.39 Done
% 24.02/24.39
% 24.02/24.39
% 24.02/24.39 Intermediate Status:
% 24.02/24.39 Generated: 72994
% 24.02/24.39 Kept: 21352
% 24.02/24.39 Inuse: 802
% 24.02/24.39 Deleted: 394
% 24.02/24.39 Deletedinuse: 1
% 24.02/24.39
% 24.02/24.39 Resimplifying inuse:
% 24.02/24.39 Done
% 24.02/24.39
% 24.02/24.39 Resimplifying inuse:
% 24.02/24.39 Done
% 24.02/24.39
% 24.02/24.39
% 24.02/24.39 Intermediate Status:
% 24.02/24.39 Generated: 82182
% 24.02/24.39 Kept: 23864
% 24.02/24.39 Inuse: 842
% 24.02/24.39 Deleted: 395
% 24.02/24.39 Deletedinuse: 2
% 24.02/24.39
% 24.02/24.39 Resimplifying inuse:
% 24.02/24.39 Done
% 24.02/24.39
% 24.02/24.39 Resimplifying inuse:
% 24.02/24.39 Done
% 24.02/24.39
% 24.02/24.39
% 24.02/24.39 Intermediate Status:
% 24.02/24.39 Generated: 90461
% 24.02/24.39 Kept: 25927
% 24.02/24.39 Inuse: 862
% 24.02/24.39 Deleted: 396
% 24.02/24.39 Deletedinuse: 3
% 24.02/24.39
% 24.02/24.39 Resimplifying inuse:
% 24.02/24.39 Done
% 24.02/24.39
% 24.02/24.39
% 24.02/24.39 Intermediate Status:
% 24.02/24.39 Generated: 109505
% 24.02/24.39 Kept: 28531
% 24.02/24.39 Inuse: 887
% 24.02/24.39 Deleted: 396
% 24.02/24.39 Deletedinuse: 3
% 24.02/24.39
% 24.02/24.39 Resimplifying inuse:
% 24.02/24.39 Done
% 24.02/24.39
% 24.02/24.39 Resimplifying inuse:
% 24.02/24.39 Done
% 24.02/24.39
% 24.02/24.39
% 24.02/24.39 Intermediate Status:
% 24.02/24.39 Generated: 118189
% 24.02/24.39 Kept: 30720
% 24.02/24.39 Inuse: 897
% 24.02/24.39 Deleted: 396
% 24.02/24.39 Deletedinuse: 3
% 24.02/24.39
% 24.02/24.39 Resimplifying inuse:
% 24.02/24.39 Done
% 24.02/24.39
% 24.02/24.39 Resimplifying inuse:
% 24.02/24.39 Done
% 24.02/24.39
% 24.02/24.39
% 24.02/24.39 Intermediate Status:
% 24.02/24.39 Generated: 125758
% 24.02/24.39 Kept: 32945
% 24.02/24.39 Inuse: 922
% 24.02/24.39 Deleted: 396
% 24.02/24.39 Deletedinuse: 3
% 24.02/24.39
% 24.02/24.39 Resimplifying inuse:
% 24.02/24.39 Done
% 24.02/24.39
% 24.02/24.39 Resimplifying inuse:
% 24.02/24.39 Done
% 24.02/24.39
% 24.02/24.39
% 24.02/24.39 Intermediate Status:
% 24.02/24.39 Generated: 134493
% 24.02/24.39 Kept: 35119
% 24.02/24.39 Inuse: 962
% 24.02/24.39 Deleted: 396
% 24.02/24.39 Deletedinuse: 3
% 24.02/24.39
% 24.02/24.39 Resimplifying inuse:
% 24.02/24.39 Done
% 24.02/24.39
% 24.02/24.39 Resimplifying inuse:
% 24.02/24.39 Done
% 24.02/24.39
% 24.02/24.39
% 24.02/24.39 Intermediate Status:
% 24.02/24.39 Generated: 146543
% 24.02/24.39 Kept: 37128
% 24.02/24.39 Inuse: 991
% 24.02/24.39 Deleted: 396
% 24.02/24.39 Deletedinuse: 3
% 24.02/24.39
% 24.02/24.39 Resimplifying inuse:
