TSTP Solution File: SWV709-1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWV709-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Wed Jul 20 16:27:58 EDT 2022
% Result : Timeout 288.43s 288.89s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWV709-1 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.13 % Command : bliksem %s
% 0.13/0.34 % Computer : n006.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % DateTime : Wed Jun 15 08:32:11 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.32/1.74 *** allocated 10000 integers for termspace/termends
% 1.32/1.74 *** allocated 10000 integers for clauses
% 1.32/1.74 *** allocated 10000 integers for justifications
% 1.32/1.74 *** allocated 15000 integers for termspace/termends
% 1.32/1.74 *** allocated 22500 integers for termspace/termends
% 1.32/1.74 *** allocated 33750 integers for termspace/termends
% 1.32/1.74 *** allocated 50625 integers for termspace/termends
% 1.32/1.74 Bliksem 1.12
% 1.32/1.74
% 1.32/1.74
% 1.32/1.74 Automatic Strategy Selection
% 1.32/1.74
% 1.32/1.74 Clauses:
% 1.32/1.74 [
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.32/1.74 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.32/1.74 Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.32/1.74 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.74 X ), X ) ) ],
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.32/1.74 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 1.32/1.74 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.32/1.74 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.74 X ), X ) ) ],
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.32/1.74 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.32/1.74 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.32/1.74 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.74 X ), X ) ) ],
% 1.32/1.74 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.32/1.74 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.32/1.74 , Y ), Z ), Z, X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 1.32/1.74 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.32/1.74 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.32/1.74 , Y ), Z ), Y, X ), 'c_Divides_Odiv__class_Omod'( Z, Y, X ) ) ],
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.32/1.74 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ), ~(
% 1.32/1.74 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X )
% 1.32/1.74 ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.32/1.74 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ), hAPP( hAPP(
% 1.32/1.74 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), U ), W ) ), hAPP( hAPP(
% 1.32/1.74 'c_Power_Opower_Opower'( X, Y, Z ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.32/1.74 X, Y, Z ), T ), U ) ), W ) ), ~( 'c_OrderedGroup_Omonoid__mult'( X, Y, Z
% 1.32/1.74 ) ) ],
% 1.32/1.74 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.32/1.74 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.32/1.74 ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ), hAPP( hAPP(
% 1.32/1.74 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z )
% 1.32/1.74 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.74 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.32/1.74 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.74 'tc_nat' ) ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.74 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y ), 'tc_nat' ),
% 1.32/1.74 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.32/1.74 [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Suc'( 'c_Suc'(
% 1.32/1.74 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ),
% 1.32/1.74 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 1.32/1.74 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.32/1.74 [ ~( =( 'c_Divides_Odiv__class_Omod'( X, 'c_Suc'( 'c_Suc'(
% 1.32/1.74 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ),
% 1.32/1.74 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ),
% 1.32/1.74 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.32/1.74 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.32/1.74 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y
% 1.32/1.74 ), 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.74 'tc_nat' ) ) ],
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.32/1.74 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.32/1.74 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.32/1.74 ), =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ),
% 1.32/1.74 'c_HOL_Ozero__class_Ozero'( X ) ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.32/1.74 , =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.74 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.74 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.32/1.74 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.32/1.74 , X ), X ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.32/1.74 ) ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.32/1.74 ), 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.32/1.74 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.32/1.74 ), X ) ],
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.74 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.74 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.74 X ), X ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'(
% 1.32/1.74 Z, X ), 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.32/1.74 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.32/1.74 ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Oinverse__class_Odivide'( T,
% 1.32/1.74 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), X ) ) ],
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.74 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.74 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.32/1.74 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.32/1.74 , X ), X ), T, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T
% 1.32/1.74 , X ) ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.32/1.74 , X ), 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.32/1.74 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.32/1.74 ), X ) ],
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.74 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.74 'class_Int_Onumber'( X ) ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.74 ), Y, X ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'(
% 1.32/1.74 Z, X ), 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.32/1.74 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.32/1.74 ), X ), ~( 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( T,
% 1.32/1.74 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ) ],
% 1.32/1.74 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.32/1.74 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), hAPP( hAPP(
% 1.32/1.74 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ), 'tc_nat' ),
% 1.32/1.74 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ), ~(
% 1.32/1.74 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.32/1.74 'tc_nat' ) ) ],
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.74 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.74 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.32/1.74 [ ~( 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.32/1.74 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.74 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.32/1.74 [ =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( 'tc_nat' ), X ),
% 1.32/1.74 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'(
% 1.32/1.74 'tc_nat' ) ) ],
% 1.32/1.74 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.32/1.74 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.32/1.74 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.32/1.74 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.32/1.74 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.32/1.74 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.32/1.74 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.32/1.74 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.32/1.74 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.74 'class_Int_Onumber'( X ) ), =( Y, 'c_HOL_Oinverse__class_Odivide'( hAPP(
% 1.32/1.74 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.32/1.74 'c_Int_Onumber__class_Onumber__of'( Z, X ) ),
% 1.32/1.74 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ), =(
% 1.32/1.74 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.74 ) ) ],
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.32/1.74 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.74 'class_Int_Onumber'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( hAPP(
% 1.32/1.74 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.32/1.74 'c_Int_Onumber__class_Onumber__of'( Z, X ) ),
% 1.32/1.74 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y ), =(
% 1.32/1.74 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.74 ) ) ],
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.32/1.74 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 1.32/1.74 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.32/1.74 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.74 X ), X ) ) ],
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.32/1.74 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.32/1.74 , Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.32/1.74 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.32/1.74 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.32/1.74 ,
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.32/1.74 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.32/1.74 , Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.32/1.74 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.32/1.74 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.32/1.74 ,
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.32/1.74 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.32/1.74 , Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.32/1.74 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.32/1.74 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 1.32/1.74 ,
% 1.32/1.74 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.32/1.74 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ), ~(
% 1.32/1.74 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ) ) ],
% 1.32/1.74 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.32/1.74 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.32/1.74 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.32/1.74 ), Z ) ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP(
% 1.32/1.74 hAPP( 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.74 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), Z ) ) ) ],
% 1.32/1.74 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( 'c_Power_Opower_Opower'( Y, Z, T ),
% 1.32/1.74 U ), W ) ), hAPP( hAPP( Z, U ), hAPP( hAPP( 'c_Power_Opower_Opower'( Y, Z
% 1.32/1.74 , T ), U ), W ) ) ) ), ~( hBOOL( hAPP( hAPP( X, Y ), U ) ) ), ~(
% 1.32/1.74 'c_Ring__and__Field_Oordered__semidom'( V0, V1, Y, Z, V2, X, T ) ) ],
% 1.32/1.74 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.32/1.74 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.32/1.74 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X ) )
% 1.32/1.74 , Z ) ), Z ) ],
% 1.32/1.74 [ =( hAPP( X, hAPP( hAPP( 'c_Power_Opower_Opower'( Y, Z, T ), U ), W ) )
% 1.32/1.74 , hAPP( hAPP( 'c_Power_Opower_Opower'( Y, Z, T ), hAPP( X, U ) ), W ) ),
% 1.32/1.74 ~( 'c_Ring__and__Field_Oordered__idom'( V0, V1, V2, V3, V4, V5, X, Y, Z,
% 1.32/1.74 V6, T ) ) ],
% 1.32/1.74 [ =( hAPP( X, hAPP( hAPP( 'c_Power_Opower_Opower'( Y, Z, T ), hAPP( U, W
% 1.32/1.74 ) ), V0 ) ), hAPP( X, hAPP( hAPP( 'c_Power_Opower_Opower'( Y, Z, T ), W
% 1.32/1.74 ), V0 ) ) ), ~( 'c_Ring__and__Field_Oordered__idom'( V1, U, V2, V3, V4,
% 1.32/1.74 V5, X, Y, Z, V6, T ) ) ],
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.32/1.74 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.32/1.74 , Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 1.32/1.74 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 1.32/1.74 ,
% 1.32/1.74 [ =( 'c_Divides_Odiv__class_Omod'( X, hAPP( hAPP(
% 1.32/1.74 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ), 'tc_nat' ), hAPP(
% 1.32/1.74 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.74 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ),
% 1.32/1.74 'c_Divides_Odiv__class_Omod'( 'c_Divides_Odiv__class_Odiv'( X, Y,
% 1.32/1.74 'tc_nat' ), Z, 'tc_nat' ) ) ), 'c_Divides_Odiv__class_Omod'( X, Y,
% 1.32/1.74 'tc_nat' ) ) ) ],
% 1.32/1.74 [ ~( =( hAPP( 'c_NthRoot_Osqrt', X ), hAPP( 'c_NthRoot_Osqrt', Y ) ) ),
% 1.32/1.74 =( X, Y ) ],
% 1.32/1.74 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.32/1.74 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.32/1.74 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.74 'tc_nat' ) ) ) ],
% 1.32/1.74 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.74 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), hAPP( hAPP(
% 1.32/1.74 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.74 'tc_nat' ) ), Y ) ) ],
% 1.32/1.74 [ ~( 'c_Ring__and__Field_Oordered__idom'( X, Y, Z, T, U, W, V0, V1, V2,
% 1.32/1.74 V3, V4 ) ), hBOOL( hAPP( hAPP( W, Z ), hAPP( hAPP(
% 1.32/1.74 'c_Power_Opower_Opower'( V1, V2, V4 ), hAPP( V0, V5 ) ),
% 1.32/1.74 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.32/1.74 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), =( Y
% 1.32/1.74 , 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.74 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.32/1.74 , X ) ) ],
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.32/1.74 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.32/1.74 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP(
% 1.32/1.74 hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), X ), ~(
% 1.32/1.74 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.32/1.74 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.32/1.74 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oinverse__class_Odivide'( Y, Z,
% 1.32/1.74 X ), X ), 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ) ) ],
% 1.32/1.74 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.74 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.32/1.74 'c_Divides_Odiv__class_Omod'( Y, Z, 'tc_nat' ) ) ), T ), hAPP( hAPP(
% 1.32/1.74 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ), 'tc_nat' ), ~(
% 1.32/1.74 'c_HOL_Oord__class_Oless'( T, X, 'tc_nat' ) ), ~(
% 1.32/1.74 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.32/1.74 'tc_nat' ) ) ],
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Omult__mono1'( X ) ), 'c_lessequals'( hAPP(
% 1.32/1.74 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.32/1.74 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~( 'c_lessequals'(
% 1.32/1.74 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Z, T, X ) )
% 1.32/1.74 ],
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ), 'c_lessequals'( hAPP(
% 1.32/1.74 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.32/1.74 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~( 'c_lessequals'(
% 1.32/1.74 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Z, T, X ) )
% 1.32/1.74 ],
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ), 'c_lessequals'( hAPP(
% 1.32/1.74 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.32/1.74 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ), ~( 'c_lessequals'(
% 1.32/1.74 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 1.32/1.74 ],
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.32/1.74 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.32/1.74 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~( 'c_lessequals'( Y,
% 1.32/1.74 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( T, Z, X ) ) ]
% 1.32/1.74 ,
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.32/1.74 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.32/1.74 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ), ~( 'c_lessequals'( Z,
% 1.32/1.74 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( T, Y, X ) ) ]
% 1.32/1.74 ,
% 1.32/1.74 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP(
% 1.32/1.74 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.32/1.74 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.32/1.74 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), T ) ) ) ), =( Z, T ), =( Y
% 1.32/1.74 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.32/1.74 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.32/1.74 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.32/1.74 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.32/1.74 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ) ) ), =( T, U ), =( Z,
% 1.32/1.74 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =( hAPP(
% 1.32/1.74 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.32/1.74 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 1.32/1.74 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.74 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =( hAPP(
% 1.32/1.74 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.32/1.74 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 1.32/1.74 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.74 X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~( =( hAPP( hAPP(
% 1.32/1.74 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), 'c_HOL_Oone__class_Oone'( X
% 1.32/1.74 ) ) ), =( 'c_HOL_Oinverse__class_Oinverse'( Y, X ), Z ) ],
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.32/1.74 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ),
% 1.32/1.74 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.32/1.74 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.32/1.74 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ), =( Z,
% 1.32/1.74 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.32/1.74 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.32/1.74 ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.32/1.74 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.32/1.74 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.32/1.74 'class_Power_Opower'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.32/1.74 , 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( hAPP( hAPP(
% 1.32/1.74 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.32/1.74 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.32/1.74 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.74 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.32/1.74 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.32/1.74 ), Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.74 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.74 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), Z, X ) ) ],
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.74 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.32/1.74 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.32/1.74 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z,
% 1.32/1.74 X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.32/1.74 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.74 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.32/1.74 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.32/1.74 , Y ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.74 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.74 Y, 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ],
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.74 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.32/1.74 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.32/1.74 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 1.32/1.74 X ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.32/1.74 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), Z, X ) ) ],
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.32/1.74 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.32/1.74 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.32/1.74 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ), ~(
% 1.32/1.74 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 1.32/1.74 ,
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.32/1.74 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.32/1.74 , X ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.32/1.74 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), Z, X ) ), ~(
% 1.32/1.74 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ]
% 1.32/1.74 ,
% 1.32/1.74 [ ~( =( hAPP( 'c_NthRoot_Oroot'( X ), Y ), hAPP( 'c_NthRoot_Oroot'( X )
% 1.32/1.74 , Z ) ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.74 'tc_nat' ), X, 'tc_nat' ) ), =( Y, Z ) ],
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.32/1.74 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oabs__class_Oabs'(
% 1.32/1.74 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OMin', X ), X ),
% 1.32/1.74 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.32/1.74 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ), hAPP( hAPP(
% 1.32/1.74 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), U ), W ) ), hAPP( hAPP( Y, hAPP(
% 1.32/1.74 hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ), U ) ), hAPP( hAPP(
% 1.32/1.74 'c_Power_Opower_Opower'( X, Y, Z ), T ), W ) ) ), ~(
% 1.32/1.74 'c_OrderedGroup_Omonoid__mult'( X, Y, Z ) ) ],
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.74 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.32/1.74 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.32/1.74 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.32/1.74 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.74 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ) ) ],
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.74 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.32/1.74 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.32/1.74 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.32/1.74 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.74 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), X ) ) ],
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.74 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.32/1.74 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.32/1.74 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.32/1.74 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.74 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ) ) ],
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.74 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.32/1.74 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.32/1.74 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.32/1.74 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.74 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), X ) ) ],
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.32/1.74 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.74 ), X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.32/1.74 , X ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.32/1.74 ,
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.32/1.74 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.74 ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z
% 1.32/1.74 , X ) ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.32/1.74 ,
% 1.32/1.74 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.32/1.74 'c_Power_Opower__class_Opower'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.32/1.74 'c_Int_OMin', X ) ), Y ), 'c_HOL_Oone__class_Oone'( X ) ), ~(
% 1.32/1.74 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ) ],
% 1.32/1.74 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =( hAPP(
% 1.32/1.74 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ), Y ) ],
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.32/1.74 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'(
% 1.32/1.74 Z, 'tc_nat' ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.32/1.74 'c_Power_Opower__class_Opower'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.74 X ), X ) ) ],
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.32/1.74 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.32/1.74 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X )
% 1.32/1.74 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.32/1.74 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.32/1.74 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.32/1.74 T, X ) ) ],
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.32/1.74 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.32/1.74 'c_Power_Opower__class_Opower'( X ), T ), Z ), X ), ~( 'c_lessequals'( Y
% 1.32/1.74 , T, X ) ), 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 1.32/1.74 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( =(
% 1.32/1.74 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.32/1.74 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ) ), =( Y, Z ) ],
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~( =(
% 1.32/1.74 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.32/1.74 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ) ), =( Y, Z ), =( Z,
% 1.32/1.74 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.32/1.74 ) ],
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 1.32/1.74 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.32/1.74 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.32/1.74 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.32/1.74 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.32/1.74 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.74 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.74 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.32/1.74 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.32/1.74 , X ) ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.74 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.74 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.32/1.74 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ],
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.74 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.74 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.32/1.74 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.32/1.74 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.32/1.74 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.32/1.74 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.32/1.74 , 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.74 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.74 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.32/1.74 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.32/1.74 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.32/1.74 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.32/1.74 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.32/1.74 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.74 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.74 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.32/1.74 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.32/1.74 , X ) ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.74 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.32/1.74 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.32/1.74 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ],
% 1.32/1.74 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.32/1.74 'tc_nat' ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 1.32/1.74 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP(
% 1.32/1.74 hAPP( 'c_Power_Opower__class_Opower'( 'tc_nat' ), X ), Y ), 'tc_nat' ) )
% 1.32/1.74 ],
% 1.32/1.74 [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 1.32/1.74 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.32/1.74 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.74 'tc_nat' ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( 'tc_nat' ), Y ),
% 1.32/1.74 X ), 'tc_nat' ) ) ],
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.74 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.74 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.32/1.74 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.32/1.74 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'(
% 1.32/1.74 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.74 ), X ) ), 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X )
% 1.32/1.74 , X ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.32/1.74 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.74 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.74 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.32/1.74 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.32/1.74 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'(
% 1.32/1.74 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.74 ), X ) ), ~( 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.74 X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ),
% 1.32/1.74 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 1.32/1.74 'c_Nat_Osemiring__1__class_Oof__nat'( hAPP( hAPP(
% 1.32/1.74 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ), X ), hAPP( hAPP(
% 1.32/1.74 'c_HOL_Oplus__class_Oplus'( X ), 'c_Nat_Osemiring__1__class_Oof__nat'( Y
% 1.32/1.74 , X ) ), 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ) ) ) ],
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =(
% 1.32/1.74 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.32/1.74 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Oord__class_Oless'(
% 1.32/1.74 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.74 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.32/1.74 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ), X ) ],
% 1.32/1.74 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.32/1.74 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.32/1.74 , Y ), 'c_Divides_Odiv__class_Omod'( Z, T, X ) ), T, X ),
% 1.32/1.74 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.32/1.74 , Y ), Z ), T, X ) ) ],
% 1.32/1.74 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.32/1.74 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.32/1.74 , 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ), T ), Z, X ),
% 1.32/1.74 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.32/1.74 , Y ), T ), Z, X ) ) ],
% 1.32/1.74 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.32/1.74 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 1.32/1.74 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 1.32/1.74 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.32/1.74 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.32/1.74 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 1.32/1.74 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_Suc'(
% 1.32/1.74 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.32/1.74 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( Y, hAPP( hAPP(
% 1.32/1.74 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.74 X ), 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ), Z ) ),
% 1.32/1.74 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ) ],
% 1.32/1.74 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 1.32/1.74 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.74 X ), 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ), Z ) ),
% 1.32/1.74 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ), Y ) ],
% 1.32/1.74 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 1.32/1.74 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.74 X ), Y ), 'c_Divides_Odiv__class_Odiv'( Z, Y, X ) ) ),
% 1.32/1.74 'c_Divides_Odiv__class_Omod'( Z, Y, X ) ), Z ) ],
% 1.32/1.74 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.32/1.74 ), =( Y, Z ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.32/1.74 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ),
% 1.32/1.74 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 1.32/1.74 ,
% 1.32/1.74 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.32/1.74 ), =( Y, Z ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.32/1.74 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.32/1.74 ), ~( 'c_lessequals'( Y, Z, X ) ), =( Y, Z ) ],
% 1.32/1.74 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Y
% 1.32/1.74 , Z, X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ) ],
% 1.32/1.74 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 1.32/1.74 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 1.32/1.74 ,
% 1.32/1.74 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.32/1.74 ), ~( 'c_lessequals'( Y, Z, X ) ), =( Z, Y ) ],
% 1.32/1.74 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.32/1.74 ), =( Z, Y ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.74 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.32/1.74 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.32/1.74 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), ~( 'c_lessequals'(
% 1.32/1.74 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 1.32/1.74 ],
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.74 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.32/1.74 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.32/1.74 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), ~( 'c_lessequals'( Z,
% 1.32/1.74 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( T, Y, X ) ) ]
% 1.32/1.74 ,
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 1.32/1.74 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.32/1.74 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.32/1.74 , X ), 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oinverse__class_Oinverse'(
% 1.32/1.74 Y, X ), X ) ) ],
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.32/1.74 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.74 X ), Y ), Z ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z
% 1.32/1.74 , X ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.32/1.74 ,
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.32/1.74 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.74 X ), Y ), Z ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.32/1.74 , X ) ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.32/1.74 ,
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.32/1.74 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.74 X ), Y ), Z ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.32/1.74 , X ) ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.32/1.74 ,
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.32/1.74 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.74 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ), X ) ],
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.32/1.74 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.74 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.32/1.74 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.32/1.74 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.32/1.74 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.74 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~( 'c_lessequals'( Z,
% 1.32/1.74 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 1.32/1.74 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.32/1.74 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.74 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.32/1.74 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.32/1.74 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =(
% 1.32/1.74 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Oone__class_Oone'( X )
% 1.32/1.74 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, Z ) ],
% 1.32/1.74 [ ~( =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ), U ), hAPP(
% 1.32/1.74 hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), W ), U ) ) ), ~(
% 1.32/1.74 'c_Ring__and__Field_Oordered__semidom'( V0, V1, X, Y, V2, V3, Z ) ), =( T
% 1.32/1.74 , W ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.32/1.74 ), U, 'tc_nat' ) ), ~( hBOOL( hAPP( hAPP( V2, V1 ), W ) ) ), ~( hBOOL(
% 1.32/1.74 hAPP( hAPP( V2, V1 ), T ) ) ) ],
% 1.32/1.74 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Ouminus__class_Ouminus'(
% 1.32/1.74 Y, X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.32/1.74 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oone__class_Oone'( X ), X ) ), Y )
% 1.32/1.74 ) ],
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.32/1.74 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.32/1.74 , 'tc_nat' ), 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.32/1.74 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.32/1.74 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.32/1.74 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.32/1.74 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.74 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.74 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y
% 1.32/1.74 ), X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ) ],
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.74 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.74 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.32/1.74 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.32/1.74 , X ), X ), T, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T
% 1.32/1.74 , X ) ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.32/1.74 , X ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y, hAPP(
% 1.32/1.74 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.32/1.74 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.74 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.74 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.32/1.74 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.32/1.74 , X ), X ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.32/1.74 ) ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.32/1.74 ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.32/1.74 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.32/1.74 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.32/1.74 [ ~( 'class_OrderedGroup_Oab__semigroup__mult'( X ) ), =( hAPP( hAPP(
% 1.32/1.74 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.32/1.74 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.32/1.74 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.32/1.74 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.74 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.32/1.74 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.32/1.74 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.32/1.74 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.74 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.74 'class_Int_Onumber'( X ) ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.74 ), 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.32/1.74 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.32/1.74 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.32/1.74 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X ),
% 1.32/1.74 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.74 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.74 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.32/1.74 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.32/1.74 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~( 'c_lessequals'(
% 1.32/1.74 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.32/1.74 ), X ) ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.32/1.74 , X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X )
% 1.32/1.74 ],
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.74 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.74 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.32/1.74 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.32/1.74 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~( 'c_lessequals'(
% 1.32/1.74 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.32/1.74 ), X ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.32/1.74 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ), ~(
% 1.32/1.74 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.32/1.74 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.32/1.74 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =( hAPP(
% 1.32/1.74 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.32/1.74 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.32/1.74 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ],
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.32/1.74 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.32/1.74 , Y ), 'c_HOL_Oone__class_Oone'( X ) ), X ) ],
% 1.32/1.74 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( 'c_Power_Opower_Opower'( Y, Z, T ),
% 1.32/1.74 U ), 'c_Suc'( W ) ) ), Y ) ), ~( hBOOL( hAPP( hAPP( X, U ), Y ) ) ), ~(
% 1.32/1.74 hBOOL( hAPP( hAPP( X, V0 ), U ) ) ), ~(
% 1.32/1.74 'c_Ring__and__Field_Oordered__semidom'( V1, V0, Y, Z, V2, X, T ) ) ],
% 1.32/1.74 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.32/1.74 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), ~(
% 1.32/1.74 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.32/1.74 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.32/1.74 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.32/1.74 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.32/1.74 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.32/1.74 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ) ],
% 1.32/1.74 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.32/1.74 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.74 'tc_nat' ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.32/1.74 ), Z ), Y ), 'tc_nat' ) ) ],
% 1.32/1.74 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.32/1.74 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.74 'tc_nat' ), X ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.32/1.74 ), Y ), Z ), 'tc_nat' ) ) ],
% 1.32/1.74 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.32/1.74 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), Z, 'tc_nat' ), hAPP(
% 1.32/1.74 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.74 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.32/1.74 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ) ),
% 1.32/1.74 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.74 'tc_nat' ), X ), 'c_Divides_Odiv__class_Omod'( Y, Z, 'tc_nat' ) ), Z,
% 1.32/1.74 'tc_nat' ) ) ) ],
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 1.32/1.74 'c_HOL_Ouminus__class_Ouminus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.74 X ), Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.32/1.74 'c_HOL_Ouminus__class_Ouminus'( Z, X ) ) ) ],
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 1.32/1.74 'c_HOL_Ouminus__class_Ouminus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.74 X ), Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.32/1.74 'c_HOL_Ouminus__class_Ouminus'( Y, X ) ), Z ) ) ],
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.32/1.74 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.32/1.74 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z
% 1.32/1.74 , X ) ), 'c_HOL_Oinverse__class_Odivide'( T, U, X ) ),
% 1.32/1.74 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.74 X ), Y ), T ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ), X
% 1.32/1.74 ) ) ],
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Opordered__ring__abs'( X ) ), =(
% 1.32/1.74 'c_HOL_Oabs__class_Oabs'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.32/1.74 Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.32/1.74 'c_HOL_Oabs__class_Oabs'( Y, X ) ), 'c_HOL_Oabs__class_Oabs'( Z, X ) ) )
% 1.32/1.74 , ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.32/1.74 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Opordered__ring__abs'( X ) ), =(
% 1.32/1.74 'c_HOL_Oabs__class_Oabs'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.32/1.74 Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.32/1.74 'c_HOL_Oabs__class_Oabs'( Y, X ) ), 'c_HOL_Oabs__class_Oabs'( Z, X ) ) )
% 1.32/1.74 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.32/1.74 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Opordered__ring__abs'( X ) ), =(
% 1.32/1.74 'c_HOL_Oabs__class_Oabs'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.32/1.74 Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.32/1.74 'c_HOL_Oabs__class_Oabs'( Y, X ) ), 'c_HOL_Oabs__class_Oabs'( Z, X ) ) )
% 1.32/1.74 , ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.32/1.74 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Opordered__ring__abs'( X ) ), =(
% 1.32/1.74 'c_HOL_Oabs__class_Oabs'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.32/1.74 Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.32/1.74 'c_HOL_Oabs__class_Oabs'( Y, X ) ), 'c_HOL_Oabs__class_Oabs'( Z, X ) ) )
% 1.32/1.74 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.32/1.74 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.32/1.74 'c_HOL_Oabs__class_Oabs'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.32/1.74 Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.32/1.74 'c_HOL_Oabs__class_Oabs'( Y, X ) ), 'c_HOL_Oabs__class_Oabs'( Z, X ) ) )
% 1.32/1.74 ],
% 1.32/1.74 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), X ), T ), X ), ~(
% 1.32/1.74 'c_OrderedGroup_Omonoid__mult'( X, Y, Z ) ) ],
% 1.32/1.74 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.32/1.74 , 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.32/1.74 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~(
% 1.32/1.74 'c_lessequals'( Y, T, X ) ) ],
% 1.32/1.74 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.32/1.74 , 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.32/1.74 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP(
% 1.32/1.74 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ],
% 1.32/1.74 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.32/1.74 , 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.32/1.74 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~(
% 1.32/1.74 'c_lessequals'( Z, T, X ) ) ],
% 1.32/1.74 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.32/1.74 , 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.32/1.74 'c_HOL_Oplus__class_Oplus'( X ), T ), Y ), hAPP( hAPP(
% 1.32/1.74 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ) ) ],
% 1.32/1.74 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 1.32/1.74 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.32/1.74 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~(
% 1.32/1.74 'c_lessequals'( Y, T, X ) ) ],
% 1.32/1.74 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 1.32/1.74 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.32/1.74 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~(
% 1.32/1.74 'c_lessequals'( Z, T, X ) ) ],
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.32/1.74 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.32/1.74 'c_Power_Opower__class_Opower'( X ), T ), Z ), X ), ~( 'c_lessequals'(
% 1.32/1.74 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Oabs__class_Oabs'( T, X ), X ) )
% 1.32/1.74 , ~( 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ) ],
% 1.32/1.74 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.32/1.74 'c_HOL_Oabs__class_Oabs'( Y, X ), Y ), ~( 'c_lessequals'(
% 1.32/1.74 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.32/1.74 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.32/1.74 ), =( Z, Y ) ],
% 1.32/1.74 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 1.32/1.74 'c_HOL_Oord__class_Oless'( Z, Y, X ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.32/1.74 ) ],
% 1.32/1.74 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 1.32/1.74 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.32/1.74 ) ],
% 1.32/1.74 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.32/1.74 , X ), =( Z, Y ), 'c_HOL_Oord__class_Oless'( Z, Y, X ) ],
% 1.32/1.74 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Y, Z
% 1.32/1.74 , X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ],
% 1.32/1.74 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 1.32/1.74 Y, X, 'tc_nat' ), =( Y, X ) ],
% 1.32/1.74 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), 'c_HOL_Oord__class_Oless'( Y, Z,
% 1.32/1.74 'tc_nat' ), =( Z, Y ), 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ],
% 1.32/1.74 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 1.32/1.74 Y, X, 'tc_nat' ), =( Y, X ) ],
% 1.32/1.74 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Z, Y
% 1.32/1.74 , X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.32/1.74 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.32/1.74 , X ), 'c_HOL_Oord__class_Oless'( Z, Y, X ), =( Z, Y ) ],
% 1.32/1.74 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Z, Y
% 1.32/1.74 , X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.32/1.74 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP(
% 1.32/1.74 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.32/1.74 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), X ), ~(
% 1.32/1.74 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.32/1.74 [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), ~( =(
% 1.32/1.74 'c_HOL_Ouminus__class_Ouminus'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Z
% 1.32/1.74 , X ) ) ), =( Y, Z ) ],
% 1.32/1.74 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 1.32/1.74 'c_HOL_Ouminus__class_Ouminus'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Z
% 1.32/1.74 , X ) ) ), =( Y, Z ) ],
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 1.32/1.74 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Oinverse__class_Odivide'(
% 1.32/1.74 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), Y, X ) ) ],
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 1.32/1.74 'c_HOL_Ozero__class_Ozero'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'(
% 1.32/1.74 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), Y, X ), Z ) ]
% 1.32/1.74 ,
% 1.32/1.74 [ ~( 'class_OrderedGroup_Olordered__ab__group__add__abs'( X ) ),
% 1.32/1.74 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ),
% 1.32/1.74 'c_HOL_Oabs__class_Oabs'( T, X ) ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.32/1.74 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), Z, X ) ) ],
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.32/1.74 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( Y,
% 1.32/1.74 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.74 X ), Y ), Z ), Z, X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.32/1.74 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.32/1.74 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.74 X ), Y ), Z ), Z, X ), Y ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.32/1.74 ,
% 1.32/1.74 [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), X ), ~(
% 1.32/1.74 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.74 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.32/1.74 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ),
% 1.32/1.74 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.32/1.74 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.74 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.32/1.74 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.32/1.74 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ),
% 1.32/1.74 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.32/1.74 [ =( hAPP( 'c_NthRoot_Oroot'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.74 'tc_nat' ), X ), Y ) ), Z ), hAPP( 'c_NthRoot_Oroot'( X ), hAPP(
% 1.32/1.74 'c_NthRoot_Oroot'( Y ), Z ) ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.74 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ), ~(
% 1.32/1.74 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.32/1.74 'tc_nat' ) ) ],
