TSTP Solution File: SWV714-1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWV714-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n014.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 16:28:00 EDT 2022
% Result : Timeout 300.01s 300.44s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SWV714-1 : TPTP v8.1.0. Released v4.1.0.
% 0.12/0.13 % Command : bliksem %s
% 0.13/0.34 % Computer : n014.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 01:09:06 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.24/1.60 *** allocated 10000 integers for termspace/termends
% 1.24/1.60 *** allocated 10000 integers for clauses
% 1.24/1.60 *** allocated 10000 integers for justifications
% 1.24/1.60 *** allocated 15000 integers for termspace/termends
% 1.24/1.60 *** allocated 22500 integers for termspace/termends
% 1.24/1.60 *** allocated 33750 integers for termspace/termends
% 1.24/1.60 *** allocated 50625 integers for termspace/termends
% 1.24/1.60 Bliksem 1.12
% 1.24/1.60
% 1.24/1.60
% 1.24/1.60 Automatic Strategy Selection
% 1.24/1.60
% 1.24/1.60 Clauses:
% 1.24/1.60 [
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.24/1.60 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.24/1.60 Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 1.24/1.60 X ), X ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.24/1.60 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.24/1.60 X ), X ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.24/1.60 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 1.24/1.60 X ), X ) ) ],
% 1.24/1.60 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.24/1.60 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.24/1.60 , Y ), Z ), Z, X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 1.24/1.60 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.24/1.60 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.24/1.60 , Y ), Z ), Y, X ), 'c_Divides_Odiv__class_Omod'( Z, Y, X ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.24/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ), ~(
% 1.24/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X )
% 1.24/1.60 ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.24/1.60 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ), hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), U ), W ) ), hAPP( hAPP(
% 1.24/1.60 'c_Power_Opower_Opower'( X, Y, Z ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.24/1.60 X, Y, Z ), T ), U ) ), W ) ), ~( 'c_OrderedGroup_Omonoid__mult'( X, Y, Z
% 1.24/1.60 ) ) ],
% 1.24/1.60 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.24/1.60 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.24/1.60 ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ), hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z )
% 1.24/1.60 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.24/1.60 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.24/1.60 'tc_nat' ) ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y ), 'tc_nat' ),
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.24/1.60 [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Suc'( 'c_Suc'(
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ),
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 1.24/1.60 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.24/1.60 [ ~( =( 'c_Divides_Odiv__class_Omod'( X, 'c_Suc'( 'c_Suc'(
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ),
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ),
% 1.24/1.60 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.24/1.60 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.24/1.60 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y
% 1.24/1.60 ), 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.24/1.60 'tc_nat' ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.24/1.60 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.24/1.60 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.24/1.60 ), =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ),
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( X ) ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.24/1.60 , =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.24/1.60 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.24/1.60 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.24/1.60 , X ), X ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.24/1.60 ) ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.24/1.60 ), 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.24/1.60 ), X ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.24/1.60 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.24/1.60 X ), X ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'(
% 1.24/1.60 Z, X ), 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.24/1.60 ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Oinverse__class_Odivide'( T,
% 1.24/1.60 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), X ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.24/1.60 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.24/1.60 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.24/1.60 , X ), X ), T, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T
% 1.24/1.60 , X ) ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.24/1.60 , X ), 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.24/1.60 ), X ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.24/1.60 'class_Int_Onumber'( X ) ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X
% 1.24/1.60 ), Y, X ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'(
% 1.24/1.60 Z, X ), 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.24/1.60 ), X ), ~( 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( T,
% 1.24/1.60 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ) ],
% 1.24/1.60 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ), 'tc_nat' ),
% 1.24/1.60 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ), ~(
% 1.24/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.24/1.60 'tc_nat' ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.24/1.60 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.24/1.60 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.24/1.60 [ ~( 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.24/1.60 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.24/1.60 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.24/1.60 [ =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( 'tc_nat' ), X ),
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'(
% 1.24/1.60 'tc_nat' ) ) ],
% 1.24/1.60 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.24/1.60 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.24/1.60 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.24/1.60 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.24/1.60 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.24/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.24/1.60 'class_Int_Onumber'( X ) ), =( Y, 'c_HOL_Oinverse__class_Odivide'( hAPP(
% 1.24/1.60 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.24/1.60 'c_Int_Onumber__class_Onumber__of'( Z, X ) ),
% 1.24/1.60 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ), =(
% 1.24/1.60 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.24/1.60 ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.24/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.24/1.60 'class_Int_Onumber'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( hAPP(
% 1.24/1.60 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.24/1.60 'c_Int_Onumber__class_Onumber__of'( Z, X ) ),
% 1.24/1.60 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y ), =(
% 1.24/1.60 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.24/1.60 ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.24/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.24/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.24/1.60 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.24/1.60 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 1.24/1.60 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.24/1.60 X ), X ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.24/1.60 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.24/1.60 , Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.24/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.24/1.60 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.24/1.60 ,
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.24/1.60 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.24/1.60 , Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.24/1.60 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.24/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.24/1.60 ,
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.24/1.60 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.24/1.60 , Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.24/1.60 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.24/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 1.24/1.60 ,
% 1.24/1.60 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.24/1.60 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ), ~(
% 1.24/1.60 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ) ) ],
% 1.24/1.60 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.24/1.60 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.24/1.60 ), Z ) ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP(
% 1.24/1.60 hAPP( 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.24/1.60 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), Z ) ) ) ],
% 1.24/1.60 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( 'c_Power_Opower_Opower'( Y, Z, T ),
% 1.24/1.60 U ), W ) ), hAPP( hAPP( Z, U ), hAPP( hAPP( 'c_Power_Opower_Opower'( Y, Z
% 1.24/1.60 , T ), U ), W ) ) ) ), ~( hBOOL( hAPP( hAPP( X, Y ), U ) ) ), ~(
% 1.24/1.60 'c_Ring__and__Field_Oordered__semidom'( V0, V1, Y, Z, V2, X, T ) ) ],
% 1.24/1.60 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.24/1.60 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.24/1.60 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X ) )
% 1.24/1.60 , Z ) ), Z ) ],
% 1.24/1.60 [ =( hAPP( X, hAPP( hAPP( 'c_Power_Opower_Opower'( Y, Z, T ), U ), W ) )
% 1.24/1.60 , hAPP( hAPP( 'c_Power_Opower_Opower'( Y, Z, T ), hAPP( X, U ) ), W ) ),
% 1.24/1.60 ~( 'c_Ring__and__Field_Oordered__idom'( V0, V1, V2, V3, V4, V5, X, Y, Z,
% 1.24/1.60 V6, T ) ) ],
% 1.24/1.60 [ =( hAPP( X, hAPP( hAPP( 'c_Power_Opower_Opower'( Y, Z, T ), hAPP( U, W
% 1.24/1.60 ) ), V0 ) ), hAPP( X, hAPP( hAPP( 'c_Power_Opower_Opower'( Y, Z, T ), W
% 1.24/1.60 ), V0 ) ) ), ~( 'c_Ring__and__Field_Oordered__idom'( V1, U, V2, V3, V4,
% 1.24/1.60 V5, X, Y, Z, V6, T ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.24/1.60 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.24/1.60 , Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 1.24/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 1.24/1.60 ,
% 1.24/1.60 [ =( 'c_Divides_Odiv__class_Omod'( X, hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ), 'tc_nat' ), hAPP(
% 1.24/1.60 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ),
% 1.24/1.60 'c_Divides_Odiv__class_Omod'( 'c_Divides_Odiv__class_Odiv'( X, Y,
% 1.24/1.60 'tc_nat' ), Z, 'tc_nat' ) ) ), 'c_Divides_Odiv__class_Omod'( X, Y,
% 1.24/1.60 'tc_nat' ) ) ) ],
% 1.24/1.60 [ ~( =( hAPP( 'c_NthRoot_Osqrt', X ), hAPP( 'c_NthRoot_Osqrt', Y ) ) ),
% 1.24/1.60 =( X, Y ) ],
% 1.24/1.60 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.24/1.60 'tc_nat' ) ) ) ],
% 1.24/1.60 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.24/1.60 'tc_nat' ) ), Y ) ) ],
% 1.24/1.60 [ ~( 'c_Ring__and__Field_Oordered__idom'( X, Y, Z, T, U, W, V0, V1, V2,
% 1.24/1.60 V3, V4 ) ), hBOOL( hAPP( hAPP( W, Z ), hAPP( hAPP(
% 1.24/1.60 'c_Power_Opower_Opower'( V1, V2, V4 ), hAPP( V0, V5 ) ),
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.24/1.60 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), =( Y
% 1.24/1.60 , 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.24/1.60 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.24/1.60 , X ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.24/1.60 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.24/1.60 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP(
% 1.24/1.60 hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), X ), ~(
% 1.24/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.24/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.24/1.60 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oinverse__class_Odivide'( Y, Z,
% 1.24/1.60 X ), X ), 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ) ) ],
% 1.24/1.60 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.24/1.60 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.24/1.60 'c_Divides_Odiv__class_Omod'( Y, Z, 'tc_nat' ) ) ), T ), hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ), 'tc_nat' ), ~(
% 1.24/1.60 'c_HOL_Oord__class_Oless'( T, X, 'tc_nat' ) ), ~(
% 1.24/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.24/1.60 'tc_nat' ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Omult__mono1'( X ) ), 'c_lessequals'( hAPP(
% 1.24/1.60 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~( 'c_lessequals'(
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Z, T, X ) )
% 1.24/1.60 ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ), 'c_lessequals'( hAPP(
% 1.24/1.60 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~( 'c_lessequals'(
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Z, T, X ) )
% 1.24/1.60 ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ), 'c_lessequals'( hAPP(
% 1.24/1.60 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ), ~( 'c_lessequals'(
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 1.24/1.60 ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.24/1.60 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~( 'c_lessequals'( Y,
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( T, Z, X ) ) ]
% 1.24/1.60 ,
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.24/1.60 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ), ~( 'c_lessequals'( Z,
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( T, Y, X ) ) ]
% 1.24/1.60 ,
% 1.24/1.60 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP(
% 1.24/1.60 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.24/1.60 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), T ) ) ) ), =( Z, T ), =( Y
% 1.24/1.60 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.24/1.60 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.24/1.60 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ) ) ), =( T, U ), =( Z,
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =( hAPP(
% 1.24/1.60 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.24/1.60 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =( hAPP(
% 1.24/1.60 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.24/1.60 X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~( =( hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), 'c_HOL_Oone__class_Oone'( X
% 1.24/1.60 ) ) ), =( 'c_HOL_Oinverse__class_Oinverse'( Y, X ), Z ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.24/1.60 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ),
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.24/1.60 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ), =( Z,
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.24/1.60 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.24/1.60 ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.24/1.60 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.24/1.60 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.24/1.60 'class_Power_Opower'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.24/1.60 , 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( hAPP( hAPP(
% 1.24/1.60 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.24/1.60 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.24/1.60 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.24/1.60 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.24/1.60 ), Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.24/1.60 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), Z, X ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.24/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.24/1.60 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z,
% 1.24/1.60 X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.24/1.60 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.24/1.60 , Y ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.24/1.60 Y, 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.24/1.60 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.24/1.60 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 1.24/1.60 X ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), Z, X ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.24/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.24/1.60 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ), ~(
% 1.24/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 1.24/1.60 ,
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.24/1.60 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.24/1.60 , X ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), Z, X ) ), ~(
% 1.24/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ]
% 1.24/1.60 ,
% 1.24/1.60 [ ~( =( hAPP( 'c_NthRoot_Oroot'( X ), Y ), hAPP( 'c_NthRoot_Oroot'( X )
% 1.24/1.60 , Z ) ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.24/1.60 'tc_nat' ), X, 'tc_nat' ) ), =( Y, Z ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.24/1.60 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oabs__class_Oabs'(
% 1.24/1.60 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OMin', X ), X ),
% 1.24/1.60 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.24/1.60 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ), hAPP( hAPP(
% 1.24/1.60 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), U ), W ) ), hAPP( hAPP( Y, hAPP(
% 1.24/1.60 hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ), U ) ), hAPP( hAPP(
% 1.24/1.60 'c_Power_Opower_Opower'( X, Y, Z ), T ), W ) ) ), ~(
% 1.24/1.60 'c_OrderedGroup_Omonoid__mult'( X, Y, Z ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.24/1.60 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.24/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.24/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.24/1.60 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.24/1.60 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.24/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.24/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.24/1.60 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), X ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.24/1.60 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.24/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.24/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.24/1.60 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.24/1.60 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.24/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.24/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.24/1.60 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), X ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.24/1.60 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.24/1.60 ), X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.24/1.60 , X ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.24/1.60 ,
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.24/1.60 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.24/1.60 ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z
% 1.24/1.60 , X ) ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.24/1.60 ,
% 1.24/1.60 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.24/1.60 'c_Power_Opower__class_Opower'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.24/1.60 'c_Int_OMin', X ) ), Y ), 'c_HOL_Oone__class_Oone'( X ) ), ~(
% 1.24/1.60 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ) ],
% 1.24/1.60 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =( hAPP(
% 1.24/1.60 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ), Y ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'(
% 1.24/1.60 Z, 'tc_nat' ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.24/1.60 'c_Power_Opower__class_Opower'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 1.24/1.60 X ), X ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.24/1.60 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.24/1.60 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X )
% 1.24/1.60 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.24/1.60 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.24/1.60 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.24/1.60 T, X ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.24/1.60 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.24/1.60 'c_Power_Opower__class_Opower'( X ), T ), Z ), X ), ~( 'c_lessequals'( Y
% 1.24/1.60 , T, X ) ), 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 1.24/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( =(
% 1.24/1.60 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.24/1.60 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ) ), =( Y, Z ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~( =(
% 1.24/1.60 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.24/1.60 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ) ), =( Y, Z ), =( Z,
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.24/1.60 ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 1.24/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.24/1.60 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.24/1.60 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.24/1.60 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.24/1.60 , X ) ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.24/1.60 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.24/1.60 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.24/1.60 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.24/1.60 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.24/1.60 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.24/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.24/1.60 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.24/1.60 , 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.24/1.60 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.24/1.60 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.24/1.60 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.24/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.24/1.60 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.24/1.60 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.24/1.60 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.24/1.60 , X ) ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.24/1.60 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.24/1.60 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ],
% 1.24/1.60 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.24/1.60 'tc_nat' ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 1.24/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP(
% 1.24/1.60 hAPP( 'c_Power_Opower__class_Opower'( 'tc_nat' ), X ), Y ), 'tc_nat' ) )
% 1.24/1.60 ],
% 1.24/1.60 [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 1.24/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.24/1.60 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.24/1.60 'tc_nat' ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( 'tc_nat' ), Y ),
% 1.24/1.60 X ), 'tc_nat' ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.24/1.60 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.24/1.60 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.24/1.60 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'(
% 1.24/1.60 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.24/1.60 ), X ) ), 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X )
% 1.24/1.60 , X ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.24/1.60 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.24/1.60 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.24/1.60 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.24/1.60 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'(
% 1.24/1.60 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.24/1.60 ), X ) ), ~( 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.24/1.60 X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ),
% 1.24/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 1.24/1.60 'c_Nat_Osemiring__1__class_Oof__nat'( hAPP( hAPP(
% 1.24/1.60 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ), X ), hAPP( hAPP(
% 1.24/1.60 'c_HOL_Oplus__class_Oplus'( X ), 'c_Nat_Osemiring__1__class_Oof__nat'( Y
% 1.24/1.60 , X ) ), 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ) ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =(
% 1.24/1.60 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Oord__class_Oless'(
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.24/1.60 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.24/1.60 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ), X ) ],
% 1.24/1.60 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.24/1.60 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.24/1.60 , Y ), 'c_Divides_Odiv__class_Omod'( Z, T, X ) ), T, X ),
% 1.24/1.60 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.24/1.60 , Y ), Z ), T, X ) ) ],
% 1.24/1.60 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.24/1.60 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.24/1.60 , 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ), T ), Z, X ),
% 1.24/1.60 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.24/1.60 , Y ), T ), Z, X ) ) ],
% 1.24/1.60 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.24/1.60 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.24/1.60 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.24/1.60 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_Suc'(
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.24/1.60 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( Y, hAPP( hAPP(
% 1.24/1.60 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.24/1.60 X ), 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ), Z ) ),
% 1.24/1.60 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ) ],
% 1.24/1.60 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 1.24/1.60 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.24/1.60 X ), 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ), Z ) ),
% 1.24/1.60 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ), Y ) ],
% 1.24/1.60 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 1.24/1.60 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.24/1.60 X ), Y ), 'c_Divides_Odiv__class_Odiv'( Z, Y, X ) ) ),
% 1.24/1.60 'c_Divides_Odiv__class_Omod'( Z, Y, X ) ), Z ) ],
% 1.24/1.60 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.24/1.60 ), =( Y, Z ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.24/1.60 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ),
% 1.24/1.60 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 1.24/1.60 ,
% 1.24/1.60 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.24/1.60 ), =( Y, Z ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.24/1.60 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.24/1.60 ), ~( 'c_lessequals'( Y, Z, X ) ), =( Y, Z ) ],
% 1.24/1.60 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Y
% 1.24/1.60 , Z, X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ) ],
% 1.24/1.60 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 1.24/1.60 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 1.24/1.60 ,
% 1.24/1.60 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.24/1.60 ), ~( 'c_lessequals'( Y, Z, X ) ), =( Z, Y ) ],
% 1.24/1.60 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.24/1.60 ), =( Z, Y ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.24/1.60 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.24/1.60 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), ~( 'c_lessequals'(
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 1.24/1.60 ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.24/1.60 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.24/1.60 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), ~( 'c_lessequals'( Z,
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( T, Y, X ) ) ]
% 1.24/1.60 ,
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 1.24/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.24/1.60 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.24/1.60 , X ), 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oinverse__class_Oinverse'(
% 1.24/1.60 Y, X ), X ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.24/1.60 X ), Y ), Z ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z
% 1.24/1.60 , X ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.24/1.60 ,
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.24/1.60 X ), Y ), Z ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.24/1.60 , X ) ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.24/1.60 ,
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.24/1.60 X ), Y ), Z ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.24/1.60 , X ) ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.24/1.60 ,
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.24/1.60 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ), X ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.24/1.60 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.24/1.60 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~( 'c_lessequals'( Z,
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.24/1.60 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =(
% 1.24/1.60 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Oone__class_Oone'( X )
% 1.24/1.60 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, Z ) ],
% 1.24/1.60 [ ~( =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ), U ), hAPP(
% 1.24/1.60 hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), W ), U ) ) ), ~(
% 1.24/1.60 'c_Ring__and__Field_Oordered__semidom'( V0, V1, X, Y, V2, V3, Z ) ), =( T
% 1.24/1.60 , W ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.24/1.60 ), U, 'tc_nat' ) ), ~( hBOOL( hAPP( hAPP( V2, V1 ), W ) ) ), ~( hBOOL(
% 1.24/1.60 hAPP( hAPP( V2, V1 ), T ) ) ) ],
% 1.24/1.60 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Ouminus__class_Ouminus'(
% 1.24/1.60 Y, X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.24/1.60 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oone__class_Oone'( X ), X ) ), Y )
% 1.24/1.60 ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.24/1.60 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.24/1.60 , 'tc_nat' ), 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.24/1.60 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.24/1.60 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.24/1.60 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y
% 1.24/1.60 ), X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.24/1.60 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.24/1.60 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.24/1.60 , X ), X ), T, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T
% 1.24/1.60 , X ) ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.24/1.60 , X ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y, hAPP(
% 1.24/1.60 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.24/1.60 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.24/1.60 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.24/1.60 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.24/1.60 , X ), X ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.24/1.60 ) ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.24/1.60 ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.24/1.60 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.24/1.60 [ ~( 'class_OrderedGroup_Oab__semigroup__mult'( X ) ), =( hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.24/1.60 'class_Int_Onumber'( X ) ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X
% 1.24/1.60 ), 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.24/1.60 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.24/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.24/1.60 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X ),
% 1.24/1.60 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.24/1.60 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.24/1.60 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.24/1.60 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~( 'c_lessequals'(
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.24/1.60 ), X ) ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.24/1.60 , X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X )
% 1.24/1.60 ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.24/1.60 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.24/1.60 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.24/1.60 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~( 'c_lessequals'(
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.24/1.60 ), X ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.24/1.60 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ), ~(
% 1.24/1.60 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.24/1.60 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.24/1.60 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =( hAPP(
% 1.24/1.60 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.24/1.60 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.24/1.60 , Y ), 'c_HOL_Oone__class_Oone'( X ) ), X ) ],
% 1.24/1.60 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( 'c_Power_Opower_Opower'( Y, Z, T ),
% 1.24/1.60 U ), 'c_Suc'( W ) ) ), Y ) ), ~( hBOOL( hAPP( hAPP( X, U ), Y ) ) ), ~(
% 1.24/1.60 hBOOL( hAPP( hAPP( X, V0 ), U ) ) ), ~(
% 1.24/1.60 'c_Ring__and__Field_Oordered__semidom'( V1, V0, Y, Z, V2, X, T ) ) ],
% 1.24/1.60 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.24/1.60 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), ~(
% 1.24/1.60 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.24/1.60 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.24/1.60 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.24/1.60 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ) ],
% 1.24/1.60 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.24/1.60 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.24/1.60 'tc_nat' ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.24/1.60 ), Z ), Y ), 'tc_nat' ) ) ],
% 1.24/1.60 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.24/1.60 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.24/1.60 'tc_nat' ), X ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.24/1.60 ), Y ), Z ), 'tc_nat' ) ) ],
% 1.24/1.60 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), Z, 'tc_nat' ), hAPP(
% 1.24/1.60 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.24/1.60 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ) ),
% 1.24/1.60 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.24/1.60 'tc_nat' ), X ), 'c_Divides_Odiv__class_Omod'( Y, Z, 'tc_nat' ) ), Z,
% 1.24/1.60 'tc_nat' ) ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 1.24/1.60 'c_HOL_Ouminus__class_Ouminus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.24/1.60 X ), Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.24/1.60 'c_HOL_Ouminus__class_Ouminus'( Z, X ) ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 1.24/1.60 'c_HOL_Ouminus__class_Ouminus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.24/1.60 X ), Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.24/1.60 'c_HOL_Ouminus__class_Ouminus'( Y, X ) ), Z ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.24/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z
% 1.24/1.60 , X ) ), 'c_HOL_Oinverse__class_Odivide'( T, U, X ) ),
% 1.24/1.60 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.24/1.60 X ), Y ), T ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ), X
% 1.24/1.60 ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Opordered__ring__abs'( X ) ), =(
% 1.24/1.60 'c_HOL_Oabs__class_Oabs'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.24/1.60 Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.24/1.60 'c_HOL_Oabs__class_Oabs'( Y, X ) ), 'c_HOL_Oabs__class_Oabs'( Z, X ) ) )
% 1.24/1.60 , ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.24/1.60 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Opordered__ring__abs'( X ) ), =(
% 1.24/1.60 'c_HOL_Oabs__class_Oabs'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.24/1.60 Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.24/1.60 'c_HOL_Oabs__class_Oabs'( Y, X ) ), 'c_HOL_Oabs__class_Oabs'( Z, X ) ) )
% 1.24/1.60 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.24/1.60 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Opordered__ring__abs'( X ) ), =(
% 1.24/1.60 'c_HOL_Oabs__class_Oabs'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.24/1.60 Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.24/1.60 'c_HOL_Oabs__class_Oabs'( Y, X ) ), 'c_HOL_Oabs__class_Oabs'( Z, X ) ) )
% 1.24/1.60 , ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.24/1.60 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Opordered__ring__abs'( X ) ), =(
% 1.24/1.60 'c_HOL_Oabs__class_Oabs'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.24/1.60 Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.24/1.60 'c_HOL_Oabs__class_Oabs'( Y, X ) ), 'c_HOL_Oabs__class_Oabs'( Z, X ) ) )
% 1.24/1.60 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.24/1.60 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.24/1.60 'c_HOL_Oabs__class_Oabs'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.24/1.60 Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.24/1.60 'c_HOL_Oabs__class_Oabs'( Y, X ) ), 'c_HOL_Oabs__class_Oabs'( Z, X ) ) )
% 1.24/1.60 ],
% 1.24/1.60 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), X ), T ), X ), ~(
% 1.24/1.60 'c_OrderedGroup_Omonoid__mult'( X, Y, Z ) ) ],
% 1.24/1.60 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.24/1.60 , 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.24/1.60 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~(
% 1.24/1.60 'c_lessequals'( Y, T, X ) ) ],
% 1.24/1.60 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.24/1.60 , 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.24/1.60 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP(
% 1.24/1.60 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ],
% 1.24/1.60 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.24/1.60 , 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.24/1.60 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~(
% 1.24/1.60 'c_lessequals'( Z, T, X ) ) ],
% 1.24/1.60 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.24/1.60 , 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.24/1.60 'c_HOL_Oplus__class_Oplus'( X ), T ), Y ), hAPP( hAPP(
% 1.24/1.60 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ) ) ],
% 1.24/1.60 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 1.24/1.60 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.24/1.60 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~(
% 1.24/1.60 'c_lessequals'( Y, T, X ) ) ],
% 1.24/1.60 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 1.24/1.60 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.24/1.60 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~(
% 1.24/1.60 'c_lessequals'( Z, T, X ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.24/1.60 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.24/1.60 'c_Power_Opower__class_Opower'( X ), T ), Z ), X ), ~( 'c_lessequals'(
% 1.24/1.60 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Oabs__class_Oabs'( T, X ), X ) )
% 1.24/1.60 , ~( 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ) ],
% 1.24/1.60 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.24/1.60 'c_HOL_Oabs__class_Oabs'( Y, X ), Y ), ~( 'c_lessequals'(
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.24/1.60 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.24/1.60 ), =( Z, Y ) ],
% 1.24/1.60 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 1.24/1.60 'c_HOL_Oord__class_Oless'( Z, Y, X ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.24/1.60 ) ],
% 1.24/1.60 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 1.24/1.60 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.24/1.60 ) ],
% 1.24/1.60 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.24/1.60 , X ), =( Z, Y ), 'c_HOL_Oord__class_Oless'( Z, Y, X ) ],
% 1.24/1.60 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Y, Z
% 1.24/1.60 , X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ],
% 1.24/1.60 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 1.24/1.60 Y, X, 'tc_nat' ), =( Y, X ) ],
% 1.24/1.60 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), 'c_HOL_Oord__class_Oless'( Y, Z,
% 1.24/1.60 'tc_nat' ), =( Z, Y ), 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ],
% 1.24/1.60 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 1.24/1.60 Y, X, 'tc_nat' ), =( Y, X ) ],
% 1.24/1.60 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Z, Y
% 1.24/1.60 , X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.24/1.60 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.24/1.60 , X ), 'c_HOL_Oord__class_Oless'( Z, Y, X ), =( Z, Y ) ],
% 1.24/1.60 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Z, Y
% 1.24/1.60 , X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.24/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.24/1.60 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), X ), ~(
% 1.24/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.24/1.60 [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), ~( =(
% 1.24/1.60 'c_HOL_Ouminus__class_Ouminus'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Z
% 1.24/1.60 , X ) ) ), =( Y, Z ) ],
% 1.24/1.60 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 1.24/1.60 'c_HOL_Ouminus__class_Ouminus'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Z
% 1.24/1.60 , X ) ) ), =( Y, Z ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Oinverse__class_Odivide'(
% 1.24/1.60 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), Y, X ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'(
% 1.24/1.60 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), Y, X ), Z ) ]
% 1.24/1.60 ,
% 1.24/1.60 [ ~( 'class_OrderedGroup_Olordered__ab__group__add__abs'( X ) ),
% 1.24/1.60 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ),
% 1.24/1.60 'c_HOL_Oabs__class_Oabs'( T, X ) ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.24/1.60 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), Z, X ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.24/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( Y,
% 1.24/1.60 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.24/1.60 X ), Y ), Z ), Z, X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.24/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.24/1.60 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.24/1.60 X ), Y ), Z ), Z, X ), Y ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.24/1.60 ,
% 1.24/1.60 [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), X ), ~(
% 1.24/1.60 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.24/1.60 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ),
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.24/1.60 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ),
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.24/1.60 [ =( hAPP( 'c_NthRoot_Oroot'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.24/1.60 'tc_nat' ), X ), Y ) ), Z ), hAPP( 'c_NthRoot_Oroot'( X ), hAPP(
% 1.24/1.60 'c_NthRoot_Oroot'( Y ), Z ) ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ), ~(
% 1.24/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.24/1.60 'tc_nat' ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.24/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.24/1.60 'class_Int_Onumber'( X ) ), ~( =( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.24/1.60 Z, X ) ) ), =( 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.24/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.24/1.60 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.24/1.60 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =(
% 1.24/1.60 'c_HOL_Oinverse__class_Odivide'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.24/1.60 , 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ],
% 1.24/1.60 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =( Y,
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'(
% 1.24/1.60 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.24/1.60 ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.24/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.24/1.60 'c_HOL_Oone__class_Oone'( X ), X ), ~( 'c_lessequals'( Y,
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), T ), hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), U ) ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), Z ), hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ) ) ],
% 1.24/1.60 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 1.24/1.60 'c_HOL_Ouminus__class_Ouminus'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.24/1.60 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.24/1.60 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( X ) ) ), hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( X ) ) ), 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.24/1.60 ],
% 1.24/1.60 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.24/1.60 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.24/1.60 ), Y ), Z ), Z, X ), Y ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.24/1.60 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.24/1.60 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.24/1.60 ), Y ), Z ), Y, X ), Z ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.24/1.60 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.24/1.60 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.24/1.60 ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.24/1.60 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.24/1.60 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.24/1.60 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.24/1.60 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.24/1.60 ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.24/1.60 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.24/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.24/1.60 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.24/1.60 Z, Y, X ) ) ],
% 1.24/1.60 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.24/1.60 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.24/1.60 'c_HOL_Ouminus__class_Ouminus'( Z, X ), 'c_HOL_Ouminus__class_Ouminus'( Y
% 1.24/1.60 , X ), X ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.24/1.60 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X )
% 1.24/1.60 , 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X
% 1.24/1.60 ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X
% 1.24/1.60 ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.24/1.60 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.24/1.60 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.24/1.60 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T
% 1.24/1.60 ), X ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.24/1.60 ), Y ), T ), Z, X ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.24/1.60 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~(
% 1.24/1.60 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.24/1.60 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ),
% 1.24/1.60 Y, X ) ), ~( 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.24/1.60 X ), T ), Z ), X ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 1.24/1.60 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.24/1.60 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.24/1.60 X ), X ) ) ],
% 1.24/1.60 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( 'c_Power_Opower_Opower'( Y, Z, T ),
% 1.24/1.60 U ), W ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( Y, Z, T ), U ), V0 ) ) )
% 1.24/1.60 , ~( 'c_HOL_Oord__class_Oless'( W, V0, 'tc_nat' ) ), ~( hBOOL( hAPP( hAPP(
% 1.24/1.60 X, Y ), U ) ) ), ~( 'c_Ring__and__Field_Oordered__semidom'( V1, V2, Y, Z
% 1.24/1.60 , V3, X, T ) ) ],
% 1.24/1.60 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~( hBOOL( hAPP( hAPP( Z,
% 1.24/1.60 hAPP( hAPP( 'c_Power_Opower_Opower'( T, U, W ), V0 ), X ) ), hAPP( hAPP(
% 1.24/1.60 'c_Power_Opower_Opower'( T, U, W ), V0 ), Y ) ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.24/1.60 Z, T ), V0 ) ) ), ~( 'c_Ring__and__Field_Oordered__semidom'( V1, V2, T, U
% 1.24/1.60 , V3, Z, W ) ) ],
% 1.24/1.60 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( 'c_Power_Opower_Opower'( Y, Z, T ),
% 1.24/1.60 U ), W ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( Y, Z, T ), U ), V0 ) ) )
% 1.24/1.60 , ~( hBOOL( hAPP( hAPP( X, Y ), U ) ) ), ~( 'c_HOL_Oord__class_Oless'( W
% 1.24/1.60 , V0, 'tc_nat' ) ), ~( 'c_Ring__and__Field_Oordered__semidom'( V1, V2, Y
% 1.24/1.60 , Z, V3, X, T ) ) ],
% 1.24/1.60 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~( hBOOL( hAPP( hAPP( Z,
% 1.24/1.60 hAPP( hAPP( 'c_Power_Opower_Opower'( T, U, W ), V0 ), X ) ), hAPP( hAPP(
% 1.24/1.60 'c_Power_Opower_Opower'( T, U, W ), V0 ), Y ) ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.24/1.60 Z, T ), V0 ) ) ), ~( 'c_Ring__and__Field_Oordered__semidom'( V1, V2, T, U
% 1.24/1.60 , V3, Z, W ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =(
% 1.24/1.60 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.24/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X )
% 1.24/1.60 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X )
% 1.24/1.60 ) ],
% 1.24/1.60 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), hBOOL( hAPP( hAPP( X, Z ), Y ) ),
% 1.24/1.60 =( Z, Y ), ~( 'c_Ring__and__Field_Oordered__idom'( T, U, W, V0, V1, X, V2
% 1.24/1.60 , V3, V4, V5, V6 ) ) ],
% 1.24/1.60 [ =( hAPP( hAPP( X, hAPP( Y, Z ) ), hAPP( Y, Z ) ), hAPP( hAPP( X, Z ),
% 1.24/1.60 Z ) ), ~( 'c_Ring__and__Field_Oordered__idom'( T, U, W, V0, V1, V2, Y, V3
% 1.24/1.60 , X, V4, V5 ) ) ],
% 1.24/1.60 [ =( hAPP( hAPP( X, hAPP( Y, Z ) ), hAPP( T, Z ) ), Z ), ~(
% 1.24/1.60 'c_Ring__and__Field_Oordered__idom'( U, W, V0, V1, V2, V3, T, V4, X, Y,
% 1.24/1.60 V5 ) ) ],
% 1.24/1.60 [ =( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), hAPP( hAPP( Y, hAPP( X, Z ) ),
% 1.24/1.60 hAPP( X, T ) ) ), ~( 'c_Ring__and__Field_Oordered__idom'( U, W, V0, V1,
% 1.24/1.60 V2, V3, V4, V5, Y, X, V6 ) ) ],
% 1.24/1.60 [ =( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), hAPP( hAPP( Y, hAPP( X, Z ) ),
% 1.24/1.60 hAPP( X, T ) ) ), ~( 'c_Ring__and__Field_Oordered__idom'( U, W, V0, V1,
% 1.24/1.60 V2, V3, X, V4, Y, V5, V6 ) ) ],
% 1.24/1.60 [ =( hAPP( X, hAPP( X, Y ) ), hAPP( X, Y ) ), ~(
% 1.24/1.60 'c_Ring__and__Field_Oordered__idom'( Z, T, U, W, V0, V1, V2, V3, V4, X,
% 1.24/1.60 V5 ) ) ],
% 1.24/1.60 [ ~( 'c_Ring__and__Field_Oordered__idom'( X, Y, Z, T, U, W, V0, V1, V2,
% 1.24/1.60 V3, V4 ) ), =( hAPP( V3, Z ), Z ) ],
% 1.24/1.60 [ ~( 'c_Ring__and__Field_Oordered__idom'( X, Y, hAPP( Z, T ), U, W, V0,
% 1.24/1.60 V1, V2, V3, Z, V4 ) ), =( T, hAPP( Z, T ) ) ],
% 1.24/1.60 [ =( hAPP( X, Y ), hAPP( hAPP( Z, Y ), hAPP( T, Y ) ) ), ~(
% 1.24/1.60 'c_Ring__and__Field_Oordered__idom'( U, W, V0, V1, V2, V3, X, V4, Z, T,
% 1.24/1.60 V5 ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.24/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.24/1.60 'class_Int_Onumber'( X ) ), =( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.24/1.60 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.24/1.60 X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.24/1.60 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 1.24/1.60 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.24/1.60 [ ~( hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( 'c_Power_Opower_Opower'( Z,
% 1.24/1.60 T, U ), hAPP( W, Y ) ), V0 ) ) ) ), ~(
% 1.24/1.60 'c_Ring__and__Field_Oordered__idom'( V1, V2, Y, V3, V4, X, W, Z, T, V5, U
% 1.24/1.60 ) ), =( V0, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.24/1.60 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), 'c_Suc'(
% 1.24/1.60 Y ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP(
% 1.24/1.60 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.24/1.60 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_Suc'( X )
% 1.24/1.60 ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), hAPP(
% 1.24/1.60 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.24/1.60 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.24/1.60 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), T ), hAPP( hAPP(
% 1.24/1.60 'c_Power_Opower__class_Opower'( X ), Z ), T ), X ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.24/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.24/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.24/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.24/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.24/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.24/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), X ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.24/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~(
% 1.24/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.24/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.24/1.60 ,
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.24/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~(
% 1.24/1.60 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.24/1.60 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.24/1.60 ,
% 1.24/1.60 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.24/1.60 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), 'tc_nat'
% 1.24/1.60 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.24/1.60 , Y, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.24/1.60 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.24/1.60 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.24/1.60 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.24/1.60 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.24/1.60 ,
% 1.24/1.60 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.24/1.60 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.24/1.60 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.24/1.60 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.24/1.60 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.24/1.60 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.24/1.60 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.24/1.60 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.24/1.60 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.24/1.60 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.24/1.60 ,
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), ~( =(
% 1.24/1.60 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 1.24/1.60 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), Z ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), Z ), hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ],
% 1.24/1.60 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.24/1.60 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.24/1.60 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.24/1.60 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.24/1.60 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.24/1.60 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.24/1.60 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.24/1.60 ) ) ],