% 24.02/24.39 Done
% 24.02/24.39
% 24.02/24.39
% 24.02/24.39 Intermediate Status:
% 24.02/24.39 Generated: 155954
% 24.02/24.39 Kept: 39567
% 24.02/24.39 Inuse: 1002
% 24.02/24.39 Deleted: 396
% 24.02/24.39 Deletedinuse: 3
% 24.02/24.39
% 24.02/24.39 Resimplifying inuse:
% 24.02/24.39 Done
% 24.02/24.39
% 24.02/24.39 Resimplifying inuse:
% 24.02/24.39 Done
% 24.02/24.39
% 24.02/24.39 Resimplifying clauses:
% 24.02/24.39 Done
% 24.02/24.39
% 24.02/24.39
% 24.02/24.39 Intermediate Status:
% 24.02/24.39 Generated: 165330
% 24.02/24.39 Kept: 41765
% 24.02/24.39 Inuse: 1012
% 24.02/24.39 Deleted: 625
% 24.02/24.39 Deletedinuse: 3
% 24.02/24.39
% 24.02/24.39 Resimplifying inuse:
% 24.02/24.39 Done
% 24.02/24.39
% 24.02/24.39
% 24.02/24.39 Intermediate Status:
% 24.02/24.39 Generated: 174142
% 24.02/24.39 Kept: 43812
% 24.02/24.39 Inuse: 1047
% 24.02/24.39 Deleted: 625
% 24.02/24.39 Deletedinuse: 3
% 24.02/24.39
% 24.02/24.39 Resimplifying inuse:
% 24.02/24.39 Done
% 24.02/24.39
% 24.02/24.39 Resimplifying inuse:
% 24.02/24.39 Done
% 24.02/24.39
% 24.02/24.39
% 24.02/24.39 Intermediate Status:
% 24.02/24.39 Generated: 184755
% 24.02/24.39 Kept: 45829
% 24.02/24.39 Inuse: 1087
% 65.13/65.49 Deleted: 625
% 65.13/65.49 Deletedinuse: 3
% 65.13/65.49
% 65.13/65.49 Resimplifying inuse:
% 65.13/65.49 Done
% 65.13/65.49
% 65.13/65.49 Resimplifying inuse:
% 65.13/65.49 Done
% 65.13/65.49
% 65.13/65.49
% 65.13/65.49 Intermediate Status:
% 65.13/65.49 Generated: 194771
% 65.13/65.49 Kept: 48468
% 65.13/65.49 Inuse: 1116
% 65.13/65.49 Deleted: 625
% 65.13/65.49 Deletedinuse: 3
% 65.13/65.49
% 65.13/65.49 Resimplifying inuse:
% 65.13/65.49 Done
% 65.13/65.49
% 65.13/65.49 Resimplifying inuse:
% 65.13/65.49 Done
% 65.13/65.49
% 65.13/65.49
% 65.13/65.49 Intermediate Status:
% 65.13/65.49 Generated: 202443
% 65.13/65.49 Kept: 50478
% 65.13/65.49 Inuse: 1131
% 65.13/65.49 Deleted: 625
% 65.13/65.49 Deletedinuse: 3
% 65.13/65.49
% 65.13/65.49 Resimplifying inuse:
% 65.13/65.49 Done
% 65.13/65.49
% 65.13/65.49
% 65.13/65.49 Intermediate Status:
% 65.13/65.49 Generated: 218006
% 65.13/65.49 Kept: 53011
% 65.13/65.49 Inuse: 1151
% 65.13/65.49 Deleted: 629
% 65.13/65.49 Deletedinuse: 6
% 65.13/65.49
% 65.13/65.49 Resimplifying inuse:
% 65.13/65.49 Done
% 65.13/65.49
% 65.13/65.49
% 65.13/65.49 Intermediate Status:
% 65.13/65.49 Generated: 229952
% 65.13/65.49 Kept: 56317
% 65.13/65.49 Inuse: 1155
% 65.13/65.49 Deleted: 629
% 65.13/65.49 Deletedinuse: 6
% 65.13/65.49
% 65.13/65.49 Resimplifying inuse:
% 65.13/65.49 Done
% 65.13/65.49