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.32/1.74 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.74 'class_Int_Onumber'( X ) ), ~( =( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.32/1.74 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.32/1.74 Z, X ) ) ), =( 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.32/1.74 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.32/1.74 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.74 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.32/1.74 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =(
% 1.32/1.74 'c_HOL_Oinverse__class_Odivide'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.32/1.74 , 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ],
% 1.32/1.74 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =( Y,
% 1.32/1.74 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'(
% 1.32/1.74 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.32/1.74 ],
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.74 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.32/1.74 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.32/1.74 'c_HOL_Oone__class_Oone'( X ), X ), ~( 'c_lessequals'( Y,
% 1.32/1.74 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.74 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.32/1.74 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.32/1.74 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.32/1.74 'c_HOL_Otimes__class_Otimes'( X ), T ), hAPP( hAPP(
% 1.32/1.74 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.32/1.74 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), U ) ) ) ],
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.74 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.32/1.74 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.32/1.74 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.32/1.74 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.32/1.74 'c_HOL_Otimes__class_Otimes'( X ), Z ), hAPP( hAPP(
% 1.32/1.74 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) ) ) ],
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.74 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.32/1.74 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.32/1.74 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.32/1.74 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.32/1.74 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.32/1.74 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ) ) ],
% 1.32/1.74 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 1.32/1.74 'c_HOL_Ouminus__class_Ouminus'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.32/1.74 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.32/1.74 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.32/1.74 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.32/1.74 'c_HOL_Ozero__class_Ozero'( X ) ) ), hAPP( hAPP(
% 1.32/1.74 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.32/1.74 'c_HOL_Ozero__class_Ozero'( X ) ) ), 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.32/1.74 ],
% 1.32/1.74 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.32/1.74 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.32/1.74 ), Y ), Z ), Z, X ), Y ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.74 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.32/1.74 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.32/1.74 ), Y ), Z ), Y, X ), Z ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.74 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.32/1.74 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.32/1.74 ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.32/1.74 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.32/1.74 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.32/1.74 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.32/1.74 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.32/1.74 ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.32/1.74 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.32/1.74 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.32/1.74 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.32/1.74 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.32/1.74 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.74 Z, Y, X ) ) ],
% 1.32/1.74 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.32/1.74 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.74 'c_HOL_Ouminus__class_Ouminus'( Z, X ), 'c_HOL_Ouminus__class_Ouminus'( Y
% 1.32/1.74 , X ), X ) ) ],
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.74 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.32/1.74 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X )
% 1.32/1.74 , 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X
% 1.32/1.74 ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X
% 1.32/1.74 ) ) ],
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.74 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.32/1.74 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.32/1.74 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.32/1.74 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T
% 1.32/1.74 ), X ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.32/1.74 ), Y ), T ), Z, X ) ) ],
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.74 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.32/1.74 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~(
% 1.32/1.74 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.32/1.74 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ),
% 1.32/1.74 Y, X ) ), ~( 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.74 X ), T ), Z ), X ) ) ],
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 1.32/1.74 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.32/1.74 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 1.32/1.74 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.74 X ), X ) ) ],
% 1.32/1.74 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( 'c_Power_Opower_Opower'( Y, Z, T ),
% 1.32/1.74 U ), W ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( Y, Z, T ), U ), V0 ) ) )
% 1.32/1.74 , ~( 'c_HOL_Oord__class_Oless'( W, V0, 'tc_nat' ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.74 X, Y ), U ) ) ), ~( 'c_Ring__and__Field_Oordered__semidom'( V1, V2, Y, Z
% 1.32/1.74 , V3, X, T ) ) ],
% 1.32/1.74 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~( hBOOL( hAPP( hAPP( Z,
% 1.32/1.74 hAPP( hAPP( 'c_Power_Opower_Opower'( T, U, W ), V0 ), X ) ), hAPP( hAPP(
% 1.32/1.74 'c_Power_Opower_Opower'( T, U, W ), V0 ), Y ) ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.74 Z, T ), V0 ) ) ), ~( 'c_Ring__and__Field_Oordered__semidom'( V1, V2, T, U
% 1.32/1.74 , V3, Z, W ) ) ],
% 1.32/1.74 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( 'c_Power_Opower_Opower'( Y, Z, T ),
% 1.32/1.74 U ), W ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( Y, Z, T ), U ), V0 ) ) )
% 1.32/1.74 , ~( hBOOL( hAPP( hAPP( X, Y ), U ) ) ), ~( 'c_HOL_Oord__class_Oless'( W
% 1.32/1.74 , V0, 'tc_nat' ) ), ~( 'c_Ring__and__Field_Oordered__semidom'( V1, V2, Y
% 1.32/1.74 , Z, V3, X, T ) ) ],
% 1.32/1.74 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~( hBOOL( hAPP( hAPP( Z,
% 1.32/1.74 hAPP( hAPP( 'c_Power_Opower_Opower'( T, U, W ), V0 ), X ) ), hAPP( hAPP(
% 1.32/1.74 'c_Power_Opower_Opower'( T, U, W ), V0 ), Y ) ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.74 Z, T ), V0 ) ) ), ~( 'c_Ring__and__Field_Oordered__semidom'( V1, V2, T, U
% 1.32/1.74 , V3, Z, W ) ) ],
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =(
% 1.32/1.74 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.32/1.74 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X )
% 1.32/1.74 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X )
% 1.32/1.74 ) ],
% 1.32/1.74 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), hBOOL( hAPP( hAPP( X, Z ), Y ) ),
% 1.32/1.74 =( Z, Y ), ~( 'c_Ring__and__Field_Oordered__idom'( T, U, W, V0, V1, X, V2
% 1.32/1.74 , V3, V4, V5, V6 ) ) ],
% 1.32/1.74 [ =( hAPP( hAPP( X, hAPP( Y, Z ) ), hAPP( Y, Z ) ), hAPP( hAPP( X, Z ),
% 1.32/1.74 Z ) ), ~( 'c_Ring__and__Field_Oordered__idom'( T, U, W, V0, V1, V2, Y, V3
% 1.32/1.74 , X, V4, V5 ) ) ],
% 1.32/1.74 [ =( hAPP( hAPP( X, hAPP( Y, Z ) ), hAPP( T, Z ) ), Z ), ~(
% 1.32/1.74 'c_Ring__and__Field_Oordered__idom'( U, W, V0, V1, V2, V3, T, V4, X, Y,
% 1.32/1.74 V5 ) ) ],
% 1.32/1.74 [ =( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), hAPP( hAPP( Y, hAPP( X, Z ) ),
% 1.32/1.74 hAPP( X, T ) ) ), ~( 'c_Ring__and__Field_Oordered__idom'( U, W, V0, V1,
% 1.32/1.74 V2, V3, V4, V5, Y, X, V6 ) ) ],
% 1.32/1.74 [ =( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), hAPP( hAPP( Y, hAPP( X, Z ) ),
% 1.32/1.74 hAPP( X, T ) ) ), ~( 'c_Ring__and__Field_Oordered__idom'( U, W, V0, V1,
% 1.32/1.74 V2, V3, X, V4, Y, V5, V6 ) ) ],
% 1.32/1.74 [ =( hAPP( X, hAPP( X, Y ) ), hAPP( X, Y ) ), ~(
% 1.32/1.74 'c_Ring__and__Field_Oordered__idom'( Z, T, U, W, V0, V1, V2, V3, V4, X,
% 1.32/1.74 V5 ) ) ],
% 1.32/1.74 [ ~( 'c_Ring__and__Field_Oordered__idom'( X, Y, Z, T, U, W, V0, V1, V2,
% 1.32/1.74 V3, V4 ) ), =( hAPP( V3, Z ), Z ) ],
% 1.32/1.74 [ ~( 'c_Ring__and__Field_Oordered__idom'( X, Y, hAPP( Z, T ), U, W, V0,
% 1.32/1.74 V1, V2, V3, Z, V4 ) ), =( T, hAPP( Z, T ) ) ],
% 1.32/1.74 [ =( hAPP( X, Y ), hAPP( hAPP( Z, Y ), hAPP( T, Y ) ) ), ~(
% 1.32/1.74 'c_Ring__and__Field_Oordered__idom'( U, W, V0, V1, V2, V3, X, V4, Z, T,
% 1.32/1.74 V5 ) ) ],
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.32/1.74 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.74 'class_Int_Onumber'( X ) ), =( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.74 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.74 X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.32/1.74 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 1.32/1.74 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.32/1.74 [ ~( hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( 'c_Power_Opower_Opower'( Z,
% 1.32/1.74 T, U ), hAPP( W, Y ) ), V0 ) ) ) ), ~(
% 1.32/1.74 'c_Ring__and__Field_Oordered__idom'( V1, V2, Y, V3, V4, X, W, Z, T, V5, U
% 1.32/1.74 ) ), =( V0, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.32/1.74 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), 'c_Suc'(
% 1.32/1.74 Y ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP(
% 1.32/1.74 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.32/1.74 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_Suc'( X )
% 1.32/1.74 ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), hAPP(
% 1.32/1.74 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.32/1.74 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.32/1.74 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.74 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), T ), hAPP( hAPP(
% 1.32/1.74 'c_Power_Opower__class_Opower'( X ), Z ), T ), X ) ) ],
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.32/1.74 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.32/1.74 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.32/1.74 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.74 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ) ) ],
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.32/1.74 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.32/1.74 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.32/1.74 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.74 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), X ) ) ],
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.32/1.74 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.74 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~(
% 1.32/1.74 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.32/1.74 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.32/1.74 ,
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.32/1.74 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.74 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~(
% 1.32/1.74 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.32/1.74 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.32/1.74 ,
% 1.32/1.74 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.32/1.74 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), 'tc_nat'
% 1.32/1.74 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.32/1.74 , Y, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.74 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.32/1.74 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.32/1.74 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.32/1.74 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.32/1.74 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.32/1.74 ,
% 1.32/1.74 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.32/1.74 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.32/1.74 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.32/1.74 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.32/1.74 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.32/1.74 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.32/1.74 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.32/1.74 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.32/1.74 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.32/1.74 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.32/1.74 ,
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.74 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.32/1.74 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.32/1.74 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.32/1.74 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), Z ) ) ],
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.74 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.32/1.74 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.32/1.74 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.32/1.74 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.74 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.32/1.74 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.32/1.74 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.32/1.74 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ) ) ],
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.74 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.32/1.74 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.32/1.74 'c_HOL_Otimes__class_Otimes'( X ), Z ), hAPP( hAPP(
% 1.32/1.74 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ],
% 1.32/1.74 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.74 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.32/1.74 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.32/1.74 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ) ) ],
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.74 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.32/1.74 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.32/1.74 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.32/1.74 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ) ) ],
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.74 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.74 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.32/1.74 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.32/1.74 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.32/1.74 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.32/1.74 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.32/1.74 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.32/1.74 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.74 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.32/1.74 ) ) ],
% 1.32/1.74 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.32/1.74 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.32/1.74 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.32/1.74 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.74 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.32/1.74 ) ) ],
% 1.32/1.74 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.32/1.74 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.74 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.32/1.74 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.32/1.74 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.32/1.74 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.32/1.74 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.74 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.32/1.74 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.32/1.74 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.32/1.74 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), hAPP(
% 1.32/1.74 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.32/1.74 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.74 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.32/1.74 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ) ],
% 1.32/1.74 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.74 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.32/1.74 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.74 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.32/1.74 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ) ) ],
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.74 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.32/1.74 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.32/1.74 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.74 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.32/1.74 ) ) ],
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Ocomm__semiring'( X ) ), =( hAPP( hAPP(
% 1.32/1.74 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.74 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.32/1.74 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.32/1.74 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.32/1.74 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.32/1.74 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.32/1.74 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ), ~( 'c_lessequals'( U, Z
% 1.32/1.74 , X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), U
% 1.32/1.74 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_lessequals'(
% 1.32/1.74 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.32/1.74 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.32/1.74 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' )
% 1.32/1.74 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y
% 1.32/1.74 , 'tc_nat' ) ) ],
% 1.32/1.74 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.32/1.74 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' )
% 1.32/1.74 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X
% 1.32/1.74 , 'tc_nat' ) ) ],
% 1.32/1.74 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.32/1.74 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.32/1.74 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ) ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.32/1.75 ,
% 1.32/1.75 [ ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), =( Y,
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( hBOOL( hAPP( Z,
% 1.32/1.75 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.75 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), T
% 1.32/1.75 ) ), X ), Y, 'tc_nat' ) ) ) ), hBOOL( hAPP( Z, X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.32/1.75 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.32/1.75 ), X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.32/1.75 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.32/1.75 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.32/1.75 ), X ), 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ouminus__class_Ouminus'(
% 1.32/1.75 Y, X ), Z, X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.75 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.32/1.75 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.32/1.75 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.75 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Z
% 1.32/1.75 , X ) ), T ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'(
% 1.32/1.75 'c_HOL_Oinverse__class_Odivide'( Y, T, X ),
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.32/1.75 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.32/1.75 X ), ~( 'c_lessequals'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.32/1.75 ,
% 1.32/1.75 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oone__class_Oone'(
% 1.32/1.75 'tc_nat' ), 'tc_nat' ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.32/1.75 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.75 X ), Y ), Z ), X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.32/1.75 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.75 X ), Z ), Y ), X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.32/1.75 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.75 X ), Y ), Z ), X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.32/1.75 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.75 X ), Z ), Y ), X ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( X, Y ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Z ),
% 1.32/1.75 ~( 'c_Groebner__Basis_Ogb__semiring'( T, U, X, W, Z, V0 ) ) ],
% 1.32/1.75 [ =( 'c_Divides_Odiv__class_Odiv'( X, 'c_Suc'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ), X ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ), ~( =(
% 1.32/1.75 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y ) ), =( Y,
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.75 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.75 'tc_nat' ) ), X ) ],
% 1.32/1.75 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.32/1.75 hAPP( hAPP( 'c_Power_Opower__class_Opower'( 'tc_nat' ), X ),
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ],
% 1.32/1.75 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ), 'c_Suc'( U ) )
% 1.32/1.75 , hAPP( hAPP( Y, hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ), U )
% 1.32/1.75 ), T ) ), ~( 'c_OrderedGroup_Omonoid__mult'( X, Y, Z ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.75 X ), 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.32/1.75 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), X
% 1.32/1.75 ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.75 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.32/1.75 X ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ) ) ), =( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.32/1.75 , X ) ), T ), Z ), =( T, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.32/1.75 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.32/1.75 'c_HOL_Oone__class_Oone'( X ), Y, X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.75 X ) ) ],
% 1.32/1.75 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.32/1.75 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.32/1.75 , Y ), Z ), Y, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.32/1.75 'c_Divides_Odiv__class_Odiv'( Z, Y, X ) ), 'c_HOL_Oone__class_Oone'( X )
% 1.32/1.75 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.75 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.32/1.75 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.32/1.75 , Y ), Z ), Z, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.32/1.75 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ), 'c_HOL_Oone__class_Oone'( X )
% 1.32/1.75 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.32/1.75 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oone__class_Oone'( X ), X ),
% 1.32/1.75 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.32/1.75 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.32/1.75 X, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), 'c_Suc'(
% 1.32/1.75 'c_Divides_Odiv__class_Odiv'( Y, X, 'tc_nat' ) ) ), 'tc_nat' ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.75 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ),
% 1.32/1.75 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.75 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.32/1.75 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.32/1.75 'c_HOL_Oone__class_Oone'( X ) ), X ) ],
% 1.32/1.75 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.32/1.75 ), Z ), 'c_HOL_Ouminus__class_Ouminus'( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ) ) ],
% 1.32/1.75 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.32/1.75 ), Z ), 'c_HOL_Ouminus__class_Ouminus'( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ) ) ],
% 1.32/1.75 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ouminus__class_Ouminus'( Z
% 1.32/1.75 , X ) ), 'c_HOL_Ouminus__class_Ouminus'( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ) ) ],
% 1.32/1.75 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ouminus__class_Ouminus'( Z
% 1.32/1.75 , X ) ), 'c_HOL_Ouminus__class_Ouminus'( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), =( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.32/1.75 ), 'c_HOL_Ouminus__class_Ouminus'( Y, X ) ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.32/1.75 ), 'c_HOL_Ouminus__class_Ouminus'( Z, X ) ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X
% 1.32/1.75 ) ), Y ), 'c_HOL_Oone__class_Oone'( X ) ), =( Y,
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X
% 1.32/1.75 ) ), Y ), 'c_HOL_Oone__class_Oone'( X ) ), =( Y,
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Oinverse__class_Oinverse'(
% 1.32/1.75 Y, X ) ), 'c_HOL_Oone__class_Oone'( X ) ), =( Y,
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ), 'c_lessequals'(
% 1.32/1.75 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X ), ~( 'c_lessequals'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( Z, U, X ) )
% 1.32/1.75 , ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ), 'c_lessequals'(
% 1.32/1.75 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X ), ~( 'c_lessequals'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Z, U, X ) )
% 1.32/1.75 , ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.32/1.75 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.32/1.75 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.32/1.75 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X
% 1.32/1.75 ), 'c_Divides_Odiv__class_Odiv'( Z, T, X ) ), =( Y,
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.75 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.32/1.75 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.32/1.75 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X
% 1.32/1.75 ), 'c_Divides_Odiv__class_Odiv'( Y, T, X ) ), =( Z,
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.75 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ), 'tc_nat' ),
% 1.32/1.75 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ), =( X,
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.32/1.75 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), Z, 'tc_nat' ), hAPP(
% 1.32/1.75 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( X,
% 1.32/1.75 Z, 'tc_nat' ) ), 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ) ),
% 1.32/1.75 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.75 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X, Z, 'tc_nat' ) ),
% 1.32/1.75 'c_Divides_Odiv__class_Omod'( Y, Z, 'tc_nat' ) ), Z, 'tc_nat' ) ) ) ]
% 1.32/1.75 ,
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.75 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.32/1.75 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =(
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.32/1.75 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.75 X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), Z ), Z, X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.32/1.75 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), Y
% 1.32/1.75 , X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.32/1.75 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 1.32/1.75 X ) ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.32/1.75 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ]
% 1.32/1.75 ,
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.32/1.75 , X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.75 X ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), Y, X ) ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.32/1.75 ), T ), Z ), X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.32/1.75 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 1.32/1.75 X ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), Y, X ) ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.32/1.75 ), T ), Z ), X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.32/1.75 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.32/1.75 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( T, Z, X )
% 1.32/1.75 , X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.32/1.75 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.32/1.75 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.75 X ) ), 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.32/1.75 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ]
% 1.32/1.75 ,
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.32/1.75 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.32/1.75 , X ), ~( 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.75 X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.32/1.75 , Y ), T ), Z, X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.32/1.75 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.32/1.75 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.75 X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.32/1.75 , Y ), T ), Z, X ) ) ],
% 1.32/1.75 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ),
% 1.32/1.75 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 1.32/1.75 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.32/1.75 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ), ~(
% 1.32/1.75 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 1.32/1.75 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.32/1.75 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ),
% 1.32/1.75 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~(
% 1.32/1.75 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ) ) ],
% 1.32/1.75 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ),
% 1.32/1.75 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~(
% 1.32/1.75 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ],
% 1.32/1.75 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ), ~(
% 1.32/1.75 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 1.32/1.75 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.32/1.75 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ),
% 1.32/1.75 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 1.32/1.75 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.32/1.75 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ), ~(
% 1.32/1.75 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 1.32/1.75 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ) ) ],
% 1.32/1.75 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ), ~(
% 1.32/1.75 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 1.32/1.75 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ],
% 1.32/1.75 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ) ),
% 1.32/1.75 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~(
% 1.32/1.75 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.32/1.75 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ) ), ~(
% 1.32/1.75 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ),
% 1.32/1.75 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.32/1.75 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ),
% 1.32/1.75 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 1.32/1.75 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ) ],
% 1.32/1.75 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ), ~(
% 1.32/1.75 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ),
% 1.32/1.75 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ],
% 1.32/1.75 [ =( 'c_Divides_Odiv__class_Odiv'( 'c_Suc'( X ), 'c_Suc'( 'c_Suc'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ), 'c_Suc'(
% 1.32/1.75 'c_Divides_Odiv__class_Odiv'( X, 'c_Suc'( 'c_Suc'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ) ) ),
% 1.32/1.75 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.32/1.75 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.32/1.75 , Y ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP(
% 1.32/1.75 hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.32/1.75 ,
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.32/1.75 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.32/1.75 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.32/1.75 ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.32/1.75 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.32/1.75 ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.32/1.75 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.32/1.75 , Z ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X )
% 1.32/1.75 ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.32/1.75 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.32/1.75 ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ) ],
% 1.32/1.75 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 1.32/1.75 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ),
% 1.32/1.75 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ouminus__class_Ouminus'(
% 1.32/1.75 'c_Divides_Odiv__class_Omod'( Y, Z, X ), X ), Z, X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.75 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.32/1.75 ,
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.75 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.32/1.75 ,
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.75 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.32/1.75 ,
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.75 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.32/1.75 ,
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.32/1.75 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.32/1.75 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X )
% 1.32/1.75 ), 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.75 X ), Y ), Z ) ), 'c_HOL_Oinverse__class_Oinverse'( Y, X ) ) ),
% 1.32/1.75 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ) ), =( Z,
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.32/1.75 ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X )
% 1.32/1.75 ), 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X
% 1.32/1.75 ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) ),
% 1.32/1.75 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ) ), =( Z,
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.32/1.75 ) ],
% 1.32/1.75 [ ~( =( 'c_Divides_Odiv__class_Omod'( X, 'c_Suc'( 'c_Suc'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ), 'c_Suc'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), ~(
% 1.32/1.75 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.32/1.75 [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Suc'( 'c_Suc'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ), 'c_Suc'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ),
% 1.32/1.75 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.32/1.75 'c_HOL_Oone__class_Oone'( X ) ), X ), Z, X ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), ~( =(
% 1.32/1.75 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.75 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =( hAPP(
% 1.32/1.75 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.75 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =( hAPP(
% 1.32/1.75 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.75 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.75 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X,
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.32/1.75 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_Suc'( 'c_Suc'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), X ), 'tc_nat' ) ],
% 1.32/1.75 [ =( 'c_Int_Onumber__class_Onumber__of'( X, 'tc_Int_Oint' ), X ) ],
% 1.32/1.75 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.32/1.75 'c_Divides_Odiv__class_Odiv'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.75 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.32/1.75 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( =(
% 1.32/1.75 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( 'c_lessequals'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Z,
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( =(
% 1.32/1.75 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( 'c_lessequals'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Y,
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.75 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.32/1.75 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), ~( =( hAPP(
% 1.32/1.75 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.75 ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.75 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.32/1.75 X ), 'c_HOL_Oinverse__class_Odivide'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.32/1.75 , X ) ) ), =( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.75 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.32/1.75 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =(
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.32/1.75 'c_HOL_Oinverse__class_Odivide'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.32/1.75 ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.75 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.32/1.75 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.75 X ), 'c_HOL_Oinverse__class_Odivide'( Z,
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.32/1.75 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.32/1.75 'c_Power_Opower__class_Opower'( X ), Y ), T ) ), hAPP( hAPP(
% 1.32/1.75 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ) ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.32/1.75 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.32/1.75 ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.32/1.75 ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oabs__if'( X ) ), =(
% 1.32/1.75 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.32/1.75 ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.32/1.75 ) ],
% 1.32/1.75 [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 1.32/1.75 'class_OrderedGroup_Olordered__ab__group__add__abs'( X ) ), =(
% 1.32/1.75 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.32/1.75 ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.32/1.75 ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( =( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ) ), =( Y,
% 1.32/1.75 'c_HOL_Ouminus__class_Ouminus'( Z, X ) ), =( Y, Z ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.32/1.75 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.75 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.32/1.75 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.75 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ),
% 1.32/1.75 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.75 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ),
% 1.32/1.75 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.75 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.32/1.75 [ =( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ),
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X
% 1.32/1.75 , Y, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'( Y
% 1.32/1.75 , 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'(
% 1.32/1.75 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), Z, X ) ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ]
% 1.32/1.75 ,
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.32/1.75 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Y
% 1.32/1.75 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 1.32/1.75 ,
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.32/1.75 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.32/1.75 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ),
% 1.32/1.75 Z, X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.32/1.75 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), T, X ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.32/1.75 'c_lessequals'( Y, 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ]
% 1.32/1.75 ,
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.32/1.75 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.32/1.75 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z
% 1.32/1.75 ), X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.32/1.75 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.32/1.75 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), Z, X ) ) ]
% 1.32/1.75 ,
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.32/1.75 X ) ), ~( =( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) )
% 1.32/1.75 , =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.75 [ ~( =( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y )
% 1.32/1.75 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.32/1.75 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), X
% 1.32/1.75 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.32/1.75 [ ~( 'class_Nat_Osemiring__char__0'( X ) ), ~( =(
% 1.32/1.75 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 1.32/1.75 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ) ) ), =( Y, Z ) ],
% 1.32/1.75 [ ~( =( 'c_Nat_Osemiring__1__class_Oof__nat'( X, 'tc_Int_Oint' ),
% 1.32/1.75 'c_Nat_Osemiring__1__class_Oof__nat'( Y, 'tc_Int_Oint' ) ) ), =( X, Y ) ]
% 1.32/1.75 ,
% 1.32/1.75 [ ~( =( 'c_Nat_Osemiring__1__class_Oof__nat'( X, 'tc_Int_Oint' ),
% 1.32/1.75 'c_Nat_Osemiring__1__class_Oof__nat'( Y, 'tc_Int_Oint' ) ) ), =( X, Y ) ]
% 1.32/1.75 ,
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.75 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.32/1.75 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.32/1.75 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ), ~(
% 1.32/1.75 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.32/1.75 [ ~( 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'( X )
% 1.32/1.75 , 'c_Power_Opower_Opower'( 'c_HOL_Oone__class_Oone'( X ),
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.75 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ), X ), ~(
% 1.32/1.75 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ),
% 1.32/1.75 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.32/1.75 , 'tc_nat' ), 'tc_nat' ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.32/1.75 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.32/1.75 , 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.75 X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ), X ) ) ],
% 1.32/1.75 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.32/1.75 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X, 'c_Suc'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.32/1.75 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.32/1.75 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.32/1.75 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oone__class_Oone'( X ),
% 1.32/1.75 X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.32/1.75 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.75 X ), Y ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z )
% 1.32/1.75 ), X ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.32/1.75 'c_HOL_Oone__class_Oone'( X ), Y, X ), X ), ~( 'c_lessequals'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.32/1.75 'c_HOL_Oone__class_Oone'( X ), Y, X ), X ) ) ],
% 1.32/1.75 [ =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_HOL_Oone__class_Oone'(
% 1.32/1.75 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.32/1.75 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.75 ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ),
% 1.32/1.75 ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.32/1.75 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.75 ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.32/1.75 ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.32/1.75 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.75 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 1.32/1.75 'tc_nat' ) ) ],
% 1.32/1.75 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.75 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z,
% 1.32/1.75 'tc_nat' ) ) ],
% 1.32/1.75 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.75 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ) ],
% 1.32/1.75 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.75 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 1.32/1.75 'tc_nat' ) ) ],
% 1.32/1.75 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.75 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z,
% 1.32/1.75 'tc_nat' ) ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.32/1.75 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 1.32/1.75 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ), ~(
% 1.32/1.75 'c_lessequals'( Y, Z, X ) ), ~( 'c_lessequals'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.32/1.75 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 1.32/1.75 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ), ~(
% 1.32/1.75 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.32/1.75 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oabs__class_Oabs'(
% 1.32/1.75 Y, X ), X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.32/1.75 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), 'tc_nat' ) ],
% 1.32/1.75 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ) ), 'tc_nat' ) ],
% 1.32/1.75 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), 'tc_nat' ) ],
% 1.32/1.75 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_Suc'(
% 1.32/1.75 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ),
% 1.32/1.75 'c_Divides_Odiv__class_Odiv'( X, 'c_Suc'( 'c_Suc'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ) ), X ), ~(
% 1.32/1.75 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.32/1.75 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.32/1.75 ), Z ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.32/1.75 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 1.32/1.75 'c_HOL_Ouminus__class_Ouminus'( Z, X ), 'c_HOL_Ouminus__class_Ouminus'( Y
% 1.32/1.75 , X ), X ) ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.32/1.75 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.32/1.75 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), ~( 'c_lessequals'( Z, Y, X )
% 1.32/1.75 ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Olordered__ring'( X ) ), 'c_lessequals'(
% 1.32/1.75 'c_HOL_Oabs__class_Oabs'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.32/1.75 Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.32/1.75 'c_HOL_Oabs__class_Oabs'( Y, X ) ), 'c_HOL_Oabs__class_Oabs'( Z, X ) ), X
% 1.32/1.75 ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.32/1.75 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( Y
% 1.32/1.75 , X ), Z, X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.32/1.75 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.32/1.75 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X )
% 1.32/1.75 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.32/1.75 T, X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.32/1.75 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.32/1.75 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.32/1.75 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Oinverse'( Y
% 1.32/1.75 , X ), 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y
% 1.32/1.75 , X ) ) ],
% 1.32/1.75 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.32/1.75 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.32/1.75 ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ), T ), Z, X ),
% 1.32/1.75 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.32/1.75 ), Y ), T ), Z, X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.75 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.32/1.75 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.32/1.75 , 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ),
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.75 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.32/1.75 , X ) ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.75 'c_HOL_Oinverse__class_Odivide'( T, Z, X ),
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.32/1.75 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), 'c_HOL_Oone__class_Oone'(
% 1.32/1.75 'tc_nat' ) ), Y ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.75 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.32/1.75 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.32/1.75 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.32/1.75 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.32/1.75 , Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.75 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.32/1.75 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.32/1.75 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.75 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.32/1.75 ), T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.75 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.32/1.75 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.32/1.75 , 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.32/1.75 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.32/1.75 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.32/1.75 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ), ~( 'c_lessequals'( Y
% 1.32/1.75 , 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Z, T, X ) )
% 1.32/1.75 ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.32/1.75 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.32/1.75 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ), ~( 'c_lessequals'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( T, Z, X ) )
% 1.32/1.75 ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.32/1.75 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ), =( Z,
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.75 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( X, hAPP( hAPP( 'c_Power_Opower_Opower'( Y, X, Z ), T )
% 1.32/1.75 , U ) ), T ), hAPP( hAPP( X, T ), hAPP( hAPP( 'c_Power_Opower_Opower'( Y
% 1.32/1.75 , X, Z ), T ), U ) ) ), ~( 'c_OrderedGroup_Omonoid__mult'( Y, X, Z ) ) ]
% 1.32/1.75 ,
% 1.32/1.75 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.75 X ), 'c_HOL_Oone__class_Oone'( X ) ), 'c_HOL_Oone__class_Oone'( X ) ) ),
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( Y ), X ) ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.32/1.75 Y ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 1.32/1.75 Y ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 1.32/1.75 Y ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 1.32/1.75 Y ) ],
% 1.32/1.75 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.75 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), X ), X ) ],
% 1.32/1.75 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.32/1.75 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), X ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.32/1.75 Y ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 1.32/1.75 Y ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.32/1.75 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( U, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), U, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 1.32/1.75 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) )
% 1.32/1.75 ],