% 1.24/1.60 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.24/1.60 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.24/1.60 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.24/1.60 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.24/1.60 ) ) ],
% 1.24/1.60 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.24/1.60 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.24/1.60 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.24/1.60 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.24/1.60 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.24/1.60 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.24/1.60 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), hAPP(
% 1.24/1.60 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.24/1.60 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ) ],
% 1.24/1.60 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.24/1.60 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.24/1.60 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.24/1.60 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.24/1.60 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.24/1.60 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.24/1.60 ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Ocomm__semiring'( X ) ), =( hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.24/1.60 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.24/1.60 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.24/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.24/1.60 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ), ~( 'c_lessequals'( U, Z
% 1.24/1.60 , X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), U
% 1.24/1.60 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_lessequals'(
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.24/1.60 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.24/1.60 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' )
% 1.24/1.60 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y
% 1.24/1.60 , 'tc_nat' ) ) ],
% 1.24/1.60 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.24/1.60 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' )
% 1.24/1.60 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X
% 1.24/1.60 , 'tc_nat' ) ) ],
% 1.24/1.60 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.24/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.24/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.24/1.60 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ) ) ],
% 1.24/1.60 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.24/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.24/1.60 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ), ~(
% 1.24/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.24/1.60 ,
% 1.24/1.60 [ ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), =( Y,
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( hBOOL( hAPP( Z,
% 1.24/1.60 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.24/1.60 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), T
% 1.24/1.60 ) ), X ), Y, 'tc_nat' ) ) ) ), hBOOL( hAPP( Z, X ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.24/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.24/1.60 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.24/1.60 ), X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.24/1.60 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.24/1.60 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.24/1.60 ), X ), 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ouminus__class_Ouminus'(
% 1.24/1.60 Y, X ), Z, X ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.24/1.60 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.24/1.60 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.24/1.60 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.24/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.24/1.60 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.24/1.60 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.24/1.60 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Z
% 1.24/1.60 , X ) ), T ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'(
% 1.24/1.60 'c_HOL_Oinverse__class_Odivide'( Y, T, X ),
% 1.24/1.60 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.24/1.60 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.24/1.60 X ), ~( 'c_lessequals'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.24/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.24/1.60 ,
% 1.24/1.60 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oone__class_Oone'(
% 1.24/1.60 'tc_nat' ), 'tc_nat' ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.24/1.60 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.24/1.60 X ), Y ), Z ), X ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.24/1.60 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.24/1.60 X ), Z ), Y ), X ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.24/1.60 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.24/1.60 X ), Y ), Z ), X ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.24/1.60 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.24/1.60 X ), Z ), Y ), X ) ) ],
% 1.24/1.60 [ =( hAPP( hAPP( X, Y ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Z ),
% 1.24/1.60 ~( 'c_Groebner__Basis_Ogb__semiring'( T, U, X, W, Z, V0 ) ) ],
% 1.24/1.60 [ =( 'c_Divides_Odiv__class_Odiv'( X, 'c_Suc'(
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ), X ) ],
% 1.24/1.60 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ), ~( =(
% 1.24/1.60 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y ) ), =( Y,
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.24/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.24/1.60 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.24/1.60 'tc_nat' ) ), X ) ],
% 1.24/1.60 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.24/1.60 hAPP( hAPP( 'c_Power_Opower__class_Opower'( 'tc_nat' ), X ),
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ],
% 1.24/1.60 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ), 'c_Suc'( U ) )
% 1.24/1.60 , hAPP( hAPP( Y, hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ), U )
% 1.24/1.60 ), T ) ), ~( 'c_OrderedGroup_Omonoid__mult'( X, Y, Z ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 1.24/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.24/1.60 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.24/1.60 X ), 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.24/1.60 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), X
% 1.24/1.60 ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.24/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.24/1.60 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.24/1.60 X ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ) ) ), =( hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.24/1.60 , X ) ), T ), Z ), =( T, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.24/1.60 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.24/1.60 'c_HOL_Oone__class_Oone'( X ), Y, X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.24/1.60 X ) ) ],
% 1.24/1.60 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.24/1.60 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.24/1.60 , Y ), Z ), Y, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.24/1.60 'c_Divides_Odiv__class_Odiv'( Z, Y, X ) ), 'c_HOL_Oone__class_Oone'( X )
% 1.24/1.60 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.24/1.60 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.24/1.60 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.24/1.60 , Y ), Z ), Z, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.24/1.60 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ), 'c_HOL_Oone__class_Oone'( X )
% 1.24/1.60 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.24/1.60 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oone__class_Oone'( X ), X ),
% 1.24/1.60 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.24/1.60 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.24/1.60 X, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), 'c_Suc'(
% 1.24/1.60 'c_Divides_Odiv__class_Odiv'( Y, X, 'tc_nat' ) ) ), 'tc_nat' ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.24/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.24/1.60 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 1.24/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ),
% 1.24/1.60 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.24/1.60 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.24/1.60 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.24/1.60 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.24/1.60 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.24/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.24/1.60 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.24/1.60 'c_HOL_Oone__class_Oone'( X ) ), X ) ],
% 1.24/1.60 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.24/1.60 ), Z ), 'c_HOL_Ouminus__class_Ouminus'( hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ) ) ],
% 1.24/1.60 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.24/1.60 ), Z ), 'c_HOL_Ouminus__class_Ouminus'( hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ) ) ],
% 1.24/1.60 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ouminus__class_Ouminus'( Z
% 1.24/1.60 , X ) ), 'c_HOL_Ouminus__class_Ouminus'( hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ) ) ],
% 1.24/1.60 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ouminus__class_Ouminus'( Z
% 1.24/1.60 , X ) ), 'c_HOL_Ouminus__class_Ouminus'( hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), =( hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.24/1.60 ), 'c_HOL_Ouminus__class_Ouminus'( Y, X ) ), hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.24/1.60 ), 'c_HOL_Ouminus__class_Ouminus'( Z, X ) ), hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X
% 1.24/1.60 ) ), Y ), 'c_HOL_Oone__class_Oone'( X ) ), =( Y,
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =( hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X
% 1.24/1.60 ) ), Y ), 'c_HOL_Oone__class_Oone'( X ) ), =( Y,
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =( hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Oinverse__class_Oinverse'(
% 1.24/1.60 Y, X ) ), 'c_HOL_Oone__class_Oone'( X ) ), =( Y,
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ), 'c_lessequals'(
% 1.24/1.60 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X ), ~( 'c_lessequals'(
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( Z, U, X ) )
% 1.24/1.60 , ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ), 'c_lessequals'(
% 1.24/1.60 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X ), ~( 'c_lessequals'(
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Z, U, X ) )
% 1.24/1.60 , ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.24/1.60 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.24/1.60 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.24/1.60 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X
% 1.24/1.60 ), 'c_Divides_Odiv__class_Odiv'( Z, T, X ) ), =( Y,
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.24/1.60 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.24/1.60 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.24/1.60 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X
% 1.24/1.60 ), 'c_Divides_Odiv__class_Odiv'( Y, T, X ) ), =( Z,
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.24/1.60 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ), 'tc_nat' ),
% 1.24/1.60 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ), =( X,
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.24/1.60 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.24/1.60 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), Z, 'tc_nat' ), hAPP(
% 1.24/1.60 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.24/1.60 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( X,
% 1.24/1.60 Z, 'tc_nat' ) ), 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ) ),
% 1.24/1.60 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.24/1.60 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X, Z, 'tc_nat' ) ),
% 1.24/1.60 'c_Divides_Odiv__class_Omod'( Y, Z, 'tc_nat' ) ), Z, 'tc_nat' ) ) ) ]
% 1.24/1.60 ,
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.24/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.24/1.60 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.24/1.60 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =(
% 1.24/1.60 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.24/1.60 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.24/1.60 X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), Z ), Z, X ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.24/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.24/1.60 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.24/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.24/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), Y
% 1.24/1.60 , X ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.24/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.24/1.60 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 1.24/1.60 X ) ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.24/1.60 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ]
% 1.24/1.60 ,
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.24/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.24/1.60 , X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.24/1.60 X ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), Y, X ) ), ~(
% 1.24/1.60 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.24/1.60 ), T ), Z ), X ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.24/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.24/1.60 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 1.24/1.60 X ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), Y, X ) ), ~(
% 1.24/1.60 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.24/1.60 ), T ), Z ), X ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.24/1.60 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.24/1.60 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.24/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.24/1.60 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( T, Z, X )
% 1.24/1.60 , X ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.24/1.60 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.24/1.60 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.24/1.60 X ) ), 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.24/1.60 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ]
% 1.24/1.60 ,
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.24/1.60 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.24/1.60 , X ), ~( 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.24/1.60 X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ), ~(
% 1.24/1.60 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.24/1.60 , Y ), T ), Z, X ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.24/1.60 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.24/1.60 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.24/1.60 X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ), ~(
% 1.24/1.60 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.24/1.60 , Y ), T ), Z, X ) ) ],
% 1.24/1.60 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.24/1.60 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ),
% 1.24/1.60 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 1.24/1.60 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.24/1.60 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.24/1.60 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ), ~(
% 1.24/1.60 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 1.24/1.60 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.24/1.60 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ),
% 1.24/1.60 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~(
% 1.24/1.60 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.24/1.60 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ) ) ],
% 1.24/1.60 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ),
% 1.24/1.60 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~(
% 1.24/1.60 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.24/1.60 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ],
% 1.24/1.60 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.24/1.60 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ), ~(
% 1.24/1.60 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 1.24/1.60 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.24/1.60 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.24/1.60 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ),
% 1.24/1.60 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 1.24/1.60 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.24/1.60 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ), ~(
% 1.24/1.60 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 1.24/1.60 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.24/1.60 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ) ) ],
% 1.24/1.60 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ), ~(
% 1.24/1.60 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 1.24/1.60 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.24/1.60 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ],
% 1.24/1.60 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.24/1.60 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ) ),
% 1.24/1.60 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~(
% 1.24/1.60 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.24/1.60 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.24/1.60 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ) ), ~(
% 1.24/1.60 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ),
% 1.24/1.60 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.24/1.60 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ),
% 1.24/1.60 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 1.24/1.60 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.24/1.60 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ) ],
% 1.24/1.60 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ), ~(
% 1.24/1.60 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ),
% 1.24/1.60 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.24/1.60 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ],
% 1.24/1.60 [ =( 'c_Divides_Odiv__class_Odiv'( 'c_Suc'( X ), 'c_Suc'( 'c_Suc'(
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ), 'c_Suc'(
% 1.24/1.60 'c_Divides_Odiv__class_Odiv'( X, 'c_Suc'( 'c_Suc'(
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ) ) ),
% 1.24/1.60 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.24/1.60 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.24/1.60 , Y ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP(
% 1.24/1.60 hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 1.24/1.60 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.24/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.24/1.60 ,
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.24/1.60 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.24/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.24/1.60 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.24/1.60 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.24/1.60 ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.24/1.60 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.24/1.60 ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.24/1.60 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.24/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.24/1.60 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.24/1.60 , Z ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X )
% 1.24/1.60 ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.24/1.60 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.24/1.60 ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ) ],
% 1.24/1.60 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 1.24/1.60 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ),
% 1.24/1.60 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ouminus__class_Ouminus'(
% 1.24/1.60 'c_Divides_Odiv__class_Omod'( Y, Z, X ), X ), Z, X ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.24/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.24/1.60 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 1.24/1.60 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.24/1.60 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.24/1.60 ,
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.24/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.24/1.60 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 1.24/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.24/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.24/1.60 ,
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.24/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.24/1.60 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 1.24/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.24/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.24/1.60 ,
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.24/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.24/1.60 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 1.24/1.60 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.24/1.60 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.24/1.60 ,
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.24/1.60 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), ~(
% 1.24/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.24/1.60 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.24/1.60 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X )
% 1.24/1.60 ), 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ), hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.24/1.60 X ), Y ), Z ) ), 'c_HOL_Oinverse__class_Oinverse'( Y, X ) ) ),
% 1.24/1.60 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ) ), =( Z,
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.24/1.60 ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =( hAPP( hAPP(
% 1.24/1.60 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X )
% 1.24/1.60 ), 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ), hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X
% 1.24/1.60 ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) ),
% 1.24/1.60 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ) ), =( Z,
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.24/1.60 ) ],
% 1.24/1.60 [ ~( =( 'c_Divides_Odiv__class_Omod'( X, 'c_Suc'( 'c_Suc'(
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ), 'c_Suc'(
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), ~(
% 1.24/1.60 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.24/1.60 [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Suc'( 'c_Suc'(
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ), 'c_Suc'(
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ),
% 1.24/1.60 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.24/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.24/1.60 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.24/1.60 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.24/1.60 'c_HOL_Oone__class_Oone'( X ) ), X ), Z, X ), ~(
% 1.24/1.60 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =( hAPP(
% 1.24/1.60 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 1.24/1.60 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =( hAPP(
% 1.24/1.60 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.24/1.60 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.24/1.60 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X,
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.24/1.60 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_Suc'( 'c_Suc'(
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), X ), 'tc_nat' ) ],
% 1.24/1.60 [ =( 'c_Int_Onumber__class_Onumber__of'( X, 'tc_Int_Oint' ), X ) ],
% 1.24/1.60 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.24/1.60 'c_Divides_Odiv__class_Odiv'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.24/1.60 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.24/1.60 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.24/1.60 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( =(
% 1.24/1.60 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( 'c_lessequals'(
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Z,
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.24/1.60 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( =(
% 1.24/1.60 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( 'c_lessequals'(
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Y,
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.24/1.60 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.24/1.60 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.24/1.60 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), ~( =( hAPP(
% 1.24/1.60 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.24/1.60 ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.24/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.24/1.60 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.24/1.60 X ), 'c_HOL_Oinverse__class_Odivide'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.24/1.60 , X ) ) ), =( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.24/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.24/1.60 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.24/1.60 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =(
% 1.24/1.60 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.24/1.60 'c_HOL_Oinverse__class_Odivide'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.24/1.60 ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.24/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.24/1.60 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.24/1.60 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( 'c_HOL_Ozero__class_Ozero'(
% 1.24/1.60 X ), 'c_HOL_Oinverse__class_Odivide'( Z,
% 1.24/1.60 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.24/1.60 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.24/1.60 'c_Power_Opower__class_Opower'( X ), Y ), T ) ), hAPP( hAPP(
% 1.24/1.60 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.24/1.60 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ) ) ],
% 1.24/1.60 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.24/1.60 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.24/1.60 ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.24/1.60 ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oabs__if'( X ) ), =(
% 1.24/1.60 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.24/1.60 ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.24/1.60 ) ],
% 1.24/1.60 [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 1.24/1.60 'class_OrderedGroup_Olordered__ab__group__add__abs'( X ) ), =(
% 1.24/1.60 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.24/1.60 ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.24/1.60 ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( =( hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ), hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ) ), =( Y,
% 1.24/1.60 'c_HOL_Ouminus__class_Ouminus'( Z, X ) ), =( Y, Z ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.24/1.60 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.24/1.60 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.24/1.60 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.24/1.60 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ),
% 1.24/1.60 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.24/1.60 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ),
% 1.24/1.60 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.24/1.60 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.24/1.60 [ =( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ),
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X
% 1.24/1.60 , Y, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'( Y
% 1.24/1.60 , 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'(
% 1.24/1.60 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), Z, X ) ), ~(
% 1.24/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ]
% 1.24/1.60 ,
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.24/1.60 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Y
% 1.24/1.60 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ), ~(
% 1.24/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 1.24/1.60 ,
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.24/1.60 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.24/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.24/1.60 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ),
% 1.24/1.60 Z, X ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.24/1.60 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), T, X ), ~(
% 1.24/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.24/1.60 'c_lessequals'( Y, 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ]
% 1.24/1.60 ,
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.24/1.60 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~(
% 1.24/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.24/1.60 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z
% 1.24/1.60 ), X ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.24/1.60 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ), ~(
% 1.24/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.24/1.60 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), Z, X ) ) ]
% 1.24/1.60 ,
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.24/1.60 X ) ), ~( =( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) )
% 1.24/1.60 , =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.24/1.60 [ ~( =( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y )
% 1.24/1.60 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.24/1.60 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), X
% 1.24/1.60 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.24/1.60 [ ~( 'class_Nat_Osemiring__char__0'( X ) ), ~( =(
% 1.24/1.60 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 1.24/1.60 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ) ) ), =( Y, Z ) ],
% 1.24/1.60 [ ~( =( 'c_Nat_Osemiring__1__class_Oof__nat'( X, 'tc_Int_Oint' ),
% 1.24/1.60 'c_Nat_Osemiring__1__class_Oof__nat'( Y, 'tc_Int_Oint' ) ) ), =( X, Y ) ]
% 1.24/1.60 ,
% 1.24/1.60 [ ~( =( 'c_Nat_Osemiring__1__class_Oof__nat'( X, 'tc_Int_Oint' ),
% 1.24/1.60 'c_Nat_Osemiring__1__class_Oof__nat'( Y, 'tc_Int_Oint' ) ) ), =( X, Y ) ]
% 1.24/1.60 ,
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.24/1.60 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.24/1.60 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.24/1.60 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.24/1.60 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.24/1.60 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.24/1.60 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ), ~(
% 1.24/1.60 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.24/1.60 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.24/1.60 [ ~( 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'( X )
% 1.24/1.60 , 'c_Power_Opower_Opower'( 'c_HOL_Oone__class_Oone'( X ),
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( X ), X ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.24/1.60 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.24/1.60 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ), X ), ~(
% 1.24/1.60 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ),
% 1.24/1.60 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.24/1.60 , 'tc_nat' ), 'tc_nat' ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.24/1.60 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.24/1.60 , 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'(
% 1.24/1.60 X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.24/1.60 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ), X ) ) ],
% 1.24/1.60 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.24/1.60 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X, 'c_Suc'(
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.24/1.60 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.24/1.60 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.24/1.60 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oone__class_Oone'( X ),
% 1.24/1.60 X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.24/1.60 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.24/1.60 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.24/1.60 X ), Y ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z )
% 1.24/1.60 ), X ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.24/1.60 'c_HOL_Oone__class_Oone'( X ), Y, X ), X ), ~( 'c_lessequals'(
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.24/1.60 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.24/1.60 'c_HOL_Oone__class_Oone'( X ), Y, X ), X ) ) ],
% 1.24/1.60 [ =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), hAPP( hAPP(
% 1.24/1.60 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_HOL_Oone__class_Oone'(
% 1.24/1.60 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.24/1.60 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.24/1.60 ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ),
% 1.24/1.60 ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.24/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.24/1.61 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.24/1.61 ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.24/1.61 ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.24/1.61 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.24/1.61 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 1.24/1.61 'tc_nat' ) ) ],
% 1.24/1.61 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.24/1.61 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z,
% 1.24/1.61 'tc_nat' ) ) ],
% 1.24/1.61 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.24/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.24/1.61 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ) ],
% 1.24/1.61 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.24/1.61 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 1.24/1.61 'tc_nat' ) ) ],
% 1.24/1.61 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.24/1.61 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z,
% 1.24/1.61 'tc_nat' ) ) ],
% 1.24/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.24/1.61 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 1.24/1.61 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ), ~(
% 1.24/1.61 'c_lessequals'( Y, Z, X ) ), ~( 'c_lessequals'(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ],
% 1.24/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.24/1.61 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 1.24/1.61 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ), ~(
% 1.24/1.61 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.24/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.24/1.61 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oabs__class_Oabs'(
% 1.24/1.61 Y, X ), X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.24/1.61 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), 'tc_nat' ) ],
% 1.24/1.61 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ) ), 'tc_nat' ) ],
% 1.24/1.61 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), 'tc_nat' ) ],
% 1.24/1.61 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_Suc'(
% 1.24/1.61 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ),
% 1.24/1.61 'c_Divides_Odiv__class_Odiv'( X, 'c_Suc'( 'c_Suc'(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ) ), X ), ~(
% 1.24/1.61 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.24/1.61 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 1.24/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.24/1.61 ), Z ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.24/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.24/1.61 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 1.24/1.61 'c_HOL_Ouminus__class_Ouminus'( Z, X ), 'c_HOL_Ouminus__class_Ouminus'( Y
% 1.24/1.61 , X ), X ) ) ],
% 1.24/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.24/1.61 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.24/1.61 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), ~( 'c_lessequals'( Z, Y, X )
% 1.24/1.61 ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Olordered__ring'( X ) ), 'c_lessequals'(
% 1.24/1.61 'c_HOL_Oabs__class_Oabs'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.24/1.61 Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.24/1.61 'c_HOL_Oabs__class_Oabs'( Y, X ) ), 'c_HOL_Oabs__class_Oabs'( Z, X ) ), X
% 1.24/1.61 ) ],
% 1.24/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.24/1.61 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( Y
% 1.24/1.61 , X ), Z, X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.24/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.24/1.61 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X )
% 1.24/1.61 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.24/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.24/1.61 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.24/1.61 T, X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.24/1.61 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.24/1.61 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.24/1.61 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Oinverse'( Y
% 1.24/1.61 , X ), 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y
% 1.24/1.61 , X ) ) ],
% 1.24/1.61 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.24/1.61 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.24/1.61 ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ), T ), Z, X ),
% 1.24/1.61 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.24/1.61 ), Y ), T ), Z, X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.24/1.61 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.24/1.61 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.24/1.61 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.24/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.24/1.61 , 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ),
% 1.24/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.24/1.61 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.24/1.61 , X ) ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.24/1.61 'c_HOL_Oinverse__class_Odivide'( T, Z, X ),
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.24/1.61 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.24/1.61 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), 'c_HOL_Oone__class_Oone'(
% 1.24/1.61 'tc_nat' ) ), Y ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.24/1.61 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.24/1.61 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.24/1.61 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.24/1.61 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ), ~(
% 1.24/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.24/1.61 , Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.24/1.61 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.24/1.61 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.24/1.61 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.24/1.61 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ), ~(
% 1.24/1.61 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.24/1.61 ), T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.24/1.61 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.24/1.61 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.24/1.61 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.24/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.24/1.61 , 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ), ~(
% 1.24/1.61 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.24/1.61 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.24/1.61 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.24/1.61 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ), ~(
% 1.24/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ), ~( 'c_lessequals'( Y
% 1.24/1.61 , 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Z, T, X ) )
% 1.24/1.61 ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.24/1.61 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.24/1.61 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ), ~(
% 1.24/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ), ~( 'c_lessequals'(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( T, Z, X ) )
% 1.24/1.61 ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.24/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.24/1.61 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ), =( Z,
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.24/1.61 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ) ) ],
% 1.24/1.61 [ =( hAPP( hAPP( X, hAPP( hAPP( 'c_Power_Opower_Opower'( Y, X, Z ), T )
% 1.24/1.61 , U ) ), T ), hAPP( hAPP( X, T ), hAPP( hAPP( 'c_Power_Opower_Opower'( Y
% 1.24/1.61 , X, Z ), T ), U ) ) ), ~( 'c_OrderedGroup_Omonoid__mult'( Y, X, Z ) ) ]
% 1.24/1.61 ,
% 1.24/1.61 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.24/1.61 X ), 'c_HOL_Oone__class_Oone'( X ) ), 'c_HOL_Oone__class_Oone'( X ) ) ),
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( Y ), X ) ) ],
% 1.24/1.61 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.24/1.61 Y ) ],
% 1.24/1.61 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 1.24/1.61 Y ) ],
% 1.24/1.61 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =( hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 1.24/1.61 Y ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 1.24/1.61 Y ) ],
% 1.24/1.61 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.24/1.61 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), X ), X ) ],
% 1.24/1.61 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.24/1.61 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), X ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.24/1.61 Y ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 1.24/1.61 Y ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.24/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.24/1.61 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ), ~(
% 1.24/1.61 'c_HOL_Oord__class_Oless'( U, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), U, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 1.24/1.61 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) )
% 1.24/1.61 ],
% 1.24/1.61 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Suc'(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.24/1.61 'tc_nat' ) ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.24/1.61 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), hAPP(
% 1.24/1.61 hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), hAPP( hAPP(
% 1.24/1.61 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.24/1.61 'c_HOL_Oone__class_Oone'( X ), Y, X ) ), Z ) ) ],
% 1.24/1.61 [ =( 'c_Suc'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.24/1.61 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), X ) ) ],
% 1.24/1.61 [ =( 'c_Suc'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X
% 1.24/1.61 ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.24/1.61 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.24/1.61 ), X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.24/1.61 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ), =( Z,
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.24/1.61 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oabs__class_Oabs'(
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.24/1.61 'c_HOL_Ouminus__class_Ouminus'( 'c_Int_Onumber__class_Onumber__of'( Y, X
% 1.24/1.61 ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.24/1.61 ), X ) ) ],
% 1.24/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.24/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.24/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.24/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.24/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.24/1.61 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.24/1.61 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.24/1.61 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.24/1.61 'c_HOL_Oone__class_Oone'( X ) ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.24/1.61 Y, Z, X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.24/1.61 ) ), T ), 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ), Z, X ) ), =( Z,
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Oinverse__class_Odivide'( Z
% 1.24/1.61 , T, X ) ), 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), T, X ) ), =( T,
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.24/1.61 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) )
% 1.24/1.61 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.24/1.61 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.24/1.61 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ),
% 1.24/1.61 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ) ), =( Z,
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.24/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.24/1.61 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), ~(
% 1.24/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.24/1.61 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.24/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.24/1.61 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), ~(
% 1.24/1.61 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.24/1.61 'c_HOL_Oord__class_Oless'( T, Y, X ) ) ],
% 1.24/1.61 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.24/1.61 'c_Power_Opower__class_Opower'( 'tc_nat' ), X ), Y ), 'tc_nat' ), ~(
% 1.24/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.24/1.61 'tc_nat' ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ]
% 1.24/1.61 ,
% 1.24/1.61 [ ~( =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ), 'c_Suc'( U
% 1.24/1.61 ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), W ), 'c_Suc'( U ) )
% 1.24/1.61 ) ), ~( 'c_Ring__and__Field_Oordered__semidom'( V0, V1, X, Y, V2, V3, Z
% 1.24/1.61 ) ), =( T, W ), ~( hBOOL( hAPP( hAPP( V2, V1 ), W ) ) ), ~( hBOOL( hAPP(
% 1.24/1.61 hAPP( V2, V1 ), T ) ) ) ],
% 1.24/1.61 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), hAPP( hAPP( Y, U ), T ) )
% 1.24/1.61 , hAPP( hAPP( Y, hAPP( hAPP( X, Z ), U ) ), T ) ), ~(
% 1.24/1.61 'c_Groebner__Basis_Ogb__semiring'( X, Y, W, V0, V1, V2 ) ) ],
% 1.24/1.61 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), T ), hAPP( hAPP( Y, hAPP(
% 1.24/1.61 hAPP( X, Z ), U ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, Y, W
% 1.24/1.61 , V0, U, V1 ) ) ],
% 1.24/1.61 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), Y ) ), hAPP( hAPP( Z, hAPP(
% 1.24/1.61 hAPP( X, T ), U ) ), Y ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, Z, W
% 1.24/1.61 , V0, U, V1 ) ) ],
% 1.24/1.61 [ =( hAPP( hAPP( X, Y ), Y ), hAPP( hAPP( Z, hAPP( hAPP( X, T ), T ) ),
% 1.24/1.61 Y ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, Z, U, W, T, V0 ) ) ],
% 1.24/1.61 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.24/1.61 X, T, U, Y, W, V0 ) ) ],
% 1.24/1.61 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.24/1.61 X, T, U, Z, W, V0 ) ) ],
% 1.24/1.61 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 1.24/1.61 'c_Groebner__Basis_Ogb__semiring'( T, X, U, W, V0, V1 ) ) ],
% 1.24/1.61 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), U ), hAPP( hAPP( Y, hAPP(
% 1.24/1.61 hAPP( X, Z ), U ) ), hAPP( hAPP( X, T ), U ) ) ), ~(
% 1.24/1.61 'c_Groebner__Basis_Ogb__semiring'( Y, X, W, V0, V1, V2 ) ) ],
% 1.24/1.61 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.24/1.61 T, X, U, Y, W, V0 ) ) ],
% 1.24/1.61 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.24/1.61 T, X, U, Z, W, V0 ) ) ],
% 1.24/1.61 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.24/1.61 T, X, U, W, Y, V0 ) ) ],
% 1.24/1.61 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.24/1.61 T, X, U, W, Z, V0 ) ) ],
% 1.24/1.61 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 1.24/1.61 , hAPP( hAPP( X, hAPP( hAPP( X, Y ), T ) ), hAPP( hAPP( X, Z ), U ) ) ),
% 1.24/1.61 ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, V0, V1, V2, V3 ) ) ],
% 1.24/1.61 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 1.24/1.61 , hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), hAPP( hAPP( X, T ), U ) ) ) ),
% 1.24/1.61 ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, V0, V1, V2, V3 ) ) ],
% 1.24/1.61 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 1.24/1.61 , hAPP( hAPP( X, T ), hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), U ) ) ),
% 1.24/1.61 ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, V0, V1, V2, V3 ) ) ],
% 1.24/1.61 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, hAPP(
% 1.24/1.61 hAPP( X, Y ), T ) ), Z ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, W
% 1.24/1.61 , V0, V1, V2 ) ) ],
% 1.24/1.61 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, Y ),
% 1.24/1.61 hAPP( hAPP( X, Z ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X,
% 1.24/1.61 W, V0, V1, V2 ) ) ],
% 1.24/1.61 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 1.24/1.61 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, W
% 1.24/1.61 , V0, V1, V2 ) ) ],
% 1.24/1.61 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, Z ),
% 1.24/1.61 hAPP( hAPP( X, Y ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X,
% 1.24/1.61 W, V0, V1, V2 ) ) ],
% 1.24/1.61 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 1.24/1.61 , hAPP( hAPP( X, hAPP( hAPP( X, Y ), T ) ), hAPP( hAPP( X, Z ), U ) ) ),
% 1.24/1.61 ~( 'c_Groebner__Basis_Ogb__semiring'( X, W, V0, V1, V2, V3 ) ) ],
% 1.24/1.61 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, Y ),
% 1.24/1.61 hAPP( hAPP( X, Z ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U,
% 1.24/1.61 W, V0, V1, V2 ) ) ],
% 1.24/1.61 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, Z ),
% 1.24/1.61 hAPP( hAPP( X, Y ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U,
% 1.24/1.61 W, V0, V1, V2 ) ) ],
% 1.24/1.61 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, hAPP(
% 1.24/1.61 hAPP( X, Y ), T ) ), Z ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U, W
% 1.24/1.61 , V0, V1, V2 ) ) ],
% 1.24/1.61 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 1.24/1.61 'c_Groebner__Basis_Ogb__semiring'( X, T, U, W, V0, V1 ) ) ],
% 1.24/1.61 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 1.24/1.61 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U, W
% 1.24/1.61 , V0, V1, V2 ) ) ],
% 1.24/1.61 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.24/1.61 X, T, U, Y, W, V0 ) ) ],
% 1.24/1.61 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 1.24/1.61 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U, W
% 1.24/1.61 , V0, V1, V2 ) ) ],
% 1.24/1.61 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 1.24/1.61 'c_Groebner__Basis_Ogb__semiring'( X, T, U, W, V0, V1 ) ) ],
% 1.24/1.61 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.24/1.61 T, X, U, Y, W, V0 ) ) ],
% 1.24/1.61 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.24/1.61 T, X, U, W, Y, V0 ) ) ],
% 1.24/1.61 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 1.24/1.61 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, W
% 1.24/1.61 , V0, V1, V2 ) ) ],
% 1.24/1.61 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 1.24/1.61 'c_Groebner__Basis_Ogb__semiring'( T, X, U, W, V0, V1 ) ) ],
% 1.24/1.61 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), U ) ), hAPP( hAPP( Z, hAPP(
% 1.24/1.61 hAPP( X, Y ), T ) ), hAPP( hAPP( X, Y ), U ) ) ), ~(
% 1.24/1.61 'c_Groebner__Basis_Ogb__semiring'( Z, X, W, V0, V1, V2 ) ) ],
% 1.24/1.61 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), U ), hAPP( hAPP( Y, hAPP(
% 1.24/1.61 hAPP( X, Z ), U ) ), hAPP( hAPP( X, T ), U ) ) ), ~(
% 1.24/1.61 'c_Groebner__Basis_Ogb__semiring'( W, Y, X, V0, V1, V2 ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.24/1.61 'c_HOL_Oabs__class_Oabs'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X
% 1.24/1.61 ), 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.24/1.61 ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z
% 1.24/1.61 , X ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.24/1.61 ,
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.24/1.61 ), X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.24/1.61 , X ) ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.24/1.61 ,
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.24/1.61 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), Z, X ), ~(
% 1.24/1.61 'c_lessequals'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.24/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.24/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.24/1.61 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), Y, X ), ~(
% 1.24/1.61 'c_lessequals'( Z, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.24/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.24/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.24/1.61 'c_HOL_Oinverse__class_Odivide'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y
% 1.24/1.61 ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.24/1.61 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.24/1.61 ,
% 1.24/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.24/1.61 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ), ~(
% 1.24/1.61 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ) ), ~(
% 1.24/1.61 'c_lessequals'( Y, Z, X ) ) ],
% 1.24/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.24/1.61 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ), ~(
% 1.24/1.61 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ) ), ~(
% 1.24/1.61 'c_lessequals'( Y, Z, X ) ) ],
% 1.24/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.24/1.61 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ),
% 1.24/1.61 'c_HOL_Oabs__class_Oabs'( Y, X ) ) ],
% 1.24/1.61 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.24/1.61 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ) ) ), =( X, Z
% 1.24/1.61 ) ],
% 1.24/1.61 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.24/1.61 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ), =( Y, Z
% 1.24/1.61 ) ],
% 1.24/1.61 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.24/1.61 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ), =( Y, Z
% 1.24/1.61 ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.24/1.61 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP(
% 1.24/1.61 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 1.24/1.61 [ ~( 'class_OrderedGroup_Ocancel__ab__semigroup__add'( X ) ), ~( =( hAPP(
% 1.24/1.61 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 1.24/1.61 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =( hAPP(
% 1.24/1.61 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 1.24/1.61 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =( hAPP(
% 1.24/1.61 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ), =( Y, T ) ],
% 1.24/1.61 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( 'c_Power_Opower_Opower'( Y, Z, T ),
% 1.24/1.61 U ), W ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( Y, Z, T ), V0 ), W ) ) )