% 65.13/65.49 Resimplifying inuse:
% 65.13/65.49 Done
% 65.13/65.49
% 65.13/65.49
% 65.13/65.49 Intermediate Status:
% 65.13/65.49 Generated: 247522
% 65.13/65.49 Kept: 58790
% 65.13/65.49 Inuse: 1161
% 65.13/65.49 Deleted: 629
% 65.13/65.49 Deletedinuse: 6
% 65.13/65.49
% 65.13/65.49 Resimplifying inuse:
% 65.13/65.49 Done
% 65.13/65.49
% 65.13/65.49 Resimplifying inuse:
% 65.13/65.49 Done
% 65.13/65.49
% 65.13/65.49
% 65.13/65.49 Intermediate Status:
% 65.13/65.49 Generated: 258704
% 65.13/65.49 Kept: 61013
% 65.13/65.49 Inuse: 1191
% 65.13/65.49 Deleted: 629
% 65.13/65.49 Deletedinuse: 6
% 65.13/65.49
% 65.13/65.49 Resimplifying inuse:
% 65.13/65.49 Done
% 65.13/65.49
% 65.13/65.49 Resimplifying clauses:
% 65.13/65.49 Done
% 65.13/65.49
% 65.13/65.49
% 65.13/65.49 Intermediate Status:
% 65.13/65.49 Generated: 269384
% 65.13/65.49 Kept: 63466
% 65.13/65.49 Inuse: 1216
% 65.13/65.49 Deleted: 1090
% 65.13/65.49 Deletedinuse: 6
% 65.13/65.49
% 65.13/65.49 Resimplifying inuse:
% 65.13/65.49 Done
% 65.13/65.49
% 65.13/65.49 Resimplifying inuse:
% 65.13/65.49 Done
% 65.13/65.49
% 65.13/65.49
% 65.13/65.49 Intermediate Status:
% 65.13/65.49 Generated: 278871
% 65.13/65.49 Kept: 65641
% 65.13/65.49 Inuse: 1231
% 65.13/65.49 Deleted: 1090
% 65.13/65.49 Deletedinuse: 6
% 65.13/65.49
% 65.13/65.49 Resimplifying inuse:
% 65.13/65.49 Done
% 65.13/65.49
% 65.13/65.49 Resimplifying inuse:
% 65.13/65.49 Done
% 65.13/65.49
% 65.13/65.49
% 65.13/65.49 Intermediate Status:
% 65.13/65.49 Generated: 295912
% 65.13/65.49 Kept: 67654
% 65.13/65.49 Inuse: 1247
% 65.13/65.49 Deleted: 1091
% 65.13/65.49 Deletedinuse: 7
% 65.13/65.49
% 65.13/65.49 Resimplifying inuse:
% 65.13/65.49 Done
% 65.13/65.49
% 65.13/65.49 Resimplifying inuse:
% 65.13/65.49 Done
% 65.13/65.49
% 65.13/65.49
% 65.13/65.49 Intermediate Status:
% 65.13/65.49 Generated: 304076
% 65.13/65.49 Kept: 69658
% 65.13/65.49 Inuse: 1274
% 65.13/65.49 Deleted: 1091
% 65.13/65.49 Deletedinuse: 7
% 65.13/65.49
% 65.13/65.49 Resimplifying inuse:
% 65.13/65.49 Done
% 65.13/65.49
% 65.13/65.49
% 65.13/65.49 Intermediate Status:
% 65.13/65.49 Generated: 312655
% 65.13/65.49 Kept: 71853
% 65.13/65.49 Inuse: 1296
% 65.13/65.49 Deleted: 1091
% 65.13/65.49 Deletedinuse: 7
% 65.13/65.49
% 65.13/65.49 Resimplifying inuse:
% 65.13/65.49 Done
% 65.13/65.49
% 65.13/65.49 Resimplifying inuse:
% 65.13/65.49 Done
% 65.13/65.49
% 65.13/65.49
% 65.13/65.49 Intermediate Status:
% 65.13/65.49 Generated: 322171
% 65.13/65.49 Kept: 74018
% 65.13/65.49 Inuse: 1326
% 65.13/65.49 Deleted: 1091