% 1.32/1.75 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Suc'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.75 'tc_nat' ) ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.32/1.75 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), hAPP(
% 1.32/1.75 hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), hAPP( hAPP(
% 1.32/1.75 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.32/1.75 'c_HOL_Oone__class_Oone'( X ), Y, X ) ), Z ) ) ],
% 1.32/1.75 [ =( 'c_Suc'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.32/1.75 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), X ) ) ],
% 1.32/1.75 [ =( 'c_Suc'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X
% 1.32/1.75 ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.32/1.75 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.32/1.75 ), X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.32/1.75 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ), =( Z,
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.32/1.75 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oabs__class_Oabs'(
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.32/1.75 'c_HOL_Ouminus__class_Ouminus'( 'c_Int_Onumber__class_Onumber__of'( Y, X
% 1.32/1.75 ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.75 ), X ) ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.32/1.75 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.32/1.75 'c_HOL_Oone__class_Oone'( X ) ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.75 Y, Z, X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.32/1.75 ) ), T ), 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ), Z, X ) ), =( Z,
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Oinverse__class_Odivide'( Z
% 1.32/1.75 , T, X ) ), 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), T, X ) ), =( T,
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.75 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) )
% 1.32/1.75 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.32/1.75 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.32/1.75 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ),
% 1.32/1.75 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ) ), =( Z,
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.32/1.75 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.32/1.75 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( T, Y, X ) ) ],
% 1.32/1.75 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.32/1.75 'c_Power_Opower__class_Opower'( 'tc_nat' ), X ), Y ), 'tc_nat' ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.32/1.75 'tc_nat' ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ]
% 1.32/1.75 ,
% 1.32/1.75 [ ~( =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ), 'c_Suc'( U
% 1.32/1.75 ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), W ), 'c_Suc'( U ) )
% 1.32/1.75 ) ), ~( 'c_Ring__and__Field_Oordered__semidom'( V0, V1, X, Y, V2, V3, Z
% 1.32/1.75 ) ), =( T, W ), ~( hBOOL( hAPP( hAPP( V2, V1 ), W ) ) ), ~( hBOOL( hAPP(
% 1.32/1.75 hAPP( V2, V1 ), T ) ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), hAPP( hAPP( Y, U ), T ) )
% 1.32/1.75 , hAPP( hAPP( Y, hAPP( hAPP( X, Z ), U ) ), T ) ), ~(
% 1.32/1.75 'c_Groebner__Basis_Ogb__semiring'( X, Y, W, V0, V1, V2 ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), T ), hAPP( hAPP( Y, hAPP(
% 1.32/1.75 hAPP( X, Z ), U ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, Y, W
% 1.32/1.75 , V0, U, V1 ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), Y ) ), hAPP( hAPP( Z, hAPP(
% 1.32/1.75 hAPP( X, T ), U ) ), Y ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, Z, W
% 1.32/1.75 , V0, U, V1 ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( X, Y ), Y ), hAPP( hAPP( Z, hAPP( hAPP( X, T ), T ) ),
% 1.32/1.75 Y ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, Z, U, W, T, V0 ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.32/1.75 X, T, U, Y, W, V0 ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.32/1.75 X, T, U, Z, W, V0 ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 1.32/1.75 'c_Groebner__Basis_Ogb__semiring'( T, X, U, W, V0, V1 ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), U ), hAPP( hAPP( Y, hAPP(
% 1.32/1.75 hAPP( X, Z ), U ) ), hAPP( hAPP( X, T ), U ) ) ), ~(
% 1.32/1.75 'c_Groebner__Basis_Ogb__semiring'( Y, X, W, V0, V1, V2 ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.32/1.75 T, X, U, Y, W, V0 ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.32/1.75 T, X, U, Z, W, V0 ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.32/1.75 T, X, U, W, Y, V0 ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.32/1.75 T, X, U, W, Z, V0 ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 1.32/1.75 , hAPP( hAPP( X, hAPP( hAPP( X, Y ), T ) ), hAPP( hAPP( X, Z ), U ) ) ),
% 1.32/1.75 ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, V0, V1, V2, V3 ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 1.32/1.75 , hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), hAPP( hAPP( X, T ), U ) ) ) ),
% 1.32/1.75 ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, V0, V1, V2, V3 ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 1.32/1.75 , hAPP( hAPP( X, T ), hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), U ) ) ),
% 1.32/1.75 ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, V0, V1, V2, V3 ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, hAPP(
% 1.32/1.75 hAPP( X, Y ), T ) ), Z ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, W
% 1.32/1.75 , V0, V1, V2 ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, Y ),
% 1.32/1.75 hAPP( hAPP( X, Z ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X,
% 1.32/1.75 W, V0, V1, V2 ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 1.32/1.75 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, W
% 1.32/1.75 , V0, V1, V2 ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, Z ),
% 1.32/1.75 hAPP( hAPP( X, Y ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X,
% 1.32/1.75 W, V0, V1, V2 ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 1.32/1.75 , hAPP( hAPP( X, hAPP( hAPP( X, Y ), T ) ), hAPP( hAPP( X, Z ), U ) ) ),
% 1.32/1.75 ~( 'c_Groebner__Basis_Ogb__semiring'( X, W, V0, V1, V2, V3 ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, Y ),
% 1.32/1.75 hAPP( hAPP( X, Z ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U,
% 1.32/1.75 W, V0, V1, V2 ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, Z ),
% 1.32/1.75 hAPP( hAPP( X, Y ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U,
% 1.32/1.75 W, V0, V1, V2 ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, hAPP(
% 1.32/1.75 hAPP( X, Y ), T ) ), Z ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U, W
% 1.32/1.75 , V0, V1, V2 ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 1.32/1.75 'c_Groebner__Basis_Ogb__semiring'( X, T, U, W, V0, V1 ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 1.32/1.75 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U, W
% 1.32/1.75 , V0, V1, V2 ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.32/1.75 X, T, U, Y, W, V0 ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 1.32/1.75 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U, W
% 1.32/1.75 , V0, V1, V2 ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 1.32/1.75 'c_Groebner__Basis_Ogb__semiring'( X, T, U, W, V0, V1 ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.32/1.75 T, X, U, Y, W, V0 ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.32/1.75 T, X, U, W, Y, V0 ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 1.32/1.75 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, W
% 1.32/1.75 , V0, V1, V2 ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 1.32/1.75 'c_Groebner__Basis_Ogb__semiring'( T, X, U, W, V0, V1 ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), U ) ), hAPP( hAPP( Z, hAPP(
% 1.32/1.75 hAPP( X, Y ), T ) ), hAPP( hAPP( X, Y ), U ) ) ), ~(
% 1.32/1.75 'c_Groebner__Basis_Ogb__semiring'( Z, X, W, V0, V1, V2 ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), U ), hAPP( hAPP( Y, hAPP(
% 1.32/1.75 hAPP( X, Z ), U ) ), hAPP( hAPP( X, T ), U ) ) ), ~(
% 1.32/1.75 'c_Groebner__Basis_Ogb__semiring'( W, Y, X, V0, V1, V2 ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.32/1.75 'c_HOL_Oabs__class_Oabs'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X
% 1.32/1.75 ), 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.32/1.75 ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z
% 1.32/1.75 , X ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.32/1.75 ,
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.32/1.75 ), X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.32/1.75 , X ) ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.32/1.75 ,
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.32/1.75 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), Z, X ), ~(
% 1.32/1.75 'c_lessequals'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.32/1.75 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.32/1.75 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.32/1.75 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), Y, X ), ~(
% 1.32/1.75 'c_lessequals'( Z, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.32/1.75 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.32/1.75 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.32/1.75 'c_HOL_Oinverse__class_Odivide'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y
% 1.32/1.75 ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.32/1.75 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.32/1.75 ,
% 1.32/1.75 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.32/1.75 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ), ~(
% 1.32/1.75 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ) ), ~(
% 1.32/1.75 'c_lessequals'( Y, Z, X ) ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.32/1.75 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ), ~(
% 1.32/1.75 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ) ), ~(
% 1.32/1.75 'c_lessequals'( Y, Z, X ) ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.32/1.75 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ),
% 1.32/1.75 'c_HOL_Oabs__class_Oabs'( Y, X ) ) ],
% 1.32/1.75 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.32/1.75 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ) ) ), =( X, Z
% 1.32/1.75 ) ],
% 1.32/1.75 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.32/1.75 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ), =( Y, Z
% 1.32/1.75 ) ],
% 1.32/1.75 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.32/1.75 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ), =( Y, Z
% 1.32/1.75 ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.32/1.75 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP(
% 1.32/1.75 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Ocancel__ab__semigroup__add'( X ) ), ~( =( hAPP(
% 1.32/1.75 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =( hAPP(
% 1.32/1.75 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =( hAPP(
% 1.32/1.75 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ), =( Y, T ) ],
% 1.32/1.75 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( 'c_Power_Opower_Opower'( Y, Z, T ),
% 1.32/1.75 U ), W ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( Y, Z, T ), V0 ), W ) ) )
% 1.32/1.75 , ~( hBOOL( hAPP( hAPP( X, V1 ), U ) ) ), ~( hBOOL( hAPP( hAPP( X, U ),
% 1.32/1.75 V0 ) ) ), ~( 'c_Ring__and__Field_Oordered__semidom'( V2, V1, Y, Z, X, V3
% 1.32/1.75 , T ) ) ],
% 1.32/1.75 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), hAPP( hAPP(
% 1.32/1.75 'c_Power_Opower_Opower'( T, Y, U ), Z ), W ) ) ), hAPP( hAPP(
% 1.32/1.75 'c_Power_Opower_Opower'( T, Y, U ), Z ), W ) ) ), ~( hBOOL( hAPP( hAPP( X
% 1.32/1.75 , Z ), T ) ) ), ~( hBOOL( hAPP( hAPP( X, V0 ), Z ) ) ), ~(
% 1.32/1.75 'c_Ring__and__Field_Oordered__semidom'( V1, V0, T, Y, V2, X, U ) ) ],
% 1.32/1.75 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), Z ) )
% 1.32/1.75 ), ~( hBOOL( hAPP( hAPP( X, hAPP( hAPP( 'c_Power_Opower_Opower'( W, V0,
% 1.32/1.75 V1 ), Y ), V2 ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( W, V0, V1 ), Z )
% 1.32/1.75 , V2 ) ) ) ), ~( 'c_Ring__and__Field_Oordered__semidom'( V3, U, W, V0, T
% 1.32/1.75 , X, V1 ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.75 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ouminus__class_Ouminus'(
% 1.32/1.75 'c_HOL_Oone__class_Oone'( X ), X ) ), Y ), 'c_HOL_Oone__class_Oone'( X )
% 1.32/1.75 ), ~( 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.32/1.75 , Y ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.32/1.75 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.32/1.75 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.32/1.75 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.32/1.75 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.32/1.75 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.32/1.75 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.32/1.75 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.32/1.75 'c_HOL_Oinverse__class_Oinverse'( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X
% 1.32/1.75 ) ), 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 1.32/1.75 'c_HOL_Oinverse__class_Oinverse'( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Oinverse'( Z, X
% 1.32/1.75 ) ), 'c_HOL_Oinverse__class_Oinverse'( Y, X ) ) ), =( Z,
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.32/1.75 ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.32/1.75 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ozero__class_Ozero'( X )
% 1.32/1.75 , X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.32/1.75 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 1.32/1.75 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oinverse__class_Oinverse'( Y, X
% 1.32/1.75 ), X ), Y ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.75 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.32/1.75 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =(
% 1.32/1.75 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.75 X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), Z ), Z, X ),
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 1.32/1.75 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.75 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.75 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), =( Y,
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'(
% 1.32/1.75 Z, 'tc_nat' ) ) ],
% 1.32/1.75 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( 'c_Power_Opower_Opower'( Y, Z,
% 1.32/1.75 T ), U ), 'c_Suc'( W ) ) ) ), ~( hBOOL( hAPP( hAPP( X, Y ), U ) ) ), ~(
% 1.32/1.75 'c_Ring__and__Field_Oordered__semidom'( V0, V1, Y, Z, V2, X, T ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.75 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Z
% 1.32/1.75 , X ) ), T ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.75 'c_HOL_Oinverse__class_Odivide'( Y, T, X ),
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.75 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.32/1.75 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.32/1.75 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.32/1.75 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( 'c_Power_Opower_Opower'( Z, T,
% 1.32/1.75 U ), hAPP( W, V0 ) ), V1 ) ) ), =( V0, Y ), ~(
% 1.32/1.75 'c_Ring__and__Field_Oordered__idom'( V2, V3, Y, V4, V5, X, W, Z, T, V6, U
% 1.32/1.75 ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.75 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.32/1.75 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.32/1.75 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.75 ), X ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.32/1.75 ), T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ), ~(
% 1.32/1.75 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.75 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.32/1.75 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.32/1.75 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.75 ), X ) ), ~( 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.75 X ), Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ), ~(
% 1.32/1.75 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.32/1.75 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), Y, X ) ),
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.32/1.75 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 'c_HOL_Oord__class_Oless'( Z,
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y, hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.32/1.75 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'( Y,
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Z, hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ),
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.32/1.75 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'( Y,
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( T,
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), Z, X ) ) ],
% 1.32/1.75 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.75 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.32/1.75 Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X, 'tc_nat' ) ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.32/1.75 ) ), Y, 'tc_nat' ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 1.32/1.75 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_Suc'( Y ), X ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.32/1.75 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ) ) ) ],
% 1.32/1.75 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( Y, 'c_Suc'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.32/1.75 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( X,
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, 'c_Suc'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ) ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 1.32/1.75 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Oone__class_Oone'( 'tc_nat'
% 1.32/1.75 ), X ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.32/1.75 [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.75 'tc_nat' ) ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ]
% 1.32/1.75 ,
% 1.32/1.75 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.32/1.75 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.32/1.75 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.75 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.32/1.75 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.75 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ), ~( 'c_lessequals'( Y,
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.32/1.75 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.32/1.75 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.32/1.75 X ) ), =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.75 X ), Y ), T ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z )
% 1.32/1.75 ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.32/1.75 X ) ), =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.75 X ), Y ), T ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z )
% 1.32/1.75 ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.32/1.75 [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.75 'tc_nat' ) ), 'tc_nat' ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =(
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.32/1.75 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ),
% 1.32/1.75 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), T ), ~(
% 1.32/1.75 'c_OrderedGroup_Omonoid__mult'( X, Y, Z ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.32/1.75 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.32/1.75 , 'c_HOL_Oabs__class_Oabs'( Y, X ) ), 'c_HOL_Oabs__class_Oabs'( Z, X ) )
% 1.32/1.75 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Z, X ), U, X ) ),
% 1.32/1.75 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Y, X ), T, X ) )
% 1.32/1.75 ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.75 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.32/1.75 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.32/1.75 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.75 ), X ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.75 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.32/1.75 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.32/1.75 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 'c_HOL_Oord__class_Oless'(
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.75 ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.32/1.75 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oinverse__class_Oinverse'( Y, X
% 1.32/1.75 ), X ), Y ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.75 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.32/1.75 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.32/1.75 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.75 ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.32/1.75 , Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.75 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.32/1.75 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.32/1.75 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.75 ), X ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.32/1.75 ), T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.32/1.75 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), 'c_Suc'( Z ) ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.32/1.75 ), Z ) ) ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.32/1.75 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), 'c_Suc'( Z ) ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.32/1.75 ), Z ) ), Y ) ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~(
% 1.32/1.75 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.32/1.75 =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.75 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =( hAPP(
% 1.32/1.75 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.32/1.75 , 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.32/1.75 ,
% 1.32/1.75 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.32/1.75 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ) ],
% 1.32/1.75 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.32/1.75 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.32/1.75 , Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X )
% 1.32/1.75 ), 'c_Divides_Odiv__class_Omod'( Z, T, X ) ), T, X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.75 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.32/1.75 , X ) ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.32/1.75 'c_HOL_Oinverse__class_Odivide'( T, Z, X ),
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.75 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.32/1.75 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.32/1.75 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ),
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.75 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y
% 1.32/1.75 ), X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.32/1.75 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.32/1.75 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 1.32/1.75 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.32/1.75 , X ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.32/1.75 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.32/1.75 ), Y ), 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ),
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.32/1.75 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.32/1.75 , 'tc_nat' ), 'tc_nat' ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.32/1.75 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.75 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.32/1.75 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.75 X ), Y ), Z ) ), T ) ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.75 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.32/1.75 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.75 X ), Y ), Z ) ), T ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.75 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.32/1.75 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.75 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.32/1.75 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 1.32/1.75 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.32/1.75 'tc_nat' ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.75 'tc_nat' ), Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X ) )
% 1.32/1.75 ), =( 'c_HOL_Ozero__class_Ozero'( X ), Y ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.32/1.75 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.32/1.75 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.32/1.75 'c_Power_Opower__class_Opower'( X ), Y ), T ) ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.32/1.75 ), ~( =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.32/1.75 ) ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.32/1.75 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oabs__class_Oabs'( Y, X ) ),
% 1.32/1.75 'c_HOL_Oabs__class_Oabs'( Z, X ) ), X ) ],
% 1.32/1.75 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( 'c_Suc'( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_Suc'( 'c_Suc'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), X ) ), 'tc_nat' ) ) ],
% 1.32/1.75 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.32/1.75 'tc_nat' ), ~( 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.32/1.75 'c_Power_Opower__class_Opower'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ],
% 1.32/1.75 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_lessequals'( Y, Z, X ) )
% 1.32/1.75 , ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.32/1.75 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.32/1.75 , X ), 'c_lessequals'( Z, Y, X ) ],
% 1.32/1.75 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'( Y, Y, X ) )
% 1.32/1.75 , ~( 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ],
% 1.32/1.75 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Y
% 1.32/1.75 , X ), 'c_lessequals'( Y, Y, X ) ],
% 1.32/1.75 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.32/1.75 , Z, X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ],
% 1.32/1.75 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 1.32/1.75 'c_HOL_Oord__class_Oless'( Z, Y, X ) ],
% 1.32/1.75 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.32/1.75 , X ), 'c_lessequals'( Z, Y, X ) ],
% 1.32/1.75 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'( Y, Z, X ) )
% 1.32/1.75 , ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y
% 1.32/1.75 , Y, X ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.32/1.75 'c_HOL_Oinverse__class_Odivide'( Y, Y, X ), 'c_HOL_Oone__class_Oone'( X )
% 1.32/1.75 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.32/1.75 'c_HOL_Oinverse__class_Odivide'( Y, Y, X ), 'c_HOL_Oone__class_Oone'( X )
% 1.32/1.75 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.75 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.32/1.75 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.32/1.75 , Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_Divides_Odiv__class_Omod'( Z, T
% 1.32/1.75 , X ) ), T, X ) ) ],
% 1.32/1.75 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.32/1.75 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.32/1.75 , Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X )
% 1.32/1.75 ), Z ), T, X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Z, Y, X
% 1.32/1.75 ), X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.32/1.75 ), X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Z, Y, X
% 1.32/1.75 ), X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.32/1.75 ), X ) ) ],
% 1.32/1.75 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.32/1.75 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), =( X, 'c_HOL_Oone__class_Oone'(
% 1.32/1.75 'tc_nat' ) ) ],
% 1.32/1.75 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.32/1.75 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), =( Y, 'c_HOL_Oone__class_Oone'(
% 1.32/1.75 'tc_nat' ) ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.32/1.75 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ),
% 1.32/1.75 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.32/1.75 , Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 1.32/1.75 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.32/1.75 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.32/1.75 'c_Power_Opower__class_Opower'( X ), T ), Z ), X ), ~( 'c_lessequals'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 1.32/1.75 ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), ~( 'class_Int_Onumber'(
% 1.32/1.75 X ) ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.75 X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), Z ) ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.32/1.75 , X ) ), T ) ) ) ],
% 1.32/1.75 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.32/1.75 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.32/1.75 'tc_nat' ) ), =( Y, Z ) ],
% 1.32/1.75 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.32/1.75 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ), 'tc_nat' ) ) ],
% 1.32/1.75 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.32/1.75 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), X ), 'tc_nat' ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.32/1.75 'c_HOL_Oone__class_Oone'( X ), Y, X ), 'c_lessequals'( Y,
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.32/1.75 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oone__class_Oone'( X ),
% 1.32/1.75 X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.32/1.75 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), =( Y,
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_lessequals'( hAPP( hAPP(
% 1.32/1.75 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y
% 1.32/1.75 ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.32/1.75 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.32/1.75 ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_lessequals'( Y,
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.32/1.75 'c_Power_Opower__class_Opower'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.75 X ), X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.32/1.75 'c_lessequals'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.32/1.75 'c_lessequals'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.32/1.75 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.32/1.75 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~(
% 1.32/1.75 'c_lessequals'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.32/1.75 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ]
% 1.32/1.75 ,
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.32/1.75 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.32/1.75 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~(
% 1.32/1.75 'c_lessequals'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.32/1.75 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.32/1.75 ,
% 1.32/1.75 [ =( X, 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X
% 1.32/1.75 , 'c_Suc'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat'
% 1.32/1.75 ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.32/1.75 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.32/1.75 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ),
% 1.32/1.75 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ) ) ],
% 1.32/1.75 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 1.32/1.75 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.32/1.75 Z, X ), 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oinverse__class_Odivide'(
% 1.32/1.75 Y, Z, X ), X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.75 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 1.32/1.75 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.75 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 1.32/1.75 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 1.32/1.75 'class_OrderedGroup_Omonoid__mult'( X ) ), 'c_lessequals'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.75 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 1.32/1.75 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ) ],
% 1.32/1.75 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.32/1.75 'c_Suc'( X ), 'tc_nat' ) ],
% 1.32/1.75 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.32/1.75 'c_Suc'( X ), 'tc_nat' ) ],
% 1.32/1.75 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Ouminus__class_Ouminus'(
% 1.32/1.75 'c_HOL_Oone__class_Oone'( X ), X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.32/1.75 'c_Int_OMin', X ) ) ],
% 1.32/1.75 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( X, T ), Z ) )
% 1.32/1.75 ), ~( hBOOL( hAPP( hAPP( X, hAPP( hAPP( 'c_Power_Opower_Opower'( U, W,
% 1.32/1.75 V0 ), Y ), 'c_Suc'( V1 ) ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( U, W,
% 1.32/1.75 V0 ), Z ), 'c_Suc'( V1 ) ) ) ) ), ~(
% 1.32/1.75 'c_Ring__and__Field_Oordered__semidom'( V2, T, U, W, X, V3, V0 ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.32/1.75 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ),
% 1.32/1.75 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP(
% 1.32/1.75 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.32/1.75 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X )
% 1.32/1.75 , Y, X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), =( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.75 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ), U ) ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.75 X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ), U )
% 1.32/1.75 ) ],
% 1.32/1.75 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ), T ) ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ), Y ) ), T ) ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X ) )
% 1.32/1.75 , Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X ) )
% 1.32/1.75 , Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ouminus__class_Ouminus'( Y,
% 1.32/1.75 X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.75 [ 'c_HOL_Oord__class_Oless'( 'c_Divides_Odiv__class_Omod'( X, Y,
% 1.32/1.75 'tc_nat' ), Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.75 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.32/1.75 ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( T
% 1.32/1.75 , 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.75 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.32/1.75 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.32/1.75 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.75 ), X ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ),
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.75 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X ),
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.32/1.75 ), X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Oinverse__class_Odivide'(
% 1.32/1.75 Y, 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.75 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.32/1.75 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.32/1.75 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.75 ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ),
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), =(
% 1.32/1.75 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ),
% 1.32/1.75 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oabs__class_Oabs'( Y, X ), X ) )
% 1.32/1.75 , =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), =(
% 1.32/1.75 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X )
% 1.32/1.75 , 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.32/1.75 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.75 X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), =( Y
% 1.32/1.75 , 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X )
% 1.32/1.75 , X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.75 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Oord__class_Oless'(
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.75 ), X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( T,
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.75 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.32/1.75 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.32/1.75 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 'c_HOL_Oord__class_Oless'(
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.75 ), X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.75 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.75 ), X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( T,
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.75 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.32/1.75 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.32/1.75 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.75 ), X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.75 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ), X ), ~(
% 1.32/1.75 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.32/1.75 , 'tc_nat' ), 'tc_nat' ) ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) ) ), =( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), U ) ],
% 1.32/1.75 [ =( 'c_Suc'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.75 'c_Suc'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ),
% 1.32/1.75 'c_Divides_Odiv__class_Odiv'( X, 'c_Suc'( 'c_Suc'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ) ) ), X ),
% 1.32/1.75 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.32/1.75 [ ~( 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.32/1.75 ), 'tc_nat' ) ) ],
% 1.32/1.75 [ ~( 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.32/1.75 ), 'tc_nat' ) ) ],
% 1.32/1.75 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OMin', 'tc_nat' ),
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.32/1.75 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.32/1.75 ), Y ), 'c_Suc'( Z ) ), 'c_HOL_Oone__class_Oone'( X ), X ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.32/1.75 ,
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.32/1.75 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.75 'c_HOL_Oinverse__class_Oinverse'( Z, X ),
% 1.32/1.75 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.32/1.75 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.32/1.75 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.75 'c_HOL_Oinverse__class_Oinverse'( Z, X ),
% 1.32/1.75 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.32/1.75 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.75 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oabs__class_Oabs'( Y, X ) ),
% 1.32/1.75 Z ), X ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.32/1.75 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.32/1.75 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.32/1.75 ), Z ) ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.32/1.75 ), T ) ) ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.32/1.75 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), X ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.32/1.75 ), T ) ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Z
% 1.32/1.75 ), T ) ) ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 1.32/1.75 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.32/1.75 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 1.32/1.75 'c_lessequals'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X )
% 1.32/1.75 , X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X )
% 1.32/1.75 , X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.32/1.75 ,
% 1.32/1.75 [ =( 'c_Divides_Odiv__class_Odiv'( 'c_Suc'( X ), Y, 'tc_nat' ), hAPP(
% 1.32/1.75 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( X,
% 1.32/1.75 Y, 'tc_nat' ) ), 'c_Divides_Odiv__class_Odiv'( 'c_Suc'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ) ),
% 1.32/1.75 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.75 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ),
% 1.32/1.75 'c_Divides_Odiv__class_Omod'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.75 'tc_nat' ) ), Y, 'tc_nat' ) ), Y, 'tc_nat' ) ) ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.32/1.75 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.32/1.75 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ) ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.32/1.75 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ), ~( 'c_lessequals'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.32/1.75 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.32/1.75 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( X ) )
% 1.32/1.75 ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'(
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ), 'tc_nat' ) ), ~(
% 1.32/1.75 'c_lessequals'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ),
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.32/1.75 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'(
% 1.32/1.75 'c_HOL_Oone__class_Oone'( X ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.32/1.75 ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'(
% 1.32/1.75 'c_HOL_Oone__class_Oone'( X ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.32/1.75 ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.32/1.75 ) ],
% 1.32/1.75 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( 'c_Power_Opower_Opower'( Y, Z, T ),
% 1.32/1.75 U ), W ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( Y, Z, T ), U ), V0 ) ) )
% 1.32/1.75 , ~( hBOOL( hAPP( hAPP( X, U ), Y ) ) ), ~( hBOOL( hAPP( hAPP( X, V1 ), U
% 1.32/1.75 ) ) ), ~( 'c_HOL_Oord__class_Oless'( V0, W, 'tc_nat' ) ), ~(
% 1.32/1.75 'c_Ring__and__Field_Oordered__semidom'( V2, V1, Y, Z, V3, X, T ) ) ],
% 1.32/1.75 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.32/1.75 'c_Divides_Odiv__class_Omod'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), Z
% 1.32/1.75 , X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 1.32/1.75 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.32/1.75 'c_Divides_Odiv__class_Odiv'( Y, Y, X ), 'c_HOL_Oone__class_Oone'( X ) )
% 1.32/1.75 , =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.32/1.75 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ),
% 1.32/1.75 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.32/1.75 , Z ), T ), X ), ~( 'c_lessequals'( Y, T, X ) ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 1.32/1.75 ,
% 1.32/1.75 [ =( hAPP( X, Y ), hAPP( Z, T ) ), ~( hBOOL( hAPP( hAPP( U, Y ), W ) ) )
% 1.32/1.75 , ~( 'c_Ring__and__Field_Oordered__idom'( V0, Z, W, V1, V2, U, V3, T, V4
% 1.32/1.75 , X, V5 ) ) ],
% 1.32/1.75 [ =( hAPP( X, Y ), Z ), ~( hBOOL( hAPP( hAPP( T, U ), Y ) ) ), ~(
% 1.32/1.75 'c_Ring__and__Field_Oordered__idom'( W, V0, U, V1, V2, T, V3, Z, V4, X,
% 1.32/1.75 V5 ) ) ],
% 1.32/1.75 [ ~( =( hAPP( X, Y ), hAPP( Z, T ) ) ), ~(
% 1.32/1.75 'c_Ring__and__Field_Oordered__idom'( U, Z, W, V0, V1, V2, V3, T, V4, X,
% 1.32/1.75 V5 ) ), hBOOL( hAPP( hAPP( V2, Y ), W ) ) ],
% 1.32/1.75 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), Y, 'tc_nat' ), X ),
% 1.32/1.75 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.32/1.75 'tc_nat' ) ) ],
% 1.32/1.75 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), X, 'tc_nat' ), Y ),
% 1.32/1.75 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.32/1.75 'tc_nat' ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.75 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.75 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.32/1.75 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.32/1.75 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.32/1.75 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ), ~(
% 1.32/1.75 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.32/1.75 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.32/1.75 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X ) ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.32/1.75 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X ), ~(
% 1.32/1.75 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ),
% 1.32/1.75 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.32/1.75 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ),
% 1.32/1.75 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ), ~(
% 1.32/1.75 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ),
% 1.32/1.75 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.32/1.75 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X ) ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ),
% 1.32/1.75 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X ), ~(
% 1.32/1.75 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.75 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X
% 1.32/1.75 ) ), Z ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ),
% 1.32/1.75 ~( 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.75 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.32/1.75 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.32/1.75 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ), ~(
% 1.32/1.75 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.32/1.75 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'(
% 1.32/1.75 X ), Y ), Z ), X ), ~( 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), Y,
% 1.32/1.75 X ) ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.32/1.75 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oabs__class_Oabs'( Y, X ), X ),
% 1.32/1.75 'c_HOL_Oabs__class_Oabs'( Y, X ) ) ],
% 1.32/1.75 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.75 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.32/1.75 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ), Z ) ),
% 1.32/1.75 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ), T ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ],
% 1.32/1.75 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.75 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.32/1.75 'c_Divides_Odiv__class_Odiv'( Z, Y, X ) ) ), 'c_Divides_Odiv__class_Omod'(
% 1.32/1.75 Z, Y, X ) ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T )
% 1.32/1.75 ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.75 'c_HOL_Oabs__class_Oabs'( Y, X ), X ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.75 X ) ) ],
% 1.32/1.75 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( 'c_Power_Opower_Opower'( Y, Z,
% 1.32/1.75 T ), U ), W ) ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), W, 'tc_nat' ) ), ~( hBOOL( hAPP(
% 1.32/1.75 hAPP( X, Y ), U ) ) ), ~( 'c_Ring__and__Field_Oordered__semidom'( V0, V1
% 1.32/1.75 , Y, Z, V2, X, T ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, Y ),
% 1.32/1.75 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ) ), ~(
% 1.32/1.75 'c_Groebner__Basis_Ogb__semiring'( U, W, X, V0, V1, V2 ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.75 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.32/1.75 ), X ), ~( 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( T,
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.75 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.32/1.75 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.32/1.75 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.75 ), X ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.32/1.75 ), T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ),
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.75 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X ),
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.32/1.75 ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.75 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.32/1.75 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.32/1.75 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.75 ), X ) ), ~( 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.75 X ), Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ),
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.32/1.75 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.32/1.75 ), Y ), Z ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), T ),
% 1.32/1.75 X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X )
% 1.32/1.75 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.32/1.75 ), ~( 'c_HOL_Oord__class_Oless'( T, Z, 'tc_nat' ) ) ],
% 1.32/1.75 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OMin', X ),
% 1.32/1.75 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oone__class_Oone'( X ), X ) ) ]
% 1.32/1.75 ,
% 1.32/1.75 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), 'tc_nat' ), ~(
% 1.32/1.75 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ) ],
% 1.32/1.75 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), 'tc_nat' ), ~(
% 1.32/1.75 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.75 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.32/1.75 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.32/1.75 , 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ),
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.75 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.32/1.75 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ),
% 1.32/1.75 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.32/1.75 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.75 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.32/1.75 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.32/1.75 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.75 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ),
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.75 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.32/1.75 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.32/1.75 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.32/1.75 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ),
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.32/1.75 [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), X, 'tc_nat' ),
% 1.32/1.75 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.75 'c_HOL_Oone__class_Oone'( 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.75 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X
% 1.32/1.75 ), X ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.32/1.75 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ),
% 1.32/1.75 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X )
% 1.32/1.75 , 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.75 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.32/1.75 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ),
% 1.32/1.75 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.75 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.32/1.75 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.32/1.75 , 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.32/1.75 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.32/1.75 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.32/1.75 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 1.32/1.75 ) ],
% 1.32/1.75 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.32/1.75 'c_Divides_Odiv__class_Omod'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.32/1.75 ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 1.32/1.75 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.32/1.75 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ) ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'(
% 1.32/1.75 X, T, 'tc_nat' ) ],
% 1.32/1.75 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), hAPP(
% 1.32/1.75 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.32/1.75 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.75 ), X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.32/1.75 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.75 ), X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'( Z,