% 1.24/1.61 , ~( hBOOL( hAPP( hAPP( X, V1 ), U ) ) ), ~( hBOOL( hAPP( hAPP( X, U ),
% 1.24/1.61 V0 ) ) ), ~( 'c_Ring__and__Field_Oordered__semidom'( V2, V1, Y, Z, X, V3
% 1.24/1.61 , T ) ) ],
% 1.24/1.61 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), hAPP( hAPP(
% 1.24/1.61 'c_Power_Opower_Opower'( T, Y, U ), Z ), W ) ) ), hAPP( hAPP(
% 1.24/1.61 'c_Power_Opower_Opower'( T, Y, U ), Z ), W ) ) ), ~( hBOOL( hAPP( hAPP( X
% 1.24/1.61 , Z ), T ) ) ), ~( hBOOL( hAPP( hAPP( X, V0 ), Z ) ) ), ~(
% 1.24/1.61 'c_Ring__and__Field_Oordered__semidom'( V1, V0, T, Y, V2, X, U ) ) ],
% 1.24/1.61 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), Z ) )
% 1.24/1.61 ), ~( hBOOL( hAPP( hAPP( X, hAPP( hAPP( 'c_Power_Opower_Opower'( W, V0,
% 1.24/1.61 V1 ), Y ), V2 ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( W, V0, V1 ), Z )
% 1.24/1.61 , V2 ) ) ) ), ~( 'c_Ring__and__Field_Oordered__semidom'( V3, U, W, V0, T
% 1.24/1.61 , X, V1 ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =( hAPP( hAPP(
% 1.24/1.61 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ouminus__class_Ouminus'(
% 1.24/1.61 'c_HOL_Oone__class_Oone'( X ), X ) ), Y ), 'c_HOL_Oone__class_Oone'( X )
% 1.24/1.61 ), ~( 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 1.24/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.24/1.61 , Y ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.24/1.61 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.24/1.61 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.24/1.61 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.24/1.61 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.24/1.61 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.24/1.61 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.24/1.61 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.24/1.61 'c_HOL_Oinverse__class_Oinverse'( hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X
% 1.24/1.61 ) ), 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 1.24/1.61 'c_HOL_Oinverse__class_Oinverse'( hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Oinverse'( Z, X
% 1.24/1.61 ) ), 'c_HOL_Oinverse__class_Oinverse'( Y, X ) ) ), =( Z,
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.24/1.61 ) ],
% 1.24/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.24/1.61 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ozero__class_Ozero'( X )
% 1.24/1.61 , X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.24/1.61 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.24/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~(
% 1.24/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.24/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.24/1.61 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.24/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 1.24/1.61 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oinverse__class_Oinverse'( Y, X
% 1.24/1.61 ), X ), Y ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.24/1.61 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.24/1.61 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =(
% 1.24/1.61 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.24/1.61 X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), Z ), Z, X ),
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 1.24/1.61 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Ozero__class_Ozero'(
% 1.24/1.61 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.24/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.24/1.61 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), =( Y,
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'(
% 1.24/1.61 Z, 'tc_nat' ) ) ],
% 1.24/1.61 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( 'c_Power_Opower_Opower'( Y, Z,
% 1.24/1.61 T ), U ), 'c_Suc'( W ) ) ) ), ~( hBOOL( hAPP( hAPP( X, Y ), U ) ) ), ~(
% 1.24/1.61 'c_Ring__and__Field_Oordered__semidom'( V0, V1, Y, Z, V2, X, T ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.24/1.61 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Z
% 1.24/1.61 , X ) ), T ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.24/1.61 'c_HOL_Oinverse__class_Odivide'( Y, T, X ),
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.24/1.61 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.24/1.61 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.24/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.24/1.61 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.24/1.61 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.24/1.61 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( 'c_Power_Opower_Opower'( Z, T,
% 1.24/1.61 U ), hAPP( W, V0 ) ), V1 ) ) ), =( V0, Y ), ~(
% 1.24/1.61 'c_Ring__and__Field_Oordered__idom'( V2, V3, Y, V4, V5, X, W, Z, T, V6, U
% 1.24/1.61 ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.24/1.61 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.24/1.61 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.24/1.61 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.24/1.61 ), X ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.24/1.61 ), T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ), ~(
% 1.24/1.61 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.24/1.61 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.24/1.61 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.24/1.61 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.24/1.61 ), X ) ), ~( 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.24/1.61 X ), Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ), ~(
% 1.24/1.61 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.24/1.61 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), Y, X ) ),
% 1.24/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.24/1.61 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 'c_HOL_Oord__class_Oless'( Z,
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y, hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.24/1.61 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'( Y,
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Z, hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ),
% 1.24/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.24/1.61 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'( Y,
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( T,
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), Z, X ) ) ],
% 1.24/1.61 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.24/1.61 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.24/1.61 Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X, 'tc_nat' ) ), ~(
% 1.24/1.61 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.24/1.61 ) ), Y, 'tc_nat' ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 1.24/1.61 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_Suc'( Y ), X ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.24/1.61 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ) ) ) ],
% 1.24/1.61 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( Y, 'c_Suc'(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.24/1.61 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( X,
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, 'c_Suc'(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ) ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 1.24/1.61 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Oone__class_Oone'( 'tc_nat'
% 1.24/1.61 ), X ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.24/1.61 [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.24/1.61 'tc_nat' ) ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ]
% 1.24/1.61 ,
% 1.24/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.24/1.61 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.24/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.24/1.61 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ],
% 1.24/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.24/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.24/1.61 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ), ~( 'c_lessequals'( Y,
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.24/1.61 X ) ), =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.24/1.61 X ), Y ), T ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z )
% 1.24/1.61 ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.24/1.61 X ) ), =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.24/1.61 X ), Y ), T ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z )
% 1.24/1.61 ) ) ],
% 1.24/1.61 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.24/1.61 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.24/1.61 [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 1.24/1.61 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.24/1.61 'tc_nat' ) ), 'tc_nat' ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =(
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.24/1.61 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.24/1.61 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ),
% 1.24/1.61 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), T ), ~(
% 1.24/1.61 'c_OrderedGroup_Omonoid__mult'( X, Y, Z ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.24/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.24/1.61 , 'c_HOL_Oabs__class_Oabs'( Y, X ) ), 'c_HOL_Oabs__class_Oabs'( Z, X ) )
% 1.24/1.61 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X ), ~(
% 1.24/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Z, X ), U, X ) ),
% 1.24/1.61 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Y, X ), T, X ) )
% 1.24/1.61 ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.24/1.61 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.24/1.61 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.24/1.61 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.24/1.61 ), X ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.24/1.61 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.24/1.61 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.24/1.61 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 'c_HOL_Oord__class_Oless'(
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.24/1.61 ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.24/1.61 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oinverse__class_Oinverse'( Y, X
% 1.24/1.61 ), X ), Y ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.24/1.61 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.24/1.61 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.24/1.61 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.24/1.61 ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ), ~(
% 1.24/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.24/1.61 , Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.24/1.61 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.24/1.61 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.24/1.61 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.24/1.61 ), X ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ), ~(
% 1.24/1.61 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.24/1.61 ), T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.24/1.61 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.24/1.61 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), 'c_Suc'( Z ) ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.24/1.61 ), Z ) ) ) ],
% 1.24/1.61 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.24/1.61 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), 'c_Suc'( Z ) ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.24/1.61 ), Z ) ), Y ) ) ],
% 1.24/1.61 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~(
% 1.24/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.24/1.61 =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ) ],
% 1.24/1.61 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.24/1.61 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.24/1.61 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =( hAPP(
% 1.24/1.61 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.24/1.61 , 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.24/1.61 ,
% 1.24/1.61 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.24/1.61 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ) ],
% 1.24/1.61 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.24/1.61 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.24/1.61 , Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X )
% 1.24/1.61 ), 'c_Divides_Odiv__class_Omod'( Z, T, X ) ), T, X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.24/1.61 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.24/1.61 , X ) ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.24/1.61 'c_HOL_Oinverse__class_Odivide'( T, Z, X ),
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.24/1.61 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.24/1.61 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.24/1.61 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.24/1.61 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ),
% 1.24/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.24/1.61 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y
% 1.24/1.61 ), X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.24/1.61 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.24/1.61 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 1.24/1.61 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 1.24/1.61 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.24/1.61 , X ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~(
% 1.24/1.61 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.24/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.24/1.61 ), Y ), 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ),
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.24/1.61 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.24/1.61 , 'tc_nat' ), 'tc_nat' ) ],
% 1.24/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.24/1.61 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.24/1.61 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 1.24/1.61 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.24/1.61 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.24/1.61 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.24/1.61 X ), Y ), Z ) ), T ) ) ],
% 1.24/1.61 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 1.24/1.61 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ) ],
% 1.24/1.61 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ) ],
% 1.24/1.61 [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =( hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.24/1.61 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.24/1.61 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.24/1.61 X ), Y ), Z ) ), T ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.24/1.61 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.24/1.61 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.24/1.61 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.24/1.61 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 1.24/1.61 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.24/1.61 'tc_nat' ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.24/1.61 'tc_nat' ), Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ],
% 1.24/1.61 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X ) )
% 1.24/1.61 ), =( 'c_HOL_Ozero__class_Ozero'( X ), Y ) ],
% 1.24/1.61 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.24/1.61 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.24/1.61 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.24/1.61 'c_Power_Opower__class_Opower'( X ), Y ), T ) ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.24/1.61 ), ~( =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.24/1.61 ) ) ],
% 1.24/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.24/1.61 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oabs__class_Oabs'( Y, X ) ),
% 1.24/1.61 'c_HOL_Oabs__class_Oabs'( Z, X ) ), X ) ],
% 1.24/1.61 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( 'c_Suc'( hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_Suc'( 'c_Suc'(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), X ) ), 'tc_nat' ) ) ],
% 1.24/1.61 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.24/1.61 'tc_nat' ), ~( 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.24/1.61 'c_Power_Opower__class_Opower'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ],
% 1.24/1.61 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_lessequals'( Y, Z, X ) )
% 1.24/1.61 , ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.24/1.61 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.24/1.61 , X ), 'c_lessequals'( Z, Y, X ) ],
% 1.24/1.61 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'( Y, Y, X ) )
% 1.24/1.61 , ~( 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ],
% 1.24/1.61 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Y
% 1.24/1.61 , X ), 'c_lessequals'( Y, Y, X ) ],
% 1.24/1.61 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.24/1.61 , Z, X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ],
% 1.24/1.61 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 1.24/1.61 'c_HOL_Oord__class_Oless'( Z, Y, X ) ],
% 1.24/1.61 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.24/1.61 , X ), 'c_lessequals'( Z, Y, X ) ],
% 1.24/1.61 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'( Y, Z, X ) )
% 1.24/1.61 , ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y
% 1.24/1.61 , Y, X ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.24/1.61 'c_HOL_Oinverse__class_Odivide'( Y, Y, X ), 'c_HOL_Oone__class_Oone'( X )
% 1.24/1.61 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.24/1.61 'c_HOL_Oinverse__class_Odivide'( Y, Y, X ), 'c_HOL_Oone__class_Oone'( X )
% 1.24/1.61 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.24/1.61 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.24/1.61 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.24/1.61 , Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_Divides_Odiv__class_Omod'( Z, T
% 1.24/1.61 , X ) ), T, X ) ) ],
% 1.24/1.61 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.24/1.61 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.24/1.61 , Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X )
% 1.24/1.61 ), Z ), T, X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Z, Y, X
% 1.24/1.61 ), X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.24/1.61 ), X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Z, Y, X
% 1.24/1.61 ), X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.24/1.61 ), X ) ) ],
% 1.24/1.61 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.24/1.61 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), =( X, 'c_HOL_Oone__class_Oone'(
% 1.24/1.61 'tc_nat' ) ) ],
% 1.24/1.61 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.24/1.61 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), =( Y, 'c_HOL_Oone__class_Oone'(
% 1.24/1.61 'tc_nat' ) ) ],
% 1.24/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.24/1.61 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ),
% 1.24/1.61 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.24/1.61 , Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 1.24/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.24/1.61 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.24/1.61 'c_Power_Opower__class_Opower'( X ), T ), Z ), X ), ~( 'c_lessequals'(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 1.24/1.61 ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), ~( 'class_Int_Onumber'(
% 1.24/1.61 X ) ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.24/1.61 X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), Z ) ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.24/1.61 , X ) ), T ) ) ) ],
% 1.24/1.61 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.24/1.61 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), ~(
% 1.24/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.24/1.61 'tc_nat' ) ), =( Y, Z ) ],
% 1.24/1.61 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.24/1.61 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ), 'tc_nat' ) ) ],
% 1.24/1.61 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.24/1.61 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), X ), 'tc_nat' ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.24/1.61 'c_HOL_Oone__class_Oone'( X ), Y, X ), 'c_lessequals'( Y,
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.24/1.61 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oone__class_Oone'( X ),
% 1.24/1.61 X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.24/1.61 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), =( Y,
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_lessequals'( hAPP( hAPP(
% 1.24/1.61 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y
% 1.24/1.61 ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.24/1.61 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.24/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.24/1.61 ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_lessequals'( Y,
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.24/1.61 'c_Power_Opower__class_Opower'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 1.24/1.61 X ), X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.24/1.61 'c_lessequals'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.24/1.61 'c_lessequals'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.24/1.61 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.24/1.61 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~(
% 1.24/1.61 'c_lessequals'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.24/1.61 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ), ~(
% 1.24/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ]
% 1.24/1.61 ,
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.24/1.61 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.24/1.61 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~(
% 1.24/1.61 'c_lessequals'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.24/1.61 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ), ~(
% 1.24/1.61 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.24/1.61 ,
% 1.24/1.61 [ =( X, 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X
% 1.24/1.61 , 'c_Suc'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat'
% 1.24/1.61 ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.24/1.61 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.24/1.61 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ),
% 1.24/1.61 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ) ) ],
% 1.24/1.61 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 1.24/1.61 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.24/1.61 Z, X ), 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oinverse__class_Odivide'(
% 1.24/1.61 Y, Z, X ), X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.24/1.61 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 1.24/1.61 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.24/1.61 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 1.24/1.61 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 1.24/1.61 'class_OrderedGroup_Omonoid__mult'( X ) ), 'c_lessequals'(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.24/1.61 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 1.24/1.61 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ) ],
% 1.24/1.61 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.24/1.61 'c_Suc'( X ), 'tc_nat' ) ],
% 1.24/1.61 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.24/1.61 'c_Suc'( X ), 'tc_nat' ) ],
% 1.24/1.61 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Ouminus__class_Ouminus'(
% 1.24/1.61 'c_HOL_Oone__class_Oone'( X ), X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.24/1.61 'c_Int_OMin', X ) ) ],
% 1.24/1.61 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( X, T ), Z ) )
% 1.24/1.61 ), ~( hBOOL( hAPP( hAPP( X, hAPP( hAPP( 'c_Power_Opower_Opower'( U, W,
% 1.24/1.61 V0 ), Y ), 'c_Suc'( V1 ) ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( U, W,
% 1.24/1.61 V0 ), Z ), 'c_Suc'( V1 ) ) ) ) ), ~(
% 1.24/1.61 'c_Ring__and__Field_Oordered__semidom'( V2, T, U, W, X, V3, V0 ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.24/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.24/1.61 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ),
% 1.24/1.61 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.24/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP(
% 1.24/1.61 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 1.24/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.24/1.61 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X )
% 1.24/1.61 , Y, X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), =( hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.24/1.61 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ), U ) ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.24/1.61 X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ), U )
% 1.24/1.61 ) ],
% 1.24/1.61 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ), T ) ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ), Y ) ), T ) ) ],
% 1.24/1.61 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X ) )
% 1.24/1.61 , Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.24/1.61 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X ) )
% 1.24/1.61 , Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.24/1.61 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ouminus__class_Ouminus'( Y,
% 1.24/1.61 X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.24/1.61 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X ) )
% 1.24/1.61 , Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.24/1.61 [ 'c_HOL_Oord__class_Oless'( 'c_Divides_Odiv__class_Omod'( X, Y,
% 1.24/1.61 'tc_nat' ), Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.24/1.61 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.24/1.61 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.24/1.61 ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( T
% 1.24/1.61 , 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.24/1.61 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.24/1.61 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.24/1.61 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.24/1.61 ), X ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ),
% 1.24/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.24/1.61 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.24/1.61 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X ),
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.24/1.61 ), X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Oinverse__class_Odivide'(
% 1.24/1.61 Y, 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.24/1.61 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.24/1.61 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.24/1.61 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.24/1.61 ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ),
% 1.24/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), =(
% 1.24/1.61 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ),
% 1.24/1.61 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oabs__class_Oabs'( Y, X ), X ) )
% 1.24/1.61 , =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), =(
% 1.24/1.61 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X )
% 1.24/1.61 , 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.24/1.61 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'(
% 1.24/1.61 X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.24/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), =( Y
% 1.24/1.61 , 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X )
% 1.24/1.61 , X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.24/1.61 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Oord__class_Oless'(
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.24/1.61 ), X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), ~(
% 1.24/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( T,
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.24/1.61 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.24/1.61 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.24/1.61 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 'c_HOL_Oord__class_Oless'(
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.24/1.61 ), X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.24/1.61 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.24/1.61 ), X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), ~(
% 1.24/1.61 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( T,
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.24/1.61 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.24/1.61 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.24/1.61 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.24/1.61 ), X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.24/1.61 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ), X ), ~(
% 1.24/1.61 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.24/1.61 , 'tc_nat' ), 'tc_nat' ) ) ],
% 1.24/1.61 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =( hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) ) ), =( hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), U ) ],
% 1.24/1.61 [ =( 'c_Suc'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.24/1.61 'c_Suc'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ),
% 1.24/1.61 'c_Divides_Odiv__class_Odiv'( X, 'c_Suc'( 'c_Suc'(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ) ) ), X ),
% 1.24/1.61 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.24/1.61 [ ~( 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.24/1.61 ), 'tc_nat' ) ) ],
% 1.24/1.61 [ ~( 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.24/1.61 ), 'tc_nat' ) ) ],
% 1.24/1.61 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OMin', 'tc_nat' ),
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.24/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.24/1.61 ), Y ), 'c_Suc'( Z ) ), 'c_HOL_Oone__class_Oone'( X ), X ), ~(
% 1.24/1.61 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.24/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.24/1.61 ,
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.24/1.61 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.24/1.61 'c_HOL_Oinverse__class_Oinverse'( Z, X ),
% 1.24/1.61 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.24/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.24/1.61 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ), ~(
% 1.24/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.24/1.61 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.24/1.61 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.24/1.61 'c_HOL_Oinverse__class_Oinverse'( Z, X ),
% 1.24/1.61 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.24/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.24/1.61 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ), ~(
% 1.24/1.61 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.24/1.61 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.24/1.61 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oabs__class_Oabs'( Y, X ) ),
% 1.24/1.61 Z ), X ) ],
% 1.24/1.61 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.24/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.24/1.61 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.24/1.61 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.24/1.61 ), Z ) ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.24/1.61 ), T ) ) ) ],
% 1.24/1.61 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.24/1.61 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( X ), X ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.24/1.61 ), T ) ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Z
% 1.24/1.61 ), T ) ) ) ],
% 1.24/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 1.24/1.61 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.24/1.61 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 1.24/1.61 'c_lessequals'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X )
% 1.24/1.61 , X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X )
% 1.24/1.61 , X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.24/1.61 ,
% 1.24/1.61 [ =( 'c_Divides_Odiv__class_Odiv'( 'c_Suc'( X ), Y, 'tc_nat' ), hAPP(
% 1.24/1.61 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( X,
% 1.24/1.61 Y, 'tc_nat' ) ), 'c_Divides_Odiv__class_Odiv'( 'c_Suc'(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ) ),
% 1.24/1.61 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.24/1.61 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ),
% 1.24/1.61 'c_Divides_Odiv__class_Omod'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.24/1.61 'tc_nat' ) ), Y, 'tc_nat' ) ), Y, 'tc_nat' ) ) ) ],
% 1.24/1.61 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.24/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.24/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ) ) ],
% 1.24/1.61 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.24/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ), ~( 'c_lessequals'(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.24/1.61 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.24/1.61 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( X ) )
% 1.24/1.61 ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'(
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ), 'tc_nat' ) ), ~(
% 1.24/1.61 'c_lessequals'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ),
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.24/1.61 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.24/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'(
% 1.24/1.61 'c_HOL_Oone__class_Oone'( X ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.24/1.61 ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.24/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'(
% 1.24/1.61 'c_HOL_Oone__class_Oone'( X ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.24/1.61 ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.24/1.61 ) ],
% 1.24/1.61 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( 'c_Power_Opower_Opower'( Y, Z, T ),
% 1.24/1.61 U ), W ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( Y, Z, T ), U ), V0 ) ) )
% 1.24/1.61 , ~( hBOOL( hAPP( hAPP( X, U ), Y ) ) ), ~( hBOOL( hAPP( hAPP( X, V1 ), U
% 1.24/1.61 ) ) ), ~( 'c_HOL_Oord__class_Oless'( V0, W, 'tc_nat' ) ), ~(
% 1.24/1.61 'c_Ring__and__Field_Oordered__semidom'( V2, V1, Y, Z, V3, X, T ) ) ],
% 1.24/1.61 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.24/1.61 'c_Divides_Odiv__class_Omod'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), Z
% 1.24/1.61 , X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 1.24/1.61 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.24/1.61 'c_Divides_Odiv__class_Odiv'( Y, Y, X ), 'c_HOL_Oone__class_Oone'( X ) )
% 1.24/1.61 , =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.24/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.24/1.61 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ),
% 1.24/1.61 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.24/1.61 , Z ), T ), X ), ~( 'c_lessequals'( Y, T, X ) ), ~(
% 1.24/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 1.24/1.61 ,
% 1.24/1.61 [ =( hAPP( X, Y ), hAPP( Z, T ) ), ~( hBOOL( hAPP( hAPP( U, Y ), W ) ) )
% 1.24/1.61 , ~( 'c_Ring__and__Field_Oordered__idom'( V0, Z, W, V1, V2, U, V3, T, V4
% 1.24/1.61 , X, V5 ) ) ],
% 1.24/1.61 [ =( hAPP( X, Y ), Z ), ~( hBOOL( hAPP( hAPP( T, U ), Y ) ) ), ~(
% 1.24/1.61 'c_Ring__and__Field_Oordered__idom'( W, V0, U, V1, V2, T, V3, Z, V4, X,
% 1.24/1.61 V5 ) ) ],
% 1.24/1.61 [ ~( =( hAPP( X, Y ), hAPP( Z, T ) ) ), ~(
% 1.24/1.61 'c_Ring__and__Field_Oordered__idom'( U, Z, W, V0, V1, V2, V3, T, V4, X,
% 1.24/1.61 V5 ) ), hBOOL( hAPP( hAPP( V2, Y ), W ) ) ],
% 1.24/1.61 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), Y, 'tc_nat' ), X ),
% 1.24/1.61 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.24/1.61 'tc_nat' ) ) ],
% 1.24/1.61 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), X, 'tc_nat' ), Y ),
% 1.24/1.61 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.24/1.61 'tc_nat' ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.24/1.61 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.24/1.61 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.24/1.61 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.24/1.61 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.24/1.61 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ],
% 1.24/1.61 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.24/1.61 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ), ~(
% 1.24/1.61 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.24/1.61 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.24/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.24/1.61 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X ) ) ],
% 1.24/1.61 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.24/1.61 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X ), ~(
% 1.24/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.24/1.61 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ),
% 1.24/1.61 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.24/1.61 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ],
% 1.24/1.61 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ),
% 1.24/1.61 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ), ~(
% 1.24/1.61 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.24/1.61 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ),
% 1.24/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.24/1.61 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X ) ) ],
% 1.24/1.61 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ),
% 1.24/1.61 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X ), ~(
% 1.24/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =( hAPP( hAPP(
% 1.24/1.61 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X
% 1.24/1.61 ) ), Z ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ),
% 1.24/1.61 ~( 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.24/1.61 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.24/1.61 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.24/1.61 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.24/1.61 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ), ~(
% 1.24/1.61 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.24/1.61 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'(
% 1.24/1.61 X ), Y ), Z ), X ), ~( 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), Y,
% 1.24/1.61 X ) ) ],
% 1.24/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.24/1.61 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oabs__class_Oabs'( Y, X ), X ),
% 1.24/1.61 'c_HOL_Oabs__class_Oabs'( Y, X ) ) ],
% 1.24/1.61 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.24/1.61 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.24/1.61 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ), Z ) ),
% 1.24/1.61 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ), T ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ],
% 1.24/1.61 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.24/1.61 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.24/1.61 'c_Divides_Odiv__class_Odiv'( Z, Y, X ) ) ), 'c_Divides_Odiv__class_Omod'(
% 1.24/1.61 Z, Y, X ) ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T )
% 1.24/1.61 ) ],
% 1.24/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.24/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.24/1.61 'c_HOL_Oabs__class_Oabs'( Y, X ), X ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.24/1.61 X ) ) ],
% 1.24/1.61 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( 'c_Power_Opower_Opower'( Y, Z,
% 1.24/1.61 T ), U ), W ) ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), W, 'tc_nat' ) ), ~( hBOOL( hAPP(
% 1.24/1.61 hAPP( X, Y ), U ) ) ), ~( 'c_Ring__and__Field_Oordered__semidom'( V0, V1
% 1.24/1.61 , Y, Z, V2, X, T ) ) ],
% 1.24/1.61 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, Y ),
% 1.24/1.61 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ) ), ~(
% 1.24/1.61 'c_Groebner__Basis_Ogb__semiring'( U, W, X, V0, V1, V2 ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.24/1.61 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.24/1.61 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.24/1.61 ), X ), ~( 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( T,
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.24/1.61 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.24/1.61 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.24/1.61 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.24/1.61 ), X ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.24/1.61 ), T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ),
% 1.24/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.24/1.61 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.24/1.61 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X ),
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.24/1.61 ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.24/1.61 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.24/1.61 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.24/1.61 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.24/1.61 ), X ) ), ~( 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.24/1.61 X ), Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ),
% 1.24/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.24/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.24/1.61 ), Y ), Z ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), T ),
% 1.24/1.61 X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X )
% 1.24/1.61 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.24/1.61 ), ~( 'c_HOL_Oord__class_Oless'( T, Z, 'tc_nat' ) ) ],
% 1.24/1.61 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OMin', X ),
% 1.24/1.61 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oone__class_Oone'( X ), X ) ) ]
% 1.24/1.61 ,
% 1.24/1.61 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), 'tc_nat' ), ~(
% 1.24/1.61 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ) ],
% 1.24/1.61 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), 'tc_nat' ), ~(
% 1.24/1.61 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.24/1.61 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.24/1.61 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.24/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~(
% 1.24/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.24/1.61 , 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ),
% 1.24/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.24/1.61 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.24/1.61 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.24/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ),
% 1.24/1.61 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.24/1.61 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.24/1.61 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.24/1.61 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.24/1.61 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.24/1.61 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.24/1.61 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ),
% 1.24/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.24/1.61 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.24/1.61 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.24/1.61 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.24/1.61 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ),
% 1.24/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.24/1.61 [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), X, 'tc_nat' ),
% 1.24/1.61 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.24/1.61 'c_HOL_Oone__class_Oone'( 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.24/1.61 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X
% 1.24/1.61 ), X ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.24/1.61 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ),
% 1.24/1.61 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X )
% 1.24/1.61 , 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.24/1.61 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.24/1.61 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.24/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ),
% 1.24/1.61 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.24/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.24/1.61 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.24/1.61 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.24/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~(
% 1.24/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.24/1.61 , 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ), ~(
% 1.24/1.61 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.24/1.61 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.24/1.61 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.24/1.61 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 1.24/1.61 ) ],
% 1.24/1.61 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.24/1.61 'c_Divides_Odiv__class_Omod'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.24/1.61 ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 1.24/1.61 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.24/1.61 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ) ), ~(
% 1.24/1.61 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'(
% 1.24/1.61 X, T, 'tc_nat' ) ],
% 1.24/1.61 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), hAPP(
% 1.24/1.61 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 1.24/1.61 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.24/1.61 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.24/1.61 ), X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.24/1.61 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.24/1.61 ), X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'( Z,
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.24/1.61 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.24/1.61 ), X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'( Y,
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.24/1.61 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.24/1.61 ), X ) ) ],
% 1.24/1.61 [ =( hAPP( 'c_NthRoot_Oroot'( X ), hAPP( 'c_NthRoot_Oroot'( Y ), Z ) ),
% 1.24/1.61 hAPP( 'c_NthRoot_Oroot'( Y ), hAPP( 'c_NthRoot_Oroot'( X ), Z ) ) ), ~(
% 1.24/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.24/1.61 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.24/1.61 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oring__1'( X ) ), =( hAPP( hAPP(
% 1.24/1.61 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X
% 1.24/1.61 ) ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.24/1.61 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ouminus__class_Ouminus'(
% 1.24/1.61 'c_HOL_Oone__class_Oone'( X ), X ) ), Z ) ), hAPP( hAPP(
% 1.24/1.61 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'( Y
% 1.24/1.61 , Z, X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.24/1.61 Z, X ) ), ~( 'c_lessequals'( 'c_HOL_Oinverse__class_Oinverse'( Z, X ),
% 1.24/1.61 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.24/1.61 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.24/1.61 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ), ~(
% 1.24/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.24/1.61 'c_lessequals'( Z, Y, X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'( Y
% 1.24/1.61 , Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.24/1.61 ), X ) ), ~( 'c_lessequals'( 'c_HOL_Oinverse__class_Oinverse'( Z, X ),
% 1.24/1.61 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.24/1.61 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.24/1.61 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ), ~(
% 1.24/1.61 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.24/1.61 'c_lessequals'( Z, Y, X ) ) ],
% 1.24/1.61 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.24/1.61 'c_Divides_Odiv__class_Odiv'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), Z
% 1.24/1.61 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.24/1.61 [ ~( 'class_Divides_Oring__div'( X ) ), ~( =(
% 1.24/1.61 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.24/1.61 , Z, X ) ) ), =( 'c_Divides_Odiv__class_Omod'(
% 1.24/1.61 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ),
% 1.24/1.61 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ouminus__class_Ouminus'( T, X ), Z,
% 1.24/1.61 X ) ) ],
% 1.24/1.61 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.24/1.61 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.24/1.61 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y
% 1.24/1.61 ), 'tc_nat' ) ) ],
% 1.24/1.61 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.24/1.61 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.24/1.61 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X
% 1.24/1.61 ), 'tc_nat' ) ) ],
% 1.24/1.61 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.24/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.24/1.61 ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.24/1.61 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.24/1.61 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.24/1.61 ,
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.24/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.24/1.61 ), Y ), Z ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), T ), Z ),
% 1.24/1.61 X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.24/1.61 , Z, 'tc_nat' ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y
% 1.24/1.61 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( Y,
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.24/1.61 X ), Z ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y )
% 1.24/1.61 ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( Y,
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.24/1.61 X ), Y ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z )
% 1.24/1.61 ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.24/1.61 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.24/1.61 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.24/1.61 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), U ), Z ) ), X ), hAPP( hAPP(
% 1.24/1.61 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.24/1.61 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), T ), hAPP( hAPP(
% 1.24/1.61 'c_Power_Opower__class_Opower'( X ), Y ), U ), X ) ), Z ) ), =( Y,
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.24/1.61 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.24/1.61 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.24/1.61 'c_HOL_Oinverse__class_Odivide'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.24/1.61 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.24/1.61 'c_HOL_Oinverse__class_Odivide'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.24/1.61 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.24/1.61 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 1.24/1.61 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.24/1.61 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.24/1.61 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ),
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.24/1.61 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.24/1.61 , 'tc_nat' ), 'tc_nat' ), =( 'c_Int_Onumber__class_Onumber__of'( Z,
% 1.24/1.61 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.24/1.61 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.24/1.61 , X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.24/1.61 ,
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.24/1.61 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.24/1.61 , X ) ) ],
% 1.24/1.61 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.24/1.61 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.24/1.61 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( X ), X ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.24/1.61 ), Z ) ), T ) ) ],
% 1.24/1.61 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.24/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.24/1.61 'tc_nat' ), 'c_Suc'( Z ) ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.24/1.61 'tc_nat' ), 'c_Suc'( Z ) ), Y ), 'tc_nat' ) ) ],
% 1.24/1.61 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.24/1.61 'tc_nat' ), 'c_Suc'( X ) ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.24/1.61 'tc_nat' ), 'c_Suc'( X ) ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.24/1.61 Y, Z, 'tc_nat' ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP( hAPP(
% 1.24/1.61 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oabs__class_Oabs'( Y, X ) ),
% 1.24/1.61 Z ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), ~(
% 1.24/1.61 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ) ],
% 1.24/1.61 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.24/1.61 'tc_nat' ), 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.24/1.61 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_OrderedGroup_Omonoid__mult'( Z
% 1.24/1.61 , X, T ) ) ],
% 1.24/1.61 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_OrderedGroup_Omonoid__mult'( Y
% 1.24/1.61 , X, T ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.24/1.61 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.24/1.61 , 'tc_nat' ), 'tc_nat' ), 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'(
% 1.24/1.61 X ), X ), ~( 'c_lessequals'( hAPP( hAPP( 'c_Power_Opower__class_Opower'(
% 1.24/1.61 X ), Z ), 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.24/1.61 [ ~( 'class_Int_Onumber__ring'( X ) ), ~( 'c_Int_Oiszero'(
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OMin', X ), X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( =(
% 1.24/1.61 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oone__class_Oone'( X ) )
% 1.24/1.61 ), =( Y, 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.24/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ),
% 1.24/1.61 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.24/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.24/1.61 'c_HOL_Oone__class_Oone'( X ), X ) ) ],
% 1.24/1.61 [ =( hAPP( 'c_NthRoot_Oroot'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.24/1.61 'tc_nat' ) ) ), X ), X ) ],
% 1.24/1.61 [ ~( =( 'c_Suc'( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), Y ) )
% 1.24/1.61 , =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.24/1.61 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.24/1.61 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.24/1.61 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.24/1.61 X ), 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~(
% 1.24/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.24/1.61 , Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.24/1.61 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.24/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ), ~(
% 1.24/1.61 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( T,
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.24/1.61 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.24/1.61 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.24/1.61 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.24/1.61 ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.24/1.61 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.24/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~(