% 65.13/65.49 Deletedinuse: 7
% 65.13/65.49
% 65.13/65.49 Resimplifying inuse:
% 65.13/65.49 Done
% 65.13/65.49
% 65.13/65.49 Resimplifying inuse:
% 65.13/65.49 Done
% 65.13/65.49
% 65.13/65.49
% 65.13/65.49 Intermediate Status:
% 65.13/65.49 Generated: 332283
% 65.13/65.49 Kept: 76315
% 65.13/65.49 Inuse: 1361
% 65.13/65.49 Deleted: 1091
% 65.13/65.49 Deletedinuse: 7
% 65.13/65.49
% 65.13/65.49 Resimplifying inuse:
% 65.13/65.49 Done
% 65.13/65.49
% 65.13/65.49
% 65.13/65.49 Intermediate Status:
% 65.13/65.49 Generated: 344051
% 65.13/65.49 Kept: 79465
% 65.13/65.49 Inuse: 1391
% 65.13/65.49 Deleted: 1091
% 65.13/65.49 Deletedinuse: 7
% 65.13/65.49
% 65.13/65.49 Resimplifying inuse:
% 65.13/65.49 Done
% 65.13/65.49
% 65.13/65.49
% 65.13/65.49 Intermediate Status:
% 65.13/65.49 Generated: 350368
% 65.13/65.49 Kept: 83425
% 65.13/65.49 Inuse: 1396
% 65.13/65.49 Deleted: 1093
% 65.13/65.49 Deletedinuse: 9
% 65.13/65.49
% 65.13/65.49 Resimplifying inuse:
% 65.13/65.49 Done
% 65.13/65.49
% 65.13/65.49 Resimplifying clauses:
% 65.13/65.49 Done
% 65.13/65.49
% 65.13/65.49
% 65.13/65.49 Intermediate Status:
% 65.13/65.49 Generated: 357067
% 65.13/65.49 Kept: 86444
% 65.13/65.49 Inuse: 1404
% 65.13/65.49 Deleted: 1464
% 65.13/65.49 Deletedinuse: 9
% 65.13/65.49
% 65.13/65.49 Resimplifying inuse:
% 65.13/65.49 Done
% 65.13/65.49
% 65.13/65.49 Resimplifying inuse:
% 65.13/65.49 Done
% 65.13/65.49
% 65.13/65.49
% 65.13/65.49 Intermediate Status:
% 65.13/65.49 Generated: 369317
% 65.13/65.49 Kept: 88461
% 65.13/65.49 Inuse: 1450
% 65.13/65.49 Deleted: 1464
% 65.13/65.49 Deletedinuse: 9
% 65.13/65.49
% 65.13/65.49 Resimplifying inuse:
% 65.13/65.49 Done
% 65.13/65.49
% 65.13/65.49 Resimplifying inuse:
% 65.13/65.49 Done
% 65.13/65.49
% 65.13/65.49
% 65.13/65.49 Intermediate Status:
% 65.13/65.49 Generated: 428169
% 65.13/65.49 Kept: 92675
% 65.13/65.49 Inuse: 1461
% 65.13/65.49 Deleted: 1464
% 65.13/65.49 Deletedinuse: 9
% 65.13/65.49
% 65.13/65.49 Resimplifying inuse:
% 65.13/65.49 Done
% 65.13/65.49
% 65.13/65.49 Resimplifying inuse:
% 65.13/65.49 Done
% 65.13/65.49
% 65.13/65.49
% 65.13/65.49 Intermediate Status:
% 65.13/65.49 Generated: 443306
% 65.13/65.49 Kept: 95878
% 65.13/65.49 Inuse: 1471
% 65.13/65.49 Deleted: 1464
% 65.13/65.49 Deletedinuse: 9
% 65.13/65.49
% 65.13/65.49 Resimplifying inuse:
% 65.13/65.49 Done
% 65.13/65.49
% 65.13/65.49
% 65.13/65.49 Intermediate Status:
% 65.13/65.49 Generated: 464318
% 65.13/65.49 Kept: 98819
% 65.13/65.49 Inuse: 1476
% 65.13/65.49 Deleted: 1464
% 65.13/65.49 Deletedinuse: 9