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.32/1.75 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.75 ), X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'( Y,
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.32/1.75 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.75 ), X ) ) ],
% 1.32/1.75 [ =( hAPP( 'c_NthRoot_Oroot'( X ), hAPP( 'c_NthRoot_Oroot'( Y ), Z ) ),
% 1.32/1.75 hAPP( 'c_NthRoot_Oroot'( Y ), hAPP( 'c_NthRoot_Oroot'( X ), Z ) ) ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.32/1.75 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.75 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.75 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X
% 1.32/1.75 ) ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.32/1.75 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ouminus__class_Ouminus'(
% 1.32/1.75 'c_HOL_Oone__class_Oone'( X ), X ) ), Z ) ), hAPP( hAPP(
% 1.32/1.75 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'( Y
% 1.32/1.75 , Z, X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.75 Z, X ) ), ~( 'c_lessequals'( 'c_HOL_Oinverse__class_Oinverse'( Z, X ),
% 1.32/1.75 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.32/1.75 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.32/1.75 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.32/1.75 'c_lessequals'( Z, Y, X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'( Y
% 1.32/1.75 , Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.75 ), X ) ), ~( 'c_lessequals'( 'c_HOL_Oinverse__class_Oinverse'( Z, X ),
% 1.32/1.75 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.32/1.75 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.32/1.75 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.32/1.75 'c_lessequals'( Z, Y, X ) ) ],
% 1.32/1.75 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.32/1.75 'c_Divides_Odiv__class_Odiv'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), Z
% 1.32/1.75 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.75 [ ~( 'class_Divides_Oring__div'( X ) ), ~( =(
% 1.32/1.75 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.32/1.75 , Z, X ) ) ), =( 'c_Divides_Odiv__class_Omod'(
% 1.32/1.75 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ),
% 1.32/1.75 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ouminus__class_Ouminus'( T, X ), Z,
% 1.32/1.75 X ) ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X ) )
% 1.32/1.75 , Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.75 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.32/1.75 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.75 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y
% 1.32/1.75 ), 'tc_nat' ) ) ],
% 1.32/1.75 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.32/1.75 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.75 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X
% 1.32/1.75 ), 'tc_nat' ) ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.32/1.75 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.32/1.75 ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.32/1.75 ,
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.32/1.75 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.32/1.75 ), Y ), Z ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), T ), Z ),
% 1.32/1.75 X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.32/1.75 , Z, 'tc_nat' ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y
% 1.32/1.75 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( Y,
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.75 X ), Z ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y )
% 1.32/1.75 ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( Y,
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.75 X ), Y ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z )
% 1.32/1.75 ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.32/1.75 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.32/1.75 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.32/1.75 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), U ), Z ) ), X ), hAPP( hAPP(
% 1.32/1.75 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.32/1.75 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), T ), hAPP( hAPP(
% 1.32/1.75 'c_Power_Opower__class_Opower'( X ), Y ), U ), X ) ), Z ) ), =( Y,
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.32/1.75 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.32/1.75 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.32/1.75 'c_HOL_Oinverse__class_Odivide'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.32/1.75 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.32/1.75 'c_HOL_Oinverse__class_Odivide'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.32/1.75 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.75 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 1.32/1.75 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.32/1.75 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.32/1.75 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ),
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.32/1.75 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.32/1.75 , 'tc_nat' ), 'tc_nat' ), =( 'c_Int_Onumber__class_Onumber__of'( Z,
% 1.32/1.75 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.32/1.75 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.32/1.75 , X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.32/1.75 ,
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.32/1.75 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.32/1.75 , X ) ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.32/1.75 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.32/1.75 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), X ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.32/1.75 ), Z ) ), T ) ) ],
% 1.32/1.75 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.75 'tc_nat' ), 'c_Suc'( Z ) ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.75 'tc_nat' ), 'c_Suc'( Z ) ), Y ), 'tc_nat' ) ) ],
% 1.32/1.75 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.75 'tc_nat' ), 'c_Suc'( X ) ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.75 'tc_nat' ), 'c_Suc'( X ) ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.75 Y, Z, 'tc_nat' ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP( hAPP(
% 1.32/1.75 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oabs__class_Oabs'( Y, X ) ),
% 1.32/1.75 Z ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), ~(
% 1.32/1.75 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ) ],
% 1.32/1.75 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.32/1.75 'tc_nat' ), 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.32/1.75 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_OrderedGroup_Omonoid__mult'( Z
% 1.32/1.75 , X, T ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_OrderedGroup_Omonoid__mult'( Y
% 1.32/1.75 , X, T ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.32/1.75 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.32/1.75 , 'tc_nat' ), 'tc_nat' ), 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.75 X ), X ), ~( 'c_lessequals'( hAPP( hAPP( 'c_Power_Opower__class_Opower'(
% 1.32/1.75 X ), Z ), 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.32/1.75 [ ~( 'class_Int_Onumber__ring'( X ) ), ~( 'c_Int_Oiszero'(
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OMin', X ), X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( =(
% 1.32/1.75 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oone__class_Oone'( X ) )
% 1.32/1.75 ), =( Y, 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ),
% 1.32/1.75 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.32/1.75 'c_HOL_Oone__class_Oone'( X ), X ) ) ],
% 1.32/1.75 [ =( hAPP( 'c_NthRoot_Oroot'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.75 'tc_nat' ) ) ), X ), X ) ],
% 1.32/1.75 [ ~( =( 'c_Suc'( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), Y ) )
% 1.32/1.75 , =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.75 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.32/1.75 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.32/1.75 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.75 X ), 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.32/1.75 , Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.75 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( T,
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.75 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.32/1.75 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.32/1.75 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.32/1.75 ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.75 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), Z, X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.32/1.75 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ),
% 1.32/1.75 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oabs__class_Oabs'( Y, X ), X ) )
% 1.32/1.75 ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.32/1.75 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X )
% 1.32/1.75 , 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.32/1.75 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.32/1.75 'c_HOL_Oabs__class_Oabs'( Y, X ), Y ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.75 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.32/1.75 ,
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.75 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.32/1.75 ,
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.75 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.32/1.75 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.32/1.75 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.32/1.75 ), Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_Divides_Odiv__class_Omod'( Z,
% 1.32/1.75 T, X ) ), T, X ) ) ],
% 1.32/1.75 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.32/1.75 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.32/1.75 ), Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X
% 1.32/1.75 ) ), Z ), T, X ) ) ],
% 1.32/1.75 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.32/1.75 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, 'c_Suc'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.32/1.75 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.32/1.75 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.32/1.75 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.32/1.75 'c_Int_OMin', X ) ), Y ), 'c_HOL_Ouminus__class_Ouminus'( Y, X ) ) ],
% 1.32/1.75 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OMin', X ) ),
% 1.32/1.75 'c_HOL_Ouminus__class_Ouminus'( Y, X ) ) ],
% 1.32/1.75 [ =( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ),
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X
% 1.32/1.75 , Y, 'tc_nat' ) ) ],
% 1.32/1.75 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), T ) ), hBOOL( hAPP(
% 1.32/1.75 hAPP( U, T ), W ) ), ~( hBOOL( hAPP( hAPP( X, Z ), V0 ) ) ), ~(
% 1.32/1.75 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, U, X, V4, V0, Y, V5,
% 1.32/1.75 V6 ) ) ],
% 1.32/1.75 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), T ) ), ~( hBOOL( hAPP(
% 1.32/1.75 hAPP( X, U ), Z ) ) ), hBOOL( hAPP( hAPP( W, V0 ), T ) ), ~(
% 1.32/1.75 'c_Ring__and__Field_Oordered__idom'( V1, V2, V0, V3, W, X, V4, U, Y, V5,
% 1.32/1.75 V6 ) ) ],
% 1.32/1.75 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), Y ) ) ), hBOOL( hAPP(
% 1.32/1.75 hAPP( U, Y ), W ) ), ~( hBOOL( hAPP( hAPP( X, V0 ), T ) ) ), ~(
% 1.32/1.75 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, U, X, V4, V0, Z, V5,
% 1.32/1.75 V6 ) ) ],
% 1.32/1.75 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), Y ) ) ), ~( hBOOL( hAPP(
% 1.32/1.75 hAPP( X, T ), U ) ) ), hBOOL( hAPP( hAPP( W, V0 ), Y ) ), ~(
% 1.32/1.75 'c_Ring__and__Field_Oordered__idom'( V1, V2, V0, V3, W, X, V4, U, Z, V5,
% 1.32/1.75 V6 ) ) ],
% 1.32/1.75 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), Z ) ), hBOOL( hAPP(
% 1.32/1.75 hAPP( U, Z ), W ) ), ~( hBOOL( hAPP( hAPP( X, T ), V0 ) ) ), ~(
% 1.32/1.75 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, U, X, V4, V0, Y, V5,
% 1.32/1.75 V6 ) ) ],
% 1.32/1.75 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), Z ) ), ~( hBOOL( hAPP(
% 1.32/1.75 hAPP( X, U ), T ) ) ), hBOOL( hAPP( hAPP( W, V0 ), Z ) ), ~(
% 1.32/1.75 'c_Ring__and__Field_Oordered__idom'( V1, V2, V0, V3, W, X, V4, U, Y, V5,
% 1.32/1.75 V6 ) ) ],
% 1.32/1.75 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, Y ), T ) ) ), hBOOL( hAPP(
% 1.32/1.75 hAPP( U, Y ), W ) ), ~( hBOOL( hAPP( hAPP( X, V0 ), T ) ) ), ~(
% 1.32/1.75 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, U, X, V4, V0, Z, V5,
% 1.32/1.75 V6 ) ) ],
% 1.32/1.75 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, Y ), T ) ) ), ~( hBOOL( hAPP(
% 1.32/1.75 hAPP( X, T ), U ) ) ), hBOOL( hAPP( hAPP( W, V0 ), Y ) ), ~(
% 1.32/1.75 'c_Ring__and__Field_Oordered__idom'( V1, V2, V0, V3, W, X, V4, U, Z, V5,
% 1.32/1.75 V6 ) ) ],
% 1.32/1.75 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), T ) ), hBOOL( hAPP(
% 1.32/1.75 hAPP( U, T ), W ) ), ~( hBOOL( hAPP( hAPP( X, Z ), V0 ) ) ), ~(
% 1.32/1.75 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, X, U, V4, V0, Y, V5,
% 1.32/1.75 V6 ) ) ],
% 1.32/1.75 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), T ) ), ~( hBOOL( hAPP(
% 1.32/1.75 hAPP( X, U ), Z ) ) ), hBOOL( hAPP( hAPP( W, V0 ), T ) ), ~(
% 1.32/1.75 'c_Ring__and__Field_Oordered__idom'( V1, V2, V0, V3, X, W, V4, U, Y, V5,
% 1.32/1.75 V6 ) ) ],
% 1.32/1.75 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), Y ) ) ), hBOOL( hAPP(
% 1.32/1.75 hAPP( U, Y ), W ) ), ~( hBOOL( hAPP( hAPP( X, V0 ), T ) ) ), ~(
% 1.32/1.75 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, X, U, V4, V0, Z, V5,
% 1.32/1.75 V6 ) ) ],
% 1.32/1.75 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), Y ) ) ), ~( hBOOL( hAPP(
% 1.32/1.75 hAPP( X, T ), U ) ) ), hBOOL( hAPP( hAPP( W, V0 ), Y ) ), ~(
% 1.32/1.75 'c_Ring__and__Field_Oordered__idom'( V1, V2, V0, V3, X, W, V4, U, Z, V5,
% 1.32/1.75 V6 ) ) ],
% 1.32/1.75 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), Z ) ), hBOOL( hAPP(
% 1.32/1.75 hAPP( U, Z ), W ) ), ~( hBOOL( hAPP( hAPP( X, T ), V0 ) ) ), ~(
% 1.32/1.75 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, X, U, V4, V0, Y, V5,
% 1.32/1.75 V6 ) ) ],
% 1.32/1.75 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), Z ) ), ~( hBOOL( hAPP(
% 1.32/1.75 hAPP( X, U ), T ) ) ), hBOOL( hAPP( hAPP( W, V0 ), Z ) ), ~(
% 1.32/1.75 'c_Ring__and__Field_Oordered__idom'( V1, V2, V0, V3, X, W, V4, U, Y, V5,
% 1.32/1.75 V6 ) ) ],
% 1.32/1.75 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, Y ), T ) ) ), hBOOL( hAPP(
% 1.32/1.75 hAPP( U, Y ), W ) ), ~( hBOOL( hAPP( hAPP( X, V0 ), T ) ) ), ~(
% 1.32/1.75 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, X, U, V4, V0, Z, V5,
% 1.32/1.75 V6 ) ) ],
% 1.32/1.75 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, Y ), T ) ) ), ~( hBOOL( hAPP(
% 1.32/1.75 hAPP( X, T ), U ) ) ), hBOOL( hAPP( hAPP( W, V0 ), Y ) ), ~(
% 1.32/1.75 'c_Ring__and__Field_Oordered__idom'( V1, V2, V0, V3, X, W, V4, U, Z, V5,
% 1.32/1.75 V6 ) ) ],
% 1.32/1.75 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( Z, T ) ) ), ~( hBOOL( hAPP( hAPP( X,
% 1.32/1.75 Y ), T ) ) ), ~( 'c_Ring__and__Field_Oordered__idom'( U, W, Y, V0, V1, X
% 1.32/1.75 , V2, V3, V4, Z, V5 ) ) ],
% 1.32/1.75 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( X, Y ), hAPP(
% 1.32/1.75 T, Z ) ) ) ), ~( 'c_Ring__and__Field_Oordered__idom'( U, W, Y, V0, V1, X
% 1.32/1.75 , V2, V3, V4, T, V5 ) ) ],
% 1.32/1.75 [ hBOOL( hAPP( hAPP( X, hAPP( Y, Z ) ), T ) ), ~( hBOOL( hAPP( hAPP( X,
% 1.32/1.75 Z ), T ) ) ), ~( 'c_Ring__and__Field_Oordered__idom'( U, W, T, V0, V1, X
% 1.32/1.75 , V2, V3, V4, Y, V5 ) ) ],
% 1.32/1.75 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( X, hAPP( T, Y
% 1.32/1.75 ) ), Z ) ) ), ~( 'c_Ring__and__Field_Oordered__idom'( U, W, Z, V0, V1, X
% 1.32/1.75 , V2, V3, V4, T, V5 ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.75 X ), Y ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z )
% 1.32/1.75 ), X ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.75 X ), Y ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z )
% 1.32/1.75 ), X ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.32/1.75 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ),
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.32/1.75 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.32/1.75 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ),
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.32/1.75 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =( hAPP( hAPP(
% 1.32/1.75 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.32/1.75 'c_Power_Opower__class_Opower'( X ), T ), Z ) ) ), =( Y, T ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.32/1.75 'tc_nat' ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X )
% 1.32/1.75 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), Z ) ), =( Y,
% 1.32/1.75 'c_HOL_Ouminus__class_Ouminus'( T, X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.32/1.75 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.75 X ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X
% 1.32/1.75 ), 'c_HOL_Oinverse__class_Odivide'( Y, T, X ) ), =( Z,
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.32/1.75 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.75 X ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X
% 1.32/1.75 ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ) ), =( Y,
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.32/1.75 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oabs__class_Oabs'( hAPP( hAPP(
% 1.32/1.75 'c_Power_Opower__class_Opower'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.32/1.75 'c_Int_OMin', X ) ), Y ), X ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.75 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.32/1.75 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.32/1.75 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.75 X ), 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~( 'c_lessequals'(
% 1.32/1.75 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.75 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ), ~( 'c_lessequals'( Y,
% 1.32/1.75 'c_HOL_Oinverse__class_Odivide'( T, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.32/1.75 , X ), X ), X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.75 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.32/1.75 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.32/1.75 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.32/1.75 ), X ) ), ~( 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.75 X ), T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.75 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~( 'c_lessequals'(
% 1.32/1.75 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( T
% 1.32/1.75 , X ), X ), Z, X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z
% 1.32/1.75 , X ) ), T ), 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), Z, X ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.75 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'(
% 1.32/1.75 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.32/1.75 'c_Groebner__Basis_Ogb__semiring'( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), 'c_Power_Opower__class_Opower'( X ),
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ), X ) ]
% 1.32/1.75 ,
% 1.32/1.75 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.32/1.75 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.32/1.75 ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.75 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), Z ),
% 1.32/1.75 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.75 'tc_nat' ), X ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.32/1.75 ), Y ), Z ), 'tc_nat' ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.32/1.75 'c_Divides_Odiv__class_Omod'( Y, Z, 'tc_nat' ) ),
% 1.32/1.75 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.75 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.32/1.75 ), X ), Z ), 'tc_nat' ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__comm__semiring__strict'( X ) ),
% 1.32/1.75 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.32/1.75 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.32/1.75 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) )
% 1.32/1.75 , ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.32/1.75 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.32/1.75 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X )
% 1.32/1.75 , ~( 'c_HOL_Oord__class_Oless'( T, Y, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.75 Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.32/1.75 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.32/1.75 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X )
% 1.32/1.75 , ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.32/1.75 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.32/1.75 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X )
% 1.32/1.75 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) )
% 1.32/1.75 , ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.32/1.75 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.32/1.75 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X )
% 1.32/1.75 , ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.32/1.75 , ~( 'c_HOL_Oord__class_Oless'( T, Y, X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.32/1.75 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.32/1.75 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.32/1.75 , ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.75 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.32/1.75 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.32/1.75 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.32/1.75 , ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.32/1.75 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.32/1.75 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.32/1.75 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) )
% 1.32/1.75 , ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.32/1.75 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.32/1.75 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.32/1.75 , ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.32/1.75 , ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.32/1.75 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.32/1.75 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.32/1.75 , ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.32/1.75 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.32/1.75 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ]
% 1.32/1.75 ,
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.32/1.75 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.32/1.75 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.32/1.75 , ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.75 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.32/1.75 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.32/1.75 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.32/1.75 ,
% 1.32/1.75 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.32/1.75 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.32/1.75 ), Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X
% 1.32/1.75 ) ), 'c_Divides_Odiv__class_Omod'( Z, T, X ) ), T, X ) ) ],
% 1.32/1.75 [ ~( =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', 'tc_Int_Oint'
% 1.32/1.75 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OMin', 'tc_Int_Oint' ) ) )
% 1.32/1.75 ],
% 1.32/1.75 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), hAPP( hAPP( Y, Z ), U ) )
% 1.32/1.75 , hAPP( hAPP( Y, Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.32/1.75 , T ), U ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, Y, V0, V1, V2
% 1.32/1.75 ) ) ],
% 1.32/1.75 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.32/1.75 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ), =( Y
% 1.32/1.75 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, Z ) ],
% 1.32/1.75 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.32/1.75 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), =( X
% 1.32/1.75 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y, Z ) ],
% 1.32/1.75 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.32/1.75 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), =( Y
% 1.32/1.75 , Z ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.32/1.75 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.32/1.75 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.32/1.75 , Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), T, X )
% 1.32/1.75 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ),
% 1.32/1.75 'c_Divides_Odiv__class_Odiv'( Y, T, X ) ) ), =( T,
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.75 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.32/1.75 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.32/1.75 , Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), Z, X )
% 1.32/1.75 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ),
% 1.32/1.75 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ) ), =( Z,
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.32/1.75 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.32/1.75 , Y ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.75 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), Y, X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.32/1.75 , X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.75 X ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), Y, X ) ),
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.32/1.75 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 1.32/1.75 X ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), Y, X ) ),
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.32/1.75 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 1.32/1.75 X ) ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.32/1.75 , ~( 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.32/1.75 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.32/1.75 ), Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( T,
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'( Z
% 1.32/1.75 , 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.32/1.75 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.32/1.75 , X ), ~( 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.75 X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ),
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.32/1.75 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.32/1.75 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.75 X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ),
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.32/1.75 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.32/1.75 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.75 X ) ), 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.32/1.75 , ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.75 X ), Y ), T ), Z, X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.75 'class_Int_Onumber'( X ) ), =( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.32/1.75 , 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.32/1.75 , X ) ), Z ), Z, X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.32/1.75 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oone__class_Oone'( X ),
% 1.32/1.75 X ), ~( 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.75 X ), 'c_HOL_Oone__class_Oone'( X ) ), 'c_HOL_Oone__class_Oone'( X ) ) ),
% 1.32/1.75 Y ) ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.32/1.75 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.32/1.75 'c_HOL_Oabs__class_Oabs'( Y, X ), X ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.75 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.32/1.75 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.32/1.75 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ),
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.75 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.32/1.75 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( T,
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.32/1.75 hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.32/1.75 [ =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'c_Suc'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.32/1.75 'c_lessequals'( Y, 'c_HOL_Oabs__class_Oabs'( Y, X ), X ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.75 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.75 ), X ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.32/1.75 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ),
% 1.32/1.75 ~( 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.32/1.75 , 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.75 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.32/1.75 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( T,
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.75 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.32/1.75 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.32/1.75 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.32/1.75 , 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.75 'class_Int_Onumber'( X ) ), =( Y, hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ),
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ), =(
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.75 ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.75 'class_Int_Onumber'( X ) ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.75 X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ),
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y ), =(
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.75 ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.32/1.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( hAPP(
% 1.32/1.75 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.32/1.75 ), Y ), Y, X ) ) ],
% 1.32/1.75 [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 1.32/1.75 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.32/1.75 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 1.32/1.75 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 1.32/1.75 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.32/1.75 , U ), Y ), Z, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), W ), T ), Z, X ) ) ],
% 1.32/1.75 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.32/1.75 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ],
% 1.32/1.75 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( X,
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.32/1.75 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( Y, 'c_Suc'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_Suc'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.32/1.75 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.32/1.75 hAPP( hAPP( 'c_Power_Opower__class_Opower'( 'tc_nat' ), X ), Y ),
% 1.32/1.75 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.75 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.75 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.32/1.75 ,
% 1.32/1.75 [ ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), =( Y,
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( hBOOL( hAPP( Z,
% 1.32/1.75 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.75 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), T
% 1.32/1.75 ) ), X ), Y, 'tc_nat' ) ) ) ), hBOOL( hAPP( Z, T ) ) ],
% 1.32/1.75 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.75 'tc_nat' ), 'tc_nat' ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.75 ) ) ), =( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.75 ) ) ), =( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.32/1.75 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.75 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 1.32/1.75 'c_Nat_Osemiring__1__class_Oof__nat'( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ), X ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), 'c_Nat_Osemiring__1__class_Oof__nat'(
% 1.32/1.75 Y, X ) ), 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ) ) ) ],
% 1.32/1.75 [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ) ), Y, 'tc_nat'
% 1.32/1.75 ), 'c_Divides_Odiv__class_Omod'( 'c_Suc'( Z ), Y, 'tc_nat' ) ) ],
% 1.32/1.75 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), T ) ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ) ), =( Y, T ), =( X
% 1.32/1.75 , Z ) ],
% 1.32/1.75 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), T ) ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ) ), =( Y, T ), =( X
% 1.32/1.75 , Z ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.32/1.75 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.76 X ), Y ), U ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.32/1.76 ) ) ), =( Z, U ), =( Y, T ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.32/1.76 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.76 X ), Y ), U ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.32/1.76 ) ) ), =( Z, U ), =( Y, T ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( 'c_Power_Opower_Opower'( Y, Z, T ),
% 1.32/1.76 U ), W ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( Y, Z, T ), V0 ), W ) ) )
% 1.32/1.76 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), W
% 1.32/1.76 , 'tc_nat' ) ), ~( hBOOL( hAPP( hAPP( V1, V2 ), U ) ) ), ~( hBOOL( hAPP(
% 1.32/1.76 hAPP( X, U ), V0 ) ) ), ~( 'c_Ring__and__Field_Oordered__semidom'( V3, V2
% 1.32/1.76 , Y, Z, V1, X, T ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oabs__class_Oabs'( Y, X ) ),
% 1.32/1.76 'c_HOL_Oabs__class_Oabs'( Y, X ) ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 1.32/1.76 'c_HOL_Oinverse__class_Oinverse'( hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y
% 1.32/1.76 , X ) ), Z ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 1.32/1.76 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.32/1.76 , X ), 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oinverse__class_Oinverse'(
% 1.32/1.76 Y, X ), X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.76 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Z
% 1.32/1.76 , X ) ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( T,
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.32/1.76 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.76 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.32/1.76 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.32/1.76 ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ),
% 1.32/1.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.32/1.76 [ ~( =( X, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y
% 1.32/1.76 ) ) ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 1.32/1.76 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.32/1.76 [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 1.32/1.76 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.32/1.76 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 1.32/1.76 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 1.32/1.76 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.32/1.76 ), U ), Y ), Z, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), W ), T ), Z, X ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.32/1.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.76 'class_Int_Onumber'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( hAPP(
% 1.32/1.76 hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), Z ), Z, X ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), =( Z,
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.76 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.32/1.76 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.32/1.76 ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ), ~(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.32/1.76 , 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.76 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.32/1.76 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.32/1.76 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ),
% 1.32/1.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.76 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Z
% 1.32/1.76 , X ) ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( T,
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_lessequals'(
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.32/1.76 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.32/1.76 ) ), 'c_HOL_Oinverse__class_Odivide'( T, U, X ) ),
% 1.32/1.76 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.76 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), U ) ), hAPP(
% 1.32/1.76 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ), X ) ), =( U,
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.32/1.76 ) ],
% 1.32/1.76 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_Suc'(
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_Suc'(
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_Suc'(
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ), X ) ),
% 1.32/1.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.32/1.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( Y, hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z
% 1.32/1.76 , X ) ), Z ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.32/1.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z
% 1.32/1.76 , X ) ), Z ), Y ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ), X ) ]
% 1.32/1.76 ,
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.32/1.76 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.32/1.76 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.76 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.32/1.76 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.76 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.32/1.76 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.76 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.76 'tc_nat' ) ) ],
% 1.32/1.76 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.76 'tc_nat' ) ) ],
% 1.32/1.76 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.32/1.76 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.76 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.32/1.76 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.32/1.76 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.32/1.76 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.32/1.76 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =( hAPP(
% 1.32/1.76 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.32/1.76 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =( hAPP(
% 1.32/1.76 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.76 X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.32/1.76 'c_HOL_Oabs__class_Oabs'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X )
% 1.32/1.76 , 'c_HOL_Ouminus__class_Ouminus'( Y, X ) ), Z ), X ),
% 1.32/1.76 'c_HOL_Oabs__class_Oabs'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X )
% 1.32/1.76 , Y ), Z ), X ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.76 X ), Y ), Z ) ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP(
% 1.32/1.76 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Oone__class_Oone'( X )
% 1.32/1.76 ) ), Z ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.76 X ), Z ), 'c_HOL_Oone__class_Oone'( X ) ) ), Y ) ) ],
% 1.32/1.76 [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Suc'(
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.32/1.76 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.32/1.76 Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.76 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.76 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), ~( 'class_Int_Onumber'(
% 1.32/1.76 X ) ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( T, X ) ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.76 X ), Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =( Y,
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_Int_Oiszero'( Y, X ) ) ],
% 1.32/1.76 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.32/1.76 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Oone__class_Oone'( X ), X ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oabs__class_Oabs'( Y, X ) ), Z
% 1.32/1.76 ), 'c_HOL_Oabs__class_Oabs'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.32/1.76 ), Y ), Z ), X ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.76 Z, X ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.32/1.76 'c_HOL_Oone__class_Oone'( X ), X ), ~( 'c_lessequals'(
% 1.32/1.76 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.32/1.76 X ) ) ],
% 1.32/1.76 [ ~( =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ), U ), hAPP(
% 1.32/1.76 hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ), W ) ) ), ~( hBOOL( hAPP(
% 1.32/1.76 hAPP( V0, X ), T ) ) ), ~( 'c_Ring__and__Field_Oordered__semidom'( V1, V2
% 1.32/1.76 , X, Y, V3, V0, Z ) ), =( U, W ) ],
% 1.32/1.76 [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Suc'(
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.76 'tc_nat' ) ) ) ],
% 1.32/1.76 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Y
% 1.32/1.76 , X ) ) ],
% 1.32/1.76 [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ],
% 1.32/1.76 [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ],
% 1.32/1.76 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.32/1.76 , Y, X ) ) ],
% 1.32/1.76 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.32/1.76 , Y, X ) ) ],
% 1.32/1.76 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.32/1.76 , X ), 'c_lessequals'( Z, Y, X ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.32/1.76 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oabs__class_Oabs'(
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), 'c_HOL_Oord__class_Oless'(
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.76 ), X ) ],
% 1.32/1.76 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.32/1.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.32/1.76 ,
% 1.32/1.76 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.76 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.32/1.76 ), X ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' )
% 1.32/1.76 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.32/1.76 , X, 'tc_nat' ) ) ],
% 1.32/1.76 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.76 'tc_nat' ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.32/1.76 ), Z ), Y ), 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_nat' ) ) ],
% 1.32/1.76 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.76 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.32/1.76 ), Z ), Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ), ~(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 1.32/1.76 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.76 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.32/1.76 ), X ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ), ~(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 1.32/1.76 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.76 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.32/1.76 ), X ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' )
% 1.32/1.76 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.32/1.76 , X, 'tc_nat' ) ) ],
% 1.32/1.76 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.76 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.32/1.76 ), Z ), Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' )
% 1.32/1.76 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.32/1.76 , Y, 'tc_nat' ) ) ],
% 1.32/1.76 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'(
% 1.32/1.76 'tc_nat' ), Z ), X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'(
% 1.32/1.76 'tc_nat' ), Z ), Y ), 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_nat' ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( 'c_Power_Opower_Opower'( Z, T,
% 1.32/1.76 U ), hAPP( W, V0 ) ), V1 ) ) ), ~( 'c_Ring__and__Field_Oordered__idom'(
% 1.32/1.76 V2, V3, Y, V4, X, V5, W, Z, T, V6, U ) ) ],
% 1.32/1.76 [ ~( hBOOL( hAPP( hAPP( X, Y ), Z ) ) ), ~(
% 1.32/1.76 'c_Ring__and__Field_Oordered__semidom'( T, Z, Y, U, W, X, V0 ) ) ],
% 1.32/1.76 [ ~( hBOOL( hAPP( hAPP( X, Y ), Z ) ) ), ~(
% 1.32/1.76 'c_Ring__and__Field_Oordered__semidom'( T, Z, Y, U, X, W, V0 ) ) ],
% 1.32/1.76 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.32/1.76 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.32/1.76 , Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), Z, X )
% 1.32/1.76 , 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 1.32/1.76 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.32/1.76 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.32/1.76 , Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), T, X )
% 1.32/1.76 , 'c_Divides_Odiv__class_Omod'( Y, T, X ) ) ],
% 1.32/1.76 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ), Y, 'tc_nat' )
% 1.32/1.76 , 'c_Divides_Odiv__class_Omod'( Z, Y, 'tc_nat' ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.32/1.76 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.32/1.76 , 'tc_nat' ), 'tc_nat' ) ), =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.32/1.76 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_lessequals'(
% 1.32/1.76 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.32/1.76 , 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ), 'c_Nat_Osemiring__1__class_Oof__nat'( Y
% 1.32/1.76 , X ), X ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ), 'c_Nat_Osemiring__1__class_Oof__nat'( Y
% 1.32/1.76 , X ), X ) ],
% 1.32/1.76 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.32/1.76 Y ) ],
% 1.32/1.76 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.32/1.76 Y ) ],
% 1.32/1.76 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.32/1.76 Y ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.32/1.76 X ) ), =( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.32/1.76 Y ) ],
% 1.32/1.76 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.32/1.76 Y ) ],
% 1.32/1.76 [ =( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.32/1.76 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ],
% 1.32/1.76 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), X ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.32/1.76 Y ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.32/1.76 Y ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.32/1.76 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'( Y,
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Z, hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ), ~( 'c_lessequals'(
% 1.32/1.76 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), Z, X ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.32/1.76 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'( Y,
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( T,
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'( Z,
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'( Y,
% 1.32/1.76 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.32/1.76 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'(
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), Y, X ) ), ~( 'c_lessequals'(
% 1.32/1.76 Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.32/1.76 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'(
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 'c_HOL_Oord__class_Oless'( Z,
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Oord__class_Oless'( Z,
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.32/1.76 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), Y, X ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.32/1.76 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.76 X ), Y ), Z ), T, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.32/1.76 'c_HOL_Oinverse__class_Odivide'( Y, T, X ) ),
% 1.32/1.76 'c_HOL_Oinverse__class_Odivide'( Z, T, X ) ) ) ],
% 1.32/1.76 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 1.32/1.76 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.76 X ), Y ), Z ), T, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.32/1.76 'c_HOL_Oinverse__class_Odivide'( Y, T, X ) ),
% 1.32/1.76 'c_HOL_Oinverse__class_Odivide'( Z, T, X ) ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.32/1.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Z, X ) ), ~(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.32/1.76 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.32/1.76 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 1.32/1.76 ), Y ) ],
% 1.32/1.76 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( Y,
% 1.32/1.76 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 1.32/1.76 ) ) ],
% 1.32/1.76 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( Y,
% 1.32/1.76 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 1.32/1.76 ) ) ],
% 1.32/1.76 [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), =(
% 1.32/1.76 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 1.32/1.76 ), Y ) ],
% 1.32/1.76 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.32/1.76 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 1.32/1.76 ), Y ) ],
% 1.32/1.76 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.32/1.76 'c_Divides_Odiv__class_Odiv'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y )
% 1.32/1.76 ],
% 1.32/1.76 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.32/1.76 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.32/1.76 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 1.32/1.76 'c_lessequals'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ]
% 1.32/1.76 ,
% 1.32/1.76 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.32/1.76 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.32/1.76 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ]
% 1.32/1.76 ,
% 1.32/1.76 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.32/1.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X )
% 1.32/1.76 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Z, X ), Y
% 1.32/1.76 , X ) ) ],
% 1.32/1.76 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.32/1.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X )
% 1.32/1.76 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Z, X ), Y
% 1.32/1.76 , X ) ) ],
% 1.32/1.76 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.32/1.76 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X )
% 1.32/1.76 , ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.32/1.76 , X ) ) ],
% 1.32/1.76 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.32/1.76 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X )
% 1.32/1.76 , ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.32/1.76 , X ) ) ],
% 1.32/1.76 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.32/1.76 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ), ~(
% 1.32/1.76 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Z, X ), Y, X ) ) ],
% 1.32/1.76 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.32/1.76 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ), ~(
% 1.32/1.76 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Z, X ), Y, X ) ) ],
% 1.32/1.76 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.32/1.76 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), ~(
% 1.32/1.76 'c_lessequals'( Z, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ],
% 1.32/1.76 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.32/1.76 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), ~(