% 1.24/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), Z, X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.24/1.61 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ),
% 1.24/1.61 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oabs__class_Oabs'( Y, X ), X ) )
% 1.24/1.61 ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.24/1.61 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X )
% 1.24/1.61 , 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.24/1.61 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ) ],
% 1.24/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.24/1.61 'c_HOL_Oabs__class_Oabs'( Y, X ), Y ), ~( 'c_HOL_Oord__class_Oless'(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.24/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.24/1.61 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ), ~(
% 1.24/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.24/1.61 ,
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.24/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.24/1.61 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ), ~(
% 1.24/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.24/1.61 ,
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.24/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.24/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.24/1.61 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.24/1.61 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.24/1.61 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.24/1.61 ), Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_Divides_Odiv__class_Omod'( Z,
% 1.24/1.61 T, X ) ), T, X ) ) ],
% 1.24/1.61 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.24/1.61 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.24/1.61 ), Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X
% 1.24/1.61 ) ), Z ), T, X ) ) ],
% 1.24/1.61 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.24/1.61 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, 'c_Suc'(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.24/1.61 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.24/1.61 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.24/1.61 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.24/1.61 'c_Int_OMin', X ) ), Y ), 'c_HOL_Ouminus__class_Ouminus'( Y, X ) ) ],
% 1.24/1.61 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OMin', X ) ),
% 1.24/1.61 'c_HOL_Ouminus__class_Ouminus'( Y, X ) ) ],
% 1.24/1.61 [ =( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ),
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X
% 1.24/1.61 , Y, 'tc_nat' ) ) ],
% 1.24/1.61 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), T ) ), hBOOL( hAPP(
% 1.24/1.61 hAPP( U, T ), W ) ), ~( hBOOL( hAPP( hAPP( X, Z ), V0 ) ) ), ~(
% 1.24/1.61 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, U, X, V4, V0, Y, V5,
% 1.24/1.61 V6 ) ) ],
% 1.24/1.61 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), T ) ), ~( hBOOL( hAPP(
% 1.24/1.61 hAPP( X, U ), Z ) ) ), hBOOL( hAPP( hAPP( W, V0 ), T ) ), ~(
% 1.24/1.61 'c_Ring__and__Field_Oordered__idom'( V1, V2, V0, V3, W, X, V4, U, Y, V5,
% 1.24/1.61 V6 ) ) ],
% 1.24/1.61 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), Y ) ) ), hBOOL( hAPP(
% 1.24/1.61 hAPP( U, Y ), W ) ), ~( hBOOL( hAPP( hAPP( X, V0 ), T ) ) ), ~(
% 1.24/1.61 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, U, X, V4, V0, Z, V5,
% 1.24/1.61 V6 ) ) ],
% 1.24/1.61 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), Y ) ) ), ~( hBOOL( hAPP(
% 1.24/1.61 hAPP( X, T ), U ) ) ), hBOOL( hAPP( hAPP( W, V0 ), Y ) ), ~(
% 1.24/1.61 'c_Ring__and__Field_Oordered__idom'( V1, V2, V0, V3, W, X, V4, U, Z, V5,
% 1.24/1.61 V6 ) ) ],
% 1.24/1.61 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), Z ) ), hBOOL( hAPP(
% 1.24/1.61 hAPP( U, Z ), W ) ), ~( hBOOL( hAPP( hAPP( X, T ), V0 ) ) ), ~(
% 1.24/1.61 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, U, X, V4, V0, Y, V5,
% 1.24/1.61 V6 ) ) ],
% 1.24/1.61 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), Z ) ), ~( hBOOL( hAPP(
% 1.24/1.61 hAPP( X, U ), T ) ) ), hBOOL( hAPP( hAPP( W, V0 ), Z ) ), ~(
% 1.24/1.61 'c_Ring__and__Field_Oordered__idom'( V1, V2, V0, V3, W, X, V4, U, Y, V5,
% 1.24/1.61 V6 ) ) ],
% 1.24/1.61 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, Y ), T ) ) ), hBOOL( hAPP(
% 1.24/1.61 hAPP( U, Y ), W ) ), ~( hBOOL( hAPP( hAPP( X, V0 ), T ) ) ), ~(
% 1.24/1.61 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, U, X, V4, V0, Z, V5,
% 1.24/1.61 V6 ) ) ],
% 1.24/1.61 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, Y ), T ) ) ), ~( hBOOL( hAPP(
% 1.24/1.61 hAPP( X, T ), U ) ) ), hBOOL( hAPP( hAPP( W, V0 ), Y ) ), ~(
% 1.24/1.61 'c_Ring__and__Field_Oordered__idom'( V1, V2, V0, V3, W, X, V4, U, Z, V5,
% 1.24/1.61 V6 ) ) ],
% 1.24/1.61 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), T ) ), hBOOL( hAPP(
% 1.24/1.61 hAPP( U, T ), W ) ), ~( hBOOL( hAPP( hAPP( X, Z ), V0 ) ) ), ~(
% 1.24/1.61 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, X, U, V4, V0, Y, V5,
% 1.24/1.61 V6 ) ) ],
% 1.24/1.61 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), T ) ), ~( hBOOL( hAPP(
% 1.24/1.61 hAPP( X, U ), Z ) ) ), hBOOL( hAPP( hAPP( W, V0 ), T ) ), ~(
% 1.24/1.61 'c_Ring__and__Field_Oordered__idom'( V1, V2, V0, V3, X, W, V4, U, Y, V5,
% 1.24/1.61 V6 ) ) ],
% 1.24/1.61 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), Y ) ) ), hBOOL( hAPP(
% 1.24/1.61 hAPP( U, Y ), W ) ), ~( hBOOL( hAPP( hAPP( X, V0 ), T ) ) ), ~(
% 1.24/1.61 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, X, U, V4, V0, Z, V5,
% 1.24/1.61 V6 ) ) ],
% 1.24/1.61 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), Y ) ) ), ~( hBOOL( hAPP(
% 1.24/1.61 hAPP( X, T ), U ) ) ), hBOOL( hAPP( hAPP( W, V0 ), Y ) ), ~(
% 1.24/1.61 'c_Ring__and__Field_Oordered__idom'( V1, V2, V0, V3, X, W, V4, U, Z, V5,
% 1.24/1.61 V6 ) ) ],
% 1.24/1.61 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), Z ) ), hBOOL( hAPP(
% 1.24/1.61 hAPP( U, Z ), W ) ), ~( hBOOL( hAPP( hAPP( X, T ), V0 ) ) ), ~(
% 1.24/1.61 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, X, U, V4, V0, Y, V5,
% 1.24/1.61 V6 ) ) ],
% 1.24/1.61 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), Z ) ), ~( hBOOL( hAPP(
% 1.24/1.61 hAPP( X, U ), T ) ) ), hBOOL( hAPP( hAPP( W, V0 ), Z ) ), ~(
% 1.24/1.61 'c_Ring__and__Field_Oordered__idom'( V1, V2, V0, V3, X, W, V4, U, Y, V5,
% 1.24/1.61 V6 ) ) ],
% 1.24/1.61 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, Y ), T ) ) ), hBOOL( hAPP(
% 1.24/1.61 hAPP( U, Y ), W ) ), ~( hBOOL( hAPP( hAPP( X, V0 ), T ) ) ), ~(
% 1.24/1.61 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, X, U, V4, V0, Z, V5,
% 1.24/1.61 V6 ) ) ],
% 1.24/1.61 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, Y ), T ) ) ), ~( hBOOL( hAPP(
% 1.24/1.61 hAPP( X, T ), U ) ) ), hBOOL( hAPP( hAPP( W, V0 ), Y ) ), ~(
% 1.24/1.61 'c_Ring__and__Field_Oordered__idom'( V1, V2, V0, V3, X, W, V4, U, Z, V5,
% 1.24/1.61 V6 ) ) ],
% 1.24/1.61 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( Z, T ) ) ), ~( hBOOL( hAPP( hAPP( X,
% 1.24/1.61 Y ), T ) ) ), ~( 'c_Ring__and__Field_Oordered__idom'( U, W, Y, V0, V1, X
% 1.24/1.61 , V2, V3, V4, Z, V5 ) ) ],
% 1.24/1.61 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( X, Y ), hAPP(
% 1.24/1.61 T, Z ) ) ) ), ~( 'c_Ring__and__Field_Oordered__idom'( U, W, Y, V0, V1, X
% 1.24/1.61 , V2, V3, V4, T, V5 ) ) ],
% 1.24/1.61 [ hBOOL( hAPP( hAPP( X, hAPP( Y, Z ) ), T ) ), ~( hBOOL( hAPP( hAPP( X,
% 1.24/1.61 Z ), T ) ) ), ~( 'c_Ring__and__Field_Oordered__idom'( U, W, T, V0, V1, X
% 1.24/1.61 , V2, V3, V4, Y, V5 ) ) ],
% 1.24/1.61 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( X, hAPP( T, Y
% 1.24/1.61 ) ), Z ) ) ), ~( 'c_Ring__and__Field_Oordered__idom'( U, W, Z, V0, V1, X
% 1.24/1.61 , V2, V3, V4, T, V5 ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.24/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.24/1.61 X ), Y ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z )
% 1.24/1.61 ), X ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.24/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.24/1.61 X ), Y ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z )
% 1.24/1.61 ), X ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 1.24/1.61 'c_HOL_Oord__class_Oless'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.24/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.24/1.61 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.24/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ),
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.24/1.61 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.24/1.61 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.24/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.24/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.24/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.24/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ),
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.24/1.61 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.24/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.24/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =( hAPP( hAPP(
% 1.24/1.61 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.24/1.61 'c_Power_Opower__class_Opower'( X ), T ), Z ) ) ), =( Y, T ), ~(
% 1.24/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.24/1.61 'tc_nat' ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X )
% 1.24/1.61 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.24/1.61 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =( hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), Z ) ), =( Y,
% 1.24/1.61 'c_HOL_Ouminus__class_Ouminus'( T, X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.24/1.61 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.24/1.61 X ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X
% 1.24/1.61 ), 'c_HOL_Oinverse__class_Odivide'( Y, T, X ) ), =( Z,
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.24/1.61 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.24/1.61 X ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X
% 1.24/1.61 ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ) ), =( Y,
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.24/1.61 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oabs__class_Oabs'( hAPP( hAPP(
% 1.24/1.61 'c_Power_Opower__class_Opower'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.24/1.61 'c_Int_OMin', X ) ), Y ), X ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.24/1.61 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.24/1.61 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.24/1.61 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.24/1.61 X ), 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~( 'c_lessequals'(
% 1.24/1.61 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.24/1.61 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.24/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ), ~( 'c_lessequals'( Y,
% 1.24/1.61 'c_HOL_Oinverse__class_Odivide'( T, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.24/1.61 , X ), X ), X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.24/1.61 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.24/1.61 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.24/1.61 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.24/1.61 ), X ) ), ~( 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.24/1.61 X ), T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.24/1.61 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.24/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~( 'c_lessequals'(
% 1.24/1.61 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( T
% 1.24/1.61 , X ), X ), Z, X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z
% 1.24/1.61 , X ) ), T ), 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), Z, X ) ) ],
% 1.24/1.61 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.24/1.61 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'(
% 1.24/1.61 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.24/1.61 'c_Groebner__Basis_Ogb__semiring'( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( X ), 'c_Power_Opower__class_Opower'( X ),
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ), X ) ]
% 1.24/1.61 ,
% 1.24/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.24/1.61 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.24/1.61 ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.24/1.61 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.24/1.61 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), Z ),
% 1.24/1.61 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.24/1.61 'tc_nat' ), X ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.24/1.61 ), Y ), Z ), 'tc_nat' ) ) ],
% 1.24/1.61 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.24/1.61 'c_Divides_Odiv__class_Omod'( Y, Z, 'tc_nat' ) ),
% 1.24/1.61 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.24/1.61 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.24/1.61 ), X ), Z ), 'tc_nat' ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__comm__semiring__strict'( X ) ),
% 1.24/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.24/1.61 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.24/1.61 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) )
% 1.24/1.61 , ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.24/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.24/1.61 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X )
% 1.24/1.61 , ~( 'c_HOL_Oord__class_Oless'( T, Y, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.24/1.61 Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.24/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.24/1.61 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X )
% 1.24/1.61 , ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.24/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.24/1.61 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X )
% 1.24/1.61 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) )
% 1.24/1.61 , ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.24/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.24/1.61 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X )
% 1.24/1.61 , ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.24/1.61 , ~( 'c_HOL_Oord__class_Oless'( T, Y, X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.24/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.24/1.61 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.24/1.61 , ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.24/1.61 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.24/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.24/1.61 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.24/1.61 , ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.24/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.24/1.61 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.24/1.61 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) )
% 1.24/1.61 , ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.24/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.24/1.61 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.24/1.61 , ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.24/1.61 , ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.24/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.24/1.61 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.24/1.61 , ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.24/1.61 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.24/1.61 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ), ~(
% 1.24/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ]
% 1.24/1.61 ,
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.24/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.24/1.61 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.24/1.61 , ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.24/1.61 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.24/1.61 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.24/1.61 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ), ~(
% 1.24/1.61 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.24/1.61 ,
% 1.24/1.61 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.24/1.61 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.24/1.61 ), X ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' )
% 1.24/1.61 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.24/1.61 , X, 'tc_nat' ) ) ],
% 1.24/1.61 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.24/1.61 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.24/1.61 ), Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X
% 1.24/1.61 ) ), 'c_Divides_Odiv__class_Omod'( Z, T, X ) ), T, X ) ) ],
% 1.24/1.61 [ ~( =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', 'tc_Int_Oint'
% 1.24/1.61 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OMin', 'tc_Int_Oint' ) ) )
% 1.24/1.61 ],
% 1.24/1.61 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), hAPP( hAPP( Y, Z ), U ) )
% 1.24/1.61 , hAPP( hAPP( Y, Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.24/1.61 , T ), U ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, Y, V0, V1, V2
% 1.24/1.61 ) ) ],
% 1.24/1.61 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.24/1.61 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ), =( Y
% 1.24/1.61 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, Z ) ],
% 1.24/1.61 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.24/1.61 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), =( X
% 1.24/1.61 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y, Z ) ],
% 1.24/1.61 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.24/1.61 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), =( Y
% 1.24/1.61 , Z ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.24/1.61 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.24/1.61 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.24/1.61 , Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), T, X )
% 1.24/1.61 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ),
% 1.24/1.61 'c_Divides_Odiv__class_Odiv'( Y, T, X ) ) ), =( T,
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.24/1.61 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.24/1.61 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.24/1.61 , Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), Z, X )
% 1.24/1.61 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ),
% 1.24/1.61 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ) ), =( Z,
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.24/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.24/1.61 , Y ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.24/1.61 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), Y, X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.24/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.24/1.61 , X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.24/1.61 X ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), Y, X ) ),
% 1.24/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.24/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.24/1.61 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 1.24/1.61 X ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), Y, X ) ),
% 1.24/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.24/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.24/1.61 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 1.24/1.61 X ) ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.24/1.61 , ~( 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.24/1.61 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.24/1.61 ), Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( T,
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'( Z
% 1.24/1.61 , 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.24/1.61 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.24/1.61 , X ), ~( 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.24/1.61 X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ),
% 1.24/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.24/1.61 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.24/1.61 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.24/1.61 X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ),
% 1.24/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.24/1.61 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.24/1.61 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.24/1.61 X ) ), 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.24/1.61 , ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.24/1.61 X ), Y ), T ), Z, X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.24/1.61 'class_Int_Onumber'( X ) ), =( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.24/1.61 , 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.24/1.61 , X ) ), Z ), Z, X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.24/1.61 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oone__class_Oone'( X ),
% 1.24/1.61 X ), ~( 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.24/1.61 X ), 'c_HOL_Oone__class_Oone'( X ) ), 'c_HOL_Oone__class_Oone'( X ) ) ),
% 1.24/1.61 Y ) ) ],
% 1.24/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.24/1.61 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.24/1.61 'c_HOL_Oabs__class_Oabs'( Y, X ), X ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.24/1.61 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.24/1.61 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.24/1.61 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.24/1.61 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ),
% 1.24/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.24/1.61 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.24/1.61 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.24/1.61 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( T,
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.24/1.61 hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.24/1.61 [ =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'c_Suc'(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.24/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.24/1.61 'c_lessequals'( Y, 'c_HOL_Oabs__class_Oabs'( Y, X ), X ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.24/1.61 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.24/1.61 ), X ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.24/1.61 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ),
% 1.24/1.61 ~( 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.24/1.61 , 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.24/1.61 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.24/1.61 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.24/1.61 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( T,
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.24/1.61 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.24/1.61 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.24/1.61 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.24/1.61 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ), ~(
% 1.24/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.24/1.61 , 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.24/1.61 'class_Int_Onumber'( X ) ), =( Y, hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ),
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ), =(
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.24/1.61 ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.24/1.61 'class_Int_Onumber'( X ) ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.24/1.61 X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ),
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y ), =(
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.24/1.61 ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( hAPP(
% 1.24/1.61 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.24/1.61 ), Y ), Y, X ) ) ],
% 1.24/1.61 [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 1.24/1.61 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.24/1.61 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 1.24/1.61 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 1.24/1.61 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.24/1.61 , U ), Y ), Z, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( X ), W ), T ), Z, X ) ) ],
% 1.24/1.61 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.24/1.61 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ],
% 1.24/1.61 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( X,
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.24/1.61 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( Y, 'c_Suc'(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_Suc'(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.24/1.61 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.24/1.61 hAPP( hAPP( 'c_Power_Opower__class_Opower'( 'tc_nat' ), X ), Y ),
% 1.24/1.61 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.24/1.61 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.24/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.24/1.61 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 1.24/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.24/1.61 ,
% 1.24/1.61 [ ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), =( Y,
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( hBOOL( hAPP( Z,
% 1.24/1.61 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.24/1.61 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), T
% 1.24/1.61 ) ), X ), Y, 'tc_nat' ) ) ) ), hBOOL( hAPP( Z, T ) ) ],
% 1.24/1.61 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Ozero__class_Ozero'(
% 1.24/1.61 'tc_nat' ), 'tc_nat' ) ],
% 1.24/1.61 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =( hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X
% 1.24/1.61 ) ) ), =( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z ) ],
% 1.24/1.61 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =( hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X
% 1.24/1.61 ) ) ), =( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 1.24/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.24/1.61 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.24/1.61 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 1.24/1.61 'c_Nat_Osemiring__1__class_Oof__nat'( hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ), X ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( X ), 'c_Nat_Osemiring__1__class_Oof__nat'(
% 1.24/1.61 Y, X ) ), 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ) ) ) ],
% 1.24/1.61 [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ) ), Y, 'tc_nat'
% 1.24/1.61 ), 'c_Divides_Odiv__class_Omod'( 'c_Suc'( Z ), Y, 'tc_nat' ) ) ],
% 1.24/1.61 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), T ) ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ) ), =( Y, T ), =( X
% 1.24/1.61 , Z ) ],
% 1.24/1.61 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), T ) ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ) ), =( Y, T ), =( X
% 1.24/1.61 , Z ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.24/1.61 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.24/1.61 X ), Y ), U ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.24/1.61 ) ) ), =( Z, U ), =( Y, T ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.24/1.61 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.24/1.61 X ), Y ), U ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.24/1.61 ) ) ), =( Z, U ), =( Y, T ) ],
% 1.24/1.61 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( 'c_Power_Opower_Opower'( Y, Z, T ),
% 1.24/1.61 U ), W ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( Y, Z, T ), V0 ), W ) ) )
% 1.24/1.61 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), W
% 1.24/1.61 , 'tc_nat' ) ), ~( hBOOL( hAPP( hAPP( V1, V2 ), U ) ) ), ~( hBOOL( hAPP(
% 1.24/1.61 hAPP( X, U ), V0 ) ) ), ~( 'c_Ring__and__Field_Oordered__semidom'( V3, V2
% 1.24/1.61 , Y, Z, V1, X, T ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oabs__class_Oabs'( Y, X ) ),
% 1.24/1.61 'c_HOL_Oabs__class_Oabs'( Y, X ) ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 1.24/1.61 'c_HOL_Oinverse__class_Oinverse'( hAPP( hAPP(
% 1.24/1.61 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), hAPP( hAPP(
% 1.24/1.61 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y
% 1.24/1.61 , X ) ), Z ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 1.24/1.61 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.24/1.61 , X ), 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oinverse__class_Oinverse'(
% 1.24/1.61 Y, X ), X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.24/1.61 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Z
% 1.24/1.61 , X ) ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( T,
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.24/1.61 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.24/1.61 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.24/1.61 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.24/1.61 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.24/1.61 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.24/1.61 ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ),
% 1.24/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.24/1.61 [ ~( =( X, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y
% 1.24/1.61 ) ) ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 1.24/1.61 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.24/1.61 [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 1.24/1.61 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.24/1.61 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 1.24/1.61 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 1.24/1.61 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.24/1.61 ), U ), Y ), Z, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( X ), W ), T ), Z, X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.24/1.61 'class_Int_Onumber'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( hAPP(
% 1.24/1.61 hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), Z ), Z, X ),
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), =( Z,
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.24/1.61 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.24/1.61 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.24/1.61 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.24/1.61 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.24/1.61 ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ), ~(
% 1.24/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.24/1.61 , 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.24/1.61 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.24/1.61 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.24/1.61 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.24/1.61 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ),
% 1.24/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.24/1.61 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Z
% 1.24/1.61 , X ) ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( T,
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_lessequals'(
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.24/1.61 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.24/1.61 ) ), 'c_HOL_Oinverse__class_Odivide'( T, U, X ) ),
% 1.24/1.61 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.24/1.61 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), U ) ), hAPP(
% 1.24/1.61 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ), X ) ), =( U,
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.24/1.61 ) ],
% 1.24/1.61 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_Suc'(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_Suc'(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_Suc'(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.24/1.61 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ), X ) ),
% 1.24/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( Y, hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z
% 1.24/1.61 , X ) ), Z ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z
% 1.24/1.61 , X ) ), Z ), Y ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ), X ) ]
% 1.24/1.61 ,
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.24/1.61 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.24/1.61 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.24/1.61 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.24/1.61 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.24/1.61 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.24/1.61 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.24/1.61 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.24/1.61 'tc_nat' ) ) ],
% 1.24/1.61 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), 'c_HOL_Ozero__class_Ozero'(
% 1.24/1.61 'tc_nat' ) ) ],
% 1.24/1.61 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.24/1.61 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.24/1.61 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.24/1.61 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.24/1.61 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =( hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.24/1.61 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =( hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.24/1.61 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =( hAPP(
% 1.24/1.61 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.24/1.61 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =( hAPP(
% 1.24/1.61 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.24/1.61 X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.24/1.61 'c_HOL_Oabs__class_Oabs'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X )
% 1.24/1.61 , 'c_HOL_Ouminus__class_Ouminus'( Y, X ) ), Z ), X ),
% 1.24/1.61 'c_HOL_Oabs__class_Oabs'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X )
% 1.24/1.61 , Y ), Z ), X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.24/1.61 X ), Y ), Z ) ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP(
% 1.24/1.61 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Oone__class_Oone'( X )
% 1.24/1.61 ) ), Z ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.24/1.61 X ), Z ), 'c_HOL_Oone__class_Oone'( X ) ) ), Y ) ) ],
% 1.24/1.61 [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Suc'(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ),
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.24/1.61 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.24/1.61 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.24/1.61 Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.24/1.61 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.24/1.61 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.24/1.61 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), ~( 'class_Int_Onumber'(
% 1.24/1.61 X ) ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ),
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ) ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.24/1.61 X ), Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =( Y,
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_Int_Oiszero'( Y, X ) ) ],
% 1.24/1.61 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.24/1.61 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Oone__class_Oone'( X ), X ),
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oabs__class_Oabs'( Y, X ) ), Z
% 1.24/1.61 ), 'c_HOL_Oabs__class_Oabs'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.24/1.61 ), Y ), Z ), X ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.24/1.61 Z, X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.24/1.61 'c_HOL_Oone__class_Oone'( X ), X ), ~( 'c_lessequals'(
% 1.24/1.61 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.24/1.61 X ) ) ],
% 1.24/1.61 [ ~( =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ), U ), hAPP(
% 1.24/1.61 hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ), W ) ) ), ~( hBOOL( hAPP(
% 1.24/1.61 hAPP( V0, X ), T ) ) ), ~( 'c_Ring__and__Field_Oordered__semidom'( V1, V2
% 1.24/1.61 , X, Y, V3, V0, Z ) ), =( U, W ) ],
% 1.24/1.61 [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Suc'(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.24/1.61 'tc_nat' ) ) ) ],
% 1.24/1.61 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Y
% 1.24/1.61 , X ) ) ],
% 1.24/1.61 [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ],
% 1.24/1.61 [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ],
% 1.24/1.61 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.24/1.61 , Y, X ) ) ],
% 1.24/1.61 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.24/1.61 , Y, X ) ) ],
% 1.24/1.61 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.24/1.61 , X ), 'c_lessequals'( Z, Y, X ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.24/1.61 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oabs__class_Oabs'(
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), 'c_HOL_Oord__class_Oless'(
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.24/1.61 ), X ) ],
% 1.24/1.61 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.24/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~(
% 1.24/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.24/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.24/1.61 ,
% 1.24/1.61 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.24/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.24/1.61 'tc_nat' ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.24/1.61 ), Z ), Y ), 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_nat' ) ) ],
% 1.24/1.61 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.24/1.61 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.24/1.61 ), Z ), Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ), ~(
% 1.24/1.61 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 1.24/1.61 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.24/1.61 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.24/1.61 ), X ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ), ~(
% 1.24/1.61 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 1.24/1.61 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.24/1.61 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.24/1.61 ), X ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' )
% 1.24/1.61 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.24/1.61 , X, 'tc_nat' ) ) ],
% 1.24/1.61 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.24/1.61 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.24/1.61 ), Z ), Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' )
% 1.24/1.61 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.24/1.61 , Y, 'tc_nat' ) ) ],
% 1.24/1.61 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.24/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'(
% 1.24/1.61 'tc_nat' ), Z ), X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'(
% 1.24/1.61 'tc_nat' ), Z ), Y ), 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_nat' ) ) ],
% 1.24/1.61 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( 'c_Power_Opower_Opower'( Z, T,
% 1.24/1.61 U ), hAPP( W, V0 ) ), V1 ) ) ), ~( 'c_Ring__and__Field_Oordered__idom'(
% 1.24/1.61 V2, V3, Y, V4, X, V5, W, Z, T, V6, U ) ) ],
% 1.24/1.61 [ ~( hBOOL( hAPP( hAPP( X, Y ), Z ) ) ), ~(
% 1.24/1.61 'c_Ring__and__Field_Oordered__semidom'( T, Z, Y, U, W, X, V0 ) ) ],
% 1.24/1.61 [ ~( hBOOL( hAPP( hAPP( X, Y ), Z ) ) ), ~(
% 1.24/1.61 'c_Ring__and__Field_Oordered__semidom'( T, Z, Y, U, X, W, V0 ) ) ],
% 1.24/1.61 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.24/1.61 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.24/1.61 , Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), Z, X )
% 1.24/1.61 , 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 1.24/1.61 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.24/1.61 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.24/1.61 , Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), T, X )
% 1.24/1.61 , 'c_Divides_Odiv__class_Omod'( Y, T, X ) ) ],
% 1.24/1.61 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ), Y, 'tc_nat' )
% 1.24/1.61 , 'c_Divides_Odiv__class_Omod'( Z, Y, 'tc_nat' ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.24/1.61 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.24/1.61 , 'tc_nat' ), 'tc_nat' ) ), =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.24/1.61 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_lessequals'(
% 1.24/1.61 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ),
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.24/1.61 , 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), 'c_Nat_Osemiring__1__class_Oof__nat'( Y
% 1.24/1.61 , X ), X ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), 'c_Nat_Osemiring__1__class_Oof__nat'( Y
% 1.24/1.61 , X ), X ) ],
% 1.24/1.61 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.24/1.61 Y ) ],
% 1.24/1.61 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.24/1.61 Y ) ],
% 1.24/1.61 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.24/1.61 Y ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.24/1.61 X ) ), =( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.24/1.61 Y ) ],
% 1.24/1.61 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.24/1.61 Y ) ],
% 1.24/1.61 [ =( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.24/1.61 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ],
% 1.24/1.61 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), X ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.24/1.61 Y ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.24/1.61 Y ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.24/1.61 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'( Y,
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Z, hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ), ~( 'c_lessequals'(
% 1.24/1.61 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), Z, X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.24/1.61 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'( Y,
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( T,
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'( Z,
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'( Y,
% 1.24/1.61 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.24/1.61 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), Y, X ) ), ~( 'c_lessequals'(
% 1.24/1.61 Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.24/1.61 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 'c_HOL_Oord__class_Oless'( Z,
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Oord__class_Oless'( Z,
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.24/1.61 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), Y, X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.24/1.61 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.24/1.61 X ), Y ), Z ), T, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.24/1.61 'c_HOL_Oinverse__class_Odivide'( Y, T, X ) ),
% 1.24/1.61 'c_HOL_Oinverse__class_Odivide'( Z, T, X ) ) ) ],
% 1.24/1.61 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 1.24/1.61 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.24/1.61 X ), Y ), Z ), T, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.24/1.61 'c_HOL_Oinverse__class_Odivide'( Y, T, X ) ),
% 1.24/1.61 'c_HOL_Oinverse__class_Odivide'( Z, T, X ) ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.24/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~(
% 1.24/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Z, X ) ), ~(
% 1.24/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.24/1.61 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.24/1.61 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 1.24/1.61 ), Y ) ],
% 1.24/1.61 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( Y,
% 1.24/1.61 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 1.24/1.61 ) ) ],
% 1.24/1.61 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( Y,
% 1.24/1.61 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 1.24/1.61 ) ) ],
% 1.24/1.61 [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), =(
% 1.24/1.61 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 1.24/1.61 ), Y ) ],
% 1.24/1.61 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.24/1.61 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 1.24/1.61 ), Y ) ],
% 1.24/1.61 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.24/1.61 'c_Divides_Odiv__class_Odiv'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y )
% 1.24/1.61 ],
% 1.24/1.61 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.24/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.24/1.61 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 1.24/1.61 'c_lessequals'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ]
% 1.24/1.61 ,
% 1.24/1.61 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.24/1.61 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.24/1.61 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 1.24/1.61 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ]
% 1.24/1.61 ,
% 1.24/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.24/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X )
% 1.24/1.61 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Z, X ), Y
% 1.24/1.61 , X ) ) ],
% 1.24/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.24/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X )
% 1.24/1.61 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Z, X ), Y
% 1.24/1.61 , X ) ) ],
% 1.24/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.24/1.61 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X )
% 1.24/1.61 , ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.24/1.61 , X ) ) ],
% 1.24/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.24/1.61 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X )
% 1.24/1.61 , ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.24/1.61 , X ) ) ],
% 1.24/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.24/1.61 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ), ~(
% 1.24/1.61 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Z, X ), Y, X ) ) ],
% 1.24/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.24/1.61 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ), ~(
% 1.24/1.61 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Z, X ), Y, X ) ) ],
% 1.24/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.24/1.61 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), ~(
% 1.24/1.61 'c_lessequals'( Z, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ],
% 1.24/1.61 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.24/1.61 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), ~(
% 1.24/1.61 'c_lessequals'( Z, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ],
% 1.24/1.61 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.24/1.61 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.24/1.61 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ),
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.61 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ), ~(
% 1.24/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.24/1.61 'tc_nat' ) ) ],
% 1.24/1.61 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( Y ), X ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.24/1.61 X ), 'c_HOL_Oone__class_Oone'( X ) ), 'c_Int_Onumber__class_Onumber__of'(
% 1.24/1.61 Y, X ) ) ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.24/1.61 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', X ), X ),
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.24/1.61 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.24/1.61 'c_Power_Opower__class_Opower'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.24/1.61 'c_Int_OMin', X ) ), Y ), 'c_Int_Onumber__class_Onumber__of'(
% 1.24/1.61 'c_Int_OMin', X ) ), 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ]
% 1.24/1.61 ,
% 1.24/1.61 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( Y ), X ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.24/1.61 X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ),
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.24/1.61 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.24/1.61 'c_HOL_Oone__class_Oone'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.24/1.61 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), X ), X ), X ) ],
% 1.24/1.61 [ =( 'c_Int_OBit1'( 'c_Int_OMin' ), 'c_Int_OMin' ) ],
% 1.24/1.61 [ ~( =( 'c_Int_OBit1'( X ), 'c_Int_OMin' ) ), =( X, 'c_Int_OMin' ) ]
% 1.24/1.61 ,
% 1.24/1.61 [ ~( =( 'c_Int_OMin', 'c_Int_OBit1'( X ) ) ), =( 'c_Int_OMin', X ) ]
% 1.24/1.61 ,
% 1.24/1.61 [ =( 'c_Int_OMin', 'c_Int_OBit1'( 'c_Int_OMin' ) ) ],
% 1.24/1.61 [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 1.24/1.61 'c_Divides_Odiv__class_Omod'( 'c_Suc'( 'c_Divides_Odiv__class_Omod'( X, Y
% 1.24/1.61 , 'tc_nat' ) ), Y, 'tc_nat' ) ) ],
% 1.24/1.61 [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.24/1.61 [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.24/1.61 [ =( X, Y ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.24/1.61 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ],
% 1.24/1.61 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_Suc'( X ), 'tc_nat' ) )
% 1.24/1.61 , 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ],
% 1.24/1.61 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) )
% 1.24/1.61 , 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ],
% 1.24/1.61 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ), 'c_Suc'( U ) )
% 1.24/1.61 , hAPP( hAPP( Y, T ), hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T )
% 1.24/1.61 , U ) ) ) ],
% 1.24/1.61 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), 'c_Suc'( Y
% 1.24/1.61 ) ), 'c_Suc'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y
% 1.24/1.61 ) ) ) ],
% 1.24/1.61 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Suc'( X ) )
% 1.24/1.61 , Y ), 'c_Suc'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.24/1.61 Y ) ) ) ],
% 1.24/1.61 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Suc'( X ) )
% 1.24/1.61 , Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), 'c_Suc'(
% 1.24/1.61 Y ) ) ) ],
% 1.24/1.61 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ),
% 1.24/1.61 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ],
% 1.24/1.61 [ ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), ~(
% 1.24/1.61 'c_HOL_Oord__class_Oless'( Y, 'c_Suc'( X ), 'tc_nat' ) ) ],
% 1.24/1.61 [ 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 1.24/1.61 X, 'c_Suc'( X ), 'tc_nat' ) ],
% 1.24/1.61 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_Suc'( X
% 1.24/1.61 ) ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_Suc'(
% 1.24/1.61 X ) ), Z ) ) ), =( Y, Z ) ],
% 1.24/1.61 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.24/1.61 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ) ) ],
% 1.24/1.61 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ), ~(
% 1.24/1.61 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.24/1.61 [ =( hAPP( hAPP( X, Y ), 'c_Suc'( Z ) ), hAPP( hAPP( T, Y ), hAPP( hAPP(
% 1.24/1.61 X, Y ), Z ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, T, X, W, V0, V1
% 1.24/1.61 ) ) ],
% 1.24/1.61 [ =( hAPP( hAPP( X, Y ), 'c_Suc'( Z ) ), hAPP( hAPP( T, Y ), hAPP( hAPP(
% 1.24/1.61 X, Y ), Z ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, T, X, W, V0, V1
% 1.24/1.61 ) ) ],
% 1.24/1.61 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), Z ), hAPP( hAPP( Y, Z ),
% 1.24/1.61 'c_Suc'( T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, Y, W, V0,
% 1.24/1.61 V1 ) ) ],
% 1.24/1.61 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, Y ), T ) ), hAPP( hAPP( Z, Y ),
% 1.24/1.61 'c_Suc'( T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, Z, W, V0,
% 1.24/1.61 V1 ) ) ],
% 1.24/1.61 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ],
% 1.24/1.61 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ],
% 1.24/1.61 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ), ~(
% 1.24/1.61 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), ~(
% 1.24/1.61 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 1.24/1.61 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( X ) ) ) ],
% 1.24/1.61 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( X ) ) ) ],
% 1.24/1.61 [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( X ), Y, 'tc_nat' ), 'c_Suc'(
% 1.24/1.61 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ) ), =( 'c_Suc'(
% 1.24/1.61 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), Y ) ],
% 1.24/1.61 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ), =( 'c_Suc'( X
% 1.24/1.61 ), Y ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.24/1.61 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ), ~(
% 1.24/1.61 'c_Parity_Oeven__odd__class_Oeven'( 'c_Suc'( X ), 'tc_nat' ) ) ],
% 1.24/1.61 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_Suc'( X ), 'tc_nat' ),
% 1.24/1.61 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.24/1.61 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ), ~(
% 1.24/1.61 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.24/1.61 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.24/1.61 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ) ) ]
% 1.24/1.61 ,
% 1.24/1.61 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ), ~(
% 1.24/1.61 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.24/1.61 [ ~( =( 'c_Int_OPls', 'c_Int_OMin' ) ) ],
% 1.24/1.61 [ ~( =( 'c_Int_OMin', 'c_Int_OPls' ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.24/1.61 Y, Z, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ),
% 1.24/1.61 ~( 'c_lessequals'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.24/1.61 'c_Suc'( T ) ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.24/1.61 'c_Suc'( T ) ), X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.24/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP(
% 1.24/1.61 'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( Z ) ), X ), ~(
% 1.24/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =( hAPP( hAPP(
% 1.24/1.61 'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( Z ) ), hAPP( hAPP(
% 1.24/1.61 'c_Power_Opower__class_Opower'( X ), T ), 'c_Suc'( Z ) ) ) ), =( Y, T ),
% 1.24/1.61 ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.24/1.61 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.24/1.61 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.24/1.61 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.24/1.61 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.24/1.61 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.24/1.61 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), T ) ) ],
% 1.24/1.61 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.24/1.61 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Oone__class_Oone'(
% 1.24/1.61 'tc_nat' ) ), Y ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 1.24/1.61 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'(
% 1.24/1.61 X ), X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.24/1.61 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.24/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.24/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.24/1.61 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.24/1.61 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.24/1.61 [ =( hAPP( hAPP( X, Y ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), Y ),
% 1.24/1.61 ~( 'c_Groebner__Basis_Ogb__semiring'( Z, T, X, U, W, V0 ) ) ],