% 65.13/65.49
% 65.13/65.49 Resimplifying inuse:
% 65.13/65.49 Done
% 65.13/65.49
% 65.13/65.49
% 65.13/65.49 Intermediate Status:
% 65.13/65.49 Generated: 485870
% 65.13/65.49 Kept: 101769
% 65.13/65.49 Inuse: 1481
% 65.13/65.49 Deleted: 1464
% 65.13/65.49 Deletedinuse: 9
% 65.13/65.49
% 65.13/65.49 Resimplifying inuse:
% 65.13/65.49 Done
% 65.13/65.49
% 65.13/65.49
% 65.13/65.49 Intermediate Status:
% 65.13/65.49 Generated: 496716
% 65.13/65.49 Kept: 103831
% 65.13/65.49 Inuse: 1496
% 65.13/65.49 Deleted: 1464
% 65.13/65.49 Deletedinuse: 9
% 65.13/65.49
% 65.13/65.49 Resimplifying inuse:
% 65.13/65.49 Done
% 65.13/65.49
% 65.13/65.49 Resimplifying clauses:
% 65.13/65.49 Done
% 65.13/65.49
% 65.13/65.49 Resimplifying inuse:
% 65.13/65.49 Done
% 65.13/65.49
% 65.13/65.49
% 65.13/65.49 Intermediate Status:
% 65.13/65.49 Generated: 507740
% 65.13/65.49 Kept: 105833
% 65.13/65.49 Inuse: 1510
% 65.13/65.49 Deleted: 1768
% 65.13/65.49 Deletedinuse: 10
% 65.13/65.49
% 65.13/65.49 Resimplifying inuse:
% 65.13/65.49 Done
% 65.13/65.49
% 65.13/65.49 Resimplifying inuse:
% 65.13/65.49 Done
% 65.13/65.49
% 65.13/65.49
% 65.13/65.49 Intermediate Status:
% 65.13/65.49 Generated: 523884
% 65.13/65.49 Kept: 110777
% 65.13/65.49 Inuse: 1543
% 65.13/65.49 Deleted: 1768
% 65.13/65.49 Deletedinuse: 10
% 65.13/65.49
% 65.13/65.49 Resimplifying inuse:
% 65.13/65.49 Done
% 65.13/65.49
% 65.13/65.49 Resimplifying inuse:
% 65.13/65.49 Done
% 65.13/65.49
% 65.13/65.49
% 65.13/65.49 Intermediate Status:
% 65.13/65.49 Generated: 535513
% 65.13/65.49 Kept: 112952
% 126.87/127.30 Inuse: 1566
% 126.87/127.30 Deleted: 1768
% 126.87/127.30 Deletedinuse: 10
% 126.87/127.30
% 126.87/127.30 Resimplifying inuse:
% 126.87/127.30 Done
% 126.87/127.30
% 126.87/127.30 Resimplifying inuse:
% 126.87/127.30 Done
% 126.87/127.30
% 126.87/127.30
% 126.87/127.30 Intermediate Status:
% 126.87/127.30 Generated: 544553
% 126.87/127.30 Kept: 114956
% 126.87/127.30 Inuse: 1585
% 126.87/127.30 Deleted: 1768
% 126.87/127.30 Deletedinuse: 10
% 126.87/127.30
% 126.87/127.30 Resimplifying inuse:
% 126.87/127.30 Done
% 126.87/127.30
% 126.87/127.30 Resimplifying inuse:
% 126.87/127.30 Done
% 126.87/127.30
% 126.87/127.30
% 126.87/127.30 Intermediate Status:
% 126.87/127.30 Generated: 554526
% 126.87/127.30 Kept: 116970
% 126.87/127.30 Inuse: 1605
% 126.87/127.30 Deleted: 1768
% 126.87/127.30 Deletedinuse: 10
% 126.87/127.30
% 126.87/127.30
% 126.87/127.30 Intermediate Status:
% 126.87/127.30 Generated: 586627
% 126.87/127.30 Kept: 120775
% 126.87/127.30 Inuse: 1611