% 1.32/1.76 'c_lessequals'( Z, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ],
% 1.32/1.76 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.32/1.76 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.76 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ), ~(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.32/1.76 'tc_nat' ) ) ],
% 1.32/1.76 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( Y ), X ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.76 X ), 'c_HOL_Oone__class_Oone'( X ) ), 'c_Int_Onumber__class_Onumber__of'(
% 1.32/1.76 Y, X ) ) ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.32/1.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.76 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', X ), X ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.76 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.32/1.76 'c_Int_OMin', X ) ), Y ), 'c_Int_Onumber__class_Onumber__of'(
% 1.32/1.76 'c_Int_OMin', X ) ), 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ]
% 1.32/1.76 ,
% 1.32/1.76 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( Y ), X ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.76 X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.76 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.32/1.76 'c_HOL_Oone__class_Oone'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.32/1.76 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), X ), X ), X ) ],
% 1.32/1.76 [ =( 'c_Int_OBit1'( 'c_Int_OMin' ), 'c_Int_OMin' ) ],
% 1.32/1.76 [ ~( =( 'c_Int_OBit1'( X ), 'c_Int_OMin' ) ), =( X, 'c_Int_OMin' ) ]
% 1.32/1.76 ,
% 1.32/1.76 [ ~( =( 'c_Int_OMin', 'c_Int_OBit1'( X ) ) ), =( 'c_Int_OMin', X ) ]
% 1.32/1.76 ,
% 1.32/1.76 [ =( 'c_Int_OMin', 'c_Int_OBit1'( 'c_Int_OMin' ) ) ],
% 1.32/1.76 [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 1.32/1.76 'c_Divides_Odiv__class_Omod'( 'c_Suc'( 'c_Divides_Odiv__class_Omod'( X, Y
% 1.32/1.76 , 'tc_nat' ) ), Y, 'tc_nat' ) ) ],
% 1.32/1.76 [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.32/1.76 [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.32/1.76 [ =( X, Y ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ],
% 1.32/1.76 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_Suc'( X ), 'tc_nat' ) )
% 1.32/1.76 , 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ],
% 1.32/1.76 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) )
% 1.32/1.76 , 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ],
% 1.32/1.76 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ), 'c_Suc'( U ) )
% 1.32/1.76 , hAPP( hAPP( Y, T ), hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T )
% 1.32/1.76 , U ) ) ) ],
% 1.32/1.76 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), 'c_Suc'( Y
% 1.32/1.76 ) ), 'c_Suc'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y
% 1.32/1.76 ) ) ) ],
% 1.32/1.76 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Suc'( X ) )
% 1.32/1.76 , Y ), 'c_Suc'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.32/1.76 Y ) ) ) ],
% 1.32/1.76 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Suc'( X ) )
% 1.32/1.76 , Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), 'c_Suc'(
% 1.32/1.76 Y ) ) ) ],
% 1.32/1.76 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ),
% 1.32/1.76 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ],
% 1.32/1.76 [ ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), ~(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( Y, 'c_Suc'( X ), 'tc_nat' ) ) ],
% 1.32/1.76 [ 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 1.32/1.76 X, 'c_Suc'( X ), 'tc_nat' ) ],
% 1.32/1.76 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_Suc'( X
% 1.32/1.76 ) ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_Suc'(
% 1.32/1.76 X ) ), Z ) ) ), =( Y, Z ) ],
% 1.32/1.76 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ) ) ],
% 1.32/1.76 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ), ~(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.32/1.76 [ =( hAPP( hAPP( X, Y ), 'c_Suc'( Z ) ), hAPP( hAPP( T, Y ), hAPP( hAPP(
% 1.32/1.76 X, Y ), Z ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, T, X, W, V0, V1
% 1.32/1.76 ) ) ],
% 1.32/1.76 [ =( hAPP( hAPP( X, Y ), 'c_Suc'( Z ) ), hAPP( hAPP( T, Y ), hAPP( hAPP(
% 1.32/1.76 X, Y ), Z ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, T, X, W, V0, V1
% 1.32/1.76 ) ) ],
% 1.32/1.76 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), Z ), hAPP( hAPP( Y, Z ),
% 1.32/1.76 'c_Suc'( T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, Y, W, V0,
% 1.32/1.76 V1 ) ) ],
% 1.32/1.76 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, Y ), T ) ), hAPP( hAPP( Z, Y ),
% 1.32/1.76 'c_Suc'( T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, Z, W, V0,
% 1.32/1.76 V1 ) ) ],
% 1.32/1.76 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ],
% 1.32/1.76 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ],
% 1.32/1.76 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ), ~(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), ~(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 1.32/1.76 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( X ) ) ) ],
% 1.32/1.76 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( X ) ) ) ],
% 1.32/1.76 [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( X ), Y, 'tc_nat' ), 'c_Suc'(
% 1.32/1.76 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ) ), =( 'c_Suc'(
% 1.32/1.76 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), Y ) ],
% 1.32/1.76 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ), =( 'c_Suc'( X
% 1.32/1.76 ), Y ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.32/1.76 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ), ~(
% 1.32/1.76 'c_Parity_Oeven__odd__class_Oeven'( 'c_Suc'( X ), 'tc_nat' ) ) ],
% 1.32/1.76 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_Suc'( X ), 'tc_nat' ),
% 1.32/1.76 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.32/1.76 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ), ~(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.32/1.76 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ) ) ]
% 1.32/1.76 ,
% 1.32/1.76 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ), ~(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.32/1.76 [ ~( =( 'c_Int_OPls', 'c_Int_OMin' ) ) ],
% 1.32/1.76 [ ~( =( 'c_Int_OMin', 'c_Int_OPls' ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.32/1.76 Y, Z, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ),
% 1.32/1.76 ~( 'c_lessequals'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.32/1.76 'c_Suc'( T ) ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.32/1.76 'c_Suc'( T ) ), X ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.32/1.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( Z ) ), X ), ~(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =( hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( Z ) ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), T ), 'c_Suc'( Z ) ) ) ), =( Y, T ),
% 1.32/1.76 ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.32/1.76 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.32/1.76 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), T ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 1.32/1.76 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.76 X ), X ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.32/1.76 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.32/1.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.32/1.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.32/1.76 [ =( hAPP( hAPP( X, Y ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), Y ),
% 1.32/1.76 ~( 'c_Groebner__Basis_Ogb__semiring'( Z, T, X, U, W, V0 ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.32/1.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.76 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OMin', X ), X ),
% 1.32/1.76 'c_HOL_Ouminus__class_Ouminus'( Y, X ) ) ],
% 1.32/1.76 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.76 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.32/1.76 , Z ), T ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, T, 'tc_nat' ) )
% 1.32/1.76 , ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 1.32/1.76 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.32/1.76 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.32/1.76 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.32/1.76 T, X ) ) ],
% 1.32/1.76 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.32/1.76 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.32/1.76 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X ) )
% 1.32/1.76 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ), Z ) ],
% 1.32/1.76 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X ) )
% 1.32/1.76 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), Z ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.32/1.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.32/1.76 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oone__class_Oone'( X ), X ),
% 1.32/1.76 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.32/1.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.32/1.76 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ), ~(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.32/1.76 ,
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 1.32/1.76 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oone__class_Oone'( X ), X ),
% 1.32/1.76 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.32/1.76 ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ),
% 1.32/1.76 ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.32/1.76 ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.32/1.76 ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.32/1.76 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.32/1.76 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ), ~( 'c_lessequals'( U, Z
% 1.32/1.76 , X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), U
% 1.32/1.76 , X ) ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'(
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.32/1.76 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), ~(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.32/1.76 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.76 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 1.32/1.76 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.32/1.76 'c_HOL_Oord__class_Oless'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 1.32/1.76 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ), ~(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( 'c_lessequals'(
% 1.32/1.76 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.32/1.76 , X ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.32/1.76 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), 'c_lessequals'( Z,
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Z ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.76 X ), X ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.32/1.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.76 'class_Int_Onumber'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( hAPP(
% 1.32/1.76 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.32/1.76 ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.32/1.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.76 'c_HOL_Oone__class_Oone'( X ), X ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.32/1.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.32/1.76 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ), ~(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ), ~(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.32/1.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.32/1.76 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ), ~(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ), ~(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.32/1.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.32/1.76 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.32/1.76 , 'tc_nat' ), 'tc_nat' ), =( 'c_Int_Onumber__class_Onumber__of'( Z,
% 1.32/1.76 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ), X ) ) ],
% 1.32/1.76 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ouminus__class_Ouminus'(
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.32/1.76 [ 'c_HOL_Oord__class_Oless'( 'c_Divides_Odiv__class_Odiv'( X, Y,
% 1.32/1.76 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ), ~(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), Y,
% 1.32/1.76 'tc_nat' ) ) ],
% 1.32/1.76 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP(
% 1.32/1.76 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), T ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), U ) ) ) ), =(
% 1.32/1.76 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ),
% 1.32/1.76 'c_Divides_Odiv__class_Omod'( T, Y, 'tc_nat' ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.32/1.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.32/1.76 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X )
% 1.32/1.76 , 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.32/1.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.76 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ), ~(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.32/1.76 'tc_nat' ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 1.32/1.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( =(
% 1.32/1.76 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.32/1.76 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~( =(
% 1.32/1.76 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.32/1.76 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.32/1.76 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.32/1.76 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X )
% 1.32/1.76 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ]
% 1.32/1.76 ,
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.32/1.76 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.32/1.76 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X )
% 1.32/1.76 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) )
% 1.32/1.76 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.32/1.76 'c_lessequals'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ]
% 1.32/1.76 ,
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =( hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Y ), T ) ) ), ~(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ), =( Z
% 1.32/1.76 , T ) ],
% 1.32/1.76 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'class_Int_Onumber'( X ) ),
% 1.32/1.76 ~( 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.32/1.76 , 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ), ~( 'c_lessequals'(
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.32/1.76 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'class_Int_Onumber'( X ) ),
% 1.32/1.76 'c_lessequals'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ),
% 1.32/1.76 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.32/1.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ), X ), ~(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ),
% 1.32/1.76 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.32/1.76 , 'tc_nat' ), 'tc_nat' ) ],
% 1.32/1.76 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.32/1.76 'tc_nat' ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.32/1.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.76 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.32/1.76 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =(
% 1.32/1.76 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( Y
% 1.32/1.76 , X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( X, 'c_Divides_Odiv__class_Odiv'( Y,
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ), ~( hBOOL( hAPP( X
% 1.32/1.76 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.32/1.76 [ ~( hBOOL( hAPP( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), hBOOL(
% 1.32/1.76 hAPP( X, 'c_Divides_Odiv__class_Odiv'( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.76 'tc_nat' ), 'tc_nat' ) ) ) ],
% 1.32/1.76 [ ~( hBOOL( hAPP( X, 'c_Divides_Odiv__class_Odiv'( Y,
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ) ), hBOOL( hAPP( X
% 1.32/1.76 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.32/1.76 ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.32/1.76 'c_HOL_Ouminus__class_Ouminus'( Z, X ) ) ) ],
% 1.32/1.76 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X
% 1.32/1.76 ) ), Z ), 'c_HOL_Ouminus__class_Ouminus'( hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ) ),
% 1.32/1.76 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.32/1.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.76 'class_Int_Onumber'( X ) ), ~( =( 'c_HOL_Oinverse__class_Odivide'( Y, Z,
% 1.32/1.76 X ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ), =( Y, hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( T
% 1.32/1.76 , X ) ), Z ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ouminus__class_Ouminus'(
% 1.32/1.76 'c_HOL_Oone__class_Oone'( X ), X ) ), Y ), 'c_HOL_Ouminus__class_Ouminus'(
% 1.32/1.76 'c_HOL_Oone__class_Oone'( X ), X ) ), 'c_Parity_Oeven__odd__class_Oeven'(
% 1.32/1.76 Y, 'tc_nat' ) ],
% 1.32/1.76 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.76 'tc_nat' ), X ), Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ), ~(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.32/1.76 ) ), X, 'tc_nat' ) ) ],
% 1.32/1.76 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.76 'tc_nat' ), Y ), X ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ), ~(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.32/1.76 ) ), X, 'tc_nat' ) ) ],
% 1.32/1.76 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.32/1.76 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.76 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ), =(
% 1.32/1.76 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.32/1.76 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Oinverse__class_Oinverse'(
% 1.32/1.76 Z, X ) ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.32/1.76 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.32/1.76 Z, X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.32/1.76 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), 'c_Int_Oiszero'(
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.32/1.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.76 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), X
% 1.32/1.76 ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.32/1.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.76 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), X
% 1.32/1.76 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.32/1.76 ) ],
% 1.32/1.76 [ =( 'c_Divides_Odiv__class_Odiv'( 'c_Suc'( X ), 'c_Suc'( 'c_Suc'(
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ),
% 1.32/1.76 'c_Divides_Odiv__class_Odiv'( X, 'c_Suc'( 'c_Suc'(
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ) ), ~(
% 1.32/1.76 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( 'class_Int_Onumber'( X )
% 1.32/1.76 ), =( 'c_HOL_Oinverse__class_Oinverse'(
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.32/1.76 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.32/1.76 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.32/1.76 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.32/1.76 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.32/1.76 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.32/1.76 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.32/1.76 [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 1.32/1.76 'class_OrderedGroup_Olordered__ab__group__add__abs'( X ) ), =(
% 1.32/1.76 'c_HOL_Oabs__class_Oabs'( Y, X ), Y ), 'c_HOL_Oord__class_Oless'( Y,
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oabs__if'( X ) ), =(
% 1.32/1.76 'c_HOL_Oabs__class_Oabs'( Y, X ), Y ), 'c_HOL_Oord__class_Oless'( Y,
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.32/1.76 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.76 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), T ), Y ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), T ), Z ), X ) ), ~(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), T, X ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.32/1.76 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.32/1.76 ), Y ), Z ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), T ),
% 1.32/1.76 X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X )
% 1.32/1.76 ), ~( 'c_HOL_Oord__class_Oless'( Z, T, 'tc_nat' ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.32/1.76 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.76 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), T ), Y ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), T ), Z ), X ) ), ~(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), T, X ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.32/1.76 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.32/1.76 ), Y ), Z ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), T ),
% 1.32/1.76 X ), ~( 'c_HOL_Oord__class_Oless'( Z, T, 'tc_nat' ) ), ~(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.76 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.32/1.76 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'(
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.76 ), X ) ), ~( 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.76 X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ), ~(
% 1.32/1.76 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.76 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.32/1.76 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'(
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.76 ), X ) ), 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X )
% 1.32/1.76 , X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X )
% 1.32/1.76 ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.76 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.76 ), X ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.32/1.76 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ),
% 1.32/1.76 ~( 'c_lessequals'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.32/1.76 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ],
% 1.32/1.76 [ ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.76 'tc_nat' ), X ), Y ), Y, 'tc_nat' ) ) ],
% 1.32/1.76 [ ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.76 'tc_nat' ), X ), Y ), X, 'tc_nat' ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.32/1.76 Z, X ) ), T ), 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Y ), T ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Z ), T ), X ) ), =( Z,
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.76 [ =( 'c_Divides_Odiv__class_Odiv'( X, hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ), 'tc_nat' ),
% 1.32/1.76 'c_Divides_Odiv__class_Odiv'( 'c_Divides_Odiv__class_Odiv'( X, Y,
% 1.32/1.76 'tc_nat' ), Z, 'tc_nat' ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( 'c_Power_Opower_Opower'( Y, Z,
% 1.32/1.76 T ), U ), W ) ) ), ~( hBOOL( hAPP( hAPP( X, Y ), U ) ) ), ~(
% 1.32/1.76 'c_Ring__and__Field_Oordered__semidom'( V0, V1, Y, Z, X, V2, T ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( 'c_Power_Opower_Opower'( Z, T,
% 1.32/1.76 U ), W ), V0 ) ) ), ~( hBOOL( hAPP( hAPP( X, Y ), W ) ) ), ~(
% 1.32/1.76 'c_Ring__and__Field_Oordered__semidom'( V1, Y, Z, T, X, V2, U ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower_Opower'( Y, Z, U ), T ), W ) ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.76 X, Y ), T ) ) ), ~( 'c_Ring__and__Field_Oordered__semidom'( V0, V1, Y, Z
% 1.32/1.76 , V2, X, U ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( 'c_Power_Opower_Opower'( Z, T,
% 1.32/1.76 U ), W ), V0 ) ) ), ~( hBOOL( hAPP( hAPP( X, Y ), W ) ) ), ~(
% 1.32/1.76 'c_Ring__and__Field_Oordered__semidom'( V1, Y, Z, T, V2, X, U ) ) ],
% 1.32/1.76 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.32/1.76 'c_HOL_Oabs__class_Oabs'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.32/1.76 'c_HOL_Oabs__class_Oabs'( Y, X ) ), 'c_HOL_Oabs__class_Oabs'( Z, X ) ), X
% 1.32/1.76 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oabs__class_Oabs'(
% 1.32/1.76 Y, X ) ), 'c_HOL_Oabs__class_Oabs'( Z, X ) ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.32/1.76 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), T, X ), ~(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.32/1.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.32/1.76 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), Y, X ) ) ]
% 1.32/1.76 ,
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.32/1.76 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.32/1.76 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ),
% 1.32/1.76 Y, X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z,
% 1.32/1.76 X ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.32/1.76 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ), ~(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.32/1.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~(
% 1.32/1.76 'c_lessequals'( Z, 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ) ) ]
% 1.32/1.76 ,
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.32/1.76 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.32/1.76 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T
% 1.32/1.76 ), X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T
% 1.32/1.76 , X ) ],
% 1.32/1.76 [ ~( 'c_Ring__and__Field_Oordered__idom'( X, Y, Z, T, U, W, V0, hAPP( V1
% 1.32/1.76 , V2 ), V3, V1, V4 ) ), hBOOL( hAPP( hAPP( W, Z ), V2 ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.32/1.76 ), ~( hBOOL( hAPP( hAPP( X, W ), hAPP( hAPP( V0, W ), Z ) ) ) ), ~(
% 1.32/1.76 'c_Ring__and__Field_Oordered__idom'( V1, V2, U, V3, X, T, V4, Y, V0, V5,
% 1.32/1.76 V6 ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.32/1.76 ), ~( hBOOL( hAPP( hAPP( X, U ), hAPP( hAPP( V0, U ), Y ) ) ) ), ~(
% 1.32/1.76 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, X, T, V4, Z, V0, V5,
% 1.32/1.76 V6 ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, Y ), T ) ) ), hBOOL( hAPP(
% 1.32/1.76 hAPP( U, Y ), W ) ), hBOOL( hAPP( hAPP( U, W ), Y ) ), ~(
% 1.32/1.76 'c_Ring__and__Field_Oordered__idom'( V0, V1, W, V2, X, U, V3, V4, Z, V5,
% 1.32/1.76 V6 ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, Y ), T ) ) ), ~( hBOOL( hAPP(
% 1.32/1.76 hAPP( X, T ), U ) ) ), ~( hBOOL( hAPP( hAPP( X, U ), T ) ) ), ~(
% 1.32/1.76 'c_Ring__and__Field_Oordered__idom'( W, V0, V1, V2, X, V3, V4, U, Z, V5,
% 1.32/1.76 V6 ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.32/1.76 ), ~( hBOOL( hAPP( hAPP( X, hAPP( hAPP( V0, W ), Y ) ), W ) ) ), ~(
% 1.32/1.76 'c_Ring__and__Field_Oordered__idom'( V1, V2, U, V3, X, T, V4, Z, V0, V5,
% 1.32/1.76 V6 ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.32/1.76 ), ~( hBOOL( hAPP( hAPP( X, hAPP( hAPP( V0, U ), Z ) ), U ) ) ), ~(
% 1.32/1.76 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, X, T, V4, Y, V0, V5,
% 1.32/1.76 V6 ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), Z ) ), hBOOL( hAPP(
% 1.32/1.76 hAPP( U, Z ), W ) ), hBOOL( hAPP( hAPP( U, W ), Z ) ), ~(
% 1.32/1.76 'c_Ring__and__Field_Oordered__idom'( V0, V1, W, V2, X, U, V3, V4, Y, V5,
% 1.32/1.76 V6 ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), Z ) ), ~( hBOOL( hAPP(
% 1.32/1.76 hAPP( X, U ), T ) ) ), ~( hBOOL( hAPP( hAPP( X, T ), U ) ) ), ~(
% 1.32/1.76 'c_Ring__and__Field_Oordered__idom'( W, V0, V1, V2, X, V3, V4, U, Y, V5,
% 1.32/1.76 V6 ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.32/1.76 ), ~( hBOOL( hAPP( hAPP( X, W ), hAPP( hAPP( V0, Z ), W ) ) ) ), ~(
% 1.32/1.76 'c_Ring__and__Field_Oordered__idom'( V1, V2, U, V3, X, T, V4, Y, V0, V5,
% 1.32/1.76 V6 ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.32/1.76 ), ~( hBOOL( hAPP( hAPP( X, U ), hAPP( hAPP( V0, Y ), U ) ) ) ), ~(
% 1.32/1.76 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, X, T, V4, Z, V0, V5,
% 1.32/1.76 V6 ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), Y ) ) ), hBOOL( hAPP(
% 1.32/1.76 hAPP( U, Y ), W ) ), hBOOL( hAPP( hAPP( U, W ), Y ) ), ~(
% 1.32/1.76 'c_Ring__and__Field_Oordered__idom'( V0, V1, W, V2, X, U, V3, V4, Z, V5,
% 1.32/1.76 V6 ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), Y ) ) ), ~( hBOOL( hAPP(
% 1.32/1.76 hAPP( X, T ), U ) ) ), ~( hBOOL( hAPP( hAPP( X, U ), T ) ) ), ~(
% 1.32/1.76 'c_Ring__and__Field_Oordered__idom'( W, V0, V1, V2, X, V3, V4, U, Z, V5,
% 1.32/1.76 V6 ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.32/1.76 ), ~( hBOOL( hAPP( hAPP( X, hAPP( hAPP( V0, Y ), W ) ), W ) ) ), ~(
% 1.32/1.76 'c_Ring__and__Field_Oordered__idom'( V1, V2, U, V3, X, T, V4, Z, V0, V5,
% 1.32/1.76 V6 ) ) ],
% 1.32/1.76 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Oone__class_Oone'(
% 1.32/1.76 'tc_nat' ) ), Y ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Oone__class_Oone'(
% 1.32/1.76 'tc_nat' ) ), Y ) ],
% 1.32/1.76 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), Y ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.32/1.76 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y )
% 1.32/1.76 , 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 1.32/1.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.32/1.76 'c_HOL_Oinverse__class_Oinverse'( hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y
% 1.32/1.76 , X ) ), Z ) ) ],
% 1.32/1.76 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Y ), T ) ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Z ), T ) ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Y ), T ) ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Z ), T ) ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oring__1__no__zero__divisors'( X ) ), ~(
% 1.32/1.76 =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.76 ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.32/1.76 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.32/1.76 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.32/1.76 ), ~( =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.76 ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.32/1.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.32/1.76 Z, X ) ), T ), 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Y ), T ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Z ), T ), X ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.32/1.76 'c_HOL_Oabs__class_Oabs'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X )
% 1.32/1.76 , Y ), Z ), X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ),
% 1.32/1.76 'c_HOL_Oabs__class_Oabs'( Y, X ) ), Z ) ) ],
% 1.32/1.76 [ ~( =( 'c_Int_OMin', 'c_Int_OBit0'( X ) ) ) ],
% 1.32/1.76 [ ~( =( 'c_Int_OBit0'( X ), 'c_Int_OMin' ) ) ],
% 1.32/1.76 [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.32/1.76 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ),
% 1.32/1.76 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X,
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ) ],
% 1.32/1.76 [ ~( =( 'c_Divides_Odiv__class_Omod'( X,
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oone__class_Oone'(
% 1.32/1.76 'tc_nat' ) ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.76 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X,
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ],
% 1.32/1.76 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.32/1.76 'c_Divides_Odiv__class_Odiv'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.32/1.76 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ),
% 1.32/1.76 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'(
% 1.32/1.76 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.32/1.76 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'(
% 1.32/1.76 'tc_nat' ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.32/1.76 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ),
% 1.32/1.76 'c_Divides_Odiv__class_Odiv'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.32/1.76 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) )
% 1.32/1.76 , ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.32/1.76 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( X ), X ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.32/1.76 ), Z ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.32/1.76 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ],
% 1.32/1.76 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.32/1.76 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ) ), Y ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oabs__class_Oabs'( Y, X ) ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ) ), ~(
% 1.32/1.76 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.32/1.76 , 'tc_nat' ), 'tc_nat' ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.32/1.76 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.32/1.76 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.32/1.76 ), =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.32/1.76 , 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ), =(
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.32/1.76 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ) ), =( 'c_Int_Onumber__class_Onumber__of'(
% 1.32/1.76 Y, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_lessequals'( Y,
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.32/1.76 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.32/1.76 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.32/1.76 ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( =( hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.32/1.76 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.32/1.76 ), Y ), 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.32/1.76 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.32/1.76 hAPP( hAPP( 'c_Power_Opower__class_Opower'( 'tc_nat' ), X ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ), 'tc_nat' ), ~(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.32/1.76 'tc_nat' ) ) ],
% 1.32/1.76 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.32/1.76 'tc_nat' ), =( 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( 'tc_nat' ), X ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ), 'tc_nat' ) ) ],
% 1.32/1.76 [ ~( =( 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Oord__class_Oless'(
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( 'tc_nat' ), Y ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ), 'tc_nat' ) ],
% 1.32/1.76 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ), ~(
% 1.32/1.76 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( 'tc_nat' ), X ), Y ), 'tc_nat' ) ) ],
% 1.32/1.76 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), 'c_Suc'( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ),
% 1.32/1.76 hAPP( hAPP( 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), Z ) ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ],
% 1.32/1.76 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'(
% 1.32/1.76 'tc_nat' ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.32/1.76 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'c_Suc'(
% 1.32/1.76 'c_Divides_Odiv__class_Odiv'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.32/1.76 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) )
% 1.32/1.76 ), 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.76 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.76 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), X ), X ), X ) ) ],
% 1.32/1.76 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), hAPP( T, X ) ),
% 1.32/1.76 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ), U ) ), X ), ~(
% 1.32/1.76 'c_Ring__and__Field_Ocomm__ring__1'( X, Y, W, T, V0, V1, Z ) ) ],
% 1.32/1.76 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), hAPP( T, U ) ),
% 1.32/1.76 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ), W ) ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower_Opower'( X, Y, Z ), U ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ), W ) ) ), ~(
% 1.32/1.76 'c_Ring__and__Field_Ocomm__ring__1'( X, Y, V0, T, V1, V2, Z ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( 'c_Power_Opower_Opower'( Z, T,
% 1.32/1.76 U ), W ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ), V0 ) ) ) ), ~(
% 1.32/1.76 'c_Ring__and__Field_Oordered__idom'( V1, V2, Y, V3, X, V4, V5, Z, T, V6,
% 1.32/1.76 U ) ) ],
% 1.32/1.76 [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.32/1.76 'c_Int_OBit0'( 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat'
% 1.32/1.76 ), 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), =(
% 1.32/1.76 'c_Divides_Odiv__class_Omod'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.32/1.76 'c_Int_OBit0'( 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat'
% 1.32/1.76 ), 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.32/1.76 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), =(
% 1.32/1.76 'c_Divides_Odiv__class_Omod'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.32/1.76 'c_Int_OBit0'( 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat'
% 1.32/1.76 ), 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), =(
% 1.32/1.76 'c_Divides_Odiv__class_Omod'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.32/1.76 'c_Int_OBit0'( 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat'
% 1.32/1.76 ), 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.32/1.76 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.32/1.76 ), Y ), Y ) ) ],
% 1.32/1.76 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ), U ) ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower_Opower'( X, Y, Z ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.32/1.76 X, Y, Z ), T ), U ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.32/1.76 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ), ~(
% 1.32/1.76 'c_OrderedGroup_Omonoid__mult'( X, Y, Z ) ) ],
% 1.32/1.76 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( Y, hAPP( hAPP( Y, T ), T ) )
% 1.32/1.76 , T ) ), ~( 'c_OrderedGroup_Omonoid__mult'( X, Y, Z ) ) ],
% 1.32/1.76 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_Int_Oint' ), 'c_Nat_Osemiring__1__class_Oof__nat'(
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_Int_Oint' ) ) ],
% 1.32/1.76 [ =( 'c_FFT__Mirabelle_OIFFT'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X
% 1.32/1.76 ), X ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( X, Y ), hAPP(
% 1.32/1.76 hAPP( 'c_Power_Opower_Opower'( T, U, W ), Z ), 'c_Suc'( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ), V0 ) ) ) ) ) ), ~(
% 1.32/1.76 'c_Ring__and__Field_Oordered__idom'( V1, V2, Y, V3, X, V4, V5, T, U, V6,
% 1.32/1.76 W ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( 'c_Power_Opower_Opower'( Y, Z, T ),
% 1.32/1.76 U ), 'c_Suc'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ), W ) ) ) ), V0 ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.76 X, U ), V0 ) ) ), ~( 'c_Ring__and__Field_Oordered__idom'( V1, V2, V0, V3
% 1.32/1.76 , V4, X, V5, Y, Z, V6, T ) ) ],
% 1.32/1.76 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ), 'c_Suc'( hAPP(
% 1.32/1.76 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ), U ) ) ), hAPP( hAPP( Y, T ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower_Opower'( X, Y, Z ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.32/1.76 X, Y, Z ), T ), U ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.32/1.76 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), ~(
% 1.32/1.76 'c_OrderedGroup_Omonoid__mult'( X, Y, Z ) ) ],
% 1.32/1.76 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), hAPP( T, X ) ),
% 1.32/1.76 'c_Suc'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ), U ) ) ), hAPP( T, X ) ), ~(
% 1.32/1.76 'c_Ring__and__Field_Ocomm__ring__1'( X, Y, W, T, V0, V1, Z ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.32/1.76 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.76 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.32/1.76 ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.32/1.76 ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ouminus__class_Ouminus'(
% 1.32/1.76 'c_HOL_Oone__class_Oone'( X ), X ) ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ), Y ) ), 'c_HOL_Oone__class_Oone'( X ) ) ]
% 1.32/1.76 ,
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), X ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.32/1.76 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ]
% 1.32/1.76 ,
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.32/1.76 ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ) ), X ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.32/1.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ) ), X ), =( Z, 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.76 X ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.32/1.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ) ), X ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.76 X ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.76 X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ) ), X ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.32/1.76 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.32/1.76 ],
% 1.32/1.76 [ ~( 'class_Int_Oring__char__0'( X ) ), ~( 'class_Int_Onumber__ring'( X
% 1.32/1.76 ) ), ~( 'c_Int_Oiszero'( 'c_Int_Onumber__class_Onumber__of'(
% 1.32/1.76 'c_Int_OBit1'( Y ), X ), X ) ) ],
% 1.32/1.76 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.76 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', X ) ) ],
% 1.32/1.76 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', X ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.76 [ ~( 'class_Int_Onumber__ring'( X ) ), 'c_Int_Oiszero'(
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', X ), X ) ],
% 1.32/1.76 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.32/1.76 'c_Int_OPls', X ) ), Y ), Y ) ],
% 1.32/1.76 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_Int_Onumber__class_Onumber__of'(
% 1.32/1.76 'c_Int_OPls', X ) ), Y ) ],
% 1.32/1.76 [ ~( 'class_Int_Oring__char__0'( X ) ), ~( 'class_Int_Onumber__ring'( X
% 1.32/1.76 ) ), 'c_Int_Oiszero'( 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.32/1.76 ~( 'c_Int_Oiszero'( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( Y
% 1.32/1.76 ), X ), X ) ) ],
% 1.32/1.76 [ ~( 'class_Int_Oring__char__0'( X ) ), ~( 'class_Int_Onumber__ring'( X
% 1.32/1.76 ) ), 'c_Int_Oiszero'( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.32/1.76 Y ), X ), X ), ~( 'c_Int_Oiszero'( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.32/1.76 , X ), X ) ) ],
% 1.32/1.76 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.32/1.76 'c_HOL_Oone__class_Oone'( X ) ), 'c_Int_Onumber__class_Onumber__of'(
% 1.32/1.76 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), X ) ) ],
% 1.32/1.76 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.32/1.76 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), X ) ), Y ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ) ) ],
% 1.32/1.76 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), X ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y )
% 1.32/1.76 , Y ) ) ],
% 1.32/1.76 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.32/1.76 'c_Int_OMin', X ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' )
% 1.32/1.76 , 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ), Y ) ), 'c_HOL_Oone__class_Oone'( X ) ) ]
% 1.32/1.76 ,
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), Y ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( Z ) ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( Z ) ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.32/1.76 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.32/1.76 'c_Suc'( Y ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( Z ) ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.32/1.76 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( Z ) ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), Y ) ) ],
% 1.32/1.76 [ ~( 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( Z ) ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( Z ) ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ouminus__class_Ouminus'(
% 1.32/1.76 'c_HOL_Oone__class_Oone'( X ), X ) ), 'c_Suc'( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ), Y ) ) ), 'c_HOL_Ouminus__class_Ouminus'(
% 1.32/1.76 'c_HOL_Oone__class_Oone'( X ), X ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.32/1.76 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.32/1.76 ), Y ), 'c_Suc'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.32/1.76 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.76 X ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ), X ) ) ],
% 1.32/1.76 [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( 'c_Suc'( 'c_Suc'( X ) ) ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), 'tc_nat' ),
% 1.32/1.76 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.76 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), X ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.32/1.76 [ =( 'c_Divides_Odiv__class_Odiv'( 'c_Suc'( 'c_Suc'( 'c_Suc'( X ) ) ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), 'tc_nat' ),
% 1.32/1.76 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.76 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), X ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.32/1.76 [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Suc'( 'c_Suc'( 'c_Suc'( Y ) ) )
% 1.32/1.76 , 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X, hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ), Y ), 'tc_nat' ) ) ],
% 1.32/1.76 [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( 'c_Suc'( 'c_Suc'( X ) ) ), Y
% 1.32/1.76 , 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), Y, 'tc_nat' ) ) ],
% 1.32/1.76 [ =( 'c_Divides_Odiv__class_Odiv'( X, 'c_Suc'( 'c_Suc'( 'c_Suc'( Y ) ) )
% 1.32/1.76 , 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( X, hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ), Y ), 'tc_nat' ) ) ],
% 1.32/1.76 [ =( 'c_Divides_Odiv__class_Odiv'( 'c_Suc'( 'c_Suc'( 'c_Suc'( X ) ) ), Y
% 1.32/1.76 , 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), Y, 'tc_nat' ) ) ],
% 1.32/1.76 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.76 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.32/1.76 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), hAPP( hAPP( T, hAPP(
% 1.32/1.76 hAPP( X, Y ), Z ) ), hAPP( hAPP( X, Y ), Z ) ) ), ~(
% 1.32/1.76 'c_Groebner__Basis_Ogb__semiring'( U, T, X, W, V0, V1 ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( 'c_Power_Opower_Opower'( Z, T,
% 1.32/1.76 U ), W ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.32/1.76 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), =( W, Y ), ~(
% 1.32/1.76 'c_Ring__and__Field_Oordered__idom'( V0, V1, Y, V2, V3, X, V4, Z, T, V5,
% 1.32/1.76 U ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower_Opower'( T, U, W ), V0 ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( T
% 1.32/1.76 , U, W ), V1 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.32/1.76 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ), =( V1, Y ), ~(
% 1.32/1.76 'c_Ring__and__Field_Oordered__idom'( V2, V3, Y, Z, V4, X, V5, T, U, V6, W
% 1.32/1.76 ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower_Opower'( T, U, W ), V0 ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( T
% 1.32/1.76 , U, W ), V1 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.32/1.76 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ), =( V0, Y ), ~(
% 1.32/1.76 'c_Ring__and__Field_Oordered__idom'( V2, V3, Y, Z, V4, X, V5, T, U, V6, W
% 1.32/1.76 ) ) ],
% 1.32/1.76 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), X ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), X ) ],
% 1.32/1.76 [ ~( hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower_Opower'( T, U, W ), Y ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( T
% 1.32/1.76 , U, W ), Y ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.32/1.76 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ) ), ~(
% 1.32/1.76 'c_Ring__and__Field_Oordered__idom'( V0, V1, Y, Z, V2, X, V3, T, U, V4, W
% 1.32/1.76 ) ) ],
% 1.32/1.76 [ ~( hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower_Opower'( Z, T, U ), W ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( Z
% 1.32/1.76 , T, U ), V0 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.32/1.76 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), V1 ) ) ), ~(
% 1.32/1.76 'c_Ring__and__Field_Oordered__idom'( V2, V3, V1, Y, V4, X, V5, Z, T, V6,
% 1.32/1.76 U ) ) ],
% 1.32/1.76 [ ~( hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( 'c_Power_Opower_Opower'( Z,
% 1.32/1.76 T, U ), Y ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.32/1.76 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ), ~(
% 1.32/1.76 'c_Ring__and__Field_Oordered__idom'( W, V0, Y, V1, V2, X, V3, Z, T, V4, U
% 1.32/1.76 ) ) ],
% 1.32/1.76 [ ~( hBOOL( hAPP( hAPP( X, hAPP( hAPP( 'c_Power_Opower_Opower'( Y, Z, T
% 1.32/1.76 ), U ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ) ), W ) ) ), ~(
% 1.32/1.76 'c_Ring__and__Field_Oordered__idom'( V0, V1, W, V2, V3, X, V4, Y, Z, V5,
% 1.32/1.76 T ) ) ],
% 1.32/1.76 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.32/1.76 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'(
% 1.32/1.76 'tc_nat' ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.32/1.76 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ],
% 1.32/1.76 [ ~( 'c_Ring__and__Field_Oordered__idom'( X, Y, Z, T, U, W, V0, V1, V2,
% 1.32/1.76 V3, V4 ) ), =( hAPP( hAPP( T, hAPP( hAPP( 'c_Power_Opower_Opower'( V1, V2
% 1.32/1.76 , V4 ), Z ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.32/1.76 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower_Opower'( V1, V2, V4 ), Z ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ) ), Z ) ],
% 1.32/1.76 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), hAPP( T, U ) ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y
% 1.32/1.76 , Z ), U ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.32/1.76 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ), ~(
% 1.32/1.76 'c_Ring__and__Field_Oordered__idom'( W, V0, V1, V2, V3, V4, T, X, Y, V5,
% 1.32/1.76 Z ) ) ],
% 1.32/1.76 [ =( hAPP( X, hAPP( hAPP( 'c_Power_Opower_Opower'( Y, Z, T ), U ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( Y
% 1.32/1.76 , Z, T ), U ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.32/1.76 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ), ~(
% 1.32/1.76 'c_Ring__and__Field_Oordered__idom'( W, V0, V1, V2, V3, V4, X, Y, Z, V5,
% 1.32/1.76 T ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.32/1.76 ), ~( hBOOL( hAPP( hAPP( X, hAPP( hAPP( V0, Z ), U ) ), U ) ) ), ~(
% 1.32/1.76 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, X, T, V4, Y, V0, V5,
% 1.32/1.76 V6 ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), T ) ), hBOOL( hAPP(
% 1.32/1.76 hAPP( U, T ), W ) ), hBOOL( hAPP( hAPP( U, W ), T ) ), ~(
% 1.32/1.76 'c_Ring__and__Field_Oordered__idom'( V0, V1, W, V2, X, U, V3, V4, Y, V5,
% 1.32/1.76 V6 ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), T ) ), ~( hBOOL( hAPP(
% 1.32/1.76 hAPP( X, U ), Z ) ) ), ~( hBOOL( hAPP( hAPP( X, Z ), U ) ) ), ~(
% 1.32/1.76 'c_Ring__and__Field_Oordered__idom'( W, V0, V1, V2, X, V3, V4, U, Y, V5,
% 1.32/1.76 V6 ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.32/1.76 ), ~( hBOOL( hAPP( hAPP( X, W ), hAPP( hAPP( V0, W ), Z ) ) ) ), ~(
% 1.32/1.76 'c_Ring__and__Field_Oordered__idom'( V1, V2, U, V3, T, X, V4, Y, V0, V5,
% 1.32/1.76 V6 ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.32/1.76 ), ~( hBOOL( hAPP( hAPP( X, U ), hAPP( hAPP( V0, U ), Y ) ) ) ), ~(
% 1.32/1.76 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, T, X, V4, Z, V0, V5,