% 1.24/1.61 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.24/1.61 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.24/1.61 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.24/1.61 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OMin', X ), X ),
% 1.24/1.61 'c_HOL_Ouminus__class_Ouminus'( Y, X ) ) ],
% 1.24/1.61 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.24/1.61 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.24/1.62 , Z ), T ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, T, 'tc_nat' ) )
% 1.24/1.62 , ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 1.24/1.62 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.24/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.24/1.62 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 1.24/1.62 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.24/1.62 T, X ) ) ],
% 1.24/1.62 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.24/1.62 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.24/1.62 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.24/1.62 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.24/1.62 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.24/1.62 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X ) )
% 1.24/1.62 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ), Z ) ],
% 1.24/1.62 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.24/1.62 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X ) )
% 1.24/1.62 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), Z ) ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.24/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.24/1.62 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oone__class_Oone'( X ), X ),
% 1.24/1.62 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.24/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.24/1.62 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ), ~(
% 1.24/1.62 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.24/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.24/1.62 ,
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 1.24/1.62 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oone__class_Oone'( X ), X ),
% 1.24/1.62 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.24/1.62 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.24/1.62 ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ),
% 1.24/1.62 ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.24/1.62 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.24/1.62 ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.24/1.62 ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.24/1.62 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.24/1.62 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ), ~( 'c_lessequals'( U, Z
% 1.24/1.62 , X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), U
% 1.24/1.62 , X ) ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'(
% 1.24/1.62 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.24/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), ~(
% 1.24/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.24/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.24/1.62 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.24/1.62 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 1.24/1.62 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ) ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.24/1.62 'c_HOL_Oord__class_Oless'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 1.24/1.62 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ), ~(
% 1.24/1.62 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( 'c_lessequals'(
% 1.24/1.62 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.24/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.24/1.62 , X ) ) ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.24/1.62 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), 'c_lessequals'( Z,
% 1.24/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( X ), Z ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.24/1.62 X ), X ) ) ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.24/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.24/1.62 'class_Int_Onumber'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( hAPP(
% 1.24/1.62 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.24/1.62 ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.24/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.24/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.24/1.62 'c_HOL_Oone__class_Oone'( X ), X ) ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.24/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.24/1.62 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ), ~(
% 1.24/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.24/1.62 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ), ~(
% 1.24/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.24/1.62 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.24/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.24/1.62 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ), ~(
% 1.24/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.24/1.62 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ), ~(
% 1.24/1.62 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.24/1.62 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.24/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.24/1.62 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.24/1.62 , 'tc_nat' ), 'tc_nat' ), =( 'c_Int_Onumber__class_Onumber__of'( Z,
% 1.24/1.62 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 1.24/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ), X ) ) ],
% 1.24/1.62 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.24/1.62 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ouminus__class_Ouminus'(
% 1.24/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.24/1.62 [ 'c_HOL_Oord__class_Oless'( 'c_Divides_Odiv__class_Odiv'( X, Y,
% 1.24/1.62 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.24/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ), ~(
% 1.24/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), Y,
% 1.24/1.62 'tc_nat' ) ) ],
% 1.24/1.62 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP(
% 1.24/1.62 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.24/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), T ), hAPP( hAPP(
% 1.24/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), U ) ) ) ), =(
% 1.24/1.62 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ),
% 1.24/1.62 'c_Divides_Odiv__class_Omod'( T, Y, 'tc_nat' ) ) ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.24/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.24/1.62 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X )
% 1.24/1.62 , 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ) ) ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.24/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.24/1.62 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ), ~(
% 1.24/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.24/1.62 'tc_nat' ) ) ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 1.24/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( =(
% 1.24/1.62 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.24/1.62 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~( =(
% 1.24/1.62 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.24/1.62 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.24/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.24/1.62 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X )
% 1.24/1.62 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.24/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.24/1.62 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ]
% 1.24/1.62 ,
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.24/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.24/1.62 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X )
% 1.24/1.62 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) )
% 1.24/1.62 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.24/1.62 'c_lessequals'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ]
% 1.24/1.62 ,
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =( hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( X ), Y ), T ) ) ), ~(
% 1.24/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ), =( Z
% 1.24/1.62 , T ) ],
% 1.24/1.62 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'class_Int_Onumber'( X ) ),
% 1.24/1.62 ~( 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.24/1.62 , 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ), ~( 'c_lessequals'(
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.24/1.62 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'class_Int_Onumber'( X ) ),
% 1.24/1.62 'c_lessequals'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ),
% 1.24/1.62 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.24/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ), X ), ~(
% 1.24/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ),
% 1.24/1.62 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.24/1.62 , 'tc_nat' ), 'tc_nat' ) ],
% 1.24/1.62 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.24/1.62 'tc_nat' ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.24/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.24/1.62 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.24/1.62 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =(
% 1.24/1.62 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( Y
% 1.24/1.62 , X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.24/1.62 [ hBOOL( hAPP( X, 'c_Divides_Odiv__class_Odiv'( Y,
% 1.24/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ), ~( hBOOL( hAPP( X
% 1.24/1.62 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.24/1.62 [ ~( hBOOL( hAPP( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), hBOOL(
% 1.24/1.62 hAPP( X, 'c_Divides_Odiv__class_Odiv'( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.24/1.62 'tc_nat' ), 'tc_nat' ) ) ) ],
% 1.24/1.62 [ ~( hBOOL( hAPP( X, 'c_Divides_Odiv__class_Odiv'( Y,
% 1.24/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ) ), hBOOL( hAPP( X
% 1.24/1.62 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP( hAPP(
% 1.24/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.24/1.62 ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.24/1.62 'c_HOL_Ouminus__class_Ouminus'( Z, X ) ) ) ],
% 1.24/1.62 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.24/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =( hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X
% 1.24/1.62 ) ), Z ), 'c_HOL_Ouminus__class_Ouminus'( hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ) ),
% 1.24/1.62 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.24/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.24/1.62 'class_Int_Onumber'( X ) ), ~( =( 'c_HOL_Oinverse__class_Odivide'( Y, Z,
% 1.24/1.62 X ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ), =( Y, hAPP( hAPP(
% 1.24/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( T
% 1.24/1.62 , X ) ), Z ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =( hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ouminus__class_Ouminus'(
% 1.24/1.62 'c_HOL_Oone__class_Oone'( X ), X ) ), Y ), 'c_HOL_Ouminus__class_Ouminus'(
% 1.24/1.62 'c_HOL_Oone__class_Oone'( X ), X ) ), 'c_Parity_Oeven__odd__class_Oeven'(
% 1.24/1.62 Y, 'tc_nat' ) ],
% 1.24/1.62 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.24/1.62 'tc_nat' ), X ), Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 1.24/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ), ~(
% 1.24/1.62 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.24/1.62 ) ), X, 'tc_nat' ) ) ],
% 1.24/1.62 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.24/1.62 'tc_nat' ), Y ), X ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 1.24/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ), ~(
% 1.24/1.62 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.24/1.62 ) ), X, 'tc_nat' ) ) ],
% 1.24/1.62 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.24/1.62 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.24/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.24/1.62 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ), =(
% 1.24/1.62 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.24/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.24/1.62 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), hAPP( hAPP(
% 1.24/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Oinverse__class_Oinverse'(
% 1.24/1.62 Z, X ) ) ) ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.24/1.62 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.24/1.62 Z, X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.24/1.62 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ) ) ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), 'c_Int_Oiszero'(
% 1.24/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.24/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.24/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.24/1.62 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), X
% 1.24/1.62 ) ) ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.24/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.24/1.62 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), X
% 1.24/1.62 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.24/1.62 ) ],
% 1.24/1.62 [ =( 'c_Divides_Odiv__class_Odiv'( 'c_Suc'( X ), 'c_Suc'( 'c_Suc'(
% 1.24/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ),
% 1.24/1.62 'c_Divides_Odiv__class_Odiv'( X, 'c_Suc'( 'c_Suc'(
% 1.24/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ) ), ~(
% 1.24/1.62 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( 'class_Int_Onumber'( X )
% 1.24/1.62 ), =( 'c_HOL_Oinverse__class_Oinverse'(
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.24/1.62 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.24/1.62 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.24/1.62 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.24/1.62 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 1.24/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.24/1.62 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.24/1.62 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 1.24/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.24/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.24/1.62 [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 1.24/1.62 'class_OrderedGroup_Olordered__ab__group__add__abs'( X ) ), =(
% 1.24/1.62 'c_HOL_Oabs__class_Oabs'( Y, X ), Y ), 'c_HOL_Oord__class_Oless'( Y,
% 1.24/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Oabs__if'( X ) ), =(
% 1.24/1.62 'c_HOL_Oabs__class_Oabs'( Y, X ), Y ), 'c_HOL_Oord__class_Oless'( Y,
% 1.24/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.24/1.62 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.24/1.62 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), T ), Y ), hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( X ), T ), Z ), X ) ), ~(
% 1.24/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), T, X ) ) ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.24/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.24/1.62 ), Y ), Z ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), T ),
% 1.24/1.62 X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X )
% 1.24/1.62 ), ~( 'c_HOL_Oord__class_Oless'( Z, T, 'tc_nat' ) ) ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.24/1.62 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.24/1.62 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), T ), Y ), hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( X ), T ), Z ), X ) ), ~(
% 1.24/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), T, X ) ) ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.24/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.24/1.62 ), Y ), Z ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), T ),
% 1.24/1.62 X ), ~( 'c_HOL_Oord__class_Oless'( Z, T, 'tc_nat' ) ), ~(
% 1.24/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.24/1.62 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.24/1.62 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'(
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.24/1.62 ), X ) ), ~( 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.24/1.62 X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ), ~(
% 1.24/1.62 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.24/1.62 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.24/1.62 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'(
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.24/1.62 ), X ) ), 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X )
% 1.24/1.62 , X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X )
% 1.24/1.62 ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.24/1.62 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.24/1.62 ), X ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.24/1.62 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ),
% 1.24/1.62 ~( 'c_lessequals'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.24/1.62 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ],
% 1.24/1.62 [ ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.24/1.62 'tc_nat' ), X ), Y ), Y, 'tc_nat' ) ) ],
% 1.24/1.62 [ ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.24/1.62 'tc_nat' ), X ), Y ), X, 'tc_nat' ) ) ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.24/1.62 Z, X ) ), T ), 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( X ), Y ), T ), hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( X ), Z ), T ), X ) ), =( Z,
% 1.24/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.24/1.62 [ =( 'c_Divides_Odiv__class_Odiv'( X, hAPP( hAPP(
% 1.24/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ), 'tc_nat' ),
% 1.24/1.62 'c_Divides_Odiv__class_Odiv'( 'c_Divides_Odiv__class_Odiv'( X, Y,
% 1.24/1.62 'tc_nat' ), Z, 'tc_nat' ) ) ],
% 1.24/1.62 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( 'c_Power_Opower_Opower'( Y, Z,
% 1.24/1.62 T ), U ), W ) ) ), ~( hBOOL( hAPP( hAPP( X, Y ), U ) ) ), ~(
% 1.24/1.62 'c_Ring__and__Field_Oordered__semidom'( V0, V1, Y, Z, X, V2, T ) ) ],
% 1.24/1.62 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( 'c_Power_Opower_Opower'( Z, T,
% 1.24/1.62 U ), W ), V0 ) ) ), ~( hBOOL( hAPP( hAPP( X, Y ), W ) ) ), ~(
% 1.24/1.62 'c_Ring__and__Field_Oordered__semidom'( V1, Y, Z, T, X, V2, U ) ) ],
% 1.24/1.62 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower_Opower'( Y, Z, U ), T ), W ) ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.24/1.62 X, Y ), T ) ) ), ~( 'c_Ring__and__Field_Oordered__semidom'( V0, V1, Y, Z
% 1.24/1.62 , V2, X, U ) ) ],
% 1.24/1.62 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( 'c_Power_Opower_Opower'( Z, T,
% 1.24/1.62 U ), W ), V0 ) ) ), ~( hBOOL( hAPP( hAPP( X, Y ), W ) ) ), ~(
% 1.24/1.62 'c_Ring__and__Field_Oordered__semidom'( V1, Y, Z, T, V2, X, U ) ) ],
% 1.24/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.24/1.62 'c_HOL_Oabs__class_Oabs'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.24/1.62 'c_HOL_Oabs__class_Oabs'( Y, X ) ), 'c_HOL_Oabs__class_Oabs'( Z, X ) ), X
% 1.24/1.62 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oabs__class_Oabs'(
% 1.24/1.62 Y, X ) ), 'c_HOL_Oabs__class_Oabs'( Z, X ) ) ) ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.24/1.62 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), T, X ), ~(
% 1.24/1.62 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.24/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.24/1.62 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), Y, X ) ) ]
% 1.24/1.62 ,
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.24/1.62 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~(
% 1.24/1.62 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.24/1.62 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ),
% 1.24/1.62 Y, X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z,
% 1.24/1.62 X ) ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.24/1.62 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ), ~(
% 1.24/1.62 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.24/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~(
% 1.24/1.62 'c_lessequals'( Z, 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ) ) ]
% 1.24/1.62 ,
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.24/1.62 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.24/1.62 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.24/1.62 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T
% 1.24/1.62 ), X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T
% 1.24/1.62 , X ) ],
% 1.24/1.62 [ ~( 'c_Ring__and__Field_Oordered__idom'( X, Y, Z, T, U, W, V0, hAPP( V1
% 1.24/1.62 , V2 ), V3, V1, V4 ) ), hBOOL( hAPP( hAPP( W, Z ), V2 ) ) ],
% 1.24/1.62 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.24/1.62 ), ~( hBOOL( hAPP( hAPP( X, W ), hAPP( hAPP( V0, W ), Z ) ) ) ), ~(
% 1.24/1.62 'c_Ring__and__Field_Oordered__idom'( V1, V2, U, V3, X, T, V4, Y, V0, V5,
% 1.24/1.62 V6 ) ) ],
% 1.24/1.62 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.24/1.62 ), ~( hBOOL( hAPP( hAPP( X, U ), hAPP( hAPP( V0, U ), Y ) ) ) ), ~(
% 1.24/1.62 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, X, T, V4, Z, V0, V5,
% 1.24/1.62 V6 ) ) ],
% 1.24/1.62 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, Y ), T ) ) ), hBOOL( hAPP(
% 1.24/1.62 hAPP( U, Y ), W ) ), hBOOL( hAPP( hAPP( U, W ), Y ) ), ~(
% 1.24/1.62 'c_Ring__and__Field_Oordered__idom'( V0, V1, W, V2, X, U, V3, V4, Z, V5,
% 1.24/1.62 V6 ) ) ],
% 1.24/1.62 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, Y ), T ) ) ), ~( hBOOL( hAPP(
% 1.24/1.62 hAPP( X, T ), U ) ) ), ~( hBOOL( hAPP( hAPP( X, U ), T ) ) ), ~(
% 1.24/1.62 'c_Ring__and__Field_Oordered__idom'( W, V0, V1, V2, X, V3, V4, U, Z, V5,
% 1.24/1.62 V6 ) ) ],
% 1.24/1.62 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.24/1.62 ), ~( hBOOL( hAPP( hAPP( X, hAPP( hAPP( V0, W ), Y ) ), W ) ) ), ~(
% 1.24/1.62 'c_Ring__and__Field_Oordered__idom'( V1, V2, U, V3, X, T, V4, Z, V0, V5,
% 1.24/1.62 V6 ) ) ],
% 1.24/1.62 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.24/1.62 ), ~( hBOOL( hAPP( hAPP( X, hAPP( hAPP( V0, U ), Z ) ), U ) ) ), ~(
% 1.24/1.62 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, X, T, V4, Y, V0, V5,
% 1.24/1.62 V6 ) ) ],
% 1.24/1.62 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), Z ) ), hBOOL( hAPP(
% 1.24/1.62 hAPP( U, Z ), W ) ), hBOOL( hAPP( hAPP( U, W ), Z ) ), ~(
% 1.24/1.62 'c_Ring__and__Field_Oordered__idom'( V0, V1, W, V2, X, U, V3, V4, Y, V5,
% 1.24/1.62 V6 ) ) ],
% 1.24/1.62 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), Z ) ), ~( hBOOL( hAPP(
% 1.24/1.62 hAPP( X, U ), T ) ) ), ~( hBOOL( hAPP( hAPP( X, T ), U ) ) ), ~(
% 1.24/1.62 'c_Ring__and__Field_Oordered__idom'( W, V0, V1, V2, X, V3, V4, U, Y, V5,
% 1.24/1.62 V6 ) ) ],
% 1.24/1.62 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.24/1.62 ), ~( hBOOL( hAPP( hAPP( X, W ), hAPP( hAPP( V0, Z ), W ) ) ) ), ~(
% 1.24/1.62 'c_Ring__and__Field_Oordered__idom'( V1, V2, U, V3, X, T, V4, Y, V0, V5,
% 1.24/1.62 V6 ) ) ],
% 1.24/1.62 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.24/1.62 ), ~( hBOOL( hAPP( hAPP( X, U ), hAPP( hAPP( V0, Y ), U ) ) ) ), ~(
% 1.24/1.62 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, X, T, V4, Z, V0, V5,
% 1.24/1.62 V6 ) ) ],
% 1.24/1.62 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), Y ) ) ), hBOOL( hAPP(
% 1.24/1.62 hAPP( U, Y ), W ) ), hBOOL( hAPP( hAPP( U, W ), Y ) ), ~(
% 1.24/1.62 'c_Ring__and__Field_Oordered__idom'( V0, V1, W, V2, X, U, V3, V4, Z, V5,
% 1.24/1.62 V6 ) ) ],
% 1.24/1.62 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), Y ) ) ), ~( hBOOL( hAPP(
% 1.24/1.62 hAPP( X, T ), U ) ) ), ~( hBOOL( hAPP( hAPP( X, U ), T ) ) ), ~(
% 1.24/1.62 'c_Ring__and__Field_Oordered__idom'( W, V0, V1, V2, X, V3, V4, U, Z, V5,
% 1.24/1.62 V6 ) ) ],
% 1.24/1.62 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.24/1.62 ), ~( hBOOL( hAPP( hAPP( X, hAPP( hAPP( V0, Y ), W ) ), W ) ) ), ~(
% 1.24/1.62 'c_Ring__and__Field_Oordered__idom'( V1, V2, U, V3, X, T, V4, Z, V0, V5,
% 1.24/1.62 V6 ) ) ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Oone__class_Oone'(
% 1.24/1.62 'tc_nat' ) ), Y ) ],
% 1.24/1.62 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.24/1.62 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), Y ), hAPP( hAPP(
% 1.24/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.24/1.62 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y )
% 1.24/1.62 , 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 1.24/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.24/1.62 'c_HOL_Oinverse__class_Oinverse'( hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y
% 1.24/1.62 , X ) ), Z ) ) ],
% 1.24/1.62 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =( hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.24/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.24/1.62 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( X ), Y ), T ) ), hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( X ), Z ), T ) ) ) ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.24/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.24/1.62 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( X ), Y ), T ) ), hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( X ), Z ), T ) ) ) ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Oring__1__no__zero__divisors'( X ) ), ~(
% 1.24/1.62 =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ),
% 1.24/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.24/1.62 ) ) ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.24/1.62 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.24/1.62 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.24/1.62 ), ~( =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ),
% 1.24/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.24/1.62 ) ) ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.24/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.24/1.62 Z, X ) ), T ), 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( X ), Y ), T ), hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( X ), Z ), T ), X ) ) ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.24/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ) ) ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.24/1.62 'c_HOL_Oabs__class_Oabs'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X )
% 1.24/1.62 , Y ), Z ), X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ),
% 1.24/1.62 'c_HOL_Oabs__class_Oabs'( Y, X ) ), Z ) ) ],
% 1.24/1.62 [ ~( =( 'c_Int_OMin', 'c_Int_OBit0'( X ) ) ) ],
% 1.24/1.62 [ ~( =( 'c_Int_OBit0'( X ), 'c_Int_OMin' ) ) ],
% 1.24/1.62 [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.24/1.62 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ),
% 1.24/1.62 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.24/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X,
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ) ],
% 1.24/1.62 [ ~( =( 'c_Divides_Odiv__class_Omod'( X,
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oone__class_Oone'(
% 1.24/1.62 'tc_nat' ) ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.24/1.62 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X,
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ],
% 1.24/1.62 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.24/1.62 'c_Divides_Odiv__class_Odiv'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.24/1.62 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ),
% 1.24/1.62 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'(
% 1.24/1.62 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.24/1.62 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.24/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'(
% 1.24/1.62 'tc_nat' ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.24/1.62 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ),
% 1.24/1.62 'c_Divides_Odiv__class_Odiv'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.24/1.62 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) )
% 1.24/1.62 , ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.24/1.62 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.24/1.62 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), hAPP( hAPP(
% 1.24/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.24/1.62 'c_HOL_Oplus__class_Oplus'( X ), X ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.24/1.62 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.24/1.62 ), Z ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.24/1.62 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ],
% 1.24/1.62 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.24/1.62 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.24/1.62 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ) ), Y ) ) ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oabs__class_Oabs'( Y, X ) ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ), hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ) ), ~(
% 1.24/1.62 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.24/1.62 , 'tc_nat' ), 'tc_nat' ) ) ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.24/1.62 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.24/1.62 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.24/1.62 ), =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ),
% 1.24/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.24/1.62 , 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ), =(
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.24/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.24/1.62 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.24/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), =( 'c_Int_Onumber__class_Onumber__of'(
% 1.24/1.62 Y, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.24/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_lessequals'( Y,
% 1.24/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ),
% 1.24/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.24/1.62 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.24/1.62 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.24/1.62 ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.24/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( =( hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.24/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.24/1.62 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.24/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.24/1.62 ), Y ), 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ),
% 1.24/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.24/1.62 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.24/1.62 hAPP( hAPP( 'c_Power_Opower__class_Opower'( 'tc_nat' ), X ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ), 'tc_nat' ), ~(
% 1.24/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.24/1.62 'tc_nat' ) ) ],
% 1.24/1.62 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.24/1.62 'tc_nat' ), =( 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.24/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.24/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( 'tc_nat' ), X ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ), 'tc_nat' ) ) ],
% 1.24/1.62 [ ~( =( 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ),
% 1.24/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Oord__class_Oless'(
% 1.24/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( 'tc_nat' ), Y ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ), 'tc_nat' ) ],
% 1.24/1.62 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ), ~(
% 1.24/1.62 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( 'tc_nat' ), X ), Y ), 'tc_nat' ) ) ],
% 1.24/1.62 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.24/1.62 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), 'c_Suc'( hAPP( hAPP(
% 1.24/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ), hAPP( hAPP(
% 1.24/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.24/1.62 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ),
% 1.24/1.62 hAPP( hAPP( 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.24/1.62 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), Z ) ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ],
% 1.24/1.62 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.24/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'(
% 1.24/1.62 'tc_nat' ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.24/1.62 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'c_Suc'(
% 1.24/1.62 'c_Divides_Odiv__class_Odiv'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.24/1.62 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) )
% 1.24/1.62 ), 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.24/1.62 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.24/1.62 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.24/1.62 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.24/1.62 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.24/1.62 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.24/1.62 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), X ), X ), X ) ) ],
% 1.24/1.62 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), hAPP( T, X ) ),
% 1.24/1.62 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ), U ) ), X ), ~(
% 1.24/1.62 'c_Ring__and__Field_Ocomm__ring__1'( X, Y, W, T, V0, V1, Z ) ) ],
% 1.24/1.62 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), hAPP( T, U ) ),
% 1.24/1.62 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ), W ) ), hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower_Opower'( X, Y, Z ), U ), hAPP( hAPP(
% 1.24/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ), W ) ) ), ~(
% 1.24/1.62 'c_Ring__and__Field_Ocomm__ring__1'( X, Y, V0, T, V1, V2, Z ) ) ],
% 1.24/1.62 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( 'c_Power_Opower_Opower'( Z, T,
% 1.24/1.62 U ), W ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ), V0 ) ) ) ), ~(
% 1.24/1.62 'c_Ring__and__Field_Oordered__idom'( V1, V2, Y, V3, X, V4, V5, Z, T, V6,
% 1.24/1.62 U ) ) ],
% 1.24/1.62 [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.24/1.62 'c_Int_OBit0'( 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat'
% 1.24/1.62 ), 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), =(
% 1.24/1.62 'c_Divides_Odiv__class_Omod'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.24/1.62 'c_Int_OBit0'( 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat'
% 1.24/1.62 ), 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.24/1.62 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), =(
% 1.24/1.62 'c_Divides_Odiv__class_Omod'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.24/1.62 'c_Int_OBit0'( 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat'
% 1.24/1.62 ), 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), =(
% 1.24/1.62 'c_Divides_Odiv__class_Omod'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.24/1.62 'c_Int_OBit0'( 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat'
% 1.24/1.62 ), 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.24/1.62 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.24/1.62 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.24/1.62 ), Y ), Y ) ) ],
% 1.24/1.62 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ), hAPP( hAPP(
% 1.24/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ), U ) ), hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower_Opower'( X, Y, Z ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.24/1.62 X, Y, Z ), T ), U ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.24/1.62 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ), ~(
% 1.24/1.62 'c_OrderedGroup_Omonoid__mult'( X, Y, Z ) ) ],
% 1.24/1.62 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( Y, hAPP( hAPP( Y, T ), T ) )
% 1.24/1.62 , T ) ), ~( 'c_OrderedGroup_Omonoid__mult'( X, Y, Z ) ) ],
% 1.24/1.62 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_Int_Oint' ), 'c_Nat_Osemiring__1__class_Oof__nat'(
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_Int_Oint' ) ) ],
% 1.24/1.62 [ =( 'c_FFT__Mirabelle_OIFFT'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X
% 1.24/1.62 ), X ) ],
% 1.24/1.62 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( X, Y ), hAPP(
% 1.24/1.62 hAPP( 'c_Power_Opower_Opower'( T, U, W ), Z ), 'c_Suc'( hAPP( hAPP(
% 1.24/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ), V0 ) ) ) ) ) ), ~(
% 1.24/1.62 'c_Ring__and__Field_Oordered__idom'( V1, V2, Y, V3, X, V4, V5, T, U, V6,
% 1.24/1.62 W ) ) ],
% 1.24/1.62 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( 'c_Power_Opower_Opower'( Y, Z, T ),
% 1.24/1.62 U ), 'c_Suc'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ), W ) ) ) ), V0 ) ), ~( hBOOL( hAPP( hAPP(
% 1.24/1.62 X, U ), V0 ) ) ), ~( 'c_Ring__and__Field_Oordered__idom'( V1, V2, V0, V3
% 1.24/1.62 , V4, X, V5, Y, Z, V6, T ) ) ],
% 1.24/1.62 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ), 'c_Suc'( hAPP(
% 1.24/1.62 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ), U ) ) ), hAPP( hAPP( Y, T ), hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower_Opower'( X, Y, Z ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.24/1.62 X, Y, Z ), T ), U ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.24/1.62 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), ~(
% 1.24/1.62 'c_OrderedGroup_Omonoid__mult'( X, Y, Z ) ) ],
% 1.24/1.62 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), hAPP( T, X ) ),
% 1.24/1.62 'c_Suc'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ), U ) ) ), hAPP( T, X ) ), ~(
% 1.24/1.62 'c_Ring__and__Field_Ocomm__ring__1'( X, Y, W, T, V0, V1, Z ) ) ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.24/1.62 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.24/1.62 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.24/1.62 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ) ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.24/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.24/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.24/1.62 ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.24/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.24/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.24/1.62 ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =( hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ouminus__class_Ouminus'(
% 1.24/1.62 'c_HOL_Oone__class_Oone'( X ), X ) ), hAPP( hAPP(
% 1.24/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ), Y ) ), 'c_HOL_Oone__class_Oone'( X ) ) ]
% 1.24/1.62 ,
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.24/1.62 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.24/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), X ) ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.24/1.62 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ]
% 1.24/1.62 ,
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.24/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.24/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.24/1.62 ) ) ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.24/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.24/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ) ), X ) ) ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.24/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.24/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ) ), X ), =( Z, 'c_HOL_Ozero__class_Ozero'(
% 1.24/1.62 X ) ) ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.24/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.24/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ) ), X ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.24/1.62 X ) ) ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.24/1.62 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.24/1.62 X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ) ), X ) ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.24/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.24/1.62 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.24/1.62 ],
% 1.24/1.62 [ ~( 'class_Int_Oring__char__0'( X ) ), ~( 'class_Int_Onumber__ring'( X
% 1.24/1.62 ) ), ~( 'c_Int_Oiszero'( 'c_Int_Onumber__class_Onumber__of'(
% 1.24/1.62 'c_Int_OBit1'( Y ), X ), X ) ) ],
% 1.24/1.62 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Ozero__class_Ozero'( X
% 1.24/1.62 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', X ) ) ],
% 1.24/1.62 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', X ),
% 1.24/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.24/1.62 [ ~( 'class_Int_Onumber__ring'( X ) ), 'c_Int_Oiszero'(
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', X ), X ) ],
% 1.24/1.62 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.24/1.62 'c_HOL_Oplus__class_Oplus'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.24/1.62 'c_Int_OPls', X ) ), Y ), Y ) ],
% 1.24/1.62 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.24/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_Int_Onumber__class_Onumber__of'(
% 1.24/1.62 'c_Int_OPls', X ) ), Y ) ],
% 1.24/1.62 [ ~( 'class_Int_Oring__char__0'( X ) ), ~( 'class_Int_Onumber__ring'( X
% 1.24/1.62 ) ), 'c_Int_Oiszero'( 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.24/1.62 ~( 'c_Int_Oiszero'( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( Y
% 1.24/1.62 ), X ), X ) ) ],
% 1.24/1.62 [ ~( 'class_Int_Oring__char__0'( X ) ), ~( 'class_Int_Onumber__ring'( X
% 1.24/1.62 ) ), 'c_Int_Oiszero'( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.24/1.62 Y ), X ), X ), ~( 'c_Int_Oiszero'( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.24/1.62 , X ), X ) ) ],
% 1.24/1.62 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.24/1.62 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.24/1.62 'c_HOL_Oone__class_Oone'( X ) ), 'c_Int_Onumber__class_Onumber__of'(
% 1.24/1.62 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), X ) ) ],
% 1.24/1.62 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.24/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.24/1.62 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), X ) ), Y ), hAPP( hAPP(
% 1.24/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ) ) ],
% 1.24/1.62 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.24/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), X ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y )
% 1.24/1.62 , Y ) ) ],
% 1.24/1.62 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.24/1.62 'c_Int_OMin', X ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' )
% 1.24/1.62 , 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ), Y ) ), 'c_HOL_Oone__class_Oone'( X ) ) ]
% 1.24/1.62 ,
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.24/1.62 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), Y ), hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( Z ) ) ) ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.24/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( Z ) ) ) ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.24/1.62 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.24/1.62 'c_Suc'( Y ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( Z ) ), hAPP( hAPP(
% 1.24/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.24/1.62 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( Z ) ), hAPP( hAPP(
% 1.24/1.62 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), Y ) ) ],
% 1.24/1.62 [ ~( 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( Z ) ), hAPP( hAPP(
% 1.24/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( Z ) ), hAPP( hAPP(
% 1.24/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =( hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ouminus__class_Ouminus'(
% 1.24/1.62 'c_HOL_Oone__class_Oone'( X ), X ) ), 'c_Suc'( hAPP( hAPP(
% 1.24/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ), Y ) ) ), 'c_HOL_Ouminus__class_Ouminus'(
% 1.24/1.62 'c_HOL_Oone__class_Oone'( X ), X ) ) ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.24/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.24/1.62 ), Y ), 'c_Suc'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.24/1.62 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.24/1.62 X ) ) ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.24/1.62 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.24/1.62 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( hAPP( hAPP(
% 1.24/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ), X ) ) ],
% 1.24/1.62 [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( 'c_Suc'( 'c_Suc'( X ) ) ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), 'tc_nat' ),
% 1.24/1.62 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.24/1.62 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), X ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.24/1.62 [ =( 'c_Divides_Odiv__class_Odiv'( 'c_Suc'( 'c_Suc'( 'c_Suc'( X ) ) ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), 'tc_nat' ),
% 1.24/1.62 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.24/1.62 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), X ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.24/1.62 [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Suc'( 'c_Suc'( 'c_Suc'( Y ) ) )
% 1.24/1.62 , 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X, hAPP( hAPP(
% 1.24/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ), Y ), 'tc_nat' ) ) ],
% 1.24/1.62 [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( 'c_Suc'( 'c_Suc'( X ) ) ), Y
% 1.24/1.62 , 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.24/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), Y, 'tc_nat' ) ) ],
% 1.24/1.62 [ =( 'c_Divides_Odiv__class_Odiv'( X, 'c_Suc'( 'c_Suc'( 'c_Suc'( Y ) ) )
% 1.24/1.62 , 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( X, hAPP( hAPP(
% 1.24/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ), Y ), 'tc_nat' ) ) ],
% 1.24/1.62 [ =( 'c_Divides_Odiv__class_Odiv'( 'c_Suc'( 'c_Suc'( 'c_Suc'( X ) ) ), Y
% 1.24/1.62 , 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.24/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), Y, 'tc_nat' ) ) ],
% 1.24/1.62 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.24/1.62 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.24/1.62 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), hAPP( hAPP( T, hAPP(
% 1.24/1.62 hAPP( X, Y ), Z ) ), hAPP( hAPP( X, Y ), Z ) ) ), ~(
% 1.24/1.62 'c_Groebner__Basis_Ogb__semiring'( U, T, X, W, V0, V1 ) ) ],
% 1.24/1.62 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( 'c_Power_Opower_Opower'( Z, T,
% 1.24/1.62 U ), W ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.24/1.62 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), =( W, Y ), ~(
% 1.24/1.62 'c_Ring__and__Field_Oordered__idom'( V0, V1, Y, V2, V3, X, V4, Z, T, V5,
% 1.24/1.62 U ) ) ],
% 1.24/1.62 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower_Opower'( T, U, W ), V0 ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( T
% 1.24/1.62 , U, W ), V1 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.24/1.62 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ), =( V1, Y ), ~(
% 1.24/1.62 'c_Ring__and__Field_Oordered__idom'( V2, V3, Y, Z, V4, X, V5, T, U, V6, W
% 1.24/1.62 ) ) ],
% 1.24/1.62 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower_Opower'( T, U, W ), V0 ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( T
% 1.24/1.62 , U, W ), V1 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.24/1.62 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ), =( V0, Y ), ~(
% 1.24/1.62 'c_Ring__and__Field_Oordered__idom'( V2, V3, Y, Z, V4, X, V5, T, U, V6, W
% 1.24/1.62 ) ) ],
% 1.24/1.62 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.24/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), X ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), X ) ],
% 1.24/1.62 [ ~( hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower_Opower'( T, U, W ), Y ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( T
% 1.24/1.62 , U, W ), Y ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.24/1.62 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ) ), ~(
% 1.24/1.62 'c_Ring__and__Field_Oordered__idom'( V0, V1, Y, Z, V2, X, V3, T, U, V4, W
% 1.24/1.62 ) ) ],
% 1.24/1.62 [ ~( hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower_Opower'( Z, T, U ), W ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( Z
% 1.24/1.62 , T, U ), V0 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.24/1.62 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), V1 ) ) ), ~(
% 1.24/1.62 'c_Ring__and__Field_Oordered__idom'( V2, V3, V1, Y, V4, X, V5, Z, T, V6,
% 1.24/1.62 U ) ) ],
% 1.24/1.62 [ ~( hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( 'c_Power_Opower_Opower'( Z,
% 1.24/1.62 T, U ), Y ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.24/1.62 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ), ~(
% 1.24/1.62 'c_Ring__and__Field_Oordered__idom'( W, V0, Y, V1, V2, X, V3, Z, T, V4, U
% 1.24/1.62 ) ) ],
% 1.24/1.62 [ ~( hBOOL( hAPP( hAPP( X, hAPP( hAPP( 'c_Power_Opower_Opower'( Y, Z, T
% 1.24/1.62 ), U ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ) ), W ) ) ), ~(
% 1.24/1.62 'c_Ring__and__Field_Oordered__idom'( V0, V1, W, V2, V3, X, V4, Y, Z, V5,
% 1.24/1.62 T ) ) ],
% 1.24/1.62 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.24/1.62 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'(
% 1.24/1.62 'tc_nat' ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.24/1.62 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ],
% 1.24/1.62 [ ~( 'c_Ring__and__Field_Oordered__idom'( X, Y, Z, T, U, W, V0, V1, V2,
% 1.24/1.62 V3, V4 ) ), =( hAPP( hAPP( T, hAPP( hAPP( 'c_Power_Opower_Opower'( V1, V2
% 1.24/1.62 , V4 ), Z ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.24/1.62 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower_Opower'( V1, V2, V4 ), Z ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ) ), Z ) ],
% 1.24/1.62 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), hAPP( T, U ) ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y
% 1.24/1.62 , Z ), U ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.24/1.62 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ), ~(
% 1.24/1.62 'c_Ring__and__Field_Oordered__idom'( W, V0, V1, V2, V3, V4, T, X, Y, V5,
% 1.24/1.62 Z ) ) ],
% 1.24/1.62 [ =( hAPP( X, hAPP( hAPP( 'c_Power_Opower_Opower'( Y, Z, T ), U ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( Y
% 1.24/1.62 , Z, T ), U ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.24/1.62 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ), ~(
% 1.24/1.62 'c_Ring__and__Field_Oordered__idom'( W, V0, V1, V2, V3, V4, X, Y, Z, V5,
% 1.24/1.62 T ) ) ],
% 1.24/1.62 [ ~( 'c_Ring__and__Field_Oordered__idom'( X, Y, hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower_Opower'( Z, T, U ), W ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ), V0, V1, V2, V3, Z, T, V4, U ) ), =( W,
% 1.24/1.62 hAPP( hAPP( 'c_Power_Opower_Opower'( Z, T, U ), W ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ],
% 1.24/1.62 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.24/1.62 ), ~( hBOOL( hAPP( hAPP( X, hAPP( hAPP( V0, Z ), U ) ), U ) ) ), ~(
% 1.24/1.62 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, X, T, V4, Y, V0, V5,
% 1.24/1.62 V6 ) ) ],
% 1.24/1.62 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), T ) ), hBOOL( hAPP(
% 1.24/1.62 hAPP( U, T ), W ) ), hBOOL( hAPP( hAPP( U, W ), T ) ), ~(
% 1.24/1.62 'c_Ring__and__Field_Oordered__idom'( V0, V1, W, V2, X, U, V3, V4, Y, V5,
% 1.24/1.62 V6 ) ) ],
% 1.24/1.62 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), T ) ), ~( hBOOL( hAPP(
% 1.24/1.62 hAPP( X, U ), Z ) ) ), ~( hBOOL( hAPP( hAPP( X, Z ), U ) ) ), ~(
% 1.24/1.62 'c_Ring__and__Field_Oordered__idom'( W, V0, V1, V2, X, V3, V4, U, Y, V5,
% 1.24/1.62 V6 ) ) ],
% 1.24/1.62 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.24/1.62 ), ~( hBOOL( hAPP( hAPP( X, W ), hAPP( hAPP( V0, W ), Z ) ) ) ), ~(
% 1.24/1.62 'c_Ring__and__Field_Oordered__idom'( V1, V2, U, V3, T, X, V4, Y, V0, V5,
% 1.24/1.62 V6 ) ) ],
% 1.24/1.62 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.24/1.62 ), ~( hBOOL( hAPP( hAPP( X, U ), hAPP( hAPP( V0, U ), Y ) ) ) ), ~(
% 1.24/1.62 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, T, X, V4, Z, V0, V5,
% 1.24/1.62 V6 ) ) ],
% 1.24/1.62 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, Y ), T ) ) ), hBOOL( hAPP(
% 1.24/1.62 hAPP( U, Y ), W ) ), hBOOL( hAPP( hAPP( U, W ), Y ) ), ~(
% 1.24/1.62 'c_Ring__and__Field_Oordered__idom'( V0, V1, W, V2, U, X, V3, V4, Z, V5,
% 1.24/1.62 V6 ) ) ],
% 1.24/1.62 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, Y ), T ) ) ), ~( hBOOL( hAPP(
% 1.24/1.62 hAPP( X, T ), U ) ) ), ~( hBOOL( hAPP( hAPP( X, U ), T ) ) ), ~(
% 1.24/1.62 'c_Ring__and__Field_Oordered__idom'( W, V0, V1, V2, V3, X, V4, U, Z, V5,
% 1.24/1.62 V6 ) ) ],
% 1.24/1.62 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.24/1.62 ), ~( hBOOL( hAPP( hAPP( X, hAPP( hAPP( V0, W ), Y ) ), W ) ) ), ~(
% 1.24/1.62 'c_Ring__and__Field_Oordered__idom'( V1, V2, U, V3, T, X, V4, Z, V0, V5,
% 1.24/1.62 V6 ) ) ],
% 1.24/1.62 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.24/1.62 ), ~( hBOOL( hAPP( hAPP( X, hAPP( hAPP( V0, U ), Z ) ), U ) ) ), ~(
% 1.24/1.62 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, T, X, V4, Y, V0, V5,
% 1.24/1.62 V6 ) ) ],
% 1.24/1.62 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), Z ) ), hBOOL( hAPP(
% 1.24/1.62 hAPP( U, Z ), W ) ), hBOOL( hAPP( hAPP( U, W ), Z ) ), ~(
% 1.24/1.62 'c_Ring__and__Field_Oordered__idom'( V0, V1, W, V2, U, X, V3, V4, Y, V5,
% 1.24/1.62 V6 ) ) ],
% 1.24/1.62 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), Z ) ), ~( hBOOL( hAPP(
% 1.24/1.62 hAPP( X, U ), T ) ) ), ~( hBOOL( hAPP( hAPP( X, T ), U ) ) ), ~(
% 1.24/1.62 'c_Ring__and__Field_Oordered__idom'( W, V0, V1, V2, V3, X, V4, U, Y, V5,
% 1.24/1.62 V6 ) ) ],
% 1.24/1.62 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.24/1.62 ), ~( hBOOL( hAPP( hAPP( X, W ), hAPP( hAPP( V0, Z ), W ) ) ) ), ~(
% 1.24/1.62 'c_Ring__and__Field_Oordered__idom'( V1, V2, U, V3, T, X, V4, Y, V0, V5,
% 1.24/1.62 V6 ) ) ],
% 1.24/1.62 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.24/1.62 ), ~( hBOOL( hAPP( hAPP( X, U ), hAPP( hAPP( V0, Y ), U ) ) ) ), ~(
% 1.24/1.62 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, T, X, V4, Z, V0, V5,
% 1.24/1.62 V6 ) ) ],
% 1.24/1.62 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), Y ) ) ), hBOOL( hAPP(
% 1.24/1.62 hAPP( U, Y ), W ) ), hBOOL( hAPP( hAPP( U, W ), Y ) ), ~(
% 1.24/1.62 'c_Ring__and__Field_Oordered__idom'( V0, V1, W, V2, U, X, V3, V4, Z, V5,
% 1.24/1.62 V6 ) ) ],
% 1.24/1.62 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), Y ) ) ), ~( hBOOL( hAPP(
% 1.24/1.62 hAPP( X, T ), U ) ) ), ~( hBOOL( hAPP( hAPP( X, U ), T ) ) ), ~(
% 1.24/1.62 'c_Ring__and__Field_Oordered__idom'( W, V0, V1, V2, V3, X, V4, U, Z, V5,
% 1.24/1.62 V6 ) ) ],
% 1.24/1.62 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.24/1.62 ), ~( hBOOL( hAPP( hAPP( X, hAPP( hAPP( V0, Y ), W ) ), W ) ) ), ~(
% 1.24/1.62 'c_Ring__and__Field_Oordered__idom'( V1, V2, U, V3, T, X, V4, Z, V0, V5,
% 1.24/1.62 V6 ) ) ],
% 1.24/1.62 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.24/1.62 ), ~( hBOOL( hAPP( hAPP( X, hAPP( hAPP( V0, Z ), U ) ), U ) ) ), ~(
% 1.24/1.62 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, T, X, V4, Y, V0, V5,
% 1.24/1.62 V6 ) ) ],
% 1.24/1.62 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), T ) ), hBOOL( hAPP(
% 1.24/1.62 hAPP( U, T ), W ) ), hBOOL( hAPP( hAPP( U, W ), T ) ), ~(