% 126.87/127.30 Deleted: 1768
% 126.87/127.30 Deletedinuse: 10
% 126.87/127.30
% 126.87/127.30 Resimplifying inuse:
% 126.87/127.30 Done
% 126.87/127.30
% 126.87/127.30 Resimplifying inuse:
% 126.87/127.30 Done
% 126.87/127.30
% 126.87/127.30
% 126.87/127.30 Intermediate Status:
% 126.87/127.30 Generated: 604428
% 126.87/127.30 Kept: 122796
% 126.87/127.30 Inuse: 1636
% 126.87/127.30 Deleted: 1768
% 126.87/127.30 Deletedinuse: 10
% 126.87/127.30
% 126.87/127.30 Resimplifying inuse:
% 126.87/127.30 Done
% 126.87/127.30
% 126.87/127.30 Resimplifying clauses:
% 126.87/127.30 Done
% 126.87/127.30
% 126.87/127.30 Resimplifying inuse:
% 126.87/127.30 Done
% 126.87/127.30
% 126.87/127.30
% 126.87/127.30 Intermediate Status:
% 126.87/127.30 Generated: 613788
% 126.87/127.30 Kept: 125547
% 126.87/127.30 Inuse: 1651
% 126.87/127.30 Deleted: 2019
% 126.87/127.30 Deletedinuse: 10
% 126.87/127.30
% 126.87/127.30 Resimplifying inuse:
% 126.87/127.30 Done
% 126.87/127.30
% 126.87/127.30 Resimplifying inuse:
% 126.87/127.30 Done
% 126.87/127.30
% 126.87/127.30
% 126.87/127.30 Intermediate Status:
% 126.87/127.30 Generated: 621278
% 126.87/127.30 Kept: 128015
% 126.87/127.30 Inuse: 1661
% 126.87/127.30 Deleted: 2019
% 126.87/127.30 Deletedinuse: 10
% 126.87/127.30
% 126.87/127.30 Resimplifying inuse:
% 126.87/127.30 Done
% 126.87/127.30
% 126.87/127.30 Resimplifying inuse:
% 126.87/127.30 Done
% 126.87/127.30
% 126.87/127.30
% 126.87/127.30 Intermediate Status:
% 126.87/127.30 Generated: 631167
% 126.87/127.30 Kept: 130143
% 126.87/127.30 Inuse: 1681
% 126.87/127.30 Deleted: 2019
% 126.87/127.30 Deletedinuse: 10
% 126.87/127.30
% 126.87/127.30 Resimplifying inuse:
% 126.87/127.30 Done
% 126.87/127.30
% 126.87/127.30
% 126.87/127.30 Intermediate Status:
% 126.87/127.30 Generated: 639742
% 126.87/127.30 Kept: 134027
% 126.87/127.30 Inuse: 1687
% 126.87/127.30 Deleted: 2019
% 126.87/127.30 Deletedinuse: 10
% 126.87/127.30
% 126.87/127.30 Resimplifying inuse:
% 126.87/127.30 Done
% 126.87/127.30
% 126.87/127.30 Resimplifying inuse:
% 126.87/127.30 Done
% 126.87/127.30
% 126.87/127.30
% 126.87/127.30 Intermediate Status:
% 126.87/127.30 Generated: 648983
% 126.87/127.30 Kept: 136055
% 126.87/127.30 Inuse: 1703
% 126.87/127.30 Deleted: 2019
% 126.87/127.30 Deletedinuse: 10
% 126.87/127.30
% 126.87/127.30 Resimplifying inuse:
% 126.87/127.30 Done
% 126.87/127.30
% 126.87/127.30 Resimplifying inuse:
% 126.87/127.30 Done
% 126.87/127.30
% 126.87/127.30
% 126.87/127.30 Intermediate Status:
% 126.87/127.30 Generated: 658223