% 1.32/1.76 V6 ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, Y ), T ) ) ), hBOOL( hAPP(
% 1.32/1.76 hAPP( U, Y ), W ) ), hBOOL( hAPP( hAPP( U, W ), Y ) ), ~(
% 1.32/1.76 'c_Ring__and__Field_Oordered__idom'( V0, V1, W, V2, U, X, V3, V4, Z, V5,
% 1.32/1.76 V6 ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, Y ), T ) ) ), ~( hBOOL( hAPP(
% 1.32/1.76 hAPP( X, T ), U ) ) ), ~( hBOOL( hAPP( hAPP( X, U ), T ) ) ), ~(
% 1.32/1.76 'c_Ring__and__Field_Oordered__idom'( W, V0, V1, V2, V3, X, V4, U, Z, V5,
% 1.32/1.76 V6 ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.32/1.76 ), ~( hBOOL( hAPP( hAPP( X, hAPP( hAPP( V0, W ), Y ) ), W ) ) ), ~(
% 1.32/1.76 'c_Ring__and__Field_Oordered__idom'( V1, V2, U, V3, T, X, V4, Z, V0, V5,
% 1.32/1.76 V6 ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.32/1.76 ), ~( hBOOL( hAPP( hAPP( X, hAPP( hAPP( V0, U ), Z ) ), U ) ) ), ~(
% 1.32/1.76 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, T, X, V4, Y, V0, V5,
% 1.32/1.76 V6 ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), Z ) ), hBOOL( hAPP(
% 1.32/1.76 hAPP( U, Z ), W ) ), hBOOL( hAPP( hAPP( U, W ), Z ) ), ~(
% 1.32/1.76 'c_Ring__and__Field_Oordered__idom'( V0, V1, W, V2, U, X, V3, V4, Y, V5,
% 1.32/1.76 V6 ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), Z ) ), ~( hBOOL( hAPP(
% 1.32/1.76 hAPP( X, U ), T ) ) ), ~( hBOOL( hAPP( hAPP( X, T ), U ) ) ), ~(
% 1.32/1.76 'c_Ring__and__Field_Oordered__idom'( W, V0, V1, V2, V3, X, V4, U, Y, V5,
% 1.32/1.76 V6 ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.32/1.76 ), ~( hBOOL( hAPP( hAPP( X, W ), hAPP( hAPP( V0, Z ), W ) ) ) ), ~(
% 1.32/1.76 'c_Ring__and__Field_Oordered__idom'( V1, V2, U, V3, T, X, V4, Y, V0, V5,
% 1.32/1.76 V6 ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.32/1.76 ), ~( hBOOL( hAPP( hAPP( X, U ), hAPP( hAPP( V0, Y ), U ) ) ) ), ~(
% 1.32/1.76 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, T, X, V4, Z, V0, V5,
% 1.32/1.76 V6 ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), Y ) ) ), hBOOL( hAPP(
% 1.32/1.76 hAPP( U, Y ), W ) ), hBOOL( hAPP( hAPP( U, W ), Y ) ), ~(
% 1.32/1.76 'c_Ring__and__Field_Oordered__idom'( V0, V1, W, V2, U, X, V3, V4, Z, V5,
% 1.32/1.76 V6 ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), Y ) ) ), ~( hBOOL( hAPP(
% 1.32/1.76 hAPP( X, T ), U ) ) ), ~( hBOOL( hAPP( hAPP( X, U ), T ) ) ), ~(
% 1.32/1.76 'c_Ring__and__Field_Oordered__idom'( W, V0, V1, V2, V3, X, V4, U, Z, V5,
% 1.32/1.76 V6 ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.32/1.76 ), ~( hBOOL( hAPP( hAPP( X, hAPP( hAPP( V0, Y ), W ) ), W ) ) ), ~(
% 1.32/1.76 'c_Ring__and__Field_Oordered__idom'( V1, V2, U, V3, T, X, V4, Z, V0, V5,
% 1.32/1.76 V6 ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.32/1.76 ), ~( hBOOL( hAPP( hAPP( X, hAPP( hAPP( V0, Z ), U ) ), U ) ) ), ~(
% 1.32/1.76 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, T, X, V4, Y, V0, V5,
% 1.32/1.76 V6 ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), T ) ), hBOOL( hAPP(
% 1.32/1.76 hAPP( U, T ), W ) ), hBOOL( hAPP( hAPP( U, W ), T ) ), ~(
% 1.32/1.76 'c_Ring__and__Field_Oordered__idom'( V0, V1, W, V2, U, X, V3, V4, Y, V5,
% 1.32/1.76 V6 ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), T ) ), ~( hBOOL( hAPP(
% 1.32/1.76 hAPP( X, U ), Z ) ) ), ~( hBOOL( hAPP( hAPP( X, Z ), U ) ) ), ~(
% 1.32/1.76 'c_Ring__and__Field_Oordered__idom'( W, V0, V1, V2, V3, X, V4, U, Y, V5,
% 1.32/1.76 V6 ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.76 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.32/1.76 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.32/1.76 , X ), X ), T, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T
% 1.32/1.76 , X ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.32/1.76 , T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ),
% 1.32/1.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.76 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.32/1.76 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.32/1.76 , X ), X ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.32/1.76 ) ), ~( 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.32/1.76 , Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ),
% 1.32/1.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.32/1.76 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ],
% 1.32/1.76 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), ~( =(
% 1.32/1.76 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.32/1.76 =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.76 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), ~(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.76 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ozero__class_Ozero'( X ), X ), X ) ) ]
% 1.32/1.76 ,
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.32/1.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.76 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.32/1.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.32/1.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.32/1.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.76 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.32/1.76 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.76 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.32/1.76 , Z ), Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) )
% 1.32/1.76 ],
% 1.32/1.76 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.76 'tc_nat' ), Z ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.32/1.76 , Z ), Y ), 'tc_nat' ) ) ],
% 1.32/1.76 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.76 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.32/1.76 , X ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) )
% 1.32/1.76 ],
% 1.32/1.76 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.32/1.76 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.76 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Y ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ) ) ],
% 1.32/1.76 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.32/1.76 , 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.32/1.76 , Y ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ),
% 1.32/1.76 ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.32/1.76 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.32/1.76 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.32/1.76 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.32/1.76 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.32/1.76 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.76 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ],
% 1.32/1.76 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.32/1.76 , 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.32/1.76 , Y ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ),
% 1.32/1.76 ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.32/1.76 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.32/1.76 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.32/1.76 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.32/1.76 [ ~( hBOOL( hAPP( X, Y ) ) ), hBOOL( hAPP( X,
% 1.32/1.76 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.32/1.76 'tc_nat' ) ) ) ],
% 1.32/1.76 [ ~( hBOOL( hAPP( X, 'c_Divides_Odiv__class_Omod'( Y,
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ) ), hBOOL( hAPP( X
% 1.32/1.76 , Y ) ) ],
% 1.32/1.76 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Y, X ) ]
% 1.32/1.76 ,
% 1.32/1.76 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Y, X ) ],
% 1.32/1.76 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.32/1.76 , X ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_lessequals'( Y, T
% 1.32/1.76 , X ) ) ],
% 1.32/1.76 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.32/1.76 , X ), ~( 'c_lessequals'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T
% 1.32/1.76 , X ) ) ],
% 1.32/1.76 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.32/1.76 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T )
% 1.32/1.76 , X ), ~( 'c_lessequals'( U, T, X ) ), ~( 'c_lessequals'( Y, hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ), X ) ) ],
% 1.32/1.76 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.32/1.76 'c_lessequals'( T, Z, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.32/1.76 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.32/1.76 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.32/1.76 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.32/1.76 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_lessequals'( T, Z, X
% 1.32/1.76 ) ) ],
% 1.32/1.76 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.32/1.76 ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X
% 1.32/1.76 ) ) ],
% 1.32/1.76 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.32/1.76 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( T, Z, X ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.32/1.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.32/1.76 'c_HOL_Oone__class_Oone'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.76 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.32/1.76 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ),
% 1.32/1.76 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~(
% 1.32/1.76 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ],
% 1.32/1.76 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_Suc'(
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_Suc'(
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.76 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.32/1.76 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~( 'c_lessequals'(
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.32/1.76 ), X ) ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.32/1.76 , X ), ~( 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.32/1.76 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.76 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.32/1.76 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~( 'c_lessequals'(
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.32/1.76 ), X ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.32/1.76 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ),
% 1.32/1.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.32/1.76 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), X, 'tc_nat' ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.32/1.76 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.32/1.76 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.32/1.76 ), Y ), Z ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.76 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.32/1.76 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.32/1.76 ), Y ), Z ), Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.76 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.32/1.76 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.32/1.76 , X ), X ), T, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T
% 1.32/1.76 , X ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.32/1.76 , T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ), ~(
% 1.32/1.76 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.32/1.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.76 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.32/1.76 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.32/1.76 , X ), X ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.32/1.76 ) ), ~( 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.32/1.76 , Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ), ~(
% 1.32/1.76 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.32/1.76 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X )
% 1.32/1.76 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.32/1.76 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ), Z ) ), Y ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( hAPP(
% 1.32/1.76 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ) ) ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.32/1.76 ,
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.32/1.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.32/1.76 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'(
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OMin', X ), Y, X ),
% 1.32/1.76 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oinverse__class_Odivide'(
% 1.32/1.76 'c_HOL_Oone__class_Oone'( X ), Y, X ), X ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.32/1.76 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.76 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.32/1.76 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.32/1.76 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.32/1.76 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.32/1.76 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.76 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.32/1.76 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.32/1.76 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.32/1.76 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.32/1.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ), X ), =( Y,
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'(
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), ~( 'c_Int_Oiszero'(
% 1.32/1.76 'c_HOL_Oone__class_Oone'( X ), X ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ), X ) ), ~(
% 1.32/1.76 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.32/1.76 , 'tc_nat' ), 'tc_nat' ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.32/1.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), U ) ) ), ~( hBOOL( hAPP(
% 1.32/1.76 hAPP( X, Y ), U ) ) ), ~( hBOOL( hAPP( hAPP( X, Y ), T ) ) ), ~(
% 1.32/1.76 'c_Ring__and__Field_Oordered__semidom'( W, V0, Y, Z, V1, X, V2 ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~(
% 1.32/1.76 'c_Ring__and__Field_Oordered__semidom'( T, Y, Z, U, X, W, V0 ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, Y ), T ) ) ), ~(
% 1.32/1.76 'c_Ring__and__Field_Oordered__semidom'( Z, U, T, W, V0, X, V1 ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~(
% 1.32/1.76 'c_Ring__and__Field_Oordered__semidom'( T, Y, Z, U, W, X, V0 ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), T ) ) ), ~(
% 1.32/1.76 'c_Ring__and__Field_Oordered__semidom'( Z, Y, T, U, W, X, V0 ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), U ) ) ), ~( hBOOL( hAPP(
% 1.32/1.76 hAPP( X, Y ), U ) ) ), ~( hBOOL( hAPP( hAPP( X, W ), T ) ) ), ~(
% 1.32/1.76 'c_Ring__and__Field_Oordered__semidom'( Z, W, V0, V1, V2, X, V3 ) ) ]
% 1.32/1.76 ,
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.32/1.76 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), 'c_lessequals'(
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Z ), Y ), X ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ),
% 1.32/1.76 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ) ),
% 1.32/1.76 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ),
% 1.32/1.76 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.32/1.76 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ), ~( 'c_lessequals'(
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ) ) ],
% 1.32/1.76 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.32/1.76 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.76 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ],
% 1.32/1.76 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.32/1.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.76 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.32/1.76 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =(
% 1.32/1.76 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.32/1.76 'c_HOL_Oinverse__class_Odivide'( T, U, X ) ) ), =( U,
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.32/1.76 ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), U ), hAPP(
% 1.32/1.76 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) ), =( Z,
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ) ), =( U, 'c_HOL_Ozero__class_Ozero'( X )
% 1.32/1.76 ), =( 'c_HOL_Oinverse__class_Odivide'( Y, U, X ),
% 1.32/1.76 'c_HOL_Oinverse__class_Odivide'( T, Z, X ) ) ],
% 1.32/1.76 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.32/1.76 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.32/1.76 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X
% 1.32/1.76 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.32/1.76 'c_Divides_Odiv__class_Omod'( Z, T, X ) ) ) ],
% 1.32/1.76 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.32/1.76 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.32/1.76 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X
% 1.32/1.76 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.32/1.76 'c_Divides_Odiv__class_Omod'( Y, T, X ) ), Z ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.32/1.76 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X )
% 1.32/1.76 ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.32/1.76 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X )
% 1.32/1.76 , ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.32/1.76 ],
% 1.32/1.76 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.32/1.76 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oabs__class_Oabs'(
% 1.32/1.76 Y, X ), X ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.32/1.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.32/1.76 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.76 X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ), Y, X ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.76 [ ~( =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ), =( Y,
% 1.32/1.76 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.32/1.76 [ ~( =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ), =( X,
% 1.32/1.76 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.32/1.76 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.32/1.76 'c_HOL_Ouminus__class_Ouminus'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.32/1.76 ), Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.32/1.76 'c_HOL_Ouminus__class_Ouminus'( Z, X ) ), 'c_HOL_Ouminus__class_Ouminus'(
% 1.32/1.76 Y, X ) ) ) ],
% 1.32/1.76 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.32/1.76 'c_HOL_Ouminus__class_Ouminus'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.32/1.76 ), Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.32/1.76 'c_HOL_Ouminus__class_Ouminus'( Y, X ) ), 'c_HOL_Ouminus__class_Ouminus'(
% 1.32/1.76 Z, X ) ) ) ],
% 1.32/1.76 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.32/1.76 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.32/1.76 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 1.32/1.76 'c_lessequals'( Z, Y, X ) ],
% 1.32/1.76 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.32/1.76 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.32/1.76 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.32/1.76 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.32/1.76 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Z
% 1.32/1.76 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.32/1.76 [ ~( 'c_Ring__and__Field_Oordered__idom'( X, Y, hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower_Opower'( Z, T, U ), W ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ), V0, V1, V2, V3, Z, T, V4, U ) ), =( W,
% 1.32/1.76 hAPP( hAPP( 'c_Power_Opower_Opower'( Z, T, U ), W ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ],
% 1.32/1.76 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_Int_Oint' ), 'c_Nat_Osemiring__1__class_Oof__nat'(
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_Int_Oint' ) ) ],
% 1.32/1.76 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) ],
% 1.32/1.76 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), 'tc_nat' ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), Z ) )
% 1.32/1.76 ), ~( hBOOL( hAPP( hAPP( X, hAPP( hAPP( 'c_Power_Opower_Opower'( W, V0,
% 1.32/1.76 V1 ), Y ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.32/1.76 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower_Opower'( W, V0, V1 ), Z ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ), ~(
% 1.32/1.76 'c_Ring__and__Field_Oordered__semidom'( V2, U, W, V0, T, X, V1 ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( X, T ), Z ) )
% 1.32/1.76 ), ~( hBOOL( hAPP( hAPP( X, hAPP( hAPP( 'c_Power_Opower_Opower'( U, W,
% 1.32/1.76 V0 ), Y ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.32/1.76 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower_Opower'( U, W, V0 ), Z ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ), ~(
% 1.32/1.76 'c_Ring__and__Field_Oordered__semidom'( V1, T, U, W, X, V2, V0 ) ) ],
% 1.32/1.76 [ =( 'c_NthRoot_Osqrt', 'c_NthRoot_Oroot'(
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ],
% 1.32/1.76 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( Y, T ), T ) ), ~(
% 1.32/1.76 'c_OrderedGroup_Omonoid__mult'( X, Y, Z ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( 'c_Power_Opower_Opower'( Z, T,
% 1.32/1.76 U ), W ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.32/1.76 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), ~(
% 1.32/1.76 'c_Ring__and__Field_Oordered__idom'( V0, V1, Y, V2, X, V3, V4, Z, T, V5,
% 1.32/1.76 U ) ) ],
% 1.32/1.76 [ ~( 'c_Ring__and__Field_Oordered__idom'( X, Y, Z, T, U, W, V0, V1, V2,
% 1.32/1.76 V3, V4 ) ), hBOOL( hAPP( hAPP( U, hAPP( hAPP( T, hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower_Opower'( V1, V2, V4 ), Z ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( V1
% 1.32/1.76 , V2, V4 ), Z ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.32/1.76 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), Z ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower_Opower'( T, U, W ), V0 ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( T
% 1.32/1.76 , U, W ), V1 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.32/1.76 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ), ~(
% 1.32/1.76 'c_Ring__and__Field_Oordered__idom'( V2, V3, Y, Z, X, V4, V5, T, U, V6, W
% 1.32/1.76 ) ) ],
% 1.32/1.76 [ ~( =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y
% 1.32/1.76 , Z ), U ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.32/1.76 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), ~(
% 1.32/1.76 'c_Ring__and__Field_Oordered__semidom'( W, V0, X, Y, V1, V2, Z ) ), =( T
% 1.32/1.76 , U ), ~( hBOOL( hAPP( hAPP( V1, V0 ), U ) ) ), ~( hBOOL( hAPP( hAPP( V1
% 1.32/1.76 , V0 ), T ) ) ) ],
% 1.32/1.76 [ ~( 'c_Ring__and__Field_Oordered__idom'( X, Y, hAPP( hAPP( Z, hAPP(
% 1.32/1.76 hAPP( 'c_Power_Opower_Opower'( T, U, W ), V0 ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( T
% 1.32/1.76 , U, W ), V1 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.32/1.76 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ), Z, V2, V3, V4, T, U, V5
% 1.32/1.76 , W ) ), =( V1, hAPP( hAPP( Z, hAPP( hAPP( 'c_Power_Opower_Opower'( T, U
% 1.32/1.76 , W ), V0 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.32/1.76 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower_Opower'( T, U, W ), V1 ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ],
% 1.32/1.76 [ ~( 'c_Ring__and__Field_Oordered__idom'( X, Y, hAPP( hAPP( Z, hAPP(
% 1.32/1.76 hAPP( 'c_Power_Opower_Opower'( T, U, W ), V0 ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( T
% 1.32/1.76 , U, W ), V1 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.32/1.76 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ), Z, V2, V3, V4, T, U, V5
% 1.32/1.76 , W ) ), =( V0, hAPP( hAPP( Z, hAPP( hAPP( 'c_Power_Opower_Opower'( T, U
% 1.32/1.76 , W ), V0 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.32/1.76 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower_Opower'( T, U, W ), V1 ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ],
% 1.32/1.76 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ), ~(
% 1.32/1.76 'c_Parity_Oeven__odd__class_Oeven'( 'c_Divides_Odiv__class_Omod'( X,
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit0'(
% 1.32/1.76 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ) ]
% 1.32/1.76 ,
% 1.32/1.76 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_Divides_Odiv__class_Omod'( X,
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit0'(
% 1.32/1.76 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ),
% 1.32/1.76 ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.32/1.76 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), hAPP( T, U ) ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y
% 1.32/1.76 , Z ), U ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.32/1.76 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ), ~(
% 1.32/1.76 'c_Ring__and__Field_Ocomm__ring__1'( X, Y, W, T, V0, V1, Z ) ) ],
% 1.32/1.76 [ =( 'c_FFT__Mirabelle_Oroot'( 'c_Int_Onumber__class_Onumber__of'(
% 1.32/1.76 'c_Int_OBit0'( 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat'
% 1.32/1.76 ) ), 'c_Complex_Oii' ) ],
% 1.32/1.76 [ =( X, Y ), ~( hBOOL( hAPP( hAPP( Z, hAPP( hAPP( T, hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower_Opower'( U, W, V0 ), V1 ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( U
% 1.32/1.76 , W, V0 ), X ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.32/1.76 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), Y ) ) ), ~(
% 1.32/1.76 'c_Ring__and__Field_Oordered__idom'( V2, V3, Y, T, Z, V4, V5, U, W, V6,
% 1.32/1.76 V0 ) ) ],
% 1.32/1.76 [ =( X, Y ), ~( hBOOL( hAPP( hAPP( Z, hAPP( hAPP( T, hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower_Opower'( U, W, V0 ), X ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( U
% 1.32/1.76 , W, V0 ), V1 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.32/1.76 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), Y ) ) ), ~(
% 1.32/1.76 'c_Ring__and__Field_Oordered__idom'( V2, V3, Y, T, Z, V4, V5, U, W, V6,
% 1.32/1.76 V0 ) ) ],
% 1.32/1.76 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.76 'tc_nat' ), X ), X ) ) ],
% 1.32/1.76 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), X ) ) ],
% 1.32/1.76 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ), T ), ~( 'c_Ring__and__Field_Osemiring__1'(
% 1.32/1.76 X, Y, T, U, Z ) ) ],
% 1.32/1.76 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), X ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), ~( 'c_Ring__and__Field_Osemiring__1'(
% 1.32/1.76 X, Y, T, U, Z ) ) ],
% 1.32/1.76 [ ~( 'c_Ring__and__Field_Oordered__idom'( X, Y, Z, T, U, W, V0, V1, V2,
% 1.32/1.76 V3, V4 ) ), =( hAPP( hAPP( 'c_Power_Opower_Opower'( V1, V2, V4 ), Z ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ],
% 1.32/1.76 [ =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', 'tc_nat' ) ) ],
% 1.32/1.76 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', 'tc_nat' ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.32/1.76 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.32/1.76 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.32/1.76 ), ~( =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.76 ) ) ],
% 1.32/1.76 [ ~( =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( 'tc_nat' ), X ), Y )
% 1.32/1.76 , 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X, 'c_Suc'(
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.32/1.76 [ =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( 'tc_nat' ), 'c_Suc'(
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), X ), 'c_Suc'(
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.32/1.76 [ =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( 'tc_nat' ), 'c_Suc'(
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), X ), 'c_Suc'(
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.32/1.76 [ =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( 'tc_nat' ), X ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_Suc'(
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 1.32/1.76 'c_Nat_Osemiring__1__class_Oof__nat'( hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( 'tc_nat' ), Y ), Z ), X ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), 'c_Nat_Osemiring__1__class_Oof__nat'(
% 1.32/1.76 Y, X ) ), Z ) ) ],
% 1.32/1.76 [ =( X, 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X
% 1.32/1.76 , 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) ) ],
% 1.32/1.76 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( 'c_Suc'( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ), 'tc_nat' ) ) ],
% 1.32/1.76 [ =( hAPP( hAPP( X, Y ), 'c_Suc'( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ), hAPP( hAPP( T, Y ), hAPP( hAPP(
% 1.32/1.76 T, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, Y ), Z ) ) ) ), ~(
% 1.32/1.76 'c_Groebner__Basis_Ogb__semiring'( U, T, X, W, V0, V1 ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.32/1.76 ,
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.32/1.76 ), Y ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.32/1.76 ,
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.32/1.76 Y, Z, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ),
% 1.32/1.76 ~( 'c_lessequals'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.32/1.76 =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.32/1.76 =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X
% 1.32/1.76 ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =( hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), =( Y, Z ), ~( 'c_lessequals'(
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.32/1.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.76 ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.32/1.76 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Oinverse'(
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ), X
% 1.32/1.76 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X
% 1.32/1.76 ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.32/1.76 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ), X
% 1.32/1.76 ), Y ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.32/1.76 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ), X
% 1.32/1.76 ), Y ) ],
% 1.32/1.76 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ),
% 1.32/1.76 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.32/1.76 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oone__class_Oone'( X )
% 1.32/1.76 , 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X )
% 1.32/1.76 ) ],
% 1.32/1.76 [ ~( 'class_Int_Onumber__ring'( X ) ), ~( 'c_Int_Oiszero'(
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ), X
% 1.32/1.76 ) ) ],
% 1.32/1.76 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.32/1.76 'c_Int_OBit1'( 'c_Int_OPls' ), X ) ), Y ), Y ) ],
% 1.32/1.76 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ) )
% 1.32/1.76 , Y ) ],
% 1.32/1.76 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.32/1.76 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.32/1.76 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), X ) ), Y ) ), Z ) ) ) ]
% 1.32/1.76 ,
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ) ],
% 1.32/1.76 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ],
% 1.32/1.76 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ),
% 1.32/1.76 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.32/1.76 [ =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ),
% 1.32/1.76 'tc_nat' ) ) ],
% 1.32/1.76 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.32/1.76 'c_Int_OMin', X ) ), 'c_Suc'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.76 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.32/1.76 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), Y ) ) ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OMin', X ) ) ],
% 1.32/1.76 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ),
% 1.32/1.76 'tc_nat' ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.32/1.76 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ), 'c_Suc'( 'c_Suc'( 'c_Suc'(
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ) ],
% 1.32/1.76 [ =( 'c_Suc'( 'c_Suc'( 'c_Suc'( X ) ) ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ) ],
% 1.32/1.76 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.76 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), Y ) ) ]
% 1.32/1.76 ,
% 1.32/1.76 [ =( hAPP( hAPP( X, Y ), Y ), hAPP( hAPP( Z, Y ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( T
% 1.32/1.76 , X, Z, U, W, V0 ) ) ],
% 1.32/1.76 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ), 'c_Suc'( 'c_Suc'(
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.32/1.76 [ =( 'c_Divides_Odiv__class_Odiv'( 'c_Suc'( 'c_Suc'( X ) ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'c_Suc'(
% 1.32/1.76 'c_Divides_Odiv__class_Odiv'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.32/1.76 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) )
% 1.32/1.76 ) ],
% 1.32/1.76 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), 'c_Suc'( 'c_Suc'( X ) ) ) ],
% 1.32/1.76 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_Suc'( 'c_Suc'( X ) ) ) ],
% 1.32/1.76 [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( 'c_Suc'( X ) ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X
% 1.32/1.76 , 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) ) ],
% 1.32/1.76 [ =( 'c_Suc'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =( hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y
% 1.32/1.76 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oabs__class_Oabs'( Y, X ) ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ],
% 1.32/1.76 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ],
% 1.32/1.76 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.76 X ), Y ), Y ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X
% 1.32/1.76 ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.32/1.76 'c_HOL_Oabs__class_Oabs'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X )
% 1.32/1.76 , Y ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ],
% 1.32/1.76 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), ~( 'class_Int_Onumber'(
% 1.32/1.76 X ) ), =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.76 X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ) ],
% 1.32/1.76 [ =( 'c_FFT__Mirabelle_OIDFT'( hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( 'tc_nat' ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ), 'v_ka____' ), X, Y ), hAPP(
% 1.32/1.76 'c_FFT__Mirabelle_OIFFT'( 'v_ka____', X ), Y ) ), ~(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_Power_Opower__class_Opower'(
% 1.32/1.76 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.32/1.76 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), 'v_ka____' ), 'tc_nat' ) )
% 1.32/1.76 ],
% 1.32/1.76 [ 'c_HOL_Oord__class_Oless'( 'v_i____', hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( 'tc_nat' ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_Suc'( 'v_ka____' ) ), 'tc_nat' ) ]
% 1.32/1.76 ,
% 1.32/1.76 [ =( 'c_Int_OBit0'( 'c_Int_OPls' ), 'c_Int_OPls' ) ],
% 1.32/1.76 [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ],
% 1.32/1.76 [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ],
% 1.32/1.76 [ ~( =( 'c_Int_OPls', 'c_Int_OBit1'( X ) ) ) ],
% 1.32/1.76 [ ~( =( 'c_Int_OBit1'( X ), 'c_Int_OPls' ) ) ],
% 1.32/1.76 [ ~( =( 'c_Int_OBit0'( X ), 'c_Int_OPls' ) ), =( X, 'c_Int_OPls' ) ]
% 1.32/1.76 ,
% 1.32/1.76 [ ~( =( 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ) ) ), =( X, Y ) ],
% 1.32/1.76 [ ~( =( 'c_Int_OBit1'( X ), 'c_Int_OBit0'( Y ) ) ) ],
% 1.32/1.76 [ =( 'c_Int_OPls', 'c_Int_OBit0'( 'c_Int_OPls' ) ) ],
% 1.32/1.76 [ ~( =( 'c_Suc'( X ), X ) ) ],
% 1.32/1.76 [ ~( =( X, 'c_Suc'( X ) ) ) ],
% 1.32/1.76 [ ~( =( 'c_Int_OPls', 'c_Int_OBit0'( X ) ) ), =( 'c_Int_OPls', X ) ]
% 1.32/1.76 ,
% 1.32/1.76 [ ~( =( 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ) ) ), =( X, Y ) ],
% 1.32/1.76 [ ~( 'class_Int_Oring__char__0'( X ) ), ~( 'class_Int_Onumber__ring'( X
% 1.32/1.76 ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ), =( Y, Z ) ],
% 1.32/1.76 [ ~( =( 'c_Int_OBit0'( X ), 'c_Int_OBit1'( Y ) ) ) ],
% 1.32/1.76 [ ~( =( 'c_FFT__Mirabelle_OIDFT'( hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( 'tc_nat' ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_Suc'( 'v_ka____' ) ), 'v_a____',
% 1.32/1.76 'v_i____' ), hAPP( 'c_FFT__Mirabelle_OIFFT'( 'c_Suc'( 'v_ka____' ),
% 1.32/1.76 'v_a____' ), 'v_i____' ) ) ) ],
% 1.32/1.76 [ 'class_Lattices_Oboolean__algebra'( 'tc_fun'( X, Y ) ), ~(
% 1.32/1.76 'class_Lattices_Oboolean__algebra'( Y ) ) ],
% 1.32/1.76 [ 'class_Orderings_Opreorder'( 'tc_fun'( X, Y ) ), ~(
% 1.32/1.76 'class_Orderings_Opreorder'( Y ) ) ],
% 1.32/1.76 [ 'class_Orderings_Oorder'( 'tc_fun'( X, Y ) ), ~(
% 1.32/1.76 'class_Orderings_Oorder'( Y ) ) ],
% 1.32/1.76 [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( 'tc_nat' )
% 1.32/1.76 ],
% 1.32/1.76 [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( 'tc_nat'
% 1.32/1.76 ) ],
% 1.32/1.76 [ 'class_Ring__and__Field_Oordered__comm__semiring__strict'( 'tc_nat' )
% 1.32/1.76 ],
% 1.32/1.76 [ 'class_Ring__and__Field_Opordered__cancel__semiring'( 'tc_nat' ) ]
% 1.32/1.76 ,
% 1.32/1.76 [ 'class_Ring__and__Field_Oordered__semiring__strict'( 'tc_nat' ) ],
% 1.32/1.76 [ 'class_OrderedGroup_Opordered__ab__semigroup__add'( 'tc_nat' ) ],
% 1.32/1.76 [ 'class_OrderedGroup_Opordered__comm__monoid__add'( 'tc_nat' ) ],
% 1.32/1.76 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'( 'tc_nat' ) ],
% 1.32/1.76 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_nat' ) ],
% 1.32/1.76 [ 'class_Ring__and__Field_Opordered__semiring'( 'tc_nat' ) ],
% 1.32/1.76 [ 'class_Ring__and__Field_Oordered__semiring'( 'tc_nat' ) ],
% 1.32/1.76 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_nat' ) ],
% 1.32/1.76 [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_nat' ) ],
% 1.32/1.76 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_nat' ) ],
% 1.32/1.76 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_nat' ) ],
% 1.32/1.76 [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_nat' ) ],
% 1.32/1.76 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_nat' ) ],
% 1.32/1.76 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_nat' ) ],
% 1.32/1.76 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_nat' ) ],
% 1.32/1.76 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_nat' ) ],
% 1.32/1.76 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_nat' ) ],
% 1.32/1.76 [ 'class_Ring__and__Field_Osemiring__0'( 'tc_nat' ) ],
% 1.32/1.76 [ 'class_Ring__and__Field_Omult__mono1'( 'tc_nat' ) ],
% 1.32/1.76 [ 'class_Ring__and__Field_Omult__zero'( 'tc_nat' ) ],
% 1.32/1.76 [ 'class_Ring__and__Field_Omult__mono'( 'tc_nat' ) ],
% 1.32/1.76 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_nat' ) ],
% 1.32/1.76 [ 'class_Ring__and__Field_Osemiring'( 'tc_nat' ) ],
% 1.32/1.76 [ 'class_OrderedGroup_Omonoid__add'( 'tc_nat' ) ],
% 1.32/1.76 [ 'class_Divides_Osemiring__div'( 'tc_nat' ) ],
% 1.32/1.76 [ 'class_Nat_Osemiring__char__0'( 'tc_nat' ) ],
% 1.32/1.76 [ 'class_Orderings_Opreorder'( 'tc_nat' ) ],
% 1.32/1.76 [ 'class_Orderings_Olinorder'( 'tc_nat' ) ],
% 1.32/1.76 [ 'class_Orderings_Oorder'( 'tc_nat' ) ],
% 1.32/1.76 [ 'class_Power_Opower'( 'tc_nat' ) ],
% 1.32/1.76 [ 'class_Int_Onumber'( 'tc_nat' ) ],
% 1.32/1.76 [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'(
% 1.32/1.76 'tc_Int_Oint' ) ],
% 1.32/1.76 [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'(
% 1.32/1.76 'tc_Int_Oint' ) ],
% 1.32/1.76 [ 'class_Ring__and__Field_Oordered__comm__semiring__strict'(
% 1.32/1.76 'tc_Int_Oint' ) ],
% 1.32/1.76 [ 'class_Ring__and__Field_Opordered__cancel__semiring'( 'tc_Int_Oint' )
% 1.32/1.76 ],
% 1.32/1.76 [ 'class_Ring__and__Field_Oring__1__no__zero__divisors'( 'tc_Int_Oint' )
% 1.32/1.76 ],
% 1.32/1.76 [ 'class_Ring__and__Field_Oordered__semiring__strict'( 'tc_Int_Oint' ) ]
% 1.32/1.76 ,
% 1.32/1.76 [ 'class_OrderedGroup_Opordered__ab__semigroup__add'( 'tc_Int_Oint' ) ]
% 1.32/1.76 ,
% 1.32/1.76 [ 'class_OrderedGroup_Opordered__ab__group__add__abs'( 'tc_Int_Oint' ) ]
% 1.32/1.76 ,
% 1.32/1.76 [ 'class_OrderedGroup_Olordered__ab__group__add__abs'( 'tc_Int_Oint' ) ]
% 1.32/1.76 ,
% 1.32/1.76 [ 'class_OrderedGroup_Opordered__comm__monoid__add'( 'tc_Int_Oint' ) ]
% 1.32/1.76 ,
% 1.32/1.76 [ 'class_Ring__and__Field_Oring__no__zero__divisors'( 'tc_Int_Oint' ) ]
% 1.32/1.76 ,
% 1.32/1.76 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'( 'tc_Int_Oint' ) ]
% 1.32/1.76 ,
% 1.32/1.76 [ 'class_Ring__and__Field_Oordered__ring__strict'( 'tc_Int_Oint' ) ]
% 1.32/1.76 ,
% 1.32/1.76 [ 'class_OrderedGroup_Opordered__ab__group__add'( 'tc_Int_Oint' ) ],
% 1.32/1.76 [ 'class_OrderedGroup_Olordered__ab__group__add'( 'tc_Int_Oint' ) ],
% 1.32/1.76 [ 'class_OrderedGroup_Oordered__ab__group__add'( 'tc_Int_Oint' ) ],
% 1.32/1.76 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_Int_Oint' ) ],
% 1.32/1.76 [ 'class_Ring__and__Field_Opordered__semiring'( 'tc_Int_Oint' ) ],
% 1.32/1.76 [ 'class_Ring__and__Field_Opordered__ring__abs'( 'tc_Int_Oint' ) ],
% 1.32/1.76 [ 'class_Ring__and__Field_Oordered__semiring'( 'tc_Int_Oint' ) ],
% 1.32/1.76 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_Int_Oint' ) ],
% 1.32/1.76 [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_Int_Oint' ) ],
% 1.32/1.76 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_Int_Oint' ) ],
% 1.32/1.76 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_Int_Oint' ) ],
% 1.32/1.76 [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_Int_Oint' ) ],
% 1.32/1.76 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_Int_Oint' ) ],
% 1.32/1.76 [ 'class_Ring__and__Field_Opordered__ring'( 'tc_Int_Oint' ) ],
% 1.32/1.76 [ 'class_Ring__and__Field_Olordered__ring'( 'tc_Int_Oint' ) ],
% 1.32/1.76 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_Int_Oint' ) ],
% 1.32/1.76 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_Int_Oint' ) ],
% 1.32/1.76 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_Int_Oint' ) ],
% 1.32/1.76 [ 'class_Ring__and__Field_Oordered__idom'( 'tc_Int_Oint' ) ],
% 1.32/1.76 [ 'class_Ring__and__Field_Ocomm__ring__1'( 'tc_Int_Oint' ) ],
% 1.32/1.76 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_Int_Oint' ) ],
% 1.32/1.76 [ 'class_Ring__and__Field_Osemiring__0'( 'tc_Int_Oint' ) ],
% 1.32/1.76 [ 'class_Ring__and__Field_Omult__mono1'( 'tc_Int_Oint' ) ],
% 1.32/1.76 [ 'class_OrderedGroup_Oab__group__add'( 'tc_Int_Oint' ) ],
% 1.32/1.76 [ 'class_Ring__and__Field_Omult__zero'( 'tc_Int_Oint' ) ],
% 1.32/1.76 [ 'class_Ring__and__Field_Omult__mono'( 'tc_Int_Oint' ) ],
% 1.32/1.76 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_Int_Oint' ) ],
% 1.32/1.76 [ 'class_Ring__and__Field_Osemiring'( 'tc_Int_Oint' ) ],
% 1.32/1.76 [ 'class_OrderedGroup_Omonoid__add'( 'tc_Int_Oint' ) ],
% 1.32/1.76 [ 'class_OrderedGroup_Ogroup__add'( 'tc_Int_Oint' ) ],
% 1.32/1.76 [ 'class_Ring__and__Field_Oring__1'( 'tc_Int_Oint' ) ],
% 1.32/1.76 [ 'class_Ring__and__Field_Oabs__if'( 'tc_Int_Oint' ) ],
% 1.32/1.76 [ 'class_Divides_Osemiring__div'( 'tc_Int_Oint' ) ],
% 1.32/1.76 [ 'class_Ring__and__Field_Oring'( 'tc_Int_Oint' ) ],
% 1.32/1.76 [ 'class_Ring__and__Field_Oidom'( 'tc_Int_Oint' ) ],
% 1.32/1.76 [ 'class_Nat_Osemiring__char__0'( 'tc_Int_Oint' ) ],
% 1.32/1.76 [ 'class_Orderings_Opreorder'( 'tc_Int_Oint' ) ],
% 1.32/1.76 [ 'class_Orderings_Olinorder'( 'tc_Int_Oint' ) ],
% 1.32/1.76 [ 'class_Divides_Oring__div'( 'tc_Int_Oint' ) ],
% 1.32/1.76 [ 'class_Orderings_Oorder'( 'tc_Int_Oint' ) ],
% 1.32/1.76 [ 'class_Int_Oring__char__0'( 'tc_Int_Oint' ) ],
% 1.32/1.76 [ 'class_Int_Onumber__ring'( 'tc_Int_Oint' ) ],
% 1.32/1.76 [ 'class_Power_Opower'( 'tc_Int_Oint' ) ],
% 1.32/1.76 [ 'class_Int_Onumber'( 'tc_Int_Oint' ) ],
% 1.32/1.76 [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'(
% 1.32/1.76 'tc_RealDef_Oreal' ) ],
% 1.32/1.76 [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'(
% 1.32/1.76 'tc_RealDef_Oreal' ) ],
% 1.32/1.76 [ 'class_Ring__and__Field_Oordered__comm__semiring__strict'(
% 1.32/1.76 'tc_RealDef_Oreal' ) ],
% 1.32/1.76 [ 'class_Ring__and__Field_Opordered__cancel__semiring'(
% 1.32/1.76 'tc_RealDef_Oreal' ) ],
% 1.32/1.76 [ 'class_Ring__and__Field_Oring__1__no__zero__divisors'(
% 1.32/1.76 'tc_RealDef_Oreal' ) ],
% 1.32/1.76 [ 'class_Ring__and__Field_Oordered__semiring__strict'(
% 1.32/1.76 'tc_RealDef_Oreal' ) ],
% 1.32/1.76 [ 'class_OrderedGroup_Opordered__ab__semigroup__add'( 'tc_RealDef_Oreal'
% 1.32/1.76 ) ],
% 1.32/1.76 [ 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 1.32/1.76 'tc_RealDef_Oreal' ) ],
% 1.32/1.76 [ 'class_OrderedGroup_Olordered__ab__group__add__abs'(
% 1.32/1.76 'tc_RealDef_Oreal' ) ],
% 1.32/1.76 [ 'class_OrderedGroup_Opordered__comm__monoid__add'( 'tc_RealDef_Oreal'
% 1.32/1.76 ) ],
% 1.32/1.76 [ 'class_Ring__and__Field_Oring__no__zero__divisors'( 'tc_RealDef_Oreal'
% 1.32/1.77 ) ],
% 1.32/1.77 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'( 'tc_RealDef_Oreal' )
% 1.32/1.77 ],
% 1.32/1.77 [ 'class_Ring__and__Field_Oordered__ring__strict'( 'tc_RealDef_Oreal' )
% 1.32/1.77 ],
% 1.32/1.77 [ 'class_OrderedGroup_Opordered__ab__group__add'( 'tc_RealDef_Oreal' ) ]
% 1.32/1.77 ,
% 1.32/1.77 [ 'class_OrderedGroup_Olordered__ab__group__add'( 'tc_RealDef_Oreal' ) ]
% 1.32/1.77 ,
% 1.32/1.77 [ 'class_OrderedGroup_Oordered__ab__group__add'( 'tc_RealDef_Oreal' ) ]
% 1.32/1.77 ,
% 1.32/1.77 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_RealDef_Oreal' ) ]
% 1.32/1.77 ,
% 1.32/1.77 [ 'class_Ring__and__Field_Opordered__semiring'( 'tc_RealDef_Oreal' ) ]
% 1.32/1.77 ,
% 1.32/1.77 [ 'class_Ring__and__Field_Opordered__ring__abs'( 'tc_RealDef_Oreal' ) ]
% 1.32/1.77 ,
% 1.32/1.77 [ 'class_Ring__and__Field_Oordered__semiring'( 'tc_RealDef_Oreal' ) ]
% 1.32/1.77 ,
% 1.32/1.77 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_RealDef_Oreal' ) ]
% 1.32/1.77 ,
% 1.32/1.77 [ 'class_Ring__and__Field_Odivision__by__zero'( 'tc_RealDef_Oreal' ) ]
% 1.32/1.77 ,
% 1.32/1.77 [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_RealDef_Oreal' ) ]
% 1.32/1.77 ,
% 1.32/1.77 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_RealDef_Oreal' ) ]
% 1.32/1.77 ,
% 1.32/1.77 [ 'class_RealVector_Oreal__normed__algebra'( 'tc_RealDef_Oreal' ) ],
% 1.32/1.77 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_RealDef_Oreal' ) ],
% 1.32/1.77 [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_RealDef_Oreal' ) ],
% 1.32/1.77 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_RealDef_Oreal' ) ],
% 1.32/1.77 [ 'class_Ring__and__Field_Opordered__ring'( 'tc_RealDef_Oreal' ) ],
% 1.32/1.77 [ 'class_Ring__and__Field_Oordered__field'( 'tc_RealDef_Oreal' ) ],
% 1.32/1.77 [ 'class_Ring__and__Field_Olordered__ring'( 'tc_RealDef_Oreal' ) ],
% 1.32/1.77 [ 'class_Ring__and__Field_Odivision__ring'( 'tc_RealDef_Oreal' ) ],
% 1.32/1.77 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_RealDef_Oreal' ) ],
% 1.32/1.77 [ 'class_RealVector_Oreal__normed__field'( 'tc_RealDef_Oreal' ) ],
% 1.32/1.77 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_RealDef_Oreal' ) ],
% 1.32/1.77 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_RealDef_Oreal' ) ],
% 1.32/1.77 [ 'class_Ring__and__Field_Oordered__idom'( 'tc_RealDef_Oreal' ) ],
% 1.32/1.77 [ 'class_Ring__and__Field_Ocomm__ring__1'( 'tc_RealDef_Oreal' ) ],
% 1.32/1.77 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_RealDef_Oreal' ) ],
% 1.32/1.77 [ 'class_Ring__and__Field_Osemiring__0'( 'tc_RealDef_Oreal' ) ],
% 1.32/1.77 [ 'class_Ring__and__Field_Omult__mono1'( 'tc_RealDef_Oreal' ) ],
% 1.32/1.77 [ 'class_OrderedGroup_Oab__group__add'( 'tc_RealDef_Oreal' ) ],
% 1.32/1.77 [ 'class_Ring__and__Field_Omult__zero'( 'tc_RealDef_Oreal' ) ],
% 1.32/1.77 [ 'class_Ring__and__Field_Omult__mono'( 'tc_RealDef_Oreal' ) ],
% 1.32/1.77 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_RealDef_Oreal' ) ],
% 1.32/1.77 [ 'class_Ring__and__Field_Osemiring'( 'tc_RealDef_Oreal' ) ],
% 1.32/1.77 [ 'class_OrderedGroup_Omonoid__add'( 'tc_RealDef_Oreal' ) ],
% 1.32/1.77 [ 'class_OrderedGroup_Ogroup__add'( 'tc_RealDef_Oreal' ) ],
% 1.32/1.77 [ 'class_Ring__and__Field_Oring__1'( 'tc_RealDef_Oreal' ) ],
% 1.32/1.77 [ 'class_Ring__and__Field_Oabs__if'( 'tc_RealDef_Oreal' ) ],
% 1.32/1.77 [ 'class_Ring__and__Field_Ofield'( 'tc_RealDef_Oreal' ) ],
% 1.32/1.77 [ 'class_Ring__and__Field_Oring'( 'tc_RealDef_Oreal' ) ],
% 1.32/1.77 [ 'class_Ring__and__Field_Oidom'( 'tc_RealDef_Oreal' ) ],
% 1.32/1.77 [ 'class_Nat_Osemiring__char__0'( 'tc_RealDef_Oreal' ) ],
% 1.32/1.77 [ 'class_Orderings_Opreorder'( 'tc_RealDef_Oreal' ) ],
% 1.32/1.77 [ 'class_Orderings_Olinorder'( 'tc_RealDef_Oreal' ) ],
% 1.32/1.77 [ 'class_Orderings_Oorder'( 'tc_RealDef_Oreal' ) ],
% 1.32/1.77 [ 'class_Int_Oring__char__0'( 'tc_RealDef_Oreal' ) ],
% 1.32/1.77 [ 'class_Int_Onumber__ring'( 'tc_RealDef_Oreal' ) ],
% 1.32/1.77 [ 'class_Power_Opower'( 'tc_RealDef_Oreal' ) ],
% 1.32/1.77 [ 'class_Int_Onumber'( 'tc_RealDef_Oreal' ) ],
% 1.32/1.77 [ 'class_Ring__and__Field_Oring__1__no__zero__divisors'(
% 1.32/1.77 'tc_Complex_Ocomplex' ) ],
% 1.32/1.77 [ 'class_Ring__and__Field_Oring__no__zero__divisors'(
% 1.32/1.77 'tc_Complex_Ocomplex' ) ],
% 1.32/1.77 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'(
% 1.32/1.77 'tc_Complex_Ocomplex' ) ],
% 1.32/1.77 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_Complex_Ocomplex' )
% 1.32/1.77 ],
% 1.32/1.77 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_Complex_Ocomplex' )
% 1.32/1.77 ],
% 1.32/1.77 [ 'class_Ring__and__Field_Odivision__by__zero'( 'tc_Complex_Ocomplex' )
% 1.32/1.77 ],
% 1.32/1.77 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_Complex_Ocomplex' ) ]
% 1.32/1.77 ,
% 1.32/1.77 [ 'class_RealVector_Oreal__normed__algebra'( 'tc_Complex_Ocomplex' ) ]
% 1.32/1.77 ,
% 1.32/1.77 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_Complex_Ocomplex' ) ]
% 1.32/1.77 ,
% 1.32/1.77 [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_Complex_Ocomplex' ) ]
% 1.32/1.77 ,
% 1.32/1.77 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_Complex_Ocomplex' ) ]
% 1.32/1.77 ,
% 1.32/1.77 [ 'class_Ring__and__Field_Odivision__ring'( 'tc_Complex_Ocomplex' ) ]
% 1.32/1.77 ,
% 1.32/1.77 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_Complex_Ocomplex' ) ]
% 1.32/1.77 ,
% 1.32/1.77 [ 'class_RealVector_Oreal__normed__field'( 'tc_Complex_Ocomplex' ) ]
% 1.32/1.77 ,
% 1.32/1.77 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_Complex_Ocomplex' ) ]
% 1.32/1.77 ,
% 1.32/1.77 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_Complex_Ocomplex' ) ]
% 1.32/1.77 ,
% 1.32/1.77 [ 'class_Ring__and__Field_Ocomm__ring__1'( 'tc_Complex_Ocomplex' ) ]
% 1.32/1.77 ,
% 1.32/1.77 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_Complex_Ocomplex' ) ],
% 1.32/1.77 [ 'class_Ring__and__Field_Osemiring__0'( 'tc_Complex_Ocomplex' ) ],
% 1.32/1.77 [ 'class_OrderedGroup_Oab__group__add'( 'tc_Complex_Ocomplex' ) ],
% 1.32/1.77 [ 'class_Ring__and__Field_Omult__zero'( 'tc_Complex_Ocomplex' ) ],
% 1.32/1.77 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_Complex_Ocomplex' ) ],
% 1.32/1.77 [ 'class_Ring__and__Field_Osemiring'( 'tc_Complex_Ocomplex' ) ],
% 1.32/1.77 [ 'class_OrderedGroup_Omonoid__add'( 'tc_Complex_Ocomplex' ) ],
% 1.32/1.77 [ 'class_OrderedGroup_Ogroup__add'( 'tc_Complex_Ocomplex' ) ],
% 1.32/1.77 [ 'class_Ring__and__Field_Oring__1'( 'tc_Complex_Ocomplex' ) ],
% 1.32/1.77 [ 'class_Ring__and__Field_Ofield'( 'tc_Complex_Ocomplex' ) ],
% 1.32/1.77 [ 'class_Ring__and__Field_Oring'( 'tc_Complex_Ocomplex' ) ],
% 1.32/1.77 [ 'class_Ring__and__Field_Oidom'( 'tc_Complex_Ocomplex' ) ],
% 1.32/1.77 [ 'class_Nat_Osemiring__char__0'( 'tc_Complex_Ocomplex' ) ],
% 1.32/1.77 [ 'class_Int_Oring__char__0'( 'tc_Complex_Ocomplex' ) ],
% 1.32/1.77 [ 'class_Int_Onumber__ring'( 'tc_Complex_Ocomplex' ) ],
% 1.32/1.77 [ 'class_Power_Opower'( 'tc_Complex_Ocomplex' ) ],
% 1.32/1.77 [ 'class_Int_Onumber'( 'tc_Complex_Ocomplex' ) ],
% 1.32/1.77 [ 'c_fequal'( X, X, Y ) ],
% 1.32/1.77 [ =( X, Y ), ~( 'c_fequal'( X, Y, Z ) ) ]
% 1.32/1.77 ] .