% 1.24/1.62 'c_Ring__and__Field_Oordered__idom'( V0, V1, W, V2, U, X, V3, V4, Y, V5,
% 1.24/1.62 V6 ) ) ],
% 1.24/1.62 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), T ) ), ~( hBOOL( hAPP(
% 1.24/1.62 hAPP( X, U ), Z ) ) ), ~( hBOOL( hAPP( hAPP( X, Z ), U ) ) ), ~(
% 1.24/1.62 'c_Ring__and__Field_Oordered__idom'( W, V0, V1, V2, V3, X, V4, U, Y, V5,
% 1.24/1.62 V6 ) ) ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.24/1.62 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.24/1.62 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.24/1.62 , X ), X ), T, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T
% 1.24/1.62 , X ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.24/1.62 , T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ),
% 1.24/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.24/1.62 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.24/1.62 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.24/1.62 , X ), X ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.24/1.62 ) ), ~( 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.24/1.62 , Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ),
% 1.24/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.24/1.62 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ),
% 1.24/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ],
% 1.24/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), ~( =(
% 1.24/1.62 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.24/1.62 =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.24/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), ~(
% 1.24/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.24/1.62 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ozero__class_Ozero'( X ), X ), X ) ) ]
% 1.24/1.62 ,
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.24/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.24/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.24/1.62 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.24/1.62 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.24/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.24/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.24/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.24/1.62 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.24/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.24/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.24/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.24/1.62 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.24/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.24/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.24/1.62 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.24/1.62 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.24/1.62 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.24/1.62 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.24/1.62 , Z ), Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) )
% 1.24/1.62 ],
% 1.24/1.62 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.24/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.24/1.62 'tc_nat' ), Z ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.24/1.62 , Z ), Y ), 'tc_nat' ) ) ],
% 1.24/1.62 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.24/1.62 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.24/1.62 , X ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) )
% 1.24/1.62 ],
% 1.24/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.24/1.62 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.24/1.62 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Y ), hAPP( hAPP(
% 1.24/1.62 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ) ) ],
% 1.24/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.24/1.62 , 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.24/1.62 , Y ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ),
% 1.24/1.62 ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.24/1.62 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.24/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.24/1.62 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~(
% 1.24/1.62 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.24/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.24/1.62 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.24/1.62 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP(
% 1.24/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ],
% 1.24/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.24/1.62 , 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.24/1.62 , Y ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ),
% 1.24/1.62 ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.24/1.62 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.24/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.24/1.62 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~(
% 1.24/1.62 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.24/1.62 [ ~( hBOOL( hAPP( X, Y ) ) ), hBOOL( hAPP( X,
% 1.24/1.62 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.24/1.62 'tc_nat' ) ) ) ],
% 1.24/1.62 [ ~( hBOOL( hAPP( X, 'c_Divides_Odiv__class_Omod'( Y,
% 1.24/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ) ), hBOOL( hAPP( X
% 1.24/1.62 , Y ) ) ],
% 1.24/1.62 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Y, X ) ]
% 1.24/1.62 ,
% 1.24/1.62 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Y, X ) ],
% 1.24/1.62 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.24/1.62 , X ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_lessequals'( Y, T
% 1.24/1.62 , X ) ) ],
% 1.24/1.62 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.24/1.62 , X ), ~( 'c_lessequals'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T
% 1.24/1.62 , X ) ) ],
% 1.24/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.24/1.62 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T )
% 1.24/1.62 , X ), ~( 'c_lessequals'( U, T, X ) ), ~( 'c_lessequals'( Y, hAPP( hAPP(
% 1.24/1.62 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ), X ) ) ],
% 1.24/1.62 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.24/1.62 'c_lessequals'( T, Z, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.24/1.62 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.24/1.62 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.24/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.24/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 1.24/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.24/1.62 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.24/1.62 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_lessequals'( T, Z, X
% 1.24/1.62 ) ) ],
% 1.24/1.62 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.24/1.62 ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X
% 1.24/1.62 ) ) ],
% 1.24/1.62 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.24/1.62 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( T, Z, X ) ) ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.24/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.24/1.62 'c_HOL_Oone__class_Oone'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.24/1.62 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.24/1.62 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ),
% 1.24/1.62 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~(
% 1.24/1.62 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.24/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ],
% 1.24/1.62 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.24/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_Suc'(
% 1.24/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_Suc'(
% 1.24/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.24/1.62 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.24/1.62 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~( 'c_lessequals'(
% 1.24/1.62 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.24/1.62 ), X ) ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.24/1.62 , X ), ~( 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.24/1.62 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.24/1.62 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.24/1.62 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~( 'c_lessequals'(
% 1.24/1.62 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.24/1.62 ), X ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.24/1.62 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ),
% 1.24/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.24/1.62 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.24/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), X, 'tc_nat' ),
% 1.24/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.24/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.24/1.62 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.24/1.62 ), Y ), Z ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.24/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.24/1.62 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.24/1.62 ), Y ), Z ), Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.24/1.62 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.24/1.62 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.24/1.62 , X ), X ), T, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T
% 1.24/1.62 , X ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.24/1.62 , T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ), ~(
% 1.24/1.62 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.24/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.24/1.62 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.24/1.62 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.24/1.62 , X ), X ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.24/1.62 ) ), ~( 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.24/1.62 , Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ), ~(
% 1.24/1.62 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.24/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 1.24/1.62 'c_HOL_Oplus__class_Oplus'( X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X )
% 1.24/1.62 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.24/1.62 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ), Z ) ), Y ) ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( hAPP(
% 1.24/1.62 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.24/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.24/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ), hAPP( hAPP(
% 1.24/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.24/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.24/1.62 ,
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.24/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.24/1.62 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'(
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OMin', X ), Y, X ),
% 1.24/1.62 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oinverse__class_Odivide'(
% 1.24/1.62 'c_HOL_Oone__class_Oone'( X ), Y, X ), X ) ) ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.24/1.62 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 1.24/1.62 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.24/1.62 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), hAPP( hAPP(
% 1.24/1.62 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ) ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.24/1.62 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.24/1.62 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.24/1.62 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.24/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ) ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.24/1.62 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 1.24/1.62 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.24/1.62 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), hAPP( hAPP(
% 1.24/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ) ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.24/1.62 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.24/1.62 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.24/1.62 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), hAPP( hAPP(
% 1.24/1.62 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ) ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.24/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ), X ), =( Y,
% 1.24/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'(
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), ~( 'c_Int_Oiszero'(
% 1.24/1.62 'c_HOL_Oone__class_Oone'( X ), X ) ) ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.24/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.24/1.62 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ), X ) ), ~(
% 1.24/1.62 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.24/1.62 , 'tc_nat' ), 'tc_nat' ) ) ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.24/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.24/1.62 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.24/1.62 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.24/1.62 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), U ) ) ), ~( hBOOL( hAPP(
% 1.24/1.62 hAPP( X, Y ), U ) ) ), ~( hBOOL( hAPP( hAPP( X, Y ), T ) ) ), ~(
% 1.24/1.62 'c_Ring__and__Field_Oordered__semidom'( W, V0, Y, Z, V1, X, V2 ) ) ],
% 1.24/1.62 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~(
% 1.24/1.62 'c_Ring__and__Field_Oordered__semidom'( T, Y, Z, U, X, W, V0 ) ) ],
% 1.24/1.62 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, Y ), T ) ) ), ~(
% 1.24/1.62 'c_Ring__and__Field_Oordered__semidom'( Z, U, T, W, V0, X, V1 ) ) ],
% 1.24/1.62 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~(
% 1.24/1.62 'c_Ring__and__Field_Oordered__semidom'( T, Y, Z, U, W, X, V0 ) ) ],
% 1.24/1.62 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), T ) ) ), ~(
% 1.24/1.62 'c_Ring__and__Field_Oordered__semidom'( Z, Y, T, U, W, X, V0 ) ) ],
% 1.24/1.62 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), U ) ) ), ~( hBOOL( hAPP(
% 1.24/1.62 hAPP( X, Y ), U ) ) ), ~( hBOOL( hAPP( hAPP( X, W ), T ) ) ), ~(
% 1.24/1.62 'c_Ring__and__Field_Oordered__semidom'( Z, W, V0, V1, V2, X, V3 ) ) ]
% 1.24/1.62 ,
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.24/1.62 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), 'c_lessequals'(
% 1.24/1.62 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.24/1.62 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( X ), Z ), Y ), X ) ) ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.24/1.62 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.24/1.62 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ),
% 1.24/1.62 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.24/1.62 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.24/1.62 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ) ),
% 1.24/1.62 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.24/1.62 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.24/1.62 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ),
% 1.24/1.62 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.24/1.62 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.24/1.62 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ), ~( 'c_lessequals'(
% 1.24/1.62 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ) ) ],
% 1.24/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.24/1.62 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.24/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.24/1.62 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ],
% 1.24/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.24/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.24/1.62 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.24/1.62 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =(
% 1.24/1.62 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.24/1.62 'c_HOL_Oinverse__class_Odivide'( T, U, X ) ) ), =( U,
% 1.24/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.24/1.62 ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), U ), hAPP(
% 1.24/1.62 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =( hAPP( hAPP(
% 1.24/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.24/1.62 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) ), =( Z,
% 1.24/1.62 'c_HOL_Ozero__class_Ozero'( X ) ), =( U, 'c_HOL_Ozero__class_Ozero'( X )
% 1.24/1.62 ), =( 'c_HOL_Oinverse__class_Odivide'( Y, U, X ),
% 1.24/1.62 'c_HOL_Oinverse__class_Odivide'( T, Z, X ) ) ],
% 1.24/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.24/1.62 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.24/1.62 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X
% 1.24/1.62 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.24/1.62 'c_Divides_Odiv__class_Omod'( Z, T, X ) ) ) ],
% 1.24/1.62 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.24/1.62 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.24/1.62 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X
% 1.24/1.62 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.24/1.62 'c_Divides_Odiv__class_Omod'( Y, T, X ) ), Z ) ) ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.24/1.62 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.24/1.62 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X )
% 1.24/1.62 ) ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.24/1.62 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X )
% 1.24/1.62 , ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.24/1.62 ],
% 1.24/1.62 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.24/1.62 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oabs__class_Oabs'(
% 1.24/1.62 Y, X ), X ) ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.24/1.62 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.24/1.62 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.24/1.62 X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ), Y, X ),
% 1.24/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.24/1.62 [ ~( =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), hAPP( hAPP(
% 1.24/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ), =( Y,
% 1.24/1.62 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.24/1.62 [ ~( =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), hAPP( hAPP(
% 1.24/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ), =( X,
% 1.24/1.62 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.24/1.62 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.24/1.62 'c_HOL_Ouminus__class_Ouminus'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.24/1.62 ), Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.24/1.62 'c_HOL_Ouminus__class_Ouminus'( Z, X ) ), 'c_HOL_Ouminus__class_Ouminus'(
% 1.24/1.62 Y, X ) ) ) ],
% 1.24/1.62 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.24/1.62 'c_HOL_Ouminus__class_Ouminus'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.24/1.62 ), Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.24/1.62 'c_HOL_Ouminus__class_Ouminus'( Y, X ) ), 'c_HOL_Ouminus__class_Ouminus'(
% 1.24/1.62 Z, X ) ) ) ],
% 1.24/1.62 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.24/1.62 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.24/1.62 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 1.24/1.62 'c_lessequals'( Z, Y, X ) ],
% 1.24/1.62 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.24/1.62 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.24/1.62 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.24/1.62 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.24/1.62 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Z
% 1.24/1.62 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.24/1.62 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_Int_Oint' ), 'c_Nat_Osemiring__1__class_Oof__nat'(
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_Int_Oint' ) ) ],
% 1.24/1.62 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) ],
% 1.24/1.62 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.24/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), 'tc_nat' ) ],
% 1.24/1.62 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), Z ) )
% 1.24/1.62 ), ~( hBOOL( hAPP( hAPP( X, hAPP( hAPP( 'c_Power_Opower_Opower'( W, V0,
% 1.24/1.62 V1 ), Y ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.24/1.62 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower_Opower'( W, V0, V1 ), Z ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ), ~(
% 1.24/1.62 'c_Ring__and__Field_Oordered__semidom'( V2, U, W, V0, T, X, V1 ) ) ],
% 1.24/1.62 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( X, T ), Z ) )
% 1.24/1.62 ), ~( hBOOL( hAPP( hAPP( X, hAPP( hAPP( 'c_Power_Opower_Opower'( U, W,
% 1.24/1.62 V0 ), Y ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.24/1.62 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower_Opower'( U, W, V0 ), Z ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ), ~(
% 1.24/1.62 'c_Ring__and__Field_Oordered__semidom'( V1, T, U, W, X, V2, V0 ) ) ],
% 1.24/1.62 [ =( 'c_NthRoot_Osqrt', 'c_NthRoot_Oroot'(
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ],
% 1.24/1.62 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( Y, T ), T ) ), ~(
% 1.24/1.62 'c_OrderedGroup_Omonoid__mult'( X, Y, Z ) ) ],
% 1.24/1.62 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( 'c_Power_Opower_Opower'( Z, T,
% 1.24/1.62 U ), W ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.24/1.62 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), ~(
% 1.24/1.62 'c_Ring__and__Field_Oordered__idom'( V0, V1, Y, V2, X, V3, V4, Z, T, V5,
% 1.24/1.62 U ) ) ],
% 1.24/1.62 [ ~( 'c_Ring__and__Field_Oordered__idom'( X, Y, Z, T, U, W, V0, V1, V2,
% 1.24/1.62 V3, V4 ) ), hBOOL( hAPP( hAPP( U, hAPP( hAPP( T, hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower_Opower'( V1, V2, V4 ), Z ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( V1
% 1.24/1.62 , V2, V4 ), Z ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.24/1.62 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), Z ) ) ],
% 1.24/1.62 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower_Opower'( T, U, W ), V0 ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( T
% 1.24/1.62 , U, W ), V1 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.24/1.62 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ), ~(
% 1.24/1.62 'c_Ring__and__Field_Oordered__idom'( V2, V3, Y, Z, X, V4, V5, T, U, V6, W
% 1.24/1.62 ) ) ],
% 1.24/1.62 [ ~( =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y
% 1.24/1.62 , Z ), U ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.24/1.62 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), ~(
% 1.24/1.62 'c_Ring__and__Field_Oordered__semidom'( W, V0, X, Y, V1, V2, Z ) ), =( T
% 1.24/1.62 , U ), ~( hBOOL( hAPP( hAPP( V1, V0 ), U ) ) ), ~( hBOOL( hAPP( hAPP( V1
% 1.24/1.62 , V0 ), T ) ) ) ],
% 1.24/1.62 [ ~( 'c_Ring__and__Field_Oordered__idom'( X, Y, hAPP( hAPP( Z, hAPP(
% 1.24/1.62 hAPP( 'c_Power_Opower_Opower'( T, U, W ), V0 ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( T
% 1.24/1.62 , U, W ), V1 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.24/1.62 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ), Z, V2, V3, V4, T, U, V5
% 1.24/1.62 , W ) ), =( V1, hAPP( hAPP( Z, hAPP( hAPP( 'c_Power_Opower_Opower'( T, U
% 1.24/1.62 , W ), V0 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.24/1.62 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower_Opower'( T, U, W ), V1 ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ],
% 1.24/1.62 [ ~( 'c_Ring__and__Field_Oordered__idom'( X, Y, hAPP( hAPP( Z, hAPP(
% 1.24/1.62 hAPP( 'c_Power_Opower_Opower'( T, U, W ), V0 ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( T
% 1.24/1.62 , U, W ), V1 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.24/1.62 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ), Z, V2, V3, V4, T, U, V5
% 1.24/1.62 , W ) ), =( V0, hAPP( hAPP( Z, hAPP( hAPP( 'c_Power_Opower_Opower'( T, U
% 1.24/1.62 , W ), V0 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.24/1.62 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower_Opower'( T, U, W ), V1 ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ],
% 1.24/1.62 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ), ~(
% 1.24/1.62 'c_Parity_Oeven__odd__class_Oeven'( 'c_Divides_Odiv__class_Omod'( X,
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit0'(
% 1.24/1.62 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ) ]
% 1.24/1.62 ,
% 1.24/1.62 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_Divides_Odiv__class_Omod'( X,
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit0'(
% 1.24/1.62 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ),
% 1.24/1.62 ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.24/1.62 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), hAPP( T, U ) ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y
% 1.24/1.62 , Z ), U ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.24/1.62 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ), ~(
% 1.24/1.62 'c_Ring__and__Field_Ocomm__ring__1'( X, Y, W, T, V0, V1, Z ) ) ],
% 1.24/1.62 [ =( 'c_FFT__Mirabelle_Oroot'( 'c_Int_Onumber__class_Onumber__of'(
% 1.24/1.62 'c_Int_OBit0'( 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat'
% 1.24/1.62 ) ), 'c_Complex_Oii' ) ],
% 1.24/1.62 [ =( X, Y ), ~( hBOOL( hAPP( hAPP( Z, hAPP( hAPP( T, hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower_Opower'( U, W, V0 ), V1 ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( U
% 1.24/1.62 , W, V0 ), X ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.24/1.62 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), Y ) ) ), ~(
% 1.24/1.62 'c_Ring__and__Field_Oordered__idom'( V2, V3, Y, T, Z, V4, V5, U, W, V6,
% 1.24/1.62 V0 ) ) ],
% 1.24/1.62 [ =( X, Y ), ~( hBOOL( hAPP( hAPP( Z, hAPP( hAPP( T, hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower_Opower'( U, W, V0 ), X ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( U
% 1.24/1.62 , W, V0 ), V1 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.24/1.62 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), Y ) ) ), ~(
% 1.24/1.62 'c_Ring__and__Field_Oordered__idom'( V2, V3, Y, T, Z, V4, V5, U, W, V6,
% 1.24/1.62 V0 ) ) ],
% 1.24/1.62 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.24/1.62 'tc_nat' ), X ), X ) ) ],
% 1.24/1.62 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), hAPP( hAPP(
% 1.24/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), X ) ) ],
% 1.24/1.62 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ), T ), ~( 'c_Ring__and__Field_Osemiring__1'(
% 1.24/1.62 X, Y, T, U, Z ) ) ],
% 1.24/1.62 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), X ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), ~( 'c_Ring__and__Field_Osemiring__1'(
% 1.24/1.62 X, Y, T, U, Z ) ) ],
% 1.24/1.62 [ ~( 'c_Ring__and__Field_Oordered__idom'( X, Y, Z, T, U, W, V0, V1, V2,
% 1.24/1.62 V3, V4 ) ), =( hAPP( hAPP( 'c_Power_Opower_Opower'( V1, V2, V4 ), Z ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ],
% 1.24/1.62 [ =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', 'tc_nat' ) ) ],
% 1.24/1.62 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', 'tc_nat' ),
% 1.24/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.24/1.62 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.24/1.62 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.24/1.62 ), ~( =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ),
% 1.24/1.62 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.24/1.62 ) ) ],
% 1.24/1.62 [ ~( =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( 'tc_nat' ), X ), Y )
% 1.24/1.62 , 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X, 'c_Suc'(
% 1.24/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.24/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.24/1.62 [ =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( 'tc_nat' ), 'c_Suc'(
% 1.24/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), X ), 'c_Suc'(
% 1.24/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.24/1.62 [ =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( 'tc_nat' ), 'c_Suc'(
% 1.24/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), X ), 'c_Suc'(
% 1.24/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.24/1.62 [ =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( 'tc_nat' ), X ),
% 1.24/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_Suc'(
% 1.24/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 1.24/1.62 'c_Nat_Osemiring__1__class_Oof__nat'( hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( 'tc_nat' ), Y ), Z ), X ), hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( X ), 'c_Nat_Osemiring__1__class_Oof__nat'(
% 1.24/1.62 Y, X ) ), Z ) ) ],
% 1.24/1.62 [ =( X, 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 1.24/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X
% 1.24/1.62 , 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) ) ],
% 1.24/1.62 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( 'c_Suc'( hAPP( hAPP(
% 1.24/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ), 'tc_nat' ) ) ],
% 1.24/1.62 [ =( hAPP( hAPP( X, Y ), 'c_Suc'( hAPP( hAPP(
% 1.24/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ), hAPP( hAPP( T, Y ), hAPP( hAPP(
% 1.24/1.62 T, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, Y ), Z ) ) ) ), ~(
% 1.24/1.62 'c_Groebner__Basis_Ogb__semiring'( U, T, X, W, V0, V1 ) ) ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP( hAPP(
% 1.24/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.24/1.62 ,
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.24/1.62 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.24/1.62 ), Y ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.24/1.62 ,
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.24/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ) ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.24/1.62 Y, Z, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ),
% 1.24/1.62 ~( 'c_lessequals'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ) ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =( hAPP( hAPP(
% 1.24/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.24/1.62 =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =( hAPP( hAPP(
% 1.24/1.62 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.24/1.62 =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =( hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X
% 1.24/1.62 ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.24/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ) ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.24/1.62 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.24/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), hAPP( hAPP(
% 1.24/1.62 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =( hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), =( Y, Z ), ~( 'c_lessequals'(
% 1.24/1.62 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.24/1.62 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.24/1.62 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.24/1.62 ) ) ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.24/1.62 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Oinverse'(
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ), X
% 1.24/1.62 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X
% 1.24/1.62 ) ) ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.24/1.62 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ), X
% 1.24/1.62 ), Y ) ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.24/1.62 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ), X
% 1.24/1.62 ), Y ) ],
% 1.24/1.62 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ),
% 1.24/1.62 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.24/1.62 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oone__class_Oone'( X )
% 1.24/1.62 , 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X )
% 1.24/1.62 ) ],
% 1.24/1.62 [ ~( 'class_Int_Onumber__ring'( X ) ), ~( 'c_Int_Oiszero'(
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ), X
% 1.24/1.62 ) ) ],
% 1.24/1.62 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.24/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.24/1.62 'c_Int_OBit1'( 'c_Int_OPls' ), X ) ), Y ), Y ) ],
% 1.24/1.62 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.24/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ) )
% 1.24/1.62 , Y ) ],
% 1.24/1.62 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.24/1.62 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.24/1.62 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), hAPP( hAPP(
% 1.24/1.62 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.24/1.62 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.24/1.62 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), X ) ), Y ) ), Z ) ) ) ]
% 1.24/1.62 ,
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( hAPP( hAPP(
% 1.24/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ), hAPP( hAPP(
% 1.24/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.24/1.62 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ) ],
% 1.24/1.62 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( hAPP( hAPP(
% 1.24/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ), hAPP( hAPP(
% 1.24/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ],
% 1.24/1.62 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ),
% 1.24/1.62 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.24/1.62 [ =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ),
% 1.24/1.62 'tc_nat' ) ) ],
% 1.24/1.62 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.24/1.62 'c_Int_OMin', X ) ), 'c_Suc'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.24/1.62 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.24/1.62 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), Y ) ) ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OMin', X ) ) ],
% 1.24/1.62 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ),
% 1.24/1.62 'tc_nat' ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.24/1.62 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ), 'c_Suc'( 'c_Suc'( 'c_Suc'(
% 1.24/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ) ],
% 1.24/1.62 [ =( 'c_Suc'( 'c_Suc'( 'c_Suc'( X ) ) ), hAPP( hAPP(
% 1.24/1.62 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ) ],
% 1.24/1.62 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.24/1.62 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), Y ) ) ]
% 1.24/1.62 ,
% 1.24/1.62 [ =( hAPP( hAPP( X, Y ), Y ), hAPP( hAPP( Z, Y ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( T
% 1.24/1.62 , X, Z, U, W, V0 ) ) ],
% 1.24/1.62 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ), 'c_Suc'( 'c_Suc'(
% 1.24/1.62 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.24/1.62 [ =( 'c_Divides_Odiv__class_Odiv'( 'c_Suc'( 'c_Suc'( X ) ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'c_Suc'(
% 1.24/1.62 'c_Divides_Odiv__class_Odiv'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.24/1.62 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) )
% 1.24/1.62 ) ],
% 1.24/1.62 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), 'c_Suc'( 'c_Suc'( X ) ) ) ],
% 1.24/1.62 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_Suc'( 'c_Suc'( X ) ) ) ],
% 1.24/1.62 [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( 'c_Suc'( X ) ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X
% 1.24/1.62 , 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) ) ],
% 1.24/1.62 [ =( 'c_Suc'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ) ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.24/1.62 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ), hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =( hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =( hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y
% 1.24/1.62 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oabs__class_Oabs'( Y, X ) ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ],
% 1.24/1.62 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.24/1.62 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ],
% 1.24/1.62 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.24/1.62 X ), Y ), Y ) ) ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =( hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =( hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X
% 1.24/1.62 ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ],
% 1.24/1.62 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.24/1.62 'c_HOL_Oabs__class_Oabs'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X )
% 1.24/1.62 , Y ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ],
% 1.24/1.62 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), ~( 'class_Int_Onumber'(
% 1.24/1.62 X ) ), =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.24/1.62 X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ) ],
% 1.24/1.62 [ ~( 'c_HOL_Oord__class_Oless'( 'v_i____', hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( 'tc_nat' ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ), 'v_ka____' ), 'tc_nat' ) ) ],
% 1.24/1.62 [ =( 'c_FFT__Mirabelle_OIDFT'( hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( 'tc_nat' ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ), 'v_ka____' ), X, Y ), hAPP(
% 1.24/1.62 'c_FFT__Mirabelle_OIFFT'( 'v_ka____', X ), Y ) ), ~(
% 1.24/1.62 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_Power_Opower__class_Opower'(
% 1.24/1.62 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.24/1.62 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), 'v_ka____' ), 'tc_nat' ) )
% 1.24/1.62 ],
% 1.24/1.62 [ 'c_HOL_Oord__class_Oless'( 'v_i____', hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( 'tc_nat' ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_Suc'( 'v_ka____' ) ), 'tc_nat' ) ]
% 1.24/1.62 ,
% 1.24/1.62 [ =( 'c_Int_OBit0'( 'c_Int_OPls' ), 'c_Int_OPls' ) ],
% 1.24/1.62 [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ],
% 1.24/1.62 [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ],
% 1.24/1.62 [ ~( =( 'c_Int_OPls', 'c_Int_OBit1'( X ) ) ) ],
% 1.24/1.62 [ ~( =( 'c_Int_OBit1'( X ), 'c_Int_OPls' ) ) ],
% 1.24/1.62 [ ~( =( 'c_Int_OBit0'( X ), 'c_Int_OPls' ) ), =( X, 'c_Int_OPls' ) ]
% 1.24/1.62 ,
% 1.24/1.62 [ ~( =( 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ) ) ), =( X, Y ) ],
% 1.24/1.62 [ ~( =( 'c_Int_OBit1'( X ), 'c_Int_OBit0'( Y ) ) ) ],
% 1.24/1.62 [ =( 'c_Int_OPls', 'c_Int_OBit0'( 'c_Int_OPls' ) ) ],
% 1.24/1.62 [ ~( =( 'c_Suc'( X ), X ) ) ],
% 1.24/1.62 [ ~( =( X, 'c_Suc'( X ) ) ) ],
% 1.24/1.62 [ ~( =( 'c_Int_OPls', 'c_Int_OBit0'( X ) ) ), =( 'c_Int_OPls', X ) ]
% 1.24/1.62 ,
% 1.24/1.62 [ ~( =( 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ) ) ), =( X, Y ) ],
% 1.24/1.62 [ ~( 'class_Int_Oring__char__0'( X ) ), ~( 'class_Int_Onumber__ring'( X
% 1.24/1.62 ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ), =( Y, Z ) ],
% 1.24/1.62 [ ~( =( 'c_Int_OBit0'( X ), 'c_Int_OBit1'( Y ) ) ) ],
% 1.24/1.62 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( 'v_i____',
% 1.24/1.62 hAPP( hAPP( 'c_Power_Opower__class_Opower'( 'tc_nat' ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ), 'v_ka____' ), 'tc_nat' ), hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( 'tc_nat' ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ), 'v_ka____' ), 'tc_nat' ) ],
% 1.24/1.62 [ 'c_HOL_Oord__class_Oless'( 'v_i____', hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( 'tc_nat' ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_Suc'( 'v_ka____' ) ), 'tc_nat' ) ]
% 1.24/1.62 ,
% 1.24/1.62 [ ~( 'c_HOL_Oord__class_Oless'( 'v_i____', hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( 'tc_nat' ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ), 'v_ka____' ), 'tc_nat' ) ) ],
% 1.24/1.62 [ ~( =( 'c_FFT__Mirabelle_OIDFT'( hAPP( hAPP(
% 1.24/1.62 'c_Power_Opower__class_Opower'( 'tc_nat' ),
% 1.24/1.62 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.24/1.62 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_Suc'( 'v_ka____' ) ), 'v_a____',
% 1.24/1.62 'v_i____' ), hAPP( 'c_FFT__Mirabelle_OIFFT'( 'c_Suc'( 'v_ka____' ),
% 1.24/1.62 'v_a____' ), 'v_i____' ) ) ) ],
% 1.24/1.62 [ 'class_Lattices_Oboolean__algebra'( 'tc_fun'( X, Y ) ), ~(
% 1.24/1.62 'class_Lattices_Oboolean__algebra'( Y ) ) ],
% 1.24/1.62 [ 'class_Orderings_Opreorder'( 'tc_fun'( X, Y ) ), ~(
% 1.24/1.62 'class_Orderings_Opreorder'( Y ) ) ],
% 1.24/1.62 [ 'class_Orderings_Oorder'( 'tc_fun'( X, Y ) ), ~(
% 1.24/1.62 'class_Orderings_Oorder'( Y ) ) ],
% 1.24/1.62 [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( 'tc_nat' )
% 1.24/1.62 ],
% 1.24/1.62 [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( 'tc_nat'
% 1.24/1.62 ) ],
% 1.24/1.62 [ 'class_Ring__and__Field_Oordered__comm__semiring__strict'( 'tc_nat' )
% 1.24/1.62 ],
% 1.24/1.62 [ 'class_Ring__and__Field_Opordered__cancel__semiring'( 'tc_nat' ) ]
% 1.24/1.62 ,
% 1.24/1.62 [ 'class_Ring__and__Field_Oordered__semiring__strict'( 'tc_nat' ) ],
% 1.24/1.62 [ 'class_OrderedGroup_Opordered__ab__semigroup__add'( 'tc_nat' ) ],
% 1.24/1.62 [ 'class_OrderedGroup_Opordered__comm__monoid__add'( 'tc_nat' ) ],
% 1.24/1.62 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'( 'tc_nat' ) ],
% 1.24/1.62 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_nat' ) ],
% 1.24/1.62 [ 'class_Ring__and__Field_Opordered__semiring'( 'tc_nat' ) ],
% 1.24/1.62 [ 'class_Ring__and__Field_Oordered__semiring'( 'tc_nat' ) ],
% 1.24/1.62 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_nat' ) ],
% 1.24/1.62 [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_nat' ) ],
% 1.24/1.62 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_nat' ) ],
% 1.24/1.62 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_nat' ) ],
% 1.24/1.62 [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_nat' ) ],
% 1.24/1.62 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_nat' ) ],
% 1.24/1.62 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_nat' ) ],
% 1.24/1.62 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_nat' ) ],
% 1.24/1.62 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_nat' ) ],
% 1.24/1.62 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_nat' ) ],
% 1.24/1.62 [ 'class_Ring__and__Field_Osemiring__0'( 'tc_nat' ) ],
% 1.24/1.62 [ 'class_Ring__and__Field_Omult__mono1'( 'tc_nat' ) ],
% 1.24/1.62 [ 'class_Ring__and__Field_Omult__zero'( 'tc_nat' ) ],
% 1.24/1.62 [ 'class_Ring__and__Field_Omult__mono'( 'tc_nat' ) ],
% 1.24/1.62 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_nat' ) ],
% 1.24/1.62 [ 'class_Ring__and__Field_Osemiring'( 'tc_nat' ) ],
% 1.24/1.62 [ 'class_OrderedGroup_Omonoid__add'( 'tc_nat' ) ],
% 1.24/1.62 [ 'class_Divides_Osemiring__div'( 'tc_nat' ) ],
% 1.24/1.62 [ 'class_Nat_Osemiring__char__0'( 'tc_nat' ) ],
% 1.24/1.62 [ 'class_Orderings_Opreorder'( 'tc_nat' ) ],
% 1.24/1.62 [ 'class_Orderings_Olinorder'( 'tc_nat' ) ],
% 1.24/1.62 [ 'class_Orderings_Oorder'( 'tc_nat' ) ],
% 1.24/1.62 [ 'class_Power_Opower'( 'tc_nat' ) ],
% 1.24/1.62 [ 'class_Int_Onumber'( 'tc_nat' ) ],
% 1.24/1.62 [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'(
% 1.24/1.62 'tc_Int_Oint' ) ],
% 1.24/1.62 [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'(
% 1.24/1.62 'tc_Int_Oint' ) ],
% 1.24/1.62 [ 'class_Ring__and__Field_Oordered__comm__semiring__strict'(
% 1.24/1.62 'tc_Int_Oint' ) ],
% 1.24/1.62 [ 'class_Ring__and__Field_Opordered__cancel__semiring'( 'tc_Int_Oint' )
% 1.24/1.62 ],
% 1.24/1.62 [ 'class_Ring__and__Field_Oring__1__no__zero__divisors'( 'tc_Int_Oint' )
% 1.24/1.62 ],
% 1.24/1.62 [ 'class_Ring__and__Field_Oordered__semiring__strict'( 'tc_Int_Oint' ) ]
% 1.24/1.62 ,
% 1.24/1.62 [ 'class_OrderedGroup_Opordered__ab__semigroup__add'( 'tc_Int_Oint' ) ]
% 1.24/1.62 ,
% 1.24/1.62 [ 'class_OrderedGroup_Opordered__ab__group__add__abs'( 'tc_Int_Oint' ) ]
% 1.24/1.62 ,
% 1.24/1.62 [ 'class_OrderedGroup_Olordered__ab__group__add__abs'( 'tc_Int_Oint' ) ]
% 1.24/1.62 ,
% 1.24/1.62 [ 'class_OrderedGroup_Opordered__comm__monoid__add'( 'tc_Int_Oint' ) ]
% 1.24/1.62 ,
% 1.24/1.62 [ 'class_Ring__and__Field_Oring__no__zero__divisors'( 'tc_Int_Oint' ) ]
% 1.24/1.62 ,
% 1.24/1.62 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'( 'tc_Int_Oint' ) ]
% 1.24/1.62 ,
% 1.24/1.62 [ 'class_Ring__and__Field_Oordered__ring__strict'( 'tc_Int_Oint' ) ]
% 1.24/1.62 ,
% 1.24/1.62 [ 'class_OrderedGroup_Opordered__ab__group__add'( 'tc_Int_Oint' ) ],
% 1.24/1.62 [ 'class_OrderedGroup_Olordered__ab__group__add'( 'tc_Int_Oint' ) ],
% 1.24/1.62 [ 'class_OrderedGroup_Oordered__ab__group__add'( 'tc_Int_Oint' ) ],
% 1.24/1.62 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_Int_Oint' ) ],
% 1.24/1.62 [ 'class_Ring__and__Field_Opordered__semiring'( 'tc_Int_Oint' ) ],
% 1.24/1.62 [ 'class_Ring__and__Field_Opordered__ring__abs'( 'tc_Int_Oint' ) ],
% 1.24/1.62 [ 'class_Ring__and__Field_Oordered__semiring'( 'tc_Int_Oint' ) ],
% 1.24/1.62 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_Int_Oint' ) ],
% 1.24/1.62 [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_Int_Oint' ) ],
% 1.24/1.62 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_Int_Oint' ) ],
% 1.24/1.62 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_Int_Oint' ) ],
% 1.24/1.62 [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_Int_Oint' ) ],
% 1.24/1.62 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_Int_Oint' ) ],
% 1.24/1.62 [ 'class_Ring__and__Field_Opordered__ring'( 'tc_Int_Oint' ) ],
% 1.24/1.62 [ 'class_Ring__and__Field_Olordered__ring'( 'tc_Int_Oint' ) ],
% 1.24/1.62 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_Int_Oint' ) ],
% 1.24/1.62 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_Int_Oint' ) ],
% 1.24/1.62 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_Int_Oint' ) ],
% 1.24/1.62 [ 'class_Ring__and__Field_Oordered__idom'( 'tc_Int_Oint' ) ],
% 1.24/1.62 [ 'class_Ring__and__Field_Ocomm__ring__1'( 'tc_Int_Oint' ) ],
% 1.24/1.62 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_Int_Oint' ) ],
% 1.24/1.62 [ 'class_Ring__and__Field_Osemiring__0'( 'tc_Int_Oint' ) ],
% 1.24/1.62 [ 'class_Ring__and__Field_Omult__mono1'( 'tc_Int_Oint' ) ],
% 1.24/1.62 [ 'class_OrderedGroup_Oab__group__add'( 'tc_Int_Oint' ) ],
% 1.24/1.62 [ 'class_Ring__and__Field_Omult__zero'( 'tc_Int_Oint' ) ],
% 1.24/1.62 [ 'class_Ring__and__Field_Omult__mono'( 'tc_Int_Oint' ) ],
% 1.24/1.62 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_Int_Oint' ) ],
% 1.24/1.62 [ 'class_Ring__and__Field_Osemiring'( 'tc_Int_Oint' ) ],
% 1.24/1.62 [ 'class_OrderedGroup_Omonoid__add'( 'tc_Int_Oint' ) ],
% 1.24/1.62 [ 'class_OrderedGroup_Ogroup__add'( 'tc_Int_Oint' ) ],
% 1.24/1.62 [ 'class_Ring__and__Field_Oring__1'( 'tc_Int_Oint' ) ],
% 1.24/1.62 [ 'class_Ring__and__Field_Oabs__if'( 'tc_Int_Oint' ) ],
% 1.24/1.62 [ 'class_Divides_Osemiring__div'( 'tc_Int_Oint' ) ],
% 1.24/1.62 [ 'class_Ring__and__Field_Oring'( 'tc_Int_Oint' ) ],
% 1.24/1.62 [ 'class_Ring__and__Field_Oidom'( 'tc_Int_Oint' ) ],
% 1.24/1.62 [ 'class_Nat_Osemiring__char__0'( 'tc_Int_Oint' ) ],
% 1.24/1.62 [ 'class_Orderings_Opreorder'( 'tc_Int_Oint' ) ],
% 1.24/1.62 [ 'class_Orderings_Olinorder'( 'tc_Int_Oint' ) ],
% 1.24/1.62 [ 'class_Divides_Oring__div'( 'tc_Int_Oint' ) ],
% 1.24/1.62 [ 'class_Orderings_Oorder'( 'tc_Int_Oint' ) ],
% 1.24/1.62 [ 'class_Int_Oring__char__0'( 'tc_Int_Oint' ) ],
% 1.24/1.62 [ 'class_Int_Onumber__ring'( 'tc_Int_Oint' ) ],
% 1.24/1.62 [ 'class_Power_Opower'( 'tc_Int_Oint' ) ],
% 1.24/1.62 [ 'class_Int_Onumber'( 'tc_Int_Oint' ) ],
% 1.24/1.62 [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'(
% 1.24/1.62 'tc_RealDef_Oreal' ) ],
% 1.24/1.62 [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'(
% 1.24/1.62 'tc_RealDef_Oreal' ) ],
% 1.24/1.62 [ 'class_Ring__and__Field_Oordered__comm__semiring__strict'(
% 1.24/1.62 'tc_RealDef_Oreal' ) ],
% 1.24/1.62 [ 'class_Ring__and__Field_Opordered__cancel__semiring'(
% 1.24/1.62 'tc_RealDef_Oreal' ) ],
% 1.24/1.62 [ 'class_Ring__and__Field_Oring__1__no__zero__divisors'(
% 1.24/1.62 'tc_RealDef_Oreal' ) ],
% 1.24/1.62 [ 'class_Ring__and__Field_Oordered__semiring__strict'(
% 1.24/1.62 'tc_RealDef_Oreal' ) ],
% 1.24/1.62 [ 'class_OrderedGroup_Opordered__ab__semigroup__add'( 'tc_RealDef_Oreal'
% 1.24/1.62 ) ],
% 1.24/1.62 [ 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 1.24/1.62 'tc_RealDef_Oreal' ) ],
% 1.24/1.62 [ 'class_OrderedGroup_Olordered__ab__group__add__abs'(
% 1.24/1.62 'tc_RealDef_Oreal' ) ],
% 1.24/1.62 [ 'class_OrderedGroup_Opordered__comm__monoid__add'( 'tc_RealDef_Oreal'
% 1.24/1.62 ) ],
% 1.24/1.62 [ 'class_Ring__and__Field_Oring__no__zero__divisors'( 'tc_RealDef_Oreal'
% 1.24/1.62 ) ],
% 1.24/1.62 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'( 'tc_RealDef_Oreal' )
% 1.24/1.62 ],
% 1.24/1.62 [ 'class_Ring__and__Field_Oordered__ring__strict'( 'tc_RealDef_Oreal' )
% 1.24/1.62 ],
% 1.24/1.62 [ 'class_OrderedGroup_Opordered__ab__group__add'( 'tc_RealDef_Oreal' ) ]
% 1.24/1.62 ,
% 1.24/1.62 [ 'class_OrderedGroup_Olordered__ab__group__add'( 'tc_RealDef_Oreal' ) ]
% 1.24/1.62 ,
% 1.24/1.62 [ 'class_OrderedGroup_Oordered__ab__group__add'( 'tc_RealDef_Oreal' ) ]
% 1.24/1.62 ,
% 1.24/1.62 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_RealDef_Oreal' ) ]
% 1.24/1.62 ,
% 1.24/1.62 [ 'class_Ring__and__Field_Opordered__semiring'( 'tc_RealDef_Oreal' ) ]
% 1.24/1.62 ,
% 1.24/1.62 [ 'class_Ring__and__Field_Opordered__ring__abs'( 'tc_RealDef_Oreal' ) ]
% 1.24/1.62 ,
% 1.24/1.62 [ 'class_Ring__and__Field_Oordered__semiring'( 'tc_RealDef_Oreal' ) ]
% 1.24/1.62 ,
% 1.24/1.62 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_RealDef_Oreal' ) ]
% 1.24/1.62 ,
% 1.24/1.62 [ 'class_Ring__and__Field_Odivision__by__zero'( 'tc_RealDef_Oreal' ) ]
% 1.24/1.62 ,
% 1.24/1.62 [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_RealDef_Oreal' ) ]
% 1.24/1.62 ,
% 1.24/1.62 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_RealDef_Oreal' ) ]
% 1.24/1.62 ,
% 1.24/1.62 [ 'class_RealVector_Oreal__normed__algebra'( 'tc_RealDef_Oreal' ) ],
% 1.24/1.62 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_RealDef_Oreal' ) ],
% 1.24/1.62 [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_RealDef_Oreal' ) ],
% 1.24/1.62 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_RealDef_Oreal' ) ],
% 1.24/1.62 [ 'class_Ring__and__Field_Opordered__ring'( 'tc_RealDef_Oreal' ) ],
% 1.24/1.62 [ 'class_Ring__and__Field_Oordered__field'( 'tc_RealDef_Oreal' ) ],
% 1.24/1.62 [ 'class_Ring__and__Field_Olordered__ring'( 'tc_RealDef_Oreal' ) ],
% 1.24/1.62 [ 'class_Ring__and__Field_Odivision__ring'( 'tc_RealDef_Oreal' ) ],
% 1.24/1.62 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_RealDef_Oreal' ) ],
% 1.24/1.62 [ 'class_RealVector_Oreal__normed__field'( 'tc_RealDef_Oreal' ) ],
% 1.24/1.62 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_RealDef_Oreal' ) ],
% 1.24/1.62 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_RealDef_Oreal' ) ],
% 1.24/1.62 [ 'class_Ring__and__Field_Oordered__idom'( 'tc_RealDef_Oreal' ) ],
% 1.24/1.62 [ 'class_Ring__and__Field_Ocomm__ring__1'( 'tc_RealDef_Oreal' ) ],
% 1.24/1.62 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_RealDef_Oreal' ) ],
% 1.24/1.62 [ 'class_Ring__and__Field_Osemiring__0'( 'tc_RealDef_Oreal' ) ],
% 1.24/1.62 [ 'class_Ring__and__Field_Omult__mono1'( 'tc_RealDef_Oreal' ) ],
% 1.24/1.62 [ 'class_OrderedGroup_Oab__group__add'( 'tc_RealDef_Oreal' ) ],
% 1.24/1.62 [ 'class_Ring__and__Field_Omult__zero'( 'tc_RealDef_Oreal' ) ],
% 1.24/1.62 [ 'class_Ring__and__Field_Omult__mono'( 'tc_RealDef_Oreal' ) ],
% 1.24/1.62 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_RealDef_Oreal' ) ],
% 1.24/1.62 [ 'class_Ring__and__Field_Osemiring'( 'tc_RealDef_Oreal' ) ],
% 1.24/1.62 [ 'class_OrderedGroup_Omonoid__add'( 'tc_RealDef_Oreal' ) ],
% 1.24/1.62 [ 'class_OrderedGroup_Ogroup__add'( 'tc_RealDef_Oreal' ) ],
% 1.24/1.62 [ 'class_Ring__and__Field_Oring__1'( 'tc_RealDef_Oreal' ) ],
% 1.24/1.62 [ 'class_Ring__and__Field_Oabs__if'( 'tc_RealDef_Oreal' ) ],
% 1.24/1.62 [ 'class_Ring__and__Field_Ofield'( 'tc_RealDef_Oreal' ) ],
% 1.24/1.62 [ 'class_Ring__and__Field_Oring'( 'tc_RealDef_Oreal' ) ],
% 1.24/1.63 [ 'class_Ring__and__Field_Oidom'( 'tc_RealDef_Oreal' ) ],
% 1.24/1.63 [ 'class_Nat_Osemiring__char__0'( 'tc_RealDef_Oreal' ) ],
% 1.24/1.63 [ 'class_Orderings_Opreorder'( 'tc_RealDef_Oreal' ) ],
% 1.24/1.63 [ 'class_Orderings_Olinorder'( 'tc_RealDef_Oreal' ) ],
% 1.24/1.63 [ 'class_Orderings_Oorder'( 'tc_RealDef_Oreal' ) ],
% 1.24/1.63 [ 'class_Int_Oring__char__0'( 'tc_RealDef_Oreal' ) ],
% 1.24/1.63 [ 'class_Int_Onumber__ring'( 'tc_RealDef_Oreal' ) ],
% 1.24/1.63 [ 'class_Power_Opower'( 'tc_RealDef_Oreal' ) ],
% 1.24/1.63 [ 'class_Int_Onumber'( 'tc_RealDef_Oreal' ) ],
% 1.24/1.63 [ 'class_Ring__and__Field_Oring__1__no__zero__divisors'(
% 1.24/1.63 'tc_Complex_Ocomplex' ) ],
% 1.24/1.63 [ 'class_Ring__and__Field_Oring__no__zero__divisors'(
% 1.24/1.63 'tc_Complex_Ocomplex' ) ],
% 1.24/1.63 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'(
% 1.24/1.63 'tc_Complex_Ocomplex' ) ],
% 1.24/1.63 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_Complex_Ocomplex' )
% 1.24/1.63 ],
% 1.24/1.63 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_Complex_Ocomplex' )
% 1.24/1.63 ],
% 1.24/1.63 [ 'class_Ring__and__Field_Odivision__by__zero'( 'tc_Complex_Ocomplex' )
% 1.24/1.63 ],
% 1.24/1.63 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_Complex_Ocomplex' ) ]
% 1.24/1.63 ,
% 1.24/1.63 [ 'class_RealVector_Oreal__normed__algebra'( 'tc_Complex_Ocomplex' ) ]
% 1.24/1.63 ,
% 1.24/1.63 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_Complex_Ocomplex' ) ]
% 1.24/1.63 ,
% 1.24/1.63 [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_Complex_Ocomplex' ) ]
% 1.24/1.63 ,
% 1.24/1.63 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_Complex_Ocomplex' ) ]
% 1.24/1.63 ,
% 1.24/1.63 [ 'class_Ring__and__Field_Odivision__ring'( 'tc_Complex_Ocomplex' ) ]
% 1.24/1.63 ,
% 1.24/1.63 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_Complex_Ocomplex' ) ]
% 1.24/1.63 ,
% 1.24/1.63 [ 'class_RealVector_Oreal__normed__field'( 'tc_Complex_Ocomplex' ) ]
% 1.24/1.63 ,
% 1.24/1.63 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_Complex_Ocomplex' ) ]
% 1.24/1.63 ,
% 1.24/1.63 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_Complex_Ocomplex' ) ]
% 1.24/1.63 ,
% 1.24/1.63 [ 'class_Ring__and__Field_Ocomm__ring__1'( 'tc_Complex_Ocomplex' ) ]
% 1.24/1.63 ,
% 1.24/1.63 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_Complex_Ocomplex' ) ],
% 1.24/1.63 [ 'class_Ring__and__Field_Osemiring__0'( 'tc_Complex_Ocomplex' ) ],
% 1.24/1.63 [ 'class_OrderedGroup_Oab__group__add'( 'tc_Complex_Ocomplex' ) ],
% 1.24/1.63 [ 'class_Ring__and__Field_Omult__zero'( 'tc_Complex_Ocomplex' ) ],
% 1.24/1.63 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_Complex_Ocomplex' ) ],
% 1.24/1.63 [ 'class_Ring__and__Field_Osemiring'( 'tc_Complex_Ocomplex' ) ],
% 1.24/1.63 [ 'class_OrderedGroup_Omonoid__add'( 'tc_Complex_Ocomplex' ) ],
% 1.24/1.63 [ 'class_OrderedGroup_Ogroup__add'( 'tc_Complex_Ocomplex' ) ],
% 1.24/1.63 [ 'class_Ring__and__Field_Oring__1'( 'tc_Complex_Ocomplex' ) ],
% 1.24/1.63 [ 'class_Ring__and__Field_Ofield'( 'tc_Complex_Ocomplex' ) ],
% 1.24/1.63 [ 'class_Ring__and__Field_Oring'( 'tc_Complex_Ocomplex' ) ],
% 1.24/1.63 [ 'class_Ring__and__Field_Oidom'( 'tc_Complex_Ocomplex' ) ],
% 1.24/1.63 [ 'class_Nat_Osemiring__char__0'( 'tc_Complex_Ocomplex' ) ],
% 1.24/1.63 [ 'class_Int_Oring__char__0'( 'tc_Complex_Ocomplex' ) ],
% 1.24/1.63 [ 'class_Int_Onumber__ring'( 'tc_Complex_Ocomplex' ) ],
% 1.24/1.63 [ 'class_Power_Opower'( 'tc_Complex_Ocomplex' ) ],
% 1.24/1.63 [ 'class_Int_Onumber'( 'tc_Complex_Ocomplex' ) ],
% 1.24/1.63 [ 'c_fequal'( X, X, Y ) ],
% 1.24/1.63 [ =( X, Y ), ~( 'c_fequal'( X, Y, Z ) ) ]
% 1.24/1.63 ] .