% 126.87/127.30 Kept: 138074
% 126.87/127.30 Inuse: 1716
% 126.87/127.30 Deleted: 2019
% 126.87/127.30 Deletedinuse: 10
% 126.87/127.30
% 126.87/127.30 Resimplifying inuse:
% 126.87/127.30 Done
% 126.87/127.30
% 126.87/127.30
% 126.87/127.30 Intermediate Status:
% 126.87/127.30 Generated: 668992
% 126.87/127.30 Kept: 140331
% 126.87/127.30 Inuse: 1731
% 126.87/127.30 Deleted: 2019
% 126.87/127.30 Deletedinuse: 10
% 126.87/127.30
% 126.87/127.30 Resimplifying inuse:
% 126.87/127.30 Done
% 126.87/127.30
% 126.87/127.30 Resimplifying inuse:
% 126.87/127.30 Done
% 126.87/127.30
% 126.87/127.30
% 126.87/127.30 Intermediate Status:
% 126.87/127.30 Generated: 679160
% 126.87/127.30 Kept: 142427
% 126.87/127.30 Inuse: 1746
% 126.87/127.30 Deleted: 2019
% 126.87/127.30 Deletedinuse: 10
% 126.87/127.30
% 126.87/127.30 Resimplifying inuse:
% 126.87/127.30 Done
% 126.87/127.30
% 126.87/127.30 Resimplifying inuse:
% 126.87/127.30 Done
% 126.87/127.30
% 126.87/127.30 Resimplifying clauses:
% 126.87/127.30 Done
% 126.87/127.30
% 126.87/127.30
% 126.87/127.30 Intermediate Status:
% 126.87/127.30 Generated: 686909
% 126.87/127.30 Kept: 144446
% 126.87/127.30 Inuse: 1761
% 126.87/127.30 Deleted: 2549
% 126.87/127.30 Deletedinuse: 10
% 126.87/127.30
% 126.87/127.30 Resimplifying inuse:
% 126.87/127.30 Done
% 126.87/127.30
% 126.87/127.30 Resimplifying inuse:
% 126.87/127.30 Done
% 126.87/127.30
% 126.87/127.30
% 126.87/127.30 Intermediate Status:
% 126.87/127.30 Generated: 704575
% 126.87/127.30 Kept: 146451
% 126.87/127.30 Inuse: 1768
% 126.87/127.30 Deleted: 2549
% 126.87/127.30 Deletedinuse: 10
% 126.87/127.30
% 126.87/127.30 Resimplifying inuse:
% 126.87/127.30 Done
% 126.87/127.30
% 126.87/127.30
% 126.87/127.30 Intermediate Status:
% 126.87/127.30 Generated: 738198
% 126.87/127.30 Kept: 150023
% 126.87/127.30 Inuse: 1776
% 126.87/127.30 Deleted: 2549
% 126.87/127.30 Deletedinuse: 10
% 126.87/127.30
% 126.87/127.30 Resimplifying inuse:
% 126.87/127.30 Done
% 126.87/127.30
% 126.87/127.30 Resimplifying inuse:
% 126.87/127.30 Done
% 126.87/127.30
% 126.87/127.30
% 126.87/127.30 Intermediate Status:
% 126.87/127.30 Generated: 772614
% 126.87/127.30 Kept: 153475
% 126.87/127.30 Inuse: 1786
% 126.87/127.30 Deleted: 2549
% 126.87/127.30 Deletedinuse: 10
% 126.87/127.30
% 126.87/127.30 Resimplifying inuse:
% 126.87/127.30 Done
% 126.87/127.30
% 126.87/127.30 Resimplifying inuse:
% 126.87/127.30 Done
% 126.87/127.30
% 126.87/127.30
% 126.87/127.30 Intermediate Status:
% 126.87/127.30 Generated: 792039
% 126.87/127.30 Kept: 155584