% 1.32/1.77
% 1.32/1.77
% 1.32/1.77 percentage equality = 0.217580, percentage horn = 0.829354
% 1.32/1.77 This is a problem with some equality
% 1.32/1.77
% 1.32/1.77
% 1.32/1.77
% 1.32/1.77 Options Used:
% 1.32/1.77
% 1.32/1.77 useres = 1
% 1.32/1.77 useparamod = 1
% 1.32/1.77 useeqrefl = 1
% 1.32/1.77 useeqfact = 1
% 1.32/1.77 usefactor = 1
% 1.32/1.77 usesimpsplitting = 0
% 1.32/1.77 usesimpdemod = 5
% 1.32/1.77 usesimpres = 3
% 1.32/1.77
% 1.32/1.77 resimpinuse = 1000
% 1.32/1.77 resimpclauses = 20000
% 1.32/1.77 substype = eqrewr
% 1.32/1.77 backwardsubs = 1
% 1.32/1.77 selectoldest = 5
% 1.32/1.77
% 1.32/1.77 litorderings [0] = split
% 1.32/1.77 litorderings [1] = extend the termordering, first sorting on arguments
% 1.32/1.77
% 1.32/1.77 termordering = kbo
% 1.32/1.77
% 1.32/1.77 litapriori = 0
% 1.32/1.77 termapriori = 1
% 1.32/1.77 litaposteriori = 0
% 1.32/1.77 termaposteriori = 0
% 1.32/1.77 demodaposteriori = 0
% 1.32/1.77 ordereqreflfact = 0
% 1.32/1.77
% 1.32/1.77 litselect = negord
% 1.32/1.77
% 1.32/1.77 maxweight = 15
% 1.32/1.77 maxdepth = 30000
% 1.32/1.77 maxlength = 115
% 1.32/1.77 maxnrvars = 195
% 1.32/1.77 excuselevel = 1
% 1.32/1.77 increasemaxweight = 1
% 1.32/1.77
% 1.32/1.77 maxselected = 10000000
% 1.32/1.77 maxnrclauses = 10000000
% 1.32/1.77
% 1.32/1.77 showgenerated = 0
% 1.32/1.77 showkept = 0
% 1.32/1.77 showselected = 0
% 1.32/1.77 showdeleted = 0
% 1.32/1.77 showresimp = 1
% 1.32/1.77 showstatus = 2000
% 1.32/1.77
% 1.32/1.77 prologoutput = 1
% 1.32/1.77 nrgoals = 5000000
% 1.32/1.77 totalproof = 1
% 1.32/1.77
% 1.32/1.77 Symbols occurring in the translation:
% 1.32/1.77
% 1.32/1.77 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 1.32/1.77 . [1, 2] (w:1, o:154, a:1, s:1, b:0),
% 1.32/1.77 ! [4, 1] (w:0, o:73, a:1, s:1, b:0),
% 1.32/1.77 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.32/1.77 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.32/1.77 'class_Ring__and__Field_Oordered__ring__strict' [40, 1] (w:1, o:83
% 1.32/1.77 , a:1, s:1, b:0),
% 1.32/1.77 'c_HOL_Ozero__class_Ozero' [42, 1] (w:1, o:84, a:1, s:1, b:0),
% 1.32/1.77 'c_lessequals' [43, 3] (w:1, o:189, a:1, s:1, b:0),
% 1.32/1.77 'c_HOL_Otimes__class_Otimes' [45, 1] (w:1, o:85, a:1, s:1, b:0),
% 1.32/1.77 hAPP [46, 2] (w:1, o:179, a:1, s:1, b:0),
% 1.32/1.77 'class_Divides_Osemiring__div' [47, 1] (w:1, o:87, a:1, s:1, b:0),
% 1.32/1.77 'c_HOL_Oplus__class_Oplus' [48, 1] (w:1, o:89, a:1, s:1, b:0),
% 1.32/1.77 'c_Divides_Odiv__class_Omod' [49, 3] (w:1, o:190, a:1, s:1, b:0),
% 1.32/1.77 'class_Ring__and__Field_Oordered__idom' [50, 1] (w:1, o:90, a:1, s:1
% 1.32/1.77 , b:0),
% 1.32/1.77 'c_HOL_Oabs__class_Oabs' [51, 2] (w:1, o:180, a:1, s:1, b:0),
% 1.32/1.77 'c_HOL_Oord__class_Oless' [52, 3] (w:1, o:191, a:1, s:1, b:0),
% 1.32/1.77 'c_HOL_Ouminus__class_Ouminus' [53, 2] (w:1, o:181, a:1, s:1, b:0),
% 1.35/1.94 'c_Power_Opower_Opower' [56, 3] (w:1, o:193, a:1, s:1, b:0),
% 1.35/1.94 'tc_nat' [57, 0] (w:1, o:31, a:1, s:1, b:0),
% 1.35/1.94 'c_OrderedGroup_Omonoid__mult' [60, 3] (w:1, o:192, a:1, s:1, b:0),
% 1.35/1.94 'c_Divides_Odiv__class_Odiv' [61, 3] (w:1, o:194, a:1, s:1, b:0),
% 1.35/1.94 'c_Suc' [63, 1] (w:1, o:91, a:1, s:1, b:0),
% 1.35/1.94 'c_Parity_Oeven__odd__class_Oeven' [64, 2] (w:1, o:182, a:1, s:1, b:0
% 1.35/1.94 ),
% 1.35/1.94 'class_Ring__and__Field_Osemiring__0' [65, 1] (w:1, o:96, a:1, s:1
% 1.35/1.94 , b:0),
% 1.35/1.94 'class_Power_Opower' [66, 1] (w:1, o:121, a:1, s:1, b:0),
% 1.35/1.94 'c_Power_Opower__class_Opower' [67, 1] (w:1, o:122, a:1, s:1, b:0),
% 1.35/1.94 'class_Ring__and__Field_Ozero__neq__one' [68, 1] (w:1, o:123, a:1, s:
% 1.35/1.94 1, b:0),
% 1.35/1.94 'class_Ring__and__Field_Ono__zero__divisors' [69, 1] (w:1, o:82, a:1
% 1.35/1.94 , s:1, b:0),
% 1.35/1.94 'class_Ring__and__Field_Omult__zero' [70, 1] (w:1, o:79, a:1, s:1, b:
% 1.35/1.94 0),
% 1.35/1.94 'class_Ring__and__Field_Oordered__field' [71, 1] (w:1, o:124, a:1, s:
% 1.35/1.94 1, b:0),
% 1.35/1.94 'class_Ring__and__Field_Odivision__by__zero' [72, 1] (w:1, o:128, a:1
% 1.35/1.94 , s:1, b:0),
% 1.35/1.94 'class_Int_Onumber' [73, 1] (w:1, o:129, a:1, s:1, b:0),
% 1.35/1.94 'c_Int_Onumber__class_Onumber__of' [75, 2] (w:1, o:184, a:1, s:1, b:0
% 1.35/1.94 ),
% 1.35/1.94 'c_HOL_Oinverse__class_Odivide' [76, 3] (w:1, o:195, a:1, s:1, b:0),
% 1.35/1.94
% 1.35/1.94 'class_Ring__and__Field_Ocomm__semiring__1' [78, 1] (w:1, o:126, a:1
% 1.35/1.94 , s:1, b:0),
% 1.35/1.94 'c_HOL_Oone__class_Oone' [79, 1] (w:1, o:88, a:1, s:1, b:0),
% 1.35/1.94 'class_OrderedGroup_Opordered__ab__group__add' [81, 1] (w:1, o:99, a:
% 1.35/1.94 1, s:1, b:0),
% 1.35/1.94 'class_Ring__and__Field_Ofield' [82, 1] (w:1, o:130, a:1, s:1, b:0),
% 1.35/1.94
% 1.35/1.94 'class_Ring__and__Field_Oordered__semiring__strict' [83, 1] (w:1, o:
% 1.35/1.94 131, a:1, s:1, b:0),
% 1.35/1.94 'class_OrderedGroup_Opordered__ab__group__add__abs' [84, 1] (w:1, o:
% 1.35/1.94 100, a:1, s:1, b:0),
% 1.35/1.94 'class_OrderedGroup_Ocomm__monoid__add' [85, 1] (w:1, o:101, a:1, s:1
% 1.35/1.94 , b:0),
% 1.35/1.94 hBOOL [87, 1] (w:1, o:132, a:1, s:1, b:0),
% 1.35/1.94 'c_Ring__and__Field_Oordered__semidom' [91, 7] (w:1, o:200, a:1, s:1
% 1.35/1.94 , b:0),
% 1.35/1.94 'class_OrderedGroup_Ogroup__add' [92, 1] (w:1, o:102, a:1, s:1, b:0)
% 1.35/1.94 ,
% 1.35/1.94 'c_Ring__and__Field_Oordered__idom' [97, 11] (w:1, o:202, a:1, s:1
% 1.35/1.94 , b:0),
% 1.35/1.94 'class_Ring__and__Field_Oordered__semidom' [98, 1] (w:1, o:133, a:1
% 1.35/1.94 , s:1, b:0),
% 1.35/1.94 'c_NthRoot_Osqrt' [100, 0] (w:1, o:52, a:1, s:1, b:0),
% 1.35/1.94 'c_HOL_Oinverse__class_Oinverse' [102, 2] (w:1, o:183, a:1, s:1, b:0)
% 1.35/1.94 ,
% 1.35/1.94 'class_Ring__and__Field_Omult__mono1' [105, 1] (w:1, o:80, a:1, s:1
% 1.35/1.94 , b:0),
% 1.35/1.94 'class_Ring__and__Field_Omult__mono' [106, 1] (w:1, o:81, a:1, s:1
% 1.35/1.94 , b:0),
% 1.35/1.94 'class_Ring__and__Field_Opordered__ring' [107, 1] (w:1, o:136, a:1
% 1.35/1.94 , s:1, b:0),
% 1.35/1.94 'class_Ring__and__Field_Oidom' [109, 1] (w:1, o:137, a:1, s:1, b:0),
% 1.35/1.94
% 1.35/1.94 'class_Int_Onumber__ring' [110, 1] (w:1, o:138, a:1, s:1, b:0),
% 1.35/1.94 'class_Ring__and__Field_Odivision__ring' [111, 1] (w:1, o:139, a:1
% 1.35/1.94 , s:1, b:0),
% 1.35/1.94 'c_NthRoot_Oroot' [113, 1] (w:1, o:140, a:1, s:1, b:0),
% 1.35/1.94 'c_Int_OMin' [114, 0] (w:1, o:57, a:1, s:1, b:0),
% 1.35/1.94 'class_OrderedGroup_Oab__semigroup__idem__mult' [115, 1] (w:1, o:103
% 1.35/1.94 , a:1, s:1, b:0),
% 1.35/1.94 'class_Ring__and__Field_Osemiring__1' [116, 1] (w:1, o:141, a:1, s:1
% 1.35/1.94 , b:0),
% 1.35/1.94 'c_Nat_Osemiring__1__class_Oof__nat' [117, 2] (w:1, o:185, a:1, s:1
% 1.35/1.94 , b:0),
% 1.35/1.94 'class_Orderings_Oorder' [118, 1] (w:1, o:104, a:1, s:1, b:0),
% 1.35/1.94 'class_Orderings_Olinorder' [119, 1] (w:1, o:105, a:1, s:1, b:0),
% 1.35/1.94 'class_Ring__and__Field_Opordered__cancel__semiring' [120, 1] (w:1
% 1.35/1.94 , o:142, a:1, s:1, b:0),
% 1.35/1.94 'class_OrderedGroup_Oab__semigroup__mult' [121, 1] (w:1, o:106, a:1
% 1.35/1.94 , s:1, b:0),
% 1.35/1.94 'class_OrderedGroup_Olordered__ab__group__add' [122, 1] (w:1, o:107
% 1.35/1.94 , a:1, s:1, b:0),
% 1.35/1.94 'class_Ring__and__Field_Oring' [123, 1] (w:1, o:92, a:1, s:1, b:0),
% 1.35/1.94 'class_Ring__and__Field_Opordered__ring__abs' [124, 1] (w:1, o:143
% 1.35/1.94 , a:1, s:1, b:0),
% 1.35/1.94 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le' [125, 1]
% 1.35/1.94 (w:1, o:108, a:1, s:1, b:0),
% 1.35/1.94 'class_OrderedGroup_Opordered__ab__semigroup__add' [126, 1] (w:1, o:
% 8.63/9.02 109, a:1, s:1, b:0),
% 8.63/9.02 'class_Lattices_Oboolean__algebra' [128, 1] (w:1, o:144, a:1, s:1, b:
% 8.63/9.02 0),
% 8.63/9.02 'class_OrderedGroup_Olordered__ab__group__add__abs' [129, 1] (w:1, o:
% 8.63/9.02 110, a:1, s:1, b:0),
% 8.63/9.02 'class_OrderedGroup_Opordered__comm__monoid__add' [134, 1] (w:1, o:
% 8.63/9.02 111, a:1, s:1, b:0),
% 8.63/9.02 'class_RealVector_Oreal__normed__algebra' [136, 1] (w:1, o:145, a:1
% 8.63/9.02 , s:1, b:0),
% 8.63/9.02 'class_Ring__and__Field_Ocomm__semiring' [141, 1] (w:1, o:127, a:1
% 8.63/9.02 , s:1, b:0),
% 8.63/9.02 'c_Groebner__Basis_Ogb__semiring' [149, 6] (w:1, o:199, a:1, s:1, b:0
% 8.63/9.02 ),
% 8.63/9.02 'class_OrderedGroup_Oordered__ab__group__add' [150, 1] (w:1, o:98, a:
% 8.63/9.02 1, s:1, b:0),
% 8.63/9.02 'class_Ring__and__Field_Opordered__semiring' [151, 1] (w:1, o:146, a:
% 8.63/9.02 1, s:1, b:0),
% 8.63/9.02 'class_Divides_Oring__div' [152, 1] (w:1, o:86, a:1, s:1, b:0),
% 8.63/9.02 'class_Ring__and__Field_Oring__no__zero__divisors' [153, 1] (w:1, o:
% 8.63/9.02 93, a:1, s:1, b:0),
% 8.63/9.02 'tc_Int_Oint' [154, 0] (w:1, o:60, a:1, s:1, b:0),
% 8.63/9.02 'class_Ring__and__Field_Oabs__if' [155, 1] (w:1, o:147, a:1, s:1, b:0
% 8.63/9.02 ),
% 8.63/9.02 'class_Ring__and__Field_Oordered__semiring' [156, 1] (w:1, o:134, a:1
% 8.63/9.02 , s:1, b:0),
% 8.63/9.02 'class_Nat_Osemiring__char__0' [157, 1] (w:1, o:97, a:1, s:1, b:0),
% 8.63/9.02 'class_Ring__and__Field_Olordered__ring' [158, 1] (w:1, o:78, a:1, s:
% 8.63/9.02 1, b:0),
% 8.63/9.02 'c_Int_OBit0' [159, 1] (w:1, o:148, a:1, s:1, b:0),
% 8.63/9.02 'class_OrderedGroup_Omonoid__mult' [160, 1] (w:1, o:112, a:1, s:1, b:
% 8.63/9.02 0),
% 8.63/9.02 'class_OrderedGroup_Ocomm__monoid__mult' [161, 1] (w:1, o:113, a:1
% 8.63/9.02 , s:1, b:0),
% 8.63/9.02 'class_OrderedGroup_Ocancel__ab__semigroup__add' [162, 1] (w:1, o:114
% 8.63/9.02 , a:1, s:1, b:0),
% 8.63/9.02 'class_OrderedGroup_Ocancel__semigroup__add' [163, 1] (w:1, o:115, a:
% 8.63/9.02 1, s:1, b:0),
% 8.63/9.02 'class_Ring__and__Field_Ocomm__ring__1' [164, 1] (w:1, o:125, a:1, s:
% 8.63/9.02 1, b:0),
% 8.63/9.02 'class_Orderings_Opreorder' [165, 1] (w:1, o:116, a:1, s:1, b:0),
% 8.63/9.02 'class_OrderedGroup_Oab__group__add' [166, 1] (w:1, o:117, a:1, s:1
% 8.63/9.02 , b:0),
% 8.63/9.02 'class_OrderedGroup_Oab__semigroup__add' [167, 1] (w:1, o:118, a:1
% 8.63/9.02 , s:1, b:0),
% 8.63/9.02 'class_Ring__and__Field_Osemiring' [168, 1] (w:1, o:149, a:1, s:1, b:
% 8.63/9.02 0),
% 8.63/9.02 'class_RealVector_Oreal__normed__field' [170, 1] (w:1, o:150, a:1, s:
% 8.63/9.02 1, b:0),
% 8.63/9.02 'class_Ring__and__Field_Oring__1' [174, 1] (w:1, o:94, a:1, s:1, b:0)
% 8.63/9.02 ,
% 8.63/9.02 'c_Int_Oiszero' [175, 2] (w:1, o:186, a:1, s:1, b:0),
% 8.63/9.02 'class_Ring__and__Field_Oordered__comm__semiring__strict' [176, 1]
% 8.63/9.02 (w:1, o:135, a:1, s:1, b:0),
% 8.63/9.02 'c_Int_OPls' [177, 0] (w:1, o:62, a:1, s:1, b:0),
% 8.63/9.02 'class_OrderedGroup_Omonoid__add' [178, 1] (w:1, o:119, a:1, s:1, b:0
% 8.63/9.02 ),
% 8.63/9.02 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add' [179, 1]
% 8.63/9.02 (w:1, o:120, a:1, s:1, b:0),
% 8.63/9.02 'c_Int_OBit1' [180, 1] (w:1, o:151, a:1, s:1, b:0),
% 8.63/9.02 'class_Ring__and__Field_Oring__1__no__zero__divisors' [183, 1] (w:1
% 8.63/9.02 , o:95, a:1, s:1, b:0),
% 8.63/9.02 'c_Ring__and__Field_Ocomm__ring__1' [184, 7] (w:1, o:201, a:1, s:1
% 8.63/9.02 , b:0),
% 8.63/9.02 'c_FFT__Mirabelle_OIFFT' [185, 2] (w:1, o:187, a:1, s:1, b:0),
% 8.63/9.02 'class_Int_Oring__char__0' [186, 1] (w:1, o:152, a:1, s:1, b:0),
% 8.63/9.02 'c_FFT__Mirabelle_Oroot' [187, 1] (w:1, o:153, a:1, s:1, b:0),
% 8.63/9.02 'c_Complex_Oii' [188, 0] (w:1, o:63, a:1, s:1, b:0),
% 8.63/9.02 'c_Ring__and__Field_Osemiring__1' [189, 5] (w:1, o:198, a:1, s:1, b:0
% 8.63/9.02 ),
% 8.63/9.02 'v_ka____' [190, 0] (w:1, o:64, a:1, s:1, b:0),
% 8.63/9.02 'c_FFT__Mirabelle_OIDFT' [191, 3] (w:1, o:196, a:1, s:1, b:0),
% 8.63/9.02 'v_i____' [192, 0] (w:1, o:65, a:1, s:1, b:0),
% 8.63/9.02 'v_a____' [194, 0] (w:1, o:66, a:1, s:1, b:0),
% 8.63/9.02 'tc_fun' [197, 2] (w:1, o:188, a:1, s:1, b:0),
% 8.63/9.02 'tc_RealDef_Oreal' [198, 0] (w:1, o:69, a:1, s:1, b:0),
% 8.63/9.02 'tc_Complex_Ocomplex' [199, 0] (w:1, o:70, a:1, s:1, b:0),
% 8.63/9.02 'c_fequal' [200, 3] (w:1, o:197, a:1, s:1, b:0).
% 8.63/9.02
% 8.63/9.02
% 8.63/9.02 Starting Search:
% 8.63/9.02
% 8.63/9.02 Resimplifying inuse:
% 8.63/9.02 Done
% 8.63/9.02
% 8.63/9.02
% 8.63/9.02 Intermediate Status:
% 8.63/9.02 Generated: 3265
% 8.63/9.02 Kept: 2003
% 8.63/9.02 Inuse: 127
% 8.63/9.02 Deleted: 9
% 8.63/9.02 Deletedinuse: 0
% 8.63/9.02
% 8.63/9.02 Resimplifying inuse:
% 8.63/9.02 Done
% 8.63/9.02
% 8.63/9.02
% 8.63/9.02 Intermediate Status:
% 8.63/9.02 Generated: 10449
% 8.63/9.02 Kept: 4134
% 43.09/43.56 Inuse: 232
% 43.09/43.56 Deleted: 14
% 43.09/43.56 Deletedinuse: 0
% 43.09/43.56
% 43.09/43.56 Resimplifying inuse:
% 43.09/43.56 Done
% 43.09/43.56
% 43.09/43.56 Resimplifying inuse:
% 43.09/43.56 Done
% 43.09/43.56
% 43.09/43.56
% 43.09/43.56 Intermediate Status:
% 43.09/43.56 Generated: 19799
% 43.09/43.56 Kept: 6478
% 43.09/43.56 Inuse: 252
% 43.09/43.56 Deleted: 14
% 43.09/43.56 Deletedinuse: 0
% 43.09/43.56
% 43.09/43.56 Resimplifying inuse:
% 43.09/43.56 Done
% 43.09/43.56
% 43.09/43.56 Resimplifying inuse:
% 43.09/43.56 Done
% 43.09/43.56
% 43.09/43.56
% 43.09/43.56 Intermediate Status:
% 43.09/43.56 Generated: 30234
% 43.09/43.56 Kept: 9012
% 43.09/43.56 Inuse: 353
% 43.09/43.56 Deleted: 18
% 43.09/43.56 Deletedinuse: 0
% 43.09/43.56
% 43.09/43.56 Resimplifying inuse:
% 43.09/43.56 Done
% 43.09/43.56
% 43.09/43.56 Resimplifying inuse:
% 43.09/43.56 Done
% 43.09/43.56
% 43.09/43.56
% 43.09/43.56 Intermediate Status:
% 43.09/43.56 Generated: 53286
% 43.09/43.56 Kept: 11520
% 43.09/43.56 Inuse: 395
% 43.09/43.56 Deleted: 21
% 43.09/43.56 Deletedinuse: 0
% 43.09/43.56
% 43.09/43.56 Resimplifying inuse:
% 43.09/43.56 Done
% 43.09/43.56
% 43.09/43.56
% 43.09/43.56 Intermediate Status:
% 43.09/43.56 Generated: 60571
% 43.09/43.56 Kept: 13651
% 43.09/43.56 Inuse: 446
% 43.09/43.56 Deleted: 25
% 43.09/43.56 Deletedinuse: 0
% 43.09/43.56
% 43.09/43.56 Resimplifying inuse:
% 43.09/43.56 Done
% 43.09/43.56
% 43.09/43.56 Resimplifying inuse:
% 43.09/43.56 Done
% 43.09/43.56
% 43.09/43.56
% 43.09/43.56 Intermediate Status:
% 43.09/43.56 Generated: 66863
% 43.09/43.56 Kept: 15744
% 43.09/43.56 Inuse: 476
% 43.09/43.56 Deleted: 25
% 43.09/43.56 Deletedinuse: 0
% 43.09/43.56
% 43.09/43.56 Resimplifying inuse:
% 43.09/43.56 Done
% 43.09/43.56
% 43.09/43.56
% 43.09/43.56 Intermediate Status:
% 43.09/43.56 Generated: 78894
% 43.09/43.56 Kept: 18378
% 43.09/43.56 Inuse: 501
% 43.09/43.56 Deleted: 25
% 43.09/43.56 Deletedinuse: 0
% 43.09/43.56
% 43.09/43.56 Resimplifying inuse:
% 43.09/43.56 Done
% 43.09/43.56
% 43.09/43.56 Resimplifying inuse:
% 43.09/43.56 Done
% 43.09/43.56
% 43.09/43.56 Resimplifying clauses:
% 43.09/43.56 Done
% 43.09/43.56
% 43.09/43.56
% 43.09/43.56 Intermediate Status:
% 43.09/43.56 Generated: 90307
% 43.09/43.56 Kept: 20449
% 43.09/43.56 Inuse: 524
% 43.09/43.56 Deleted: 287
% 43.09/43.56 Deletedinuse: 0
% 43.09/43.56
% 43.09/43.56 Resimplifying inuse:
% 43.09/43.56 Done
% 43.09/43.56
% 43.09/43.56 Resimplifying inuse:
% 43.09/43.56 Done
% 43.09/43.56
% 43.09/43.56
% 43.09/43.56 Intermediate Status:
% 43.09/43.56 Generated: 95288
% 43.09/43.56 Kept: 22512
% 43.09/43.56 Inuse: 534
% 43.09/43.56 Deleted: 287
% 43.09/43.56 Deletedinuse: 0
% 43.09/43.56
% 43.09/43.56 Resimplifying inuse:
% 43.09/43.56 Done
% 43.09/43.56
% 43.09/43.56 Resimplifying inuse:
% 43.09/43.56 Done
% 43.09/43.56
% 43.09/43.56
% 43.09/43.56 Intermediate Status:
% 43.09/43.56 Generated: 103809
% 43.09/43.56 Kept: 24704
% 43.09/43.56 Inuse: 584
% 43.09/43.56 Deleted: 287
% 43.09/43.56 Deletedinuse: 0
% 43.09/43.56
% 43.09/43.56 Resimplifying inuse:
% 43.09/43.56 Done
% 43.09/43.56
% 43.09/43.56 Resimplifying inuse:
% 43.09/43.56 Done
% 43.09/43.56
% 43.09/43.56
% 43.09/43.56 Intermediate Status:
% 43.09/43.56 Generated: 111272
% 43.09/43.56 Kept: 26707
% 43.09/43.56 Inuse: 636
% 43.09/43.56 Deleted: 287
% 43.09/43.56 Deletedinuse: 0
% 43.09/43.56
% 43.09/43.56 Resimplifying inuse:
% 43.09/43.56 Done
% 43.09/43.56
% 43.09/43.56
% 43.09/43.56 Intermediate Status:
% 43.09/43.56 Generated: 121775
% 43.09/43.56 Kept: 29003
% 43.09/43.56 Inuse: 654
% 43.09/43.56 Deleted: 288
% 43.09/43.56 Deletedinuse: 1
% 43.09/43.56
% 43.09/43.56 Resimplifying inuse:
% 43.09/43.56 Done
% 43.09/43.56
% 43.09/43.56
% 43.09/43.56 Intermediate Status:
% 43.09/43.56 Generated: 131651
% 43.09/43.56 Kept: 31090
% 43.09/43.56 Inuse: 664
% 43.09/43.56 Deleted: 288
% 43.09/43.56 Deletedinuse: 1
% 43.09/43.56
% 43.09/43.56 Resimplifying inuse:
% 43.09/43.56 Done
% 43.09/43.56
% 43.09/43.56 Resimplifying inuse:
% 43.09/43.56 Done
% 43.09/43.56
% 43.09/43.56
% 43.09/43.56 Intermediate Status:
% 43.09/43.56 Generated: 142636
% 43.09/43.56 Kept: 33696
% 43.09/43.56 Inuse: 679
% 43.09/43.56 Deleted: 288
% 43.09/43.56 Deletedinuse: 1
% 43.09/43.56
% 43.09/43.56 Resimplifying inuse:
% 43.09/43.56 Done
% 43.09/43.56
% 43.09/43.56 Resimplifying inuse:
% 43.09/43.56 Done
% 43.09/43.56
% 43.09/43.56
% 43.09/43.56 Intermediate Status:
% 43.09/43.56 Generated: 150730
% 43.09/43.56 Kept: 35712
% 43.09/43.56 Inuse: 709
% 43.09/43.56 Deleted: 288
% 43.09/43.56 Deletedinuse: 1
% 43.09/43.56
% 43.09/43.56 Resimplifying inuse:
% 43.09/43.56 Done
% 43.09/43.56
% 43.09/43.56
% 43.09/43.56 Intermediate Status:
% 43.09/43.56 Generated: 157348
% 43.09/43.56 Kept: 38407
% 43.09/43.56 Inuse: 724
% 43.09/43.56 Deleted: 288
% 43.09/43.56 Deletedinuse: 1
% 43.09/43.56
% 43.09/43.56 Resimplifying inuse:
% 43.09/43.56 Done
% 43.09/43.56
% 43.09/43.56 Resimplifying inuse:
% 43.09/43.56 Done
% 43.09/43.56
% 43.09/43.56
% 43.09/43.56 Intermediate Status:
% 43.09/43.56 Generated: 165145
% 43.09/43.56 Kept: 40421
% 43.09/43.56 Inuse: 734
% 43.09/43.56 Deleted: 288
% 43.09/43.56 Deletedinuse: 1
% 43.09/43.56
% 43.09/43.56 Resimplifying inuse:
% 43.09/43.56 Done
% 43.09/43.56
% 43.09/43.56 Resimplifying clauses:
% 43.09/43.56 Done
% 43.09/43.56
% 43.09/43.56 Resimplifying inuse:
% 43.09/43.56 Done
% 43.09/43.56
% 43.09/43.56
% 43.09/43.56 Intermediate Status:
% 43.09/43.56 Generated: 172648
% 43.09/43.56 Kept: 42500
% 43.09/43.56 Inuse: 774
% 43.09/43.56 Deleted: 398
% 43.09/43.56 Deletedinuse: 1
% 43.09/43.56
% 43.09/43.56 Resimplifying inuse:
% 43.09/43.56 Done
% 43.09/43.56
% 43.09/43.56 Resimplifying inuse:
% 43.09/43.56 Done
% 43.09/43.56
% 43.09/43.56
% 43.09/43.56 Intermediate Status:
% 43.09/43.56 Generated: 182058
% 43.09/43.56 Kept: 44732
% 43.09/43.56 Inuse: 799
% 43.09/43.56 Deleted: 398
% 43.09/43.56 Deletedinuse: 1
% 43.09/43.56
% 43.09/43.56 Resimplifying inuse:
% 43.09/43.56 Done
% 43.09/43.56
% 43.09/43.56 Resimplifying inuse:
% 43.09/43.56 Done
% 43.09/43.56
% 43.09/43.56
% 43.09/43.56 Intermediate Status:
% 43.09/43.56 Generated: 188436
% 43.09/43.56 Kept: 46854
% 43.09/43.56 Inuse: 829
% 43.09/43.56 Deleted: 398
% 43.09/43.56 Deletedinuse: 1
% 43.09/43.56
% 43.09/43.56 Resimplifying inuse:
% 43.09/43.56 Done
% 43.09/43.56
% 43.09/43.56 Resimplifying inuse:
% 43.09/43.56 Done
% 43.09/43.56
% 43.09/43.56
% 43.09/43.56 Intermediate Status:
% 43.09/43.56 Generated: 195618
% 43.09/43.56 Kept: 49232
% 43.09/43.56 Inuse: 844
% 43.09/43.56 Deleted: 398
% 43.09/43.56 Deletedinuse: 1
% 43.09/43.56
% 43.09/43.56 Resimplifying inuse:
% 43.09/43.56 Done
% 43.09/43.56
% 43.09/43.56 Resimplifying inuse:
% 43.09/43.56 Done
% 43.09/43.56
% 43.09/43.56
% 43.09/43.56 Intermediate Status:
% 43.09/43.56 Generated: 202588
% 43.09/43.56 Kept: 51289
% 43.09/43.56 Inuse: 874
% 43.09/43.56 Deleted: 398
% 43.09/43.56 Deletedinuse: 1
% 43.09/43.56
% 43.09/43.56 Resimplifying inuse:
% 43.09/43.56 Done
% 43.09/43.56
% 43.09/43.56 Resimplifying inuse:
% 43.09/43.56 Done
% 43.09/43.56
% 43.09/43.56
% 43.09/43.56 Intermediate Status:
% 43.09/43.56 Generated: 210739
% 43.09/43.56 Kept: 53295
% 43.09/43.56 Inuse: 910
% 43.09/43.56 Deleted: 398
% 43.09/43.56 Deletedinuse: 1
% 43.09/43.56
% 43.09/43.56 Resimplifying inuse:
% 43.09/43.56 Done
% 43.09/43.56
% 43.09/43.56 Resimplifying inuse:
% 43.09/43.56 Done
% 43.09/43.56
% 43.09/43.56
% 43.09/43.56 Intermediate Status:
% 43.09/43.56 Generated: 220109
% 43.09/43.56 Kept: 55614
% 43.09/43.56 Inuse: 944
% 43.09/43.56 Deleted: 398
% 43.09/43.56 Deletedinuse: 1
% 43.09/43.56
% 43.09/43.56 Resimplifying inuse:
% 43.09/43.56 Done
% 43.09/43.56
% 43.09/43.56 Resimplifying inuse:
% 43.09/43.56 Done
% 43.09/43.56
% 43.09/43.56
% 43.09/43.56 Intermediate Status:
% 43.09/43.56 Generated: 227817
% 43.09/43.56 Kept: 57759
% 43.09/43.56 Inuse: 974
% 43.09/43.56 Deleted: 398
% 43.09/43.56 Deletedinuse: 1
% 43.09/43.56
% 43.09/43.56 Resimplifying inuse:
% 43.09/43.56 Done
% 43.09/43.56
% 43.09/43.56
% 43.09/43.56 Intermediate Status:
% 99.04/99.47 Generated: 236014
% 99.04/99.47 Kept: 59767
% 99.04/99.47 Inuse: 999
% 99.04/99.47 Deleted: 399
% 99.04/99.47 Deletedinuse: 2
% 99.04/99.47
% 99.04/99.47 Resimplifying inuse:
% 99.04/99.47 Done
% 99.04/99.47
% 99.04/99.47 Resimplifying clauses:
% 99.04/99.47 Done
% 99.04/99.47
% 99.04/99.47
% 99.04/99.47 Intermediate Status:
% 99.04/99.47 Generated: 242823
% 99.04/99.47 Kept: 61838
% 99.04/99.47 Inuse: 1014
% 99.04/99.47 Deleted: 1514
% 99.04/99.47 Deletedinuse: 5
% 99.04/99.47
% 99.04/99.47 Resimplifying inuse:
% 99.04/99.47 Done
% 99.04/99.47
% 99.04/99.47 Resimplifying inuse:
% 99.04/99.47 Done
% 99.04/99.47
% 99.04/99.47
% 99.04/99.47 Intermediate Status:
% 99.04/99.47 Generated: 247989
% 99.04/99.47 Kept: 63838
% 99.04/99.47 Inuse: 1022
% 99.04/99.47 Deleted: 1514
% 99.04/99.47 Deletedinuse: 5
% 99.04/99.47
% 99.04/99.47
% 99.04/99.47 Intermediate Status:
% 99.04/99.47 Generated: 264564
% 99.04/99.47 Kept: 67166
% 99.04/99.47 Inuse: 1034
% 99.04/99.47 Deleted: 1514
% 99.04/99.47 Deletedinuse: 5
% 99.04/99.47
% 99.04/99.47 Resimplifying inuse:
% 99.04/99.47 Done
% 99.04/99.47
% 99.04/99.47 Resimplifying inuse:
% 99.04/99.47 Done
% 99.04/99.47
% 99.04/99.47
% 99.04/99.47 Intermediate Status:
% 99.04/99.47 Generated: 279311
% 99.04/99.47 Kept: 70227
% 99.04/99.47 Inuse: 1044
% 99.04/99.47 Deleted: 1514
% 99.04/99.47 Deletedinuse: 5
% 99.04/99.47
% 99.04/99.47 Resimplifying inuse:
% 99.04/99.47 Done
% 99.04/99.47
% 99.04/99.47 Resimplifying inuse:
% 99.04/99.47 Done
% 99.04/99.47
% 99.04/99.47
% 99.04/99.47 Intermediate Status:
% 99.04/99.47 Generated: 294834
% 99.04/99.47 Kept: 73495
% 99.04/99.47 Inuse: 1084
% 99.04/99.47 Deleted: 1514
% 99.04/99.47 Deletedinuse: 5
% 99.04/99.47
% 99.04/99.47 Resimplifying inuse:
% 99.04/99.47 Done
% 99.04/99.47
% 99.04/99.47 Resimplifying inuse:
% 99.04/99.47 Done
% 99.04/99.47
% 99.04/99.47
% 99.04/99.47 Intermediate Status:
% 99.04/99.47 Generated: 303968
% 99.04/99.47 Kept: 76882
% 99.04/99.47 Inuse: 1090
% 99.04/99.47 Deleted: 1514
% 99.04/99.47 Deletedinuse: 5
% 99.04/99.47
% 99.04/99.47 Resimplifying inuse:
% 99.04/99.47 Done
% 99.04/99.47
% 99.04/99.47 Resimplifying inuse:
% 99.04/99.47 Done
% 99.04/99.47
% 99.04/99.47
% 99.04/99.47 Intermediate Status:
% 99.04/99.47 Generated: 314535
% 99.04/99.47 Kept: 79122
% 99.04/99.47 Inuse: 1099
% 99.04/99.47 Deleted: 1514
% 99.04/99.47 Deletedinuse: 5