% 1.24/1.63
% 1.24/1.63
% 1.24/1.63 percentage equality = 0.217469, percentage horn = 0.829593
% 1.24/1.63 This is a problem with some equality
% 1.24/1.63
% 1.24/1.63
% 1.24/1.63
% 1.24/1.63 Options Used:
% 1.24/1.63
% 1.24/1.63 useres = 1
% 1.24/1.63 useparamod = 1
% 1.24/1.63 useeqrefl = 1
% 1.24/1.63 useeqfact = 1
% 1.24/1.63 usefactor = 1
% 1.24/1.63 usesimpsplitting = 0
% 1.24/1.63 usesimpdemod = 5
% 1.24/1.63 usesimpres = 3
% 1.24/1.63
% 1.24/1.63 resimpinuse = 1000
% 1.24/1.63 resimpclauses = 20000
% 1.24/1.63 substype = eqrewr
% 1.24/1.63 backwardsubs = 1
% 1.24/1.63 selectoldest = 5
% 1.24/1.63
% 1.24/1.63 litorderings [0] = split
% 1.24/1.63 litorderings [1] = extend the termordering, first sorting on arguments
% 1.24/1.63
% 1.24/1.63 termordering = kbo
% 1.24/1.63
% 1.24/1.63 litapriori = 0
% 1.24/1.63 termapriori = 1
% 1.24/1.63 litaposteriori = 0
% 1.24/1.63 termaposteriori = 0
% 1.24/1.63 demodaposteriori = 0
% 1.24/1.63 ordereqreflfact = 0
% 1.24/1.63
% 1.24/1.63 litselect = negord
% 1.24/1.63
% 1.24/1.63 maxweight = 15
% 1.24/1.63 maxdepth = 30000
% 1.24/1.63 maxlength = 115
% 1.24/1.63 maxnrvars = 195
% 1.24/1.63 excuselevel = 1
% 1.24/1.63 increasemaxweight = 1
% 1.24/1.63
% 1.24/1.63 maxselected = 10000000
% 1.24/1.63 maxnrclauses = 10000000
% 1.24/1.63
% 1.24/1.63 showgenerated = 0
% 1.24/1.63 showkept = 0
% 1.24/1.63 showselected = 0
% 1.24/1.63 showdeleted = 0
% 1.24/1.63 showresimp = 1
% 1.24/1.63 showstatus = 2000
% 1.24/1.63
% 1.24/1.63 prologoutput = 1
% 1.24/1.63 nrgoals = 5000000
% 1.24/1.63 totalproof = 1
% 1.24/1.63
% 1.24/1.63 Symbols occurring in the translation:
% 1.24/1.63
% 1.24/1.63 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 1.24/1.63 . [1, 2] (w:1, o:154, a:1, s:1, b:0),
% 1.24/1.63 ! [4, 1] (w:0, o:73, a:1, s:1, b:0),
% 1.24/1.63 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.24/1.63 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.24/1.63 'class_Ring__and__Field_Oordered__ring__strict' [40, 1] (w:1, o:83
% 1.24/1.63 , a:1, s:1, b:0),
% 1.24/1.63 'c_HOL_Ozero__class_Ozero' [42, 1] (w:1, o:84, a:1, s:1, b:0),
% 1.24/1.63 'c_lessequals' [43, 3] (w:1, o:189, a:1, s:1, b:0),
% 1.24/1.63 'c_HOL_Otimes__class_Otimes' [45, 1] (w:1, o:85, a:1, s:1, b:0),
% 1.24/1.63 hAPP [46, 2] (w:1, o:179, a:1, s:1, b:0),
% 1.24/1.63 'class_Divides_Osemiring__div' [47, 1] (w:1, o:87, a:1, s:1, b:0),
% 1.24/1.63 'c_HOL_Oplus__class_Oplus' [48, 1] (w:1, o:89, a:1, s:1, b:0),
% 1.24/1.63 'c_Divides_Odiv__class_Omod' [49, 3] (w:1, o:190, a:1, s:1, b:0),
% 1.24/1.63 'class_Ring__and__Field_Oordered__idom' [50, 1] (w:1, o:90, a:1, s:1
% 1.24/1.63 , b:0),
% 1.24/1.63 'c_HOL_Oabs__class_Oabs' [51, 2] (w:1, o:180, a:1, s:1, b:0),
% 1.24/1.63 'c_HOL_Oord__class_Oless' [52, 3] (w:1, o:191, a:1, s:1, b:0),
% 1.24/1.63 'c_HOL_Ouminus__class_Ouminus' [53, 2] (w:1, o:181, a:1, s:1, b:0),
% 1.24/1.63 'c_Power_Opower_Opower' [56, 3] (w:1, o:193, a:1, s:1, b:0),
% 1.24/1.63 'tc_nat' [57, 0] (w:1, o:31, a:1, s:1, b:0),
% 1.24/1.63 'c_OrderedGroup_Omonoid__mult' [60, 3] (w:1, o:192, a:1, s:1, b:0),
% 1.24/1.63 'c_Divides_Odiv__class_Odiv' [61, 3] (w:1, o:194, a:1, s:1, b:0),
% 1.24/1.63 'c_Suc' [63, 1] (w:1, o:91, a:1, s:1, b:0),
% 1.24/1.63 'c_Parity_Oeven__odd__class_Oeven' [64, 2] (w:1, o:182, a:1, s:1, b:0
% 1.24/1.63 ),
% 1.24/1.63 'class_Ring__and__Field_Osemiring__0' [65, 1] (w:1, o:96, a:1, s:1
% 1.24/1.63 , b:0),
% 1.24/1.63 'class_Power_Opower' [66, 1] (w:1, o:121, a:1, s:1, b:0),
% 1.24/1.63 'c_Power_Opower__class_Opower' [67, 1] (w:1, o:122, a:1, s:1, b:0),
% 1.24/1.63 'class_Ring__and__Field_Ozero__neq__one' [68, 1] (w:1, o:123, a:1, s:
% 1.24/1.63 1, b:0),
% 1.24/1.63 'class_Ring__and__Field_Ono__zero__divisors' [69, 1] (w:1, o:82, a:1
% 1.24/1.63 , s:1, b:0),
% 1.24/1.63 'class_Ring__and__Field_Omult__zero' [70, 1] (w:1, o:79, a:1, s:1, b:
% 1.24/1.63 0),
% 1.24/1.63 'class_Ring__and__Field_Oordered__field' [71, 1] (w:1, o:124, a:1, s:
% 1.24/1.63 1, b:0),
% 1.24/1.63 'class_Ring__and__Field_Odivision__by__zero' [72, 1] (w:1, o:128, a:1
% 1.24/1.63 , s:1, b:0),
% 1.24/1.63 'class_Int_Onumber' [73, 1] (w:1, o:129, a:1, s:1, b:0),
% 1.24/1.63 'c_Int_Onumber__class_Onumber__of' [75, 2] (w:1, o:184, a:1, s:1, b:0
% 1.24/1.63 ),
% 1.24/1.63 'c_HOL_Oinverse__class_Odivide' [76, 3] (w:1, o:195, a:1, s:1, b:0),
% 1.24/1.63
% 1.24/1.63 'class_Ring__and__Field_Ocomm__semiring__1' [78, 1] (w:1, o:126, a:1
% 1.24/1.63 , s:1, b:0),
% 1.24/1.63 'c_HOL_Oone__class_Oone' [79, 1] (w:1, o:88, a:1, s:1, b:0),
% 1.24/1.63 'class_OrderedGroup_Opordered__ab__group__add' [81, 1] (w:1, o:99, a:
% 1.24/1.63 1, s:1, b:0),
% 1.24/1.63 'class_Ring__and__Field_Ofield' [82, 1] (w:1, o:130, a:1, s:1, b:0),
% 1.24/1.63
% 1.24/1.63 'c_HOL_Oinverse__class_Oinverse' [83, 2] (w:1, o:183, a:1, s:1, b:0)
% 1.24/1.63 ,
% 1.24/1.63 'class_Ring__and__Field_Oordered__semiring__strict' [84, 1] (w:1, o:
% 1.24/1.63 131, a:1, s:1, b:0),
% 1.24/1.63 'class_OrderedGroup_Opordered__ab__group__add__abs' [85, 1] (w:1, o:
% 1.24/1.63 100, a:1, s:1, b:0),
% 1.24/1.63 'class_OrderedGroup_Ocomm__monoid__add' [86, 1] (w:1, o:101, a:1, s:1
% 1.24/1.63 , b:0),
% 1.24/1.63 hBOOL [88, 1] (w:1, o:132, a:1, s:1, b:0),
% 1.24/1.63 'c_Ring__and__Field_Oordered__semidom' [92, 7] (w:1, o:201, a:1, s:1
% 1.24/1.63 , b:0),
% 1.24/1.63 'class_OrderedGroup_Ogroup__add' [93, 1] (w:1, o:102, a:1, s:1, b:0)
% 1.24/1.63 ,
% 1.24/1.63 'c_Ring__and__Field_Oordered__idom' [98, 11] (w:1, o:203, a:1, s:1
% 1.24/1.63 , b:0),
% 1.24/1.63 'class_Ring__and__Field_Oordered__semidom' [99, 1] (w:1, o:133, a:1
% 1.24/1.63 , s:1, b:0),
% 1.24/1.63 'c_NthRoot_Osqrt' [101, 0] (w:1, o:52, a:1, s:1, b:0),
% 1.24/1.63 'class_Ring__and__Field_Omult__mono1' [105, 1] (w:1, o:80, a:1, s:1
% 1.24/1.63 , b:0),
% 1.24/1.63 'class_Ring__and__Field_Omult__mono' [106, 1] (w:1, o:81, a:1, s:1
% 1.24/1.63 , b:0),
% 1.24/1.63 'class_Ring__and__Field_Opordered__ring' [107, 1] (w:1, o:136, a:1
% 1.24/1.63 , s:1, b:0),
% 1.24/1.63 'class_Ring__and__Field_Oidom' [109, 1] (w:1, o:137, a:1, s:1, b:0),
% 1.24/1.63
% 1.24/1.63 'class_Int_Onumber__ring' [110, 1] (w:1, o:138, a:1, s:1, b:0),
% 1.24/1.63 'class_Ring__and__Field_Odivision__ring' [111, 1] (w:1, o:139, a:1
% 6.88/7.23 , s:1, b:0),
% 6.88/7.23 'c_NthRoot_Oroot' [113, 1] (w:1, o:140, a:1, s:1, b:0),
% 6.88/7.23 'c_Int_OMin' [114, 0] (w:1, o:57, a:1, s:1, b:0),
% 6.88/7.23 'class_OrderedGroup_Oab__semigroup__idem__mult' [115, 1] (w:1, o:103
% 6.88/7.23 , a:1, s:1, b:0),
% 6.88/7.23 'class_Ring__and__Field_Osemiring__1' [116, 1] (w:1, o:141, a:1, s:1
% 6.88/7.23 , b:0),
% 6.88/7.23 'c_Nat_Osemiring__1__class_Oof__nat' [117, 2] (w:1, o:185, a:1, s:1
% 6.88/7.23 , b:0),
% 6.88/7.23 'class_Orderings_Oorder' [118, 1] (w:1, o:104, a:1, s:1, b:0),
% 6.88/7.23 'class_Orderings_Olinorder' [119, 1] (w:1, o:105, a:1, s:1, b:0),
% 6.88/7.23 'class_Ring__and__Field_Opordered__cancel__semiring' [120, 1] (w:1
% 6.88/7.23 , o:142, a:1, s:1, b:0),
% 6.88/7.23 'class_OrderedGroup_Oab__semigroup__mult' [121, 1] (w:1, o:106, a:1
% 6.88/7.23 , s:1, b:0),
% 6.88/7.23 'class_OrderedGroup_Olordered__ab__group__add' [122, 1] (w:1, o:107
% 6.88/7.23 , a:1, s:1, b:0),
% 6.88/7.23 'class_Ring__and__Field_Oring' [123, 1] (w:1, o:92, a:1, s:1, b:0),
% 6.88/7.23 'class_Ring__and__Field_Opordered__ring__abs' [124, 1] (w:1, o:143
% 6.88/7.23 , a:1, s:1, b:0),
% 6.88/7.23 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le' [125, 1]
% 6.88/7.23 (w:1, o:108, a:1, s:1, b:0),
% 6.88/7.23 'class_OrderedGroup_Opordered__ab__semigroup__add' [126, 1] (w:1, o:
% 6.88/7.23 109, a:1, s:1, b:0),
% 6.88/7.23 'class_Lattices_Oboolean__algebra' [128, 1] (w:1, o:144, a:1, s:1, b:
% 6.88/7.23 0),
% 6.88/7.23 'class_OrderedGroup_Olordered__ab__group__add__abs' [129, 1] (w:1, o:
% 6.88/7.23 110, a:1, s:1, b:0),
% 6.88/7.23 'class_OrderedGroup_Opordered__comm__monoid__add' [134, 1] (w:1, o:
% 6.88/7.23 111, a:1, s:1, b:0),
% 6.88/7.23 'class_Ring__and__Field_Oring__no__zero__divisors' [136, 1] (w:1, o:
% 6.88/7.23 93, a:1, s:1, b:0),
% 6.88/7.23 'class_RealVector_Oreal__normed__algebra' [137, 1] (w:1, o:145, a:1
% 6.88/7.23 , s:1, b:0),
% 6.88/7.23 'class_Ring__and__Field_Ocomm__semiring' [142, 1] (w:1, o:127, a:1
% 6.88/7.23 , s:1, b:0),
% 6.88/7.23 'c_Groebner__Basis_Ogb__semiring' [150, 6] (w:1, o:200, a:1, s:1, b:0
% 6.88/7.23 ),
% 6.88/7.23 'class_OrderedGroup_Oordered__ab__group__add' [151, 1] (w:1, o:98, a:
% 6.88/7.23 1, s:1, b:0),
% 6.88/7.23 'class_Ring__and__Field_Opordered__semiring' [152, 1] (w:1, o:146, a:
% 6.88/7.23 1, s:1, b:0),
% 6.88/7.23 'class_Divides_Oring__div' [153, 1] (w:1, o:86, a:1, s:1, b:0),
% 6.88/7.23 'tc_Int_Oint' [154, 0] (w:1, o:60, a:1, s:1, b:0),
% 6.88/7.23 'class_Ring__and__Field_Oabs__if' [155, 1] (w:1, o:147, a:1, s:1, b:0
% 6.88/7.23 ),
% 6.88/7.23 'class_Ring__and__Field_Oordered__semiring' [156, 1] (w:1, o:134, a:1
% 6.88/7.23 , s:1, b:0),
% 6.88/7.23 'class_Nat_Osemiring__char__0' [157, 1] (w:1, o:97, a:1, s:1, b:0),
% 6.88/7.23 'class_Ring__and__Field_Olordered__ring' [158, 1] (w:1, o:78, a:1, s:
% 6.88/7.23 1, b:0),
% 6.88/7.23 'c_Int_OBit0' [159, 1] (w:1, o:148, a:1, s:1, b:0),
% 6.88/7.23 'class_OrderedGroup_Omonoid__mult' [160, 1] (w:1, o:112, a:1, s:1, b:
% 6.88/7.23 0),
% 6.88/7.23 'class_OrderedGroup_Ocomm__monoid__mult' [161, 1] (w:1, o:113, a:1
% 6.88/7.23 , s:1, b:0),
% 6.88/7.23 'class_OrderedGroup_Ocancel__ab__semigroup__add' [162, 1] (w:1, o:114
% 6.88/7.23 , a:1, s:1, b:0),
% 6.88/7.23 'class_OrderedGroup_Ocancel__semigroup__add' [163, 1] (w:1, o:115, a:
% 6.88/7.23 1, s:1, b:0),
% 6.88/7.23 'class_Ring__and__Field_Ocomm__ring__1' [164, 1] (w:1, o:125, a:1, s:
% 6.88/7.23 1, b:0),
% 6.88/7.23 'class_Orderings_Opreorder' [165, 1] (w:1, o:116, a:1, s:1, b:0),
% 6.88/7.23 'class_OrderedGroup_Oab__group__add' [166, 1] (w:1, o:117, a:1, s:1
% 6.88/7.23 , b:0),
% 6.88/7.23 'class_OrderedGroup_Oab__semigroup__add' [167, 1] (w:1, o:118, a:1
% 6.88/7.23 , s:1, b:0),
% 6.88/7.23 'class_Ring__and__Field_Osemiring' [168, 1] (w:1, o:149, a:1, s:1, b:
% 6.88/7.23 0),
% 6.88/7.23 'class_RealVector_Oreal__normed__field' [170, 1] (w:1, o:150, a:1, s:
% 6.88/7.23 1, b:0),
% 6.88/7.23 'class_Ring__and__Field_Oring__1' [174, 1] (w:1, o:94, a:1, s:1, b:0)
% 6.88/7.23 ,
% 6.88/7.23 'c_Int_Oiszero' [175, 2] (w:1, o:186, a:1, s:1, b:0),
% 6.88/7.23 'class_Ring__and__Field_Oordered__comm__semiring__strict' [176, 1]
% 6.88/7.23 (w:1, o:135, a:1, s:1, b:0),
% 6.88/7.23 'c_Int_OPls' [177, 0] (w:1, o:62, a:1, s:1, b:0),
% 6.88/7.23 'class_OrderedGroup_Omonoid__add' [178, 1] (w:1, o:119, a:1, s:1, b:0
% 6.88/7.23 ),
% 6.88/7.23 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add' [179, 1]
% 6.88/7.23 (w:1, o:120, a:1, s:1, b:0),
% 6.88/7.23 'c_Int_OBit1' [180, 1] (w:1, o:151, a:1, s:1, b:0),
% 6.88/7.23 'class_Ring__and__Field_Oring__1__no__zero__divisors' [183, 1] (w:1
% 32.64/32.98 , o:95, a:1, s:1, b:0),
% 32.64/32.98 'c_Ring__and__Field_Ocomm__ring__1' [184, 7] (w:1, o:202, a:1, s:1
% 32.64/32.98 , b:0),
% 32.64/32.98 'c_FFT__Mirabelle_OIFFT' [185, 2] (w:1, o:187, a:1, s:1, b:0),
% 32.64/32.98 'class_Int_Oring__char__0' [186, 1] (w:1, o:152, a:1, s:1, b:0),
% 32.64/32.98 'c_FFT__Mirabelle_Oroot' [187, 1] (w:1, o:153, a:1, s:1, b:0),
% 32.64/32.98 'c_Complex_Oii' [188, 0] (w:1, o:63, a:1, s:1, b:0),
% 32.64/32.98 'c_Ring__and__Field_Osemiring__1' [189, 5] (w:1, o:199, a:1, s:1, b:0
% 32.64/32.98 ),
% 32.64/32.98 'v_i____' [190, 0] (w:1, o:64, a:1, s:1, b:0),
% 32.64/32.98 'v_ka____' [191, 0] (w:1, o:65, a:1, s:1, b:0),
% 32.64/32.98 'c_FFT__Mirabelle_OIDFT' [192, 3] (w:1, o:196, a:1, s:1, b:0),
% 32.64/32.98 'c_HOL_Ominus__class_Ominus' [194, 3] (w:1, o:197, a:1, s:1, b:0),
% 32.64/32.98 'v_a____' [195, 0] (w:1, o:66, a:1, s:1, b:0),
% 32.64/32.98 'tc_fun' [198, 2] (w:1, o:188, a:1, s:1, b:0),
% 32.64/32.98 'tc_RealDef_Oreal' [199, 0] (w:1, o:69, a:1, s:1, b:0),
% 32.64/32.98 'tc_Complex_Ocomplex' [200, 0] (w:1, o:70, a:1, s:1, b:0),
% 32.64/32.98 'c_fequal' [201, 3] (w:1, o:198, a:1, s:1, b:0).