% 126.87/127.30 Inuse: 1796
% 126.87/127.30 Deleted: 2549
% 126.87/127.30 Deletedinuse: 10
% 126.87/127.30
% 126.87/127.30 Resimplifying inuse:
% 126.87/127.30 Done
% 126.87/127.30
% 126.87/127.30
% 126.87/127.30 Intermediate Status:
% 126.87/127.30 Generated: 838020
% 126.87/127.30 Kept: 161265
% 126.87/127.30 Inuse: 1821
% 126.87/127.30 Deleted: 2549
% 126.87/127.30 Deletedinuse: 10
% 126.87/127.30
% 126.87/127.30 Resimplifying inuse:
% 126.87/127.30 Done
% 126.87/127.30
% 126.87/127.30 Resimplifying inuse:
% 126.87/127.30 Done
% 126.87/127.30
% 126.87/127.30
% 126.87/127.30 Intermediate Status:
% 126.87/127.30 Generated: 848911
% 126.87/127.30 Kept: 163732
% 126.87/127.30 Inuse: 1841
% 126.87/127.30 Deleted: 2549
% 126.87/127.30 Deletedinuse: 10
% 126.87/127.30
% 126.87/127.30 Resimplifying inuse:
% 126.87/127.30 Done
% 126.87/127.30
% 126.87/127.30 Resimplifying clauses:
% 126.87/127.30 Done
% 126.87/127.30
% 126.87/127.30 Resimplifying inuse:
% 126.87/127.30 Done
% 126.87/127.30
% 126.87/127.30
% 126.87/127.30 Intermediate Status:
% 126.87/127.30 Generated: 869158
% 126.87/127.30 Kept: 167424
% 126.87/127.30 Inuse: 1866
% 126.87/127.30 Deleted: 2766
% 126.87/127.30 Deletedinuse: 10
% 126.87/127.30
% 126.87/127.30 Resimplifying inuse:
% 126.87/127.30 Done
% 126.87/127.30
% 126.87/127.30
% 126.87/127.30 Intermediate Status:
% 126.87/127.30 Generated: 880985
% 126.87/127.30 Kept: 169674
% 126.87/127.30 Inuse: 1871
% 126.87/127.30 Deleted: 2767
% 126.87/127.30 Deletedinuse: 11
% 126.87/127.30
% 126.87/127.30 Resimplifying inuse:
% 126.87/127.30 Done
% 126.87/127.30
% 126.87/127.30
% 126.87/127.30 Intermediate Status:
% 126.87/127.30 Generated: 913153
% 126.87/127.30 Kept: 174246
% 126.87/127.30 Inuse: 1886
% 126.87/127.30 Deleted: 2767
% 126.87/127.30 Deletedinuse: 11
% 126.87/127.30
% 126.87/127.30 Resimplifying inuse:
% 126.87/127.30 Done
% 126.87/127.30
% 126.87/127.30 Resimplifying inuse:
% 126.87/127.30 Done
% 126.87/127.30
% 126.87/127.30
% 126.87/127.30 Intermediate Status:
% 126.87/127.30 Generated: 923292
% 126.87/127.30 Kept: 176503
% 126.87/127.30 Inuse: 1911
% 126.87/127.30 Deleted: 2767
% 126.87/127.30 Deletedinuse: 11
% 126.87/127.30
% 126.87/127.30 Resimplifying inuse:
% 126.87/127.30 Done
% 126.87/127.30
% 126.87/127.30 Resimplifying inuse:
% 126.87/127.30 Done
% 126.87/127.30
% 126.87/127.30
% 126.87/127.30 Intermediate Status:
% 126.87/127.30 Generated: 942685
% 126.87/127.30 Kept: 179976
% 126.87/127.30 Inuse: 1926
% 126.87/127.30 Deleted: 27Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------