% 99.04/99.47
% 99.04/99.47 Resimplifying inuse:
% 99.04/99.47 Done
% 99.04/99.47
% 99.04/99.47
% 99.04/99.47 Intermediate Status:
% 99.04/99.47 Generated: 326441
% 99.04/99.47 Kept: 81438
% 99.04/99.47 Inuse: 1109
% 99.04/99.47 Deleted: 1514
% 99.04/99.47 Deletedinuse: 5
% 99.04/99.47
% 99.04/99.47 Resimplifying inuse:
% 99.04/99.47 Done
% 99.04/99.47
% 99.04/99.47 Resimplifying clauses:
% 99.04/99.47 Done
% 99.04/99.47
% 99.04/99.47 Resimplifying inuse:
% 99.04/99.47 Done
% 99.04/99.47
% 99.04/99.47
% 99.04/99.47 Intermediate Status:
% 99.04/99.47 Generated: 337043
% 99.04/99.47 Kept: 83992
% 99.04/99.47 Inuse: 1119
% 99.04/99.47 Deleted: 1569
% 99.04/99.47 Deletedinuse: 5
% 99.04/99.47
% 99.04/99.47 Resimplifying inuse:
% 99.04/99.47 Done
% 99.04/99.47
% 99.04/99.47 Resimplifying inuse:
% 99.04/99.47 Done
% 99.04/99.47
% 99.04/99.47
% 99.04/99.47 Intermediate Status:
% 99.04/99.47 Generated: 347326
% 99.04/99.47 Kept: 86017
% 99.04/99.47 Inuse: 1141
% 99.04/99.47 Deleted: 1569
% 99.04/99.47 Deletedinuse: 5
% 99.04/99.47
% 99.04/99.47 Resimplifying inuse:
% 99.04/99.47 Done
% 99.04/99.47
% 99.04/99.47 Resimplifying inuse:
% 99.04/99.47 Done
% 99.04/99.47
% 99.04/99.47
% 99.04/99.47 Intermediate Status:
% 99.04/99.47 Generated: 357591
% 99.04/99.47 Kept: 88019
% 99.04/99.47 Inuse: 1162
% 99.04/99.47 Deleted: 1569
% 99.04/99.47 Deletedinuse: 5
% 99.04/99.47
% 99.04/99.47 Resimplifying inuse:
% 99.04/99.47 Done
% 99.04/99.47
% 99.04/99.47 Resimplifying inuse:
% 99.04/99.47 Done
% 99.04/99.47
% 99.04/99.47
% 99.04/99.47 Intermediate Status:
% 99.04/99.47 Generated: 366606
% 99.04/99.47 Kept: 90274
% 99.04/99.47 Inuse: 1184
% 99.04/99.47 Deleted: 1569
% 99.04/99.47 Deletedinuse: 5
% 99.04/99.47
% 99.04/99.47 Resimplifying inuse:
% 99.04/99.47 Done
% 99.04/99.47
% 99.04/99.47 Resimplifying inuse:
% 99.04/99.47 Done
% 99.04/99.47
% 99.04/99.47
% 99.04/99.47 Intermediate Status:
% 99.04/99.47 Generated: 376270
% 99.04/99.47 Kept: 92712
% 99.04/99.47 Inuse: 1204
% 99.04/99.47 Deleted: 1569
% 99.04/99.47 Deletedinuse: 5
% 99.04/99.47
% 99.04/99.47 Resimplifying inuse:
% 99.04/99.47 Done
% 99.04/99.47
% 99.04/99.47 Resimplifying inuse:
% 99.04/99.47 Done
% 99.04/99.47
% 99.04/99.47
% 99.04/99.47 Intermediate Status:
% 99.04/99.47 Generated: 409976
% 99.04/99.47 Kept: 97513
% 99.04/99.47 Inuse: 1229
% 99.04/99.47 Deleted: 1569
% 99.04/99.47 Deletedinuse: 5
% 99.04/99.47
% 99.04/99.47 Resimplifying inuse:
% 99.04/99.47 Done
% 99.04/99.47
% 99.04/99.47
% 99.04/99.47 Intermediate Status:
% 99.04/99.47 Generated: 432496
% 99.04/99.47 Kept: 101229
% 99.04/99.47 Inuse: 1239
% 99.04/99.47 Deleted: 1569
% 99.04/99.47 Deletedinuse: 5
% 99.04/99.47
% 99.04/99.47 Resimplifying inuse:
% 99.04/99.47 Done
% 99.04/99.47
% 99.04/99.47
% 99.04/99.47 Intermediate Status:
% 99.04/99.47 Generated: 453425
% 99.04/99.47 Kept: 104257
% 99.04/99.47 Inuse: 1244
% 99.04/99.47 Deleted: 1569
% 99.04/99.47 Deletedinuse: 5
% 99.04/99.47
% 99.04/99.47 Resimplifying inuse:
% 99.04/99.47 Done
% 99.04/99.47
% 99.04/99.47 Resimplifying clauses:
% 99.04/99.47 Done
% 99.04/99.47
% 99.04/99.47
% 99.04/99.47 Intermediate Status:
% 99.04/99.47 Generated: 474498
% 99.04/99.47 Kept: 107170
% 99.04/99.47 Inuse: 1249
% 99.04/99.47 Deleted: 1707
% 99.04/99.47 Deletedinuse: 5
% 99.04/99.47
% 99.04/99.47 Resimplifying inuse:
% 99.04/99.47 Done
% 99.04/99.47
% 99.04/99.47
% 99.04/99.47 Intermediate Status:
% 99.04/99.47 Generated: 486851
% 99.04/99.47 Kept: 109504
% 99.04/99.47 Inuse: 1264
% 99.04/99.47 Deleted: 1707
% 99.04/99.47 Deletedinuse: 5
% 99.04/99.47
% 99.04/99.47 Resimplifying inuse:
% 99.04/99.47 Done
% 99.04/99.47
% 99.04/99.47 Resimplifying inuse:
% 99.04/99.47 Done
% 99.04/99.47
% 99.04/99.47
% 99.04/99.47 Intermediate Status:
% 99.04/99.47 Generated: 503665
% 99.04/99.47 Kept: 113369
% 99.04/99.47 Inuse: 1274
% 99.04/99.47 Deleted: 1707
% 99.04/99.47 Deletedinuse: 5
% 99.04/99.47
% 99.04/99.47 Resimplifying inuse:
% 99.04/99.47 Done
% 99.04/99.47
% 99.04/99.47
% 99.04/99.47 Intermediate Status:
% 99.04/99.47 Generated: 513661
% 99.04/99.47 Kept: 115390
% 99.04/99.47 Inuse: 1279
% 99.04/99.47 Deleted: 1707
% 99.04/99.47 Deletedinuse: 5
% 99.04/99.47
% 99.04/99.47 Resimplifying inuse:
% 99.04/99.47 Done
% 99.04/99.47
% 99.04/99.47 Resimplifying inuse:
% 99.04/99.47 Done
% 99.04/99.47
% 99.04/99.47
% 99.04/99.47 Intermediate Status:
% 99.04/99.47 Generated: 521346
% 99.04/99.47 Kept: 117412
% 99.04/99.47 Inuse: 1289
% 99.04/99.47 Deleted: 1708
% 99.04/99.47 Deletedinuse: 6
% 99.04/99.47
% 99.04/99.47 Resimplifying inuse:
% 99.04/99.47 Done
% 99.04/99.47
% 99.04/99.47
% 99.04/99.47 Intermediate Status:
% 99.04/99.47 Generated: 555679
% 99.04/99.47 Kept: 123022
% 99.04/99.47 Inuse: 1308
% 99.04/99.47 Deleted: 1714
% 99.04/99.47 Deletedinuse: 6
% 99.04/99.47
% 99.04/99.47 Resimplifying inuse:
% 99.04/99.47 Done
% 99.04/99.47
% 99.04/99.47 Resimplifying inuse:
% 99.04/99.47 Done
% 99.04/99.47
% 99.04/99.47 Resimplifying clauses:
% 99.04/99.47 Done
% 99.04/99.47
% 99.04/99.47
% 99.04/99.47 Intermediate Status:
% 99.04/99.47 Generated: 563168
% 99.04/99.47 Kept: 125311
% 99.04/99.47 Inuse: 1323
% 99.04/99.47 Deleted: 1990
% 99.04/99.47 Deletedinuse: 6
% 99.04/99.47
% 99.04/99.47 Resimplifying inuse:
% 99.04/99.47 Done
% 99.04/99.47
% 99.04/99.47
% 99.04/99.47 Intermediate Status:
% 99.04/99.47 Generated: 569936
% 99.04/99.47 Kept: 127418
% 99.04/99.47 Inuse: 1338
% 99.04/99.47 Deleted: 1990
% 99.04/99.47 Deletedinuse: 6
% 99.04/99.47
% 99.04/99.47 Resimplifying inuse:
% 99.04/99.47 Done
% 99.04/99.47
% 99.04/99.47 Resimplifying inuse:
% 183.75/184.15 Done
% 183.75/184.15
% 183.75/184.15
% 183.75/184.15 Intermediate Status:
% 183.75/184.15 Generated: 581820
% 183.75/184.15 Kept: 130729
% 183.75/184.15 Inuse: 1353
% 183.75/184.15 Deleted: 1990
% 183.75/184.15 Deletedinuse: 6
% 183.75/184.15
% 183.75/184.15 Resimplifying inuse:
% 183.75/184.15 Done
% 183.75/184.15
% 183.75/184.15
% 183.75/184.15 Intermediate Status:
% 183.75/184.15 Generated: 589644
% 183.75/184.15 Kept: 133725
% 183.75/184.15 Inuse: 1358
% 183.75/184.15 Deleted: 1990
% 183.75/184.15 Deletedinuse: 6
% 183.75/184.15
% 183.75/184.15 Resimplifying inuse:
% 183.75/184.15 Done
% 183.75/184.15
% 183.75/184.15
% 183.75/184.15 Intermediate Status:
% 183.75/184.15 Generated: 602417
% 183.75/184.15 Kept: 136943
% 183.75/184.15 Inuse: 1363
% 183.75/184.15 Deleted: 1990
% 183.75/184.15 Deletedinuse: 6
% 183.75/184.15
% 183.75/184.15 Resimplifying inuse:
% 183.75/184.15 Done
% 183.75/184.15
% 183.75/184.15
% 183.75/184.15 Intermediate Status:
% 183.75/184.15 Generated: 616106
% 183.75/184.15 Kept: 140192
% 183.75/184.15 Inuse: 1368
% 183.75/184.15 Deleted: 1990
% 183.75/184.15 Deletedinuse: 6
% 183.75/184.15
% 183.75/184.15 Resimplifying inuse:
% 183.75/184.15 Done
% 183.75/184.15
% 183.75/184.15 Resimplifying inuse:
% 183.75/184.15 Done
% 183.75/184.15
% 183.75/184.15
% 183.75/184.15 Intermediate Status:
% 183.75/184.15 Generated: 624936
% 183.75/184.15 Kept: 142206
% 183.75/184.15 Inuse: 1392
% 183.75/184.15 Deleted: 1990
% 183.75/184.15 Deletedinuse: 6
% 183.75/184.15
% 183.75/184.15 Resimplifying inuse:
% 183.75/184.15 Done
% 183.75/184.15
% 183.75/184.15
% 183.75/184.15 Intermediate Status:
% 183.75/184.15 Generated: 635832
% 183.75/184.15 Kept: 144223
% 183.75/184.15 Inuse: 1413
% 183.75/184.15 Deleted: 1990
% 183.75/184.15 Deletedinuse: 6
% 183.75/184.15
% 183.75/184.15 Resimplifying inuse:
% 183.75/184.15 Done
% 183.75/184.15
% 183.75/184.15 Resimplifying clauses:
% 183.75/184.15 Done
% 183.75/184.15
% 183.75/184.15 Resimplifying inuse:
% 183.75/184.15 Done
% 183.75/184.15
% 183.75/184.15
% 183.75/184.15 Intermediate Status:
% 183.75/184.15 Generated: 646898
% 183.75/184.15 Kept: 146240
% 183.75/184.15 Inuse: 1435
% 183.75/184.15 Deleted: 2684
% 183.75/184.15 Deletedinuse: 13
% 183.75/184.15
% 183.75/184.15 Resimplifying inuse:
% 183.75/184.15 Done
% 183.75/184.15
% 183.75/184.15 Resimplifying inuse:
% 183.75/184.15 Done
% 183.75/184.15
% 183.75/184.15
% 183.75/184.15 Intermediate Status:
% 183.75/184.15 Generated: 656601
% 183.75/184.15 Kept: 148276
% 183.75/184.15 Inuse: 1458
% 183.75/184.15 Deleted: 2684
% 183.75/184.15 Deletedinuse: 13
% 183.75/184.15
% 183.75/184.15 Resimplifying inuse:
% 183.75/184.15 Done
% 183.75/184.15
% 183.75/184.15 Resimplifying inuse:
% 183.75/184.15 Done
% 183.75/184.15
% 183.75/184.15
% 183.75/184.15 Intermediate Status:
% 183.75/184.15 Generated: 668159
% 183.75/184.15 Kept: 150318
% 183.75/184.15 Inuse: 1478
% 183.75/184.15 Deleted: 2684
% 183.75/184.15 Deletedinuse: 13
% 183.75/184.15
% 183.75/184.15 Resimplifying inuse:
% 183.75/184.15 Done
% 183.75/184.15
% 183.75/184.15
% 183.75/184.15 Intermediate Status:
% 183.75/184.15 Generated: 680220
% 183.75/184.15 Kept: 152749
% 183.75/184.15 Inuse: 1498
% 183.75/184.15 Deleted: 2684
% 183.75/184.15 Deletedinuse: 13
% 183.75/184.15
% 183.75/184.15 Resimplifying inuse:
% 183.75/184.15 Done
% 183.75/184.15
% 183.75/184.15 Resimplifying inuse:
% 183.75/184.15 Done
% 183.75/184.15
% 183.75/184.15
% 183.75/184.15 Intermediate Status:
% 183.75/184.15 Generated: 692074
% 183.75/184.15 Kept: 154770
% 183.75/184.15 Inuse: 1523
% 183.75/184.15 Deleted: 2684
% 183.75/184.15 Deletedinuse: 13
% 183.75/184.15
% 183.75/184.15 Resimplifying inuse:
% 183.75/184.15 Done
% 183.75/184.15
% 183.75/184.15 Resimplifying inuse:
% 183.75/184.15 Done
% 183.75/184.15
% 183.75/184.15
% 183.75/184.15 Intermediate Status:
% 183.75/184.15 Generated: 707661
% 183.75/184.15 Kept: 157024
% 183.75/184.15 Inuse: 1553
% 183.75/184.15 Deleted: 2684
% 183.75/184.15 Deletedinuse: 13
% 183.75/184.15
% 183.75/184.15 Resimplifying inuse:
% 183.75/184.15 Done
% 183.75/184.15
% 183.75/184.15
% 183.75/184.15 Intermediate Status:
% 183.75/184.15 Generated: 718531
% 183.75/184.15 Kept: 159061
% 183.75/184.15 Inuse: 1563
% 183.75/184.15 Deleted: 2684
% 183.75/184.15 Deletedinuse: 13
% 183.75/184.15
% 183.75/184.15 Resimplifying inuse:
% 183.75/184.15 Done
% 183.75/184.15
% 183.75/184.15
% 183.75/184.15 Intermediate Status:
% 183.75/184.15 Generated: 735488
% 183.75/184.15 Kept: 162802
% 183.75/184.15 Inuse: 1583
% 183.75/184.15 Deleted: 2684
% 183.75/184.15 Deletedinuse: 13
% 183.75/184.15
% 183.75/184.15 Resimplifying inuse:
% 183.75/184.15 Done
% 183.75/184.15
% 183.75/184.15 Resimplifying inuse:
% 183.75/184.15 Done
% 183.75/184.15
% 183.75/184.15
% 183.75/184.15 Intermediate Status:
% 183.75/184.15 Generated: 775097
% 183.75/184.15 Kept: 166448
% 183.75/184.15 Inuse: 1613
% 183.75/184.15 Deleted: 2685
% 183.75/184.15 Deletedinuse: 14
% 183.75/184.15
% 183.75/184.15 Resimplifying inuse:
% 183.75/184.15 Done
% 183.75/184.15
% 183.75/184.15 Resimplifying clauses:
% 183.75/184.15 Done
% 183.75/184.15
% 183.75/184.15 Resimplifying inuse:
% 183.75/184.15 Done
% 183.75/184.15
% 183.75/184.15
% 183.75/184.15 Intermediate Status:
% 183.75/184.15 Generated: 784056
% 183.75/184.15 Kept: 169093
% 183.75/184.15 Inuse: 1623
% 183.75/184.15 Deleted: 2944
% 183.75/184.15 Deletedinuse: 15
% 183.75/184.15
% 183.75/184.15 Resimplifying inuse:
% 183.75/184.15 Done
% 183.75/184.15
% 183.75/184.15 Resimplifying inuse:
% 183.75/184.15 Done
% 183.75/184.15
% 183.75/184.15
% 183.75/184.15 Intermediate Status:
% 183.75/184.15 Generated: 793455
% 183.75/184.15 Kept: 171999
% 183.75/184.15 Inuse: 1633
% 183.75/184.15 Deleted: 2944
% 183.75/184.15 Deletedinuse: 15
% 183.75/184.15
% 183.75/184.15 Resimplifying inuse:
% 183.75/184.15 Done
% 183.75/184.15
% 183.75/184.15 Resimplifying inuse:
% 183.75/184.15 Done
% 183.75/184.15
% 183.75/184.15
% 183.75/184.15 Intermediate Status:
% 183.75/184.15 Generated: 805657
% 183.75/184.15 Kept: 174310
% 183.75/184.15 Inuse: 1653
% 183.75/184.15 Deleted: 2944
% 183.75/184.15 Deletedinuse: 15
% 183.75/184.15
% 183.75/184.15 Resimplifying inuse:
% 183.75/184.15 Done
% 183.75/184.15
% 183.75/184.15 Resimplifying inuse:
% 183.75/184.15 Done
% 183.75/184.15
% 183.75/184.15
% 183.75/184.15 Intermediate Status:
% 183.75/184.15 Generated: 819419
% 183.75/184.15 Kept: 177111
% 183.75/184.15 Inuse: 1673
% 183.75/184.15 Deleted: 2944
% 183.75/184.15 Deletedinuse: 15
% 183.75/184.15
% 183.75/184.15 Resimplifying inuse:
% 183.75/184.15 Done
% 183.75/184.15
% 183.75/184.15 Resimplifying inuse:
% 183.75/184.15 Done
% 183.75/184.15
% 183.75/184.15
% 183.75/184.15 Intermediate Status:
% 183.75/184.15 Generated: 831292
% 183.75/184.15 Kept: 179490
% 183.75/184.15 Inuse: 1688
% 183.75/184.15 Deleted: 2944
% 183.75/184.15 Deletedinuse: 15
% 183.75/184.15
% 183.75/184.15 Resimplifying inuse:
% 183.75/184.15 Done
% 183.75/184.15
% 183.75/184.15
% 183.75/184.15 Intermediate Status:
% 183.75/184.15 Generated: 840997
% 183.75/184.15 Kept: 181494
% 183.75/184.15 Inuse: 1701
% 183.75/184.15 Deleted: 2944
% 183.75/184.15 Deletedinuse: 15
% 183.75/184.15
% 183.75/184.15 Resimplifying inuse:
% 183.75/184.15 Done
% 183.75/184.15
% 183.75/184.15
% 183.75/184.15 Intermediate Status:
% 183.75/184.15 Generated: 852449
% 183.75/184.15 Kept: 183541
% 183.75/184.15 Inuse: 1713
% 183.75/184.15 Deleted: 2944
% 183.75/184.15 Deletedinuse: 15
% 183.75/184.15
% 183.75/184.15 Resimplifying inuse:
% 183.75/184.15 Done
% 183.75/184.15
% 183.75/184.15 Resimplifying inuse:
% 183.75/184.15 Done
% 183.75/184.15
% 183.75/184.15
% 183.75/184.15 Intermediate Status:
% 183.75/184.15 Generated: 860575
% 183.75/184.15 Kept: 185821
% 183.75/184.15 Inuse: 1723
% 183.75/184.15 Deleted: 2944
% 183.75/184.15 Deletedinuse: 15
% 183.75/184.15
% 183.75/184.15 Resimplifying inuse:
% 183.75/184.15 Done
% 183.75/184.15
% 183.75/184.15 Resimplifying clauses:
% 183.75/184.15 Done
% 183.75/184.15
% 183.75/184.15 Resimplifying inuse:
% 183.75/184.15 Done
% 183.75/184.15
% 183.75/184.15
% 183.75/184.15 Intermediate Status:
% 183.75/184.15 Generated: 875441
% 183.75/184.15 Kept: 188159
% 183.75/184.15 Inuse: 1748
% 183.75/184.15 Deleted: 3296
% 183.75/184.15 Deletedinuse: 15
% 183.75/184.15
% 183.75/184.15 Resimplifying inuse:
% 183.75/184.15 Done
% 183.75/184.15
% 183.75/184.15
% 183.75/184.15 Intermediate Status:
% 183.75/184.15 Generated: 897697
% 183.75/184.15 Kept: 190833
% 183.75/184.15 Inuse: 1768
% 183.75/184.15 Deleted: 3296
% 288.43/288.89 Deletedinuse: 15
% 288.43/288.89
% 288.43/288.89 Resimplifying inuse:
% 288.43/288.89 Done
% 288.43/288.89
% 288.43/288.89 Resimplifying inuse:
% 288.43/288.89 Done
% 288.43/288.89
% 288.43/288.89
% 288.43/288.89 Intermediate Status:
% 288.43/288.89 Generated: 915342
% 288.43/288.89 Kept: 192846
% 288.43/288.89 Inuse: 1776
% 288.43/288.89 Deleted: 3296
% 288.43/288.89 Deletedinuse: 15
% 288.43/288.89
% 288.43/288.89 Resimplifying inuse:
% 288.43/288.89 Done
% 288.43/288.89
% 288.43/288.89
% 288.43/288.89 Intermediate Status:
% 288.43/288.89 Generated: 946639
% 288.43/288.89 Kept: 196600
% 288.43/288.89 Inuse: 1783
% 288.43/288.89 Deleted: 3296
% 288.43/288.89 Deletedinuse: 15
% 288.43/288.89
% 288.43/288.89 Resimplifying inuse:
% 288.43/288.89 Done
% 288.43/288.89
% 288.43/288.89 Resimplifying inuse:
% 288.43/288.89 Done
% 288.43/288.89
% 288.43/288.89
% 288.43/288.89 Intermediate Status:
% 288.43/288.89 Generated: 979341
% 288.43/288.89 Kept: 200444
% 288.43/288.89 Inuse: 1793
% 288.43/288.89 Deleted: 3296
% 288.43/288.89 Deletedinuse: 15
% 288.43/288.89
% 288.43/288.89 Resimplifying inuse:
% 288.43/288.89 Done
% 288.43/288.89
% 288.43/288.89 Resimplifying inuse:
% 288.43/288.89 Done
% 288.43/288.89
% 288.43/288.89
% 288.43/288.89 Intermediate Status:
% 288.43/288.89 Generated: 989121
% 288.43/288.89 Kept: 203442
% 288.43/288.89 Inuse: 1803
% 288.43/288.89 Deleted: 3296
% 288.43/288.89 Deletedinuse: 15
% 288.43/288.89
% 288.43/288.89 Resimplifying inuse:
% 288.43/288.89 Done
% 288.43/288.89
% 288.43/288.89 Resimplifying inuse:
% 288.43/288.89 Done
% 288.43/288.89
% 288.43/288.89
% 288.43/288.89 Intermediate Status:
% 288.43/288.89 Generated: 1002194
% 288.43/288.89 Kept: 205714
% 288.43/288.89 Inuse: 1823
% 288.43/288.89 Deleted: 3296
% 288.43/288.89 Deletedinuse: 15
% 288.43/288.89
% 288.43/288.89 Resimplifying inuse:
% 288.43/288.89 Done
% 288.43/288.89
% 288.43/288.89
% 288.43/288.89 Intermediate Status:
% 288.43/288.89 Generated: 1043170
% 288.43/288.89 Kept: 210506
% 288.43/288.89 Inuse: 1833
% 288.43/288.89 Deleted: 3296
% 288.43/288.89 Deletedinuse: 15
% 288.43/288.89
% 288.43/288.89 Resimplifying inuse:
% 288.43/288.89 Done
% 288.43/288.89
% 288.43/288.89 Resimplifying clauses:
% 288.43/288.89 Done
% 288.43/288.89
% 288.43/288.89 Resimplifying inuse:
% 288.43/288.89 Done
% 288.43/288.89
% 288.43/288.89
% 288.43/288.89 Intermediate Status:
% 288.43/288.89 Generated: 1060785
% 288.43/288.89 Kept: 214016
% 288.43/288.89 Inuse: 1848
% 288.43/288.89 Deleted: 3421
% 288.43/288.89 Deletedinuse: 15
% 288.43/288.89
% 288.43/288.89 Resimplifying inuse:
% 288.43/288.89 Done
% 288.43/288.89
% 288.43/288.89
% 288.43/288.89 Intermediate Status:
% 288.43/288.89 Generated: 1074459
% 288.43/288.89 Kept: 216702
% 288.43/288.89 Inuse: 1858
% 288.43/288.89 Deleted: 3421
% 288.43/288.89 Deletedinuse: 15
% 288.43/288.89
% 288.43/288.89 Resimplifying inuse:
% 288.43/288.89 Done
% 288.43/288.89
% 288.43/288.89
% 288.43/288.89 Intermediate Status:
% 288.43/288.89 Generated: 1096019
% 288.43/288.89 Kept: 221670
% 288.43/288.89 Inuse: 1868
% 288.43/288.89 Deleted: 3421
% 288.43/288.89 Deletedinuse: 15
% 288.43/288.89
% 288.43/288.89 Resimplifying inuse:
% 288.43/288.89 Done
% 288.43/288.89
% 288.43/288.89 Resimplifying inuse:
% 288.43/288.89 Done
% 288.43/288.89
% 288.43/288.89
% 288.43/288.89 Intermediate Status:
% 288.43/288.89 Generated: 1107048
% 288.43/288.89 Kept: 224335
% 288.43/288.89 Inuse: 1883
% 288.43/288.89 Deleted: 3421
% 288.43/288.89 Deletedinuse: 15
% 288.43/288.89
% 288.43/288.89 Resimplifying inuse:
% 288.43/288.89 Done
% 288.43/288.89
% 288.43/288.89 Resimplifying inuse:
% 288.43/288.89 Done
% 288.43/288.89
% 288.43/288.89
% 288.43/288.89 Intermediate Status:
% 288.43/288.89 Generated: 1118378
% 288.43/288.89 Kept: 228147
% 288.43/288.89 Inuse: 1889
% 288.43/288.89 Deleted: 3421
% 288.43/288.89 Deletedinuse: 15
% 288.43/288.89
% 288.43/288.89 Resimplifying inuse:
% 288.43/288.89 Done
% 288.43/288.89
% 288.43/288.89 Resimplifying inuse:
% 288.43/288.89 Done
% 288.43/288.89
% 288.43/288.89
% 288.43/288.89 Intermediate Status:
% 288.43/288.89 Generated: 1127029
% 288.43/288.89 Kept: 230286
% 288.43/288.89 Inuse: 1908
% 288.43/288.89 Deleted: 3421
% 288.43/288.89 Deletedinuse: 15
% 288.43/288.89
% 288.43/288.89 Resimplifying inuse:
% 288.43/288.89 Done
% 288.43/288.89
% 288.43/288.89 Resimplifying clauses:
% 288.43/288.89 Done
% 288.43/288.89
% 288.43/288.89 Resimplifying inuse:
% 288.43/288.89 Done
% 288.43/288.89
% 288.43/288.89
% 288.43/288.89 Intermediate Status:
% 288.43/288.89 Generated: 1141438
% 288.43/288.89 Kept: 232520
% 288.43/288.89 Inuse: 1928
% 288.43/288.89 Deleted: 3547
% 288.43/288.89 Deletedinuse: 15
% 288.43/288.89
% 288.43/288.89 Resimplifying inuse:
% 288.43/288.89 Done
% 288.43/288.89
% 288.43/288.89 Resimplifying inuse:
% 288.43/288.89 Done
% 288.43/288.89
% 288.43/288.89
% 288.43/288.89 Intermediate Status:
% 288.43/288.89 Generated: 1155220
% 288.43/288.89 Kept: 234548
% 288.43/288.89 Inuse: 1954
% 288.43/288.89 Deleted: 3547
% 288.43/288.89 Deletedinuse: 15
% 288.43/288.89
% 288.43/288.89 Resimplifying inuse:
% 288.43/288.89 Done
% 288.43/288.89
% 288.43/288.89 Resimplifying inuse:
% 288.43/288.89 Done
% 288.43/288.89
% 288.43/288.89
% 288.43/288.89 Intermediate Status:
% 288.43/288.89 Generated: 1166041
% 288.43/288.89 Kept: 236595
% 288.43/288.89 Inuse: 1970
% 288.43/288.89 Deleted: 3547
% 288.43/288.89 Deletedinuse: 15
% 288.43/288.89
% 288.43/288.89 Resimplifying inuse:
% 288.43/288.89 Done
% 288.43/288.89
% 288.43/288.89 Resimplifying inuse:
% 288.43/288.89 Done
% 288.43/288.89
% 288.43/288.89
% 288.43/288.89 Intermediate Status:
% 288.43/288.89 Generated: 1175061
% 288.43/288.89 Kept: 238602
% 288.43/288.89 Inuse: 1988
% 288.43/288.89 Deleted: 3547
% 288.43/288.89 Deletedinuse: 15
% 288.43/288.89
% 288.43/288.89 Resimplifying inuse:
% 288.43/288.89 Done
% 288.43/288.89
% 288.43/288.89
% 288.43/288.89 Intermediate Status:
% 288.43/288.89 Generated: 1185631
% 288.43/288.89 Kept: 240822
% 288.43/288.89 Inuse: 2003
% 288.43/288.89 Deleted: 3547
% 288.43/288.89 Deletedinuse: 15
% 288.43/288.89
% 288.43/288.89 Resimplifying inuse:
% 288.43/288.89 Done
% 288.43/288.89
% 288.43/288.89 Resimplifying inuse:
% 288.43/288.89 Done
% 288.43/288.89
% 288.43/288.89
% 288.43/288.89 Intermediate Status:
% 288.43/288.89 Generated: 1201496
% 288.43/288.89 Kept: 242852
% 288.43/288.89 Inuse: 2024
% 288.43/288.89 Deleted: 3547
% 288.43/288.89 Deletedinuse: 15
% 288.43/288.89
% 288.43/288.89 Resimplifying inuse:
% 288.43/288.89 Done
% 288.43/288.89
% 288.43/288.89 Resimplifying inuse:
% 288.43/288.89 Done
% 288.43/288.89
% 288.43/288.89
% 288.43/288.89 Intermediate Status:
% 288.43/288.89 Generated: 1212027
% 288.43/288.89 Kept: 245538
% 288.43/288.89 Inuse: 2038
% 288.43/288.89 Deleted: 3548
% 288.43/288.89 Deletedinuse: 16
% 288.43/288.89
% 288.43/288.89 Resimplifying inuse:
% 288.43/288.89 Done
% 288.43/288.89
% 288.43/288.89 Resimplifying inuse:
% 288.43/288.89 Done
% 288.43/288.89
% 288.43/288.89
% 288.43/288.89 Intermediate Status:
% 288.43/288.89 Generated: 1229240
% 288.43/288.89 Kept: 249297
% 288.43/288.89 Inuse: 2058
% 288.43/288.89 Deleted: 3548
% 288.43/288.89 Deletedinuse: 16
% 288.43/288.89
% 288.43/288.89 Resimplifying inuse:
% 288.43/288.89 Done
% 288.43/288.89
% 288.43/288.89 Resimplifying inuse:
% 288.43/288.89 Done
% 288.43/288.89
% 288.43/288.89 Resimplifying clauses:
% 288.43/288.89 Done
% 288.43/288.89
% 288.43/288.89
% 288.43/288.89 Intermediate Status:
% 288.43/288.89 Generated: 1239080
% 288.43/288.89 Kept: 251306
% 288.43/288.89 Inuse: 2074
% 288.43/288.89 Deleted: 4295
% 288.43/288.89 Deletedinuse: 16
% 288.43/288.89
% 288.43/288.89 Resimplifying inuse:
% 288.43/288.89 Done
% 288.43/288.89
% 288.43/288.89
% 288.43/288.89 Intermediate Status:
% 288.43/288.89 Generated: 1252270
% 288.43/288.89 Kept: 254501
% 288.43/288.89 Inuse: 2083
% 288.43/288.89 Deleted: 4295
% 288.43/288.89 Deletedinuse: 16
% 288.43/288.89
% 288.43/288.89 Resimplifying inuse:
% 288.43/288.89 Done
% 288.43/288.89
% 288.43/288.89
% 288.43/288.89 Intermediate Status:
% 288.43/288.89 Generated: 1263056
% 288.43/288.89 Kept: 257156
% 288.43/288.89 Inuse: 2088
% 288.43/288.89 Deleted: 4295
% 288.43/288.89 Deletedinuse: 16
% 288.43/288.89
% 288.43/288.89 Resimplifying inuse:
% 288.43/288.89 Done
% 288.43/288.89
% 288.43/288.89 Resimplifying inuse:
% 288.43/288.89 Done
% 288.43/288.89
% 288.43/288.89
% 288.43/288.89 Intermediate Status:
% 288.43/288.89 Generated: 1271308
% 288.43/288.89 Kept: 259203
% 288.43/288.89 Inuse: 2102
% 288.43/288.89 Deleted: 4295Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------