% 32.64/32.98
% 32.64/32.98
% 32.64/32.98 Starting Search:
% 32.64/32.98
% 32.64/32.98 Resimplifying inuse:
% 32.64/32.98 Done
% 32.64/32.98
% 32.64/32.98
% 32.64/32.98 Intermediate Status:
% 32.64/32.98 Generated: 3236
% 32.64/32.98 Kept: 2001
% 32.64/32.98 Inuse: 127
% 32.64/32.98 Deleted: 9
% 32.64/32.98 Deletedinuse: 0
% 32.64/32.98
% 32.64/32.98 Resimplifying inuse:
% 32.64/32.98 Done
% 32.64/32.98
% 32.64/32.98
% 32.64/32.98 Intermediate Status:
% 32.64/32.98 Generated: 10641
% 32.64/32.98 Kept: 4211
% 32.64/32.98 Inuse: 237
% 32.64/32.98 Deleted: 14
% 32.64/32.98 Deletedinuse: 0
% 32.64/32.98
% 32.64/32.98 Resimplifying inuse:
% 32.64/32.98 Done
% 32.64/32.98
% 32.64/32.98 Resimplifying inuse:
% 32.64/32.98 Done
% 32.64/32.98
% 32.64/32.98
% 32.64/32.98 Intermediate Status:
% 32.64/32.98 Generated: 20135
% 32.64/32.98 Kept: 6315
% 32.64/32.98 Inuse: 253
% 32.64/32.98 Deleted: 14
% 32.64/32.98 Deletedinuse: 0
% 32.64/32.98
% 32.64/32.98 Resimplifying inuse:
% 32.64/32.98 Done
% 32.64/32.98
% 32.64/32.98 Resimplifying inuse:
% 32.64/32.98 Done
% 32.64/32.98
% 32.64/32.98
% 32.64/32.98 Intermediate Status:
% 32.64/32.98 Generated: 28218
% 32.64/32.98 Kept: 8371
% 32.64/32.98 Inuse: 343
% 32.64/32.98 Deleted: 18
% 32.64/32.98 Deletedinuse: 0
% 32.64/32.98
% 32.64/32.98 Resimplifying inuse:
% 32.64/32.98 Done
% 32.64/32.98
% 32.64/32.98
% 32.64/32.98 Intermediate Status:
% 32.64/32.98 Generated: 50534
% 32.64/32.98 Kept: 10937
% 32.64/32.98 Inuse: 378
% 32.64/32.98 Deleted: 18
% 32.64/32.98 Deletedinuse: 0
% 32.64/32.98
% 32.64/32.98 Resimplifying inuse:
% 32.64/32.98 Done
% 32.64/32.98
% 32.64/32.98 Resimplifying inuse:
% 32.64/32.98 Done
% 32.64/32.98
% 32.64/32.98
% 32.64/32.98 Intermediate Status:
% 32.64/32.98 Generated: 60976
% 32.64/32.98 Kept: 13766
% 32.64/32.98 Inuse: 451
% 32.64/32.98 Deleted: 25
% 32.64/32.98 Deletedinuse: 0
% 32.64/32.98
% 32.64/32.98 Resimplifying inuse:
% 32.64/32.98 Done
% 32.64/32.98
% 32.64/32.98 Resimplifying inuse:
% 32.64/32.98 Done
% 32.64/32.98
% 32.64/32.98
% 32.64/32.98 Intermediate Status:
% 32.64/32.98 Generated: 66843
% 32.64/32.98 Kept: 15786
% 32.64/32.98 Inuse: 478
% 32.64/32.98 Deleted: 25
% 32.64/32.98 Deletedinuse: 0
% 32.64/32.98
% 32.64/32.98 Resimplifying inuse:
% 32.64/32.98 Done
% 32.64/32.98
% 32.64/32.98
% 32.64/32.98 Intermediate Status:
% 32.64/32.98 Generated: 79454
% 32.64/32.98 Kept: 18554
% 32.64/32.98 Inuse: 506
% 32.64/32.98 Deleted: 25
% 32.64/32.98 Deletedinuse: 0
% 32.64/32.98
% 32.64/32.98 Resimplifying inuse:
% 32.64/32.98 Done
% 32.64/32.98
% 32.64/32.98 Resimplifying inuse:
% 32.64/32.98 Done
% 32.64/32.98
% 32.64/32.98 Resimplifying clauses:
% 32.64/32.98 Done
% 32.64/32.98
% 32.64/32.98
% 32.64/32.98 Intermediate Status:
% 32.64/32.98 Generated: 91277
% 32.64/32.98 Kept: 20660
% 32.64/32.98 Inuse: 529
% 32.64/32.98 Deleted: 285
% 32.64/32.98 Deletedinuse: 0
% 32.64/32.98
% 32.64/32.98 Resimplifying inuse:
% 32.64/32.98 Done
% 32.64/32.98
% 32.64/32.98 Resimplifying inuse:
% 32.64/32.98 Done
% 32.64/32.98
% 32.64/32.98
% 32.64/32.98 Intermediate Status:
% 32.64/32.98 Generated: 95980
% 32.64/32.98 Kept: 22688
% 32.64/32.98 Inuse: 539
% 32.64/32.98 Deleted: 285
% 32.64/32.98 Deletedinuse: 0
% 32.64/32.98
% 32.64/32.98 Resimplifying inuse:
% 32.64/32.98 Done
% 32.64/32.98
% 32.64/32.98 Resimplifying inuse:
% 32.64/32.98 Done
% 32.64/32.98
% 32.64/32.98
% 32.64/32.98 Intermediate Status:
% 32.64/32.98 Generated: 103963
% 32.64/32.98 Kept: 24712
% 32.64/32.98 Inuse: 584
% 32.64/32.98 Deleted: 285
% 32.64/32.98 Deletedinuse: 0
% 32.64/32.98
% 32.64/32.98 Resimplifying inuse:
% 32.64/32.98 Done
% 32.64/32.98
% 32.64/32.98 Resimplifying inuse:
% 32.64/32.98 Done
% 32.64/32.98
% 32.64/32.98
% 32.64/32.98 Intermediate Status:
% 32.64/32.98 Generated: 111382
% 32.64/32.98 Kept: 26712
% 32.64/32.98 Inuse: 635
% 32.64/32.98 Deleted: 285
% 32.64/32.98 Deletedinuse: 0
% 32.64/32.98
% 32.64/32.98 Resimplifying inuse:
% 32.64/32.98 Done
% 32.64/32.98
% 32.64/32.98
% 32.64/32.98 Intermediate Status:
% 32.64/32.98 Generated: 121951
% 32.64/32.98 Kept: 29013
% 32.64/32.98 Inuse: 654
% 32.64/32.99 Deleted: 286
% 32.64/32.99 Deletedinuse: 1
% 32.64/32.99
% 32.64/32.99 Resimplifying inuse:
% 32.64/32.99 Done
% 32.64/32.99
% 32.64/32.99
% 32.64/32.99 Intermediate Status:
% 32.64/32.99 Generated: 131840
% 32.64/32.99 Kept: 31100
% 32.64/32.99 Inuse: 664
% 32.64/32.99 Deleted: 286
% 32.64/32.99 Deletedinuse: 1
% 32.64/32.99
% 32.64/32.99 Resimplifying inuse:
% 32.64/32.99 Done
% 32.64/32.99
% 32.64/32.99 Resimplifying inuse:
% 32.64/32.99 Done
% 32.64/32.99
% 32.64/32.99
% 32.64/32.99 Intermediate Status:
% 32.64/32.99 Generated: 142851
% 32.64/32.99 Kept: 33712
% 32.64/32.99 Inuse: 679
% 32.64/32.99 Deleted: 286
% 32.64/32.99 Deletedinuse: 1
% 32.64/32.99
% 32.64/32.99 Resimplifying inuse:
% 32.64/32.99 Done
% 32.64/32.99
% 32.64/32.99 Resimplifying inuse:
% 32.64/32.99 Done
% 32.64/32.99
% 32.64/32.99
% 32.64/32.99 Intermediate Status:
% 32.64/32.99 Generated: 150950
% 32.64/32.99 Kept: 35728
% 32.64/32.99 Inuse: 709
% 32.64/32.99 Deleted: 286
% 32.64/32.99 Deletedinuse: 1
% 32.64/32.99
% 32.64/32.99 Resimplifying inuse:
% 32.64/32.99 Done
% 32.64/32.99
% 32.64/32.99
% 32.64/32.99 Intermediate Status:
% 32.64/32.99 Generated: 157578
% 32.64/32.99 Kept: 38426
% 32.64/32.99 Inuse: 724
% 32.64/32.99 Deleted: 286
% 32.64/32.99 Deletedinuse: 1
% 32.64/32.99
% 32.64/32.99 Resimplifying inuse:
% 32.64/32.99 Done
% 32.64/32.99
% 32.64/32.99 Resimplifying inuse:
% 32.64/32.99 Done
% 32.64/32.99
% 32.64/32.99
% 32.64/32.99 Intermediate Status:
% 32.64/32.99 Generated: 165381
% 32.64/32.99 Kept: 40440
% 32.64/32.99 Inuse: 734
% 32.64/32.99 Deleted: 286
% 32.64/32.99 Deletedinuse: 1
% 32.64/32.99
% 32.64/32.99 Resimplifying inuse:
% 32.64/32.99 Done
% 32.64/32.99
% 32.64/32.99 Resimplifying clauses:
% 32.64/32.99 Done
% 32.64/32.99
% 32.64/32.99 Resimplifying inuse:
% 32.64/32.99 Done
% 32.64/32.99
% 32.64/32.99
% 32.64/32.99 Intermediate Status:
% 32.64/32.99 Generated: 172888
% 32.64/32.99 Kept: 42519
% 32.64/32.99 Inuse: 774
% 32.64/32.99 Deleted: 395
% 32.64/32.99 Deletedinuse: 1
% 82.26/82.64
% 82.26/82.64 Resimplifying inuse:
% 82.26/82.64 Done
% 82.26/82.64
% 82.26/82.64 Resimplifying inuse:
% 82.26/82.64 Done
% 82.26/82.64
% 82.26/82.64
% 82.26/82.64 Intermediate Status:
% 82.26/82.64 Generated: 182306
% 82.26/82.64 Kept: 44751
% 82.26/82.64 Inuse: 799
% 82.26/82.64 Deleted: 395
% 82.26/82.64 Deletedinuse: 1
% 82.26/82.64
% 82.26/82.64 Resimplifying inuse:
% 82.26/82.64 Done
% 82.26/82.64
% 82.26/82.64 Resimplifying inuse:
% 82.26/82.64 Done
% 82.26/82.64
% 82.26/82.64
% 82.26/82.64 Intermediate Status:
% 82.26/82.64 Generated: 188682
% 82.26/82.64 Kept: 46873
% 82.26/82.64 Inuse: 829
% 82.26/82.64 Deleted: 395
% 82.26/82.64 Deletedinuse: 1
% 82.26/82.64
% 82.26/82.64 Resimplifying inuse:
% 82.26/82.64 Done
% 82.26/82.64
% 82.26/82.64 Resimplifying inuse:
% 82.26/82.64 Done
% 82.26/82.64
% 82.26/82.64
% 82.26/82.64 Intermediate Status:
% 82.26/82.64 Generated: 195866
% 82.26/82.64 Kept: 49251
% 82.26/82.64 Inuse: 844
% 82.26/82.64 Deleted: 395
% 82.26/82.64 Deletedinuse: 1
% 82.26/82.64
% 82.26/82.64 Resimplifying inuse:
% 82.26/82.64 Done
% 82.26/82.64
% 82.26/82.64 Resimplifying inuse:
% 82.26/82.64 Done
% 82.26/82.64
% 82.26/82.64
% 82.26/82.64 Intermediate Status:
% 82.26/82.64 Generated: 202837
% 82.26/82.64 Kept: 51306
% 82.26/82.64 Inuse: 874
% 82.26/82.64 Deleted: 395
% 82.26/82.64 Deletedinuse: 1
% 82.26/82.64
% 82.26/82.64 Resimplifying inuse:
% 82.26/82.64 Done
% 82.26/82.64
% 82.26/82.64 Resimplifying inuse:
% 82.26/82.64 Done
% 82.26/82.64
% 82.26/82.64
% 82.26/82.64 Intermediate Status:
% 82.26/82.64 Generated: 221999
% 82.26/82.64 Kept: 55106
% 82.26/82.64 Inuse: 909
% 82.26/82.64 Deleted: 395
% 82.26/82.64 Deletedinuse: 1
% 82.26/82.64
% 82.26/82.64 Resimplifying inuse:
% 82.26/82.64 Done
% 82.26/82.64
% 82.26/82.64 Resimplifying inuse:
% 82.26/82.64 Done
% 82.26/82.64
% 82.26/82.64
% 82.26/82.64 Intermediate Status:
% 82.26/82.64 Generated: 232079
% 82.26/82.64 Kept: 57465
% 82.26/82.64 Inuse: 944
% 82.26/82.64 Deleted: 395
% 82.26/82.64 Deletedinuse: 1
% 82.28/82.64
% 82.28/82.64 Resimplifying inuse:
% 82.28/82.64 Done
% 82.28/82.64
% 82.28/82.64 Resimplifying inuse:
% 82.28/82.64 Done
% 82.28/82.64
% 82.28/82.64
% 82.28/82.64 Intermediate Status:
% 82.28/82.64 Generated: 239893
% 82.28/82.64 Kept: 59518
% 82.28/82.64 Inuse: 969
% 82.28/82.64 Deleted: 395
% 82.28/82.64 Deletedinuse: 1
% 82.28/82.64
% 82.28/82.64 Resimplifying inuse:
% 82.28/82.64 Done
% 82.28/82.64
% 82.28/82.64
% 82.28/82.64 Intermediate Status:
% 82.28/82.64 Generated: 247570
% 82.28/82.64 Kept: 61563
% 82.28/82.64 Inuse: 984
% 82.28/82.64 Deleted: 395
% 82.28/82.64 Deletedinuse: 1
% 82.28/82.64
% 82.28/82.64 Resimplifying inuse:
% 82.28/82.64 Done
% 82.28/82.64
% 82.28/82.64 Resimplifying clauses:
% 82.28/82.64 Done
% 82.28/82.64
% 82.28/82.64 Resimplifying inuse:
% 82.28/82.64 Done
% 82.28/82.64
% 82.28/82.64
% 82.28/82.64 Intermediate Status:
% 82.28/82.64 Generated: 259034
% 82.28/82.64 Kept: 64399
% 82.28/82.64 Inuse: 1023
% 82.28/82.64 Deleted: 1194
% 82.28/82.64 Deletedinuse: 5
% 82.28/82.64
% 82.28/82.64 Resimplifying inuse:
% 82.28/82.64 Done
% 82.28/82.64
% 82.28/82.64 Resimplifying inuse:
% 82.28/82.64 Done
% 82.28/82.64
% 82.28/82.64
% 82.28/82.64 Intermediate Status:
% 82.28/82.64 Generated: 264303
% 82.28/82.64 Kept: 66399
% 82.28/82.64 Inuse: 1031
% 82.28/82.64 Deleted: 1194
% 82.28/82.64 Deletedinuse: 5
% 82.28/82.64
% 82.28/82.64
% 82.28/82.64 Intermediate Status:
% 82.28/82.64 Generated: 280903
% 82.28/82.64 Kept: 69698
% 82.28/82.64 Inuse: 1043
% 82.28/82.64 Deleted: 1194
% 82.28/82.64 Deletedinuse: 5
% 82.28/82.64
% 82.28/82.64 Resimplifying inuse:
% 82.28/82.64 Done
% 82.28/82.64
% 82.28/82.64 Resimplifying inuse:
% 82.28/82.64 Done
% 82.28/82.64
% 82.28/82.64
% 82.28/82.64 Intermediate Status:
% 82.28/82.64 Generated: 296590
% 82.28/82.64 Kept: 72810
% 82.28/82.64 Inuse: 1053
% 82.28/82.64 Deleted: 1194
% 82.28/82.64 Deletedinuse: 5
% 82.28/82.64
% 82.28/82.64 Resimplifying inuse:
% 82.28/82.64 Done
% 82.28/82.64
% 82.28/82.64 Resimplifying inuse:
% 82.28/82.64 Done
% 82.28/82.64
% 82.28/82.64
% 82.28/82.64 Intermediate Status:
% 82.28/82.64 Generated: 310581
% 82.28/82.64 Kept: 76583
% 82.28/82.64 Inuse: 1090
% 82.28/82.64 Deleted: 1194
% 82.28/82.64 Deletedinuse: 5
% 82.28/82.64
% 82.28/82.64 Resimplifying inuse:
% 82.28/82.64 Done
% 82.28/82.64
% 82.28/82.64 Resimplifying inuse:
% 82.28/82.64 Done
% 82.28/82.64
% 82.28/82.64
% 82.28/82.64 Intermediate Status:
% 82.28/82.64 Generated: 322111
% 82.28/82.64 Kept: 79736
% 82.28/82.64 Inuse: 1098
% 82.28/82.64 Deleted: 1194
% 82.28/82.64 Deletedinuse: 5
% 82.28/82.64
% 82.28/82.64 Resimplifying inuse:
% 82.28/82.64 Done
% 82.28/82.64
% 82.28/82.64 Resimplifying inuse:
% 82.28/82.64 Done
% 82.28/82.64
% 82.28/82.64
% 82.28/82.64 Intermediate Status:
% 82.28/82.64 Generated: 333473
% 82.28/82.64 Kept: 82031
% 82.28/82.64 Inuse: 1108
% 82.28/82.64 Deleted: 1194
% 82.28/82.64 Deletedinuse: 5
% 82.28/82.64
% 82.28/82.64 Resimplifying clauses:
% 82.28/82.64 Done
% 82.28/82.64
% 82.28/82.64 Resimplifying inuse:
% 82.28/82.64 Done
% 82.28/82.64
% 82.28/82.64
% 82.28/82.64 Intermediate Status:
% 82.28/82.64 Generated: 345983
% 82.28/82.64 Kept: 84378
% 82.28/82.64 Inuse: 1118
% 82.28/82.64 Deleted: 1585
% 82.28/82.64 Deletedinuse: 5
% 82.28/82.64
% 82.28/82.64 Resimplifying inuse:
% 82.28/82.64 Done
% 82.28/82.64
% 82.28/82.64 Resimplifying inuse:
% 82.28/82.64 Done
% 82.28/82.64
% 82.28/82.64
% 82.28/82.64 Intermediate Status:
% 82.28/82.64 Generated: 356698
% 82.28/82.64 Kept: 86980
% 82.28/82.64 Inuse: 1128
% 82.28/82.64 Deleted: 1585
% 82.28/82.64 Deletedinuse: 5
% 82.28/82.64
% 82.28/82.64 Resimplifying inuse:
% 82.28/82.64 Done
% 82.28/82.64
% 82.28/82.64 Resimplifying inuse:
% 82.28/82.64 Done
% 82.28/82.64
% 82.28/82.64
% 82.28/82.64 Intermediate Status:
% 82.28/82.64 Generated: 366977
% 82.28/82.64 Kept: 89003
% 82.28/82.64 Inuse: 1149
% 82.28/82.64 Deleted: 1585
% 82.28/82.64 Deletedinuse: 5
% 82.28/82.64
% 82.28/82.64 Resimplifying inuse:
% 82.28/82.64 Done
% 82.28/82.64
% 82.28/82.64 Resimplifying inuse:
% 82.28/82.64 Done
% 82.28/82.64
% 82.28/82.64
% 82.28/82.64 Intermediate Status:
% 82.28/82.64 Generated: 377231
% 82.28/82.64 Kept: 91004
% 82.28/82.64 Inuse: 1169
% 82.28/82.64 Deleted: 1585
% 82.28/82.64 Deletedinuse: 5
% 82.28/82.64
% 82.28/82.64 Resimplifying inuse:
% 82.28/82.64 Done
% 82.28/82.64
% 82.28/82.64 Resimplifying inuse:
% 82.28/82.64 Done
% 82.28/82.64
% 82.28/82.64
% 82.28/82.64 Intermediate Status:
% 82.28/82.64 Generated: 386950
% 82.28/82.64 Kept: 93384
% 82.28/82.64 Inuse: 1193
% 82.28/82.64 Deleted: 1585
% 82.28/82.64 Deletedinuse: 5
% 82.28/82.64
% 82.28/82.64 Resimplifying inuse:
% 82.28/82.64 Done
% 82.28/82.64
% 82.28/82.64 Resimplifying inuse:
% 82.28/82.64 Done
% 82.28/82.64
% 82.28/82.64
% 82.28/82.64 Intermediate Status:
% 82.28/82.64 Generated: 396831
% 82.28/82.64 Kept: 95868
% 82.28/82.64 Inuse: 1213
% 82.28/82.64 Deleted: 1585
% 82.28/82.64 Deletedinuse: 5
% 82.28/82.64
% 82.28/82.64 Resimplifying inuse:
% 82.28/82.64 Done
% 82.28/82.64
% 82.28/82.64 Resimplifying inuse:
% 82.28/82.64 Done
% 82.28/82.64
% 82.28/82.64
% 82.28/82.64 Intermediate Status:
% 82.28/82.64 Generated: 431805
% 82.28/82.64 Kept: 100722
% 82.28/82.64 Inuse: 1238
% 82.28/82.64 Deleted: 1585
% 82.28/82.64 Deletedinuse: 5
% 82.28/82.64
% 82.28/82.64 Resimplifying inuse:
% 82.28/82.64 Done
% 82.28/82.64
% 82.28/82.64
% 82.28/82.64 Intermediate Status:
% 82.28/82.64 Generated: 454915
% 82.28/82.64 Kept: 104465
% 82.28/82.64 Inuse: 1248
% 82.28/82.64 Deleted: 1585
% 82.28/82.64 Deletedinuse: 5
% 82.28/82.64
% 82.28/82.64 Resimplifying inuse:
% 82.28/82.64 Done
% 82.28/82.64
% 82.28/82.64 Resimplifying clauses:
% 82.28/82.64 Done
% 82.28/82.64
% 82.28/82.64
% 82.28/82.64 Intermediate Status:
% 82.28/82.64 Generated: 476039
% 82.28/82.64 Kept: 107375
% 82.28/82.64 Inuse: 1253
% 82.28/82.64 Deleted: 1730
% 82.28/82.64 Deletedinuse: 5
% 82.28/82.64
% 82.28/82.64 Resimplifying inuse:
% 82.28/82.64 Done
% 82.28/82.64
% 82.28/82.64
% 82.28/82.64 Intermediate Status:
% 157.21/157.60 Generated: 488369
% 157.21/157.60 Kept: 109709
% 157.21/157.60 Inuse: 1268
% 157.21/157.60 Deleted: 1730
% 157.21/157.60 Deletedinuse: 5
% 157.21/157.60
% 157.21/157.60 Resimplifying inuse:
% 157.21/157.60 Done
% 157.21/157.60
% 157.21/157.60 Resimplifying inuse:
% 157.21/157.60 Done
% 157.21/157.60
% 157.21/157.60
% 157.21/157.60 Intermediate Status:
% 157.21/157.60 Generated: 505215
% 157.21/157.60 Kept: 113576
% 157.21/157.60 Inuse: 1278
% 157.21/157.60 Deleted: 1730
% 157.21/157.60 Deletedinuse: 5
% 157.21/157.60
% 157.21/157.60 Resimplifying inuse:
% 157.21/157.60 Done
% 157.21/157.60
% 157.21/157.60
% 157.21/157.60 Intermediate Status:
% 157.21/157.60 Generated: 515235
% 157.21/157.60 Kept: 115597
% 157.21/157.60 Inuse: 1283
% 157.21/157.60 Deleted: 1730
% 157.21/157.60 Deletedinuse: 5
% 157.21/157.60
% 157.21/157.60 Resimplifying inuse:
% 157.21/157.60 Done
% 157.21/157.60
% 157.21/157.60 Resimplifying inuse:
% 157.21/157.60 Done
% 157.21/157.60
% 157.21/157.60
% 157.21/157.60 Intermediate Status:
% 157.21/157.60 Generated: 522934
% 157.21/157.60 Kept: 117619
% 157.21/157.60 Inuse: 1293
% 157.21/157.60 Deleted: 1731
% 157.21/157.60 Deletedinuse: 6
% 157.21/157.60
% 157.21/157.60 Resimplifying inuse:
% 157.21/157.60 Done
% 157.21/157.60
% 157.21/157.60
% 157.21/157.60 Intermediate Status:
% 157.21/157.60 Generated: 557306
% 157.21/157.60 Kept: 123229
% 157.21/157.60 Inuse: 1312
% 157.21/157.60 Deleted: 1737
% 157.21/157.60 Deletedinuse: 6
% 157.21/157.60
% 157.21/157.60 Resimplifying inuse:
% 157.21/157.60 Done
% 157.21/157.60
% 157.21/157.60 Resimplifying inuse:
% 157.21/157.60 Done
% 157.21/157.60
% 157.21/157.60 Resimplifying clauses:
% 157.21/157.60 Done
% 157.21/157.60
% 157.21/157.60
% 157.21/157.60 Intermediate Status:
% 157.21/157.60 Generated: 564791
% 157.21/157.60 Kept: 125517
% 157.21/157.60 Inuse: 1327
% 157.21/157.60 Deleted: 2013
% 157.21/157.60 Deletedinuse: 6
% 157.21/157.60
% 157.21/157.60 Resimplifying inuse:
% 157.21/157.60 Done
% 157.21/157.60
% 157.21/157.60
% 157.21/157.60 Intermediate Status:
% 157.21/157.60 Generated: 571549
% 157.21/157.60 Kept: 127623
% 157.21/157.60 Inuse: 1342
% 157.21/157.60 Deleted: 2013
% 157.21/157.60 Deletedinuse: 6
% 157.21/157.60
% 157.21/157.60 Resimplifying inuse:
% 157.21/157.60 Done
% 157.21/157.60
% 157.21/157.60 Resimplifying inuse:
% 157.21/157.60 Done
% 157.21/157.60
% 157.21/157.60
% 157.21/157.60 Intermediate Status:
% 157.21/157.60 Generated: 583454
% 157.21/157.60 Kept: 130935
% 157.21/157.60 Inuse: 1357
% 157.21/157.60 Deleted: 2013
% 157.21/157.60 Deletedinuse: 6
% 157.21/157.60
% 157.21/157.60 Resimplifying inuse:
% 157.21/157.60 Done
% 157.21/157.60
% 157.21/157.60
% 157.21/157.60 Intermediate Status:
% 157.21/157.60 Generated: 591393
% 157.21/157.60 Kept: 133884
% 157.21/157.60 Inuse: 1362
% 157.21/157.60 Deleted: 2013
% 157.21/157.60 Deletedinuse: 6
% 157.21/157.60
% 157.21/157.60 Resimplifying inuse:
% 157.21/157.60 Done
% 157.21/157.60
% 157.21/157.60
% 157.21/157.60 Intermediate Status:
% 157.21/157.60 Generated: 604324
% 157.21/157.60 Kept: 137156
% 157.21/157.60 Inuse: 1367
% 157.21/157.60 Deleted: 2013
% 157.21/157.60 Deletedinuse: 6
% 157.21/157.60
% 157.21/157.60 Resimplifying inuse:
% 157.21/157.60 Done
% 157.21/157.60
% 157.21/157.60
% 157.21/157.60 Intermediate Status:
% 157.21/157.60 Generated: 617669
% 157.21/157.60 Kept: 140340
% 157.21/157.60 Inuse: 1372
% 157.21/157.60 Deleted: 2013
% 157.21/157.60 Deletedinuse: 6
% 157.21/157.60
% 157.21/157.60 Resimplifying inuse:
% 157.21/157.60 Done
% 157.21/157.60
% 157.21/157.60 Resimplifying inuse:
% 157.21/157.60 Done
% 157.21/157.60
% 157.21/157.60
% 157.21/157.60 Intermediate Status:
% 157.21/157.60 Generated: 627608
% 157.21/157.60 Kept: 142681
% 157.21/157.60 Inuse: 1397
% 157.21/157.60 Deleted: 2013
% 157.21/157.60 Deletedinuse: 6
% 157.21/157.60
% 157.21/157.60 Resimplifying inuse:
% 157.21/157.60 Done
% 157.21/157.60
% 157.21/157.60 Resimplifying inuse:
% 157.21/157.60 Done
% 157.21/157.60
% 157.21/157.60
% 157.21/157.60 Intermediate Status:
% 157.21/157.60 Generated: 640312
% 157.21/157.60 Kept: 144838
% 157.21/157.60 Inuse: 1422
% 157.21/157.60 Deleted: 2013
% 157.21/157.60 Deletedinuse: 6
% 157.21/157.60
% 157.21/157.60 Resimplifying clauses:
% 157.21/157.60 Done
% 157.21/157.60
% 157.21/157.60 Resimplifying inuse:
% 157.21/157.60 Done
% 157.21/157.60
% 157.21/157.60 Resimplifying inuse:
% 157.21/157.60 Done
% 157.21/157.60
% 157.21/157.60
% 157.21/157.60 Intermediate Status:
% 157.21/157.60 Generated: 651456
% 157.21/157.60 Kept: 146853
% 157.21/157.60 Inuse: 1445
% 157.21/157.60 Deleted: 2707
% 157.21/157.60 Deletedinuse: 13
% 157.21/157.60
% 157.21/157.60 Resimplifying inuse:
% 157.21/157.60 Done
% 157.21/157.60
% 157.21/157.60
% 157.21/157.60 Intermediate Status:
% 157.21/157.60 Generated: 661297
% 157.21/157.60 Kept: 149115
% 157.21/157.60 Inuse: 1467
% 157.21/157.60 Deleted: 2707
% 157.21/157.60 Deletedinuse: 13
% 157.21/157.60
% 157.21/157.60 Resimplifying inuse:
% 157.21/157.60 Done
% 157.21/157.60
% 157.21/157.60 Resimplifying inuse:
% 157.21/157.60 Done
% 157.21/157.60
% 157.21/157.60
% 157.21/157.60 Intermediate Status:
% 157.21/157.60 Generated: 675239
% 157.21/157.60 Kept: 151406
% 157.21/157.60 Inuse: 1492
% 157.21/157.60 Deleted: 2707
% 157.21/157.60 Deletedinuse: 13
% 157.21/157.60
% 157.21/157.60 Resimplifying inuse:
% 157.21/157.60 Done
% 157.21/157.60
% 157.21/157.60 Resimplifying inuse:
% 157.21/157.60 Done
% 157.21/157.60
% 157.21/157.60
% 157.21/157.60 Intermediate Status:
% 157.21/157.60 Generated: 686935
% 157.21/157.60 Kept: 153711
% 157.21/157.60 Inuse: 1512
% 157.21/157.60 Deleted: 2707
% 157.21/157.60 Deletedinuse: 13
% 157.21/157.60
% 157.21/157.60 Resimplifying inuse:
% 157.21/157.60 Done
% 157.21/157.60
% 157.21/157.60 Resimplifying inuse:
% 157.21/157.60 Done
% 157.21/157.60
% 157.21/157.60
% 157.21/157.60 Intermediate Status:
% 157.21/157.60 Generated: 700076
% 157.21/157.60 Kept: 155716
% 157.21/157.60 Inuse: 1540
% 157.21/157.60 Deleted: 2707
% 157.21/157.60 Deletedinuse: 13
% 157.21/157.60
% 157.21/157.60 Resimplifying inuse:
% 157.21/157.60 Done
% 157.21/157.60
% 157.21/157.60
% 157.21/157.60 Intermediate Status:
% 157.21/157.60 Generated: 718347
% 157.21/157.60 Kept: 158896
% 157.21/157.60 Inuse: 1562
% 157.21/157.60 Deleted: 2707
% 157.21/157.60 Deletedinuse: 13
% 157.21/157.60
% 157.21/157.60 Resimplifying inuse:
% 157.21/157.60 Done
% 157.21/157.60
% 157.21/157.60 Resimplifying inuse:
% 157.21/157.60 Done
% 157.21/157.60
% 157.21/157.60
% 157.21/157.60 Intermediate Status:
% 157.21/157.60 Generated: 728375
% 157.21/157.60 Kept: 160896
% 157.21/157.60 Inuse: 1587
% 157.21/157.60 Deleted: 2707
% 157.21/157.60 Deletedinuse: 13
% 157.21/157.60
% 157.21/157.60 Resimplifying inuse:
% 157.21/157.60 Done
% 157.21/157.60
% 157.21/157.60
% 157.21/157.60 Intermediate Status:
% 157.21/157.60 Generated: 739375
% 157.21/157.60 Kept: 163132
% 157.21/157.60 Inuse: 1592
% 157.21/157.60 Deleted: 2707
% 157.21/157.60 Deletedinuse: 13
% 157.21/157.60
% 157.21/157.60 Resimplifying inuse:
% 157.21/157.60 Done
% 157.21/157.60
% 157.21/157.60 Resimplifying inuse:
% 157.21/157.60 Done
% 157.21/157.60
% 157.21/157.60
% 157.21/157.60 Intermediate Status:
% 157.21/157.60 Generated: 779144
% 157.21/157.60 Kept: 166779
% 157.21/157.60 Inuse: 1622
% 157.21/157.60 Deleted: 2708
% 157.21/157.60 Deletedinuse: 14
% 157.21/157.60
% 157.21/157.60 Resimplifying inuse:
% 157.21/157.60 Done
% 157.21/157.60
% 157.21/157.60 Resimplifying clauses:
% 157.21/157.60 Done
% 157.21/157.60
% 157.21/157.60 Resimplifying inuse:
% 157.21/157.60 Done
% 157.21/157.60
% 157.21/157.60
% 157.21/157.60 Intermediate Status:
% 157.21/157.60 Generated: 788068
% 157.21/157.60 Kept: 169428
% 157.21/157.60 Inuse: 1632
% 157.21/157.60 Deleted: 2967
% 157.21/157.60 Deletedinuse: 15
% 157.21/157.60
% 157.21/157.60 Resimplifying inuse:
% 157.21/157.60 Done
% 157.21/157.60
% 157.21/157.60 Resimplifying inuse:
% 157.21/157.60 Done
% 157.21/157.60
% 157.21/157.60
% 157.21/157.60 Intermediate Status:
% 157.21/157.60 Generated: 797462
% 157.21/157.60 Kept: 172328
% 157.21/157.60 Inuse: 1642
% 157.21/157.60 Deleted: 2967
% 157.21/157.60 Deletedinuse: 15
% 157.21/157.60
% 157.21/157.60 Resimplifying inuse:
% 157.21/157.60 Done
% 157.21/157.60
% 157.21/157.60 Resimplifying inuse:
% 157.21/157.60 Done
% 157.21/157.60
% 157.21/157.60
% 157.21/157.60 Intermediate Status:
% 157.21/157.60 Generated: 809671
% 157.21/157.60 Kept: 174653
% 157.21/157.60 Inuse: 1662
% 157.21/157.60 Deleted: 2967
% 157.21/157.60 Deletedinuse: 15
% 255.39/255.81
% 255.39/255.81 Resimplifying inuse:
% 255.39/255.81 Done
% 255.39/255.81
% 255.39/255.81 Resimplifying inuse:
% 255.39/255.81 Done
% 255.39/255.81
% 255.39/255.81
% 255.39/255.81 Intermediate Status:
% 255.39/255.81 Generated: 823446
% 255.39/255.81 Kept: 177446
% 255.39/255.81 Inuse: 1682
% 255.39/255.81 Deleted: 2967
% 255.39/255.81 Deletedinuse: 15
% 255.39/255.81
% 255.39/255.81 Resimplifying inuse:
% 255.39/255.81 Done
% 255.39/255.81
% 255.39/255.81 Resimplifying inuse:
% 255.39/255.81 Done
% 255.39/255.81
% 255.39/255.81
% 255.39/255.81 Intermediate Status:
% 255.39/255.81 Generated: 835288
% 255.39/255.81 Kept: 179825
% 255.39/255.81 Inuse: 1697
% 255.39/255.81 Deleted: 2967
% 255.39/255.81 Deletedinuse: 15
% 255.39/255.81
% 255.39/255.81 Resimplifying inuse:
% 255.39/255.81 Done
% 255.39/255.81
% 255.39/255.81
% 255.39/255.81 Intermediate Status:
% 255.39/255.81 Generated: 844994
% 255.39/255.81 Kept: 181825
% 255.39/255.81 Inuse: 1710
% 255.39/255.81 Deleted: 2967
% 255.39/255.81 Deletedinuse: 15
% 255.39/255.81
% 255.39/255.81 Resimplifying inuse:
% 255.39/255.81 Done
% 255.39/255.81
% 255.39/255.81
% 255.39/255.81 Intermediate Status:
% 255.39/255.81 Generated: 856466
% 255.39/255.81 Kept: 183876
% 255.39/255.81 Inuse: 1722
% 255.39/255.81 Deleted: 2967
% 255.39/255.81 Deletedinuse: 15
% 255.39/255.81
% 255.39/255.81 Resimplifying inuse:
% 255.39/255.81 Done
% 255.39/255.81
% 255.39/255.81 Resimplifying inuse:
% 255.39/255.81 Done
% 255.39/255.81
% 255.39/255.81
% 255.39/255.81 Intermediate Status:
% 255.39/255.81 Generated: 864574
% 255.39/255.81 Kept: 186152
% 255.39/255.81 Inuse: 1732
% 255.39/255.81 Deleted: 2967
% 255.39/255.81 Deletedinuse: 15
% 255.39/255.81
% 255.39/255.81 Resimplifying inuse:
% 255.39/255.81 Done
% 255.39/255.81
% 255.39/255.81 Resimplifying clauses:
% 255.39/255.81 Done
% 255.39/255.81
% 255.39/255.81 Resimplifying inuse:
% 255.39/255.81 Done
% 255.39/255.81
% 255.39/255.81
% 255.39/255.81 Intermediate Status:
% 255.39/255.81 Generated: 879460
% 255.39/255.81 Kept: 188492
% 255.39/255.81 Inuse: 1757
% 255.39/255.81 Deleted: 3319
% 255.39/255.81 Deletedinuse: 15
% 255.39/255.81
% 255.39/255.81 Resimplifying inuse:
% 255.39/255.81 Done
% 255.39/255.81
% 255.39/255.81
% 255.39/255.81 Intermediate Status:
% 255.39/255.81 Generated: 901790
% 255.39/255.81 Kept: 191173
% 255.39/255.81 Inuse: 1777
% 255.39/255.81 Deleted: 3319
% 255.39/255.81 Deletedinuse: 15
% 255.39/255.81
% 255.39/255.81 Resimplifying inuse:
% 255.39/255.81 Done
% 255.39/255.81
% 255.39/255.81 Resimplifying inuse:
% 255.39/255.81 Done
% 255.39/255.81
% 255.39/255.81
% 255.39/255.81 Intermediate Status:
% 255.39/255.81 Generated: 919487
% 255.39/255.81 Kept: 193179
% 255.39/255.81 Inuse: 1785
% 255.39/255.81 Deleted: 3319
% 255.39/255.81 Deletedinuse: 15
% 255.39/255.81
% 255.39/255.81 Resimplifying inuse:
% 255.39/255.81 Done
% 255.39/255.81
% 255.39/255.81
% 255.39/255.81 Intermediate Status:
% 255.39/255.81 Generated: 950917
% 255.39/255.81 Kept: 196935
% 255.39/255.81 Inuse: 1792
% 255.39/255.81 Deleted: 3319
% 255.39/255.81 Deletedinuse: 15
% 255.39/255.81
% 255.39/255.81 Resimplifying inuse:
% 255.39/255.81 Done
% 255.39/255.81
% 255.39/255.81 Resimplifying inuse:
% 255.39/255.81 Done
% 255.39/255.81
% 255.39/255.81
% 255.39/255.81 Intermediate Status:
% 255.39/255.81 Generated: 969038
% 255.39/255.81 Kept: 198939
% 255.39/255.81 Inuse: 1801
% 255.39/255.81 Deleted: 3319
% 255.39/255.81 Deletedinuse: 15
% 255.39/255.81
% 255.39/255.81 Resimplifying inuse:
% 255.39/255.81 Done
% 255.39/255.81
% 255.39/255.81
% 255.39/255.81 Intermediate Status:
% 255.39/255.81 Generated: 989020
% 255.39/255.81 Kept: 202285
% 255.39/255.81 Inuse: 1807
% 255.39/255.81 Deleted: 3319
% 255.39/255.81 Deletedinuse: 15
% 255.39/255.81
% 255.39/255.81 Resimplifying inuse:
% 255.39/255.81 Done
% 255.39/255.81
% 255.39/255.81 Resimplifying inuse:
% 255.39/255.81 Done
% 255.39/255.81
% 255.39/255.81
% 255.39/255.81 Intermediate Status:
% 255.39/255.81 Generated: 996062
% 255.39/255.81 Kept: 204301
% 255.39/255.81 Inuse: 1817
% 255.39/255.81 Deleted: 3319
% 255.39/255.81 Deletedinuse: 15
% 255.39/255.81
% 255.39/255.81 Resimplifying inuse:
% 255.39/255.81 Done
% 255.39/255.81
% 255.39/255.81 Resimplifying inuse:
% 255.39/255.81 Done
% 255.39/255.81
% 255.39/255.81
% 255.39/255.81 Intermediate Status:
% 255.39/255.81 Generated: 1010125
% 255.39/255.81 Kept: 206626
% 255.39/255.81 Inuse: 1837
% 255.39/255.81 Deleted: 3319
% 255.39/255.81 Deletedinuse: 15
% 255.39/255.81
% 255.39/255.81
% 255.39/255.81 Intermediate Status:
% 255.39/255.81 Generated: 1047659
% 255.39/255.81 Kept: 210849
% 255.39/255.81 Inuse: 1842
% 255.39/255.81 Deleted: 3319
% 255.39/255.81 Deletedinuse: 15
% 255.39/255.81
% 255.39/255.81 Resimplifying inuse:
% 255.39/255.81 Done
% 255.39/255.81
% 255.39/255.81 Resimplifying clauses:
% 255.39/255.81 Done
% 255.39/255.81
% 255.39/255.81 Resimplifying inuse:
% 255.39/255.81 Done
% 255.39/255.81
% 255.39/255.81
% 255.39/255.81 Intermediate Status:
% 255.39/255.81 Generated: 1065322
% 255.39/255.81 Kept: 214362
% 255.39/255.81 Inuse: 1857
% 255.39/255.81 Deleted: 3444
% 255.39/255.81 Deletedinuse: 15
% 255.39/255.81
% 255.39/255.81 Resimplifying inuse:
% 255.39/255.81 Done
% 255.39/255.81
% 255.39/255.81
% 255.39/255.81 Intermediate Status:
% 255.39/255.81 Generated: 1079039
% 255.39/255.81 Kept: 217049
% 255.39/255.81 Inuse: 1867
% 255.39/255.81 Deleted: 3444
% 255.39/255.81 Deletedinuse: 15
% 255.39/255.81
% 255.39/255.81 Resimplifying inuse:
% 255.39/255.81 Done
% 255.39/255.81
% 255.39/255.81
% 255.39/255.81 Intermediate Status:
% 255.39/255.81 Generated: 1100665
% 255.39/255.81 Kept: 222019
% 255.39/255.81 Inuse: 1877
% 255.39/255.81 Deleted: 3444
% 255.39/255.81 Deletedinuse: 15
% 255.39/255.81
% 255.39/255.81 Resimplifying inuse:
% 255.39/255.81 Done
% 255.39/255.81
% 255.39/255.81 Resimplifying inuse:
% 255.39/255.81 Done
% 255.39/255.81
% 255.39/255.81
% 255.39/255.81 Intermediate Status:
% 255.39/255.81 Generated: 1108032
% 255.39/255.81 Kept: 224073
% 255.39/255.81 Inuse: 1887
% 255.39/255.81 Deleted: 3444
% 255.39/255.81 Deletedinuse: 15
% 255.39/255.81
% 255.39/255.81 Resimplifying inuse:
% 255.39/255.81 Done
% 255.39/255.81
% 255.39/255.81
% 255.39/255.81 Intermediate Status:
% 255.39/255.81 Generated: 1115448
% 255.39/255.81 Kept: 226784
% 255.39/255.81 Inuse: 1888
% 255.39/255.81 Deleted: 3444
% 255.39/255.81 Deletedinuse: 15
% 255.39/255.81
% 255.39/255.81 Resimplifying inuse:
% 255.39/255.81 Done
% 255.39/255.81
% 255.39/255.81 Resimplifying inuse:
% 255.39/255.81 Done
% 255.39/255.81
% 255.39/255.81
% 255.39/255.81 Intermediate Status:
% 255.39/255.81 Generated: 1122123
% 255.39/255.81 Kept: 228786
% 255.39/255.81 Inuse: 1898
% 255.39/255.81 Deleted: 3444
% 255.39/255.81 Deletedinuse: 15
% 255.39/255.81
% 255.39/255.81 Resimplifying inuse:
% 255.39/255.81 Done
% 255.39/255.81
% 255.39/255.81 Resimplifying inuse:
% 255.39/255.81 Done
% 255.39/255.81
% 255.39/255.81
% 255.39/255.81 Intermediate Status:
% 255.39/255.81 Generated: 1131052
% 255.39/255.81 Kept: 230877
% 255.39/255.81 Inuse: 1917
% 255.39/255.81 Deleted: 3444
% 255.39/255.81 Deletedinuse: 15
% 255.39/255.81
% 255.39/255.81 Resimplifying inuse:
% 255.39/255.81 Done
% 255.39/255.81
% 255.39/255.81 Resimplifying clauses:
% 255.39/255.81 Done
% 255.39/255.81
% 255.39/255.81 Resimplifying inuse:
% 255.39/255.81 Done
% 255.39/255.81
% 255.39/255.81
% 255.39/255.81 Intermediate Status:
% 255.39/255.81 Generated: 1144644
% 255.39/255.81 Kept: 232920
% 255.39/255.81 Inuse: 1935
% 255.39/255.81 Deleted: 3570
% 255.39/255.81 Deletedinuse: 15
% 255.39/255.81
% 255.39/255.81 Resimplifying inuse:
% 255.39/255.81 Done
% 255.39/255.81
% 255.39/255.81 Resimplifying inuse:
% 255.39/255.81 Done
% 255.39/255.81
% 255.39/255.81
% 255.39/255.81 Intermediate Status:
% 255.39/255.81 Generated: 1158452
% 255.39/255.81 Kept: 234949
% 255.39/255.81 Inuse: 1961
% 255.39/255.81 Deleted: 3570
% 255.39/255.81 Deletedinuse: 15
% 255.39/255.81
% 255.39/255.81 Resimplifying inuse:
% 255.39/255.81 Done
% 255.39/255.81
% 255.39/255.81 Resimplifying inuse:
% 255.39/255.81 Done
% 255.39/255.81
% 255.39/255.81
% 255.39/255.81 Intermediate Status:
% 255.39/255.81 Generated: 1169771
% 255.39/255.81 Kept: 237275
% 255.39/255.81 Inuse: 1977
% 255.39/255.81 Deleted: 3570
% 255.39/255.81 Deletedinuse: 15
% 255.39/255.81
% 255.39/255.81 Resimplifying inuse:
% 255.39/255.81 Done
% 255.39/255.81
% 255.39/255.81 Resimplifying inuse:
% 255.39/255.81 Done
% 255.39/255.81
% 255.39/255.81
% 255.39/255.81 Intermediate Status:Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------