TSTP Solution File: SWV707-1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWV707-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Wed Jul 20 16:27:57 EDT 2022
% Result : Timeout 300.03s 300.43s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.14 % Problem : SWV707-1 : TPTP v8.1.0. Released v4.1.0.
% 0.09/0.15 % Command : bliksem %s
% 0.14/0.36 % Computer : n018.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % DateTime : Tue Jun 14 18:41:29 EDT 2022
% 0.14/0.36 % CPUTime :
% 1.29/1.64 *** allocated 10000 integers for termspace/termends
% 1.29/1.64 *** allocated 10000 integers for clauses
% 1.29/1.64 *** allocated 10000 integers for justifications
% 1.29/1.64 *** allocated 15000 integers for termspace/termends
% 1.29/1.64 *** allocated 22500 integers for termspace/termends
% 1.29/1.64 *** allocated 33750 integers for termspace/termends
% 1.29/1.64 *** allocated 50625 integers for termspace/termends
% 1.29/1.64 Bliksem 1.12
% 1.29/1.64
% 1.29/1.64
% 1.29/1.64 Automatic Strategy Selection
% 1.29/1.64
% 1.29/1.64 Clauses:
% 1.29/1.64 [
% 1.29/1.64 [ =( hAPP( X, hAPP( X, Y ) ), hAPP( X, Y ) ), ~(
% 1.29/1.64 'c_Ring__and__Field_Oordered__idom'( Z, T, U, W, V0, V1, V2, V3, V4, X,
% 1.29/1.64 V5 ) ) ],
% 1.29/1.64 [ ~( 'c_Ring__and__Field_Oordered__idom'( X, Y, Z, T, U, W, V0, V1, V2,
% 1.29/1.64 V3, V4 ) ), =( hAPP( V3, Z ), Z ) ],
% 1.29/1.64 [ ~( 'c_Ring__and__Field_Oordered__idom'( X, Y, hAPP( Z, T ), U, W, V0,
% 1.29/1.64 V1, V2, V3, Z, V4 ) ), =( T, hAPP( Z, T ) ) ],
% 1.29/1.64 [ =( hAPP( X, Y ), hAPP( hAPP( Z, Y ), hAPP( T, Y ) ) ), ~(
% 1.29/1.64 'c_Ring__and__Field_Oordered__idom'( U, W, V0, V1, V2, V3, X, V4, Z, T,
% 1.29/1.64 V5 ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.29/1.64 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.29/1.64 'class_Int_Onumber'( X ) ), =( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.29/1.64 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.29/1.64 X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.29/1.64 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 1.29/1.64 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.29/1.64 [ ~( hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( 'c_Power_Opower_Opower'( Z,
% 1.29/1.64 T, U ), hAPP( W, Y ) ), V0 ) ) ) ), ~(
% 1.29/1.64 'c_Ring__and__Field_Oordered__idom'( V1, V2, Y, V3, V4, X, W, Z, T, V5, U
% 1.29/1.64 ) ), =( V0, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.29/1.64 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), 'c_Suc'(
% 1.29/1.64 Y ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP(
% 1.29/1.64 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.29/1.64 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_Suc'( X )
% 1.29/1.64 ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), hAPP(
% 1.29/1.64 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.29/1.64 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.29/1.64 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.29/1.64 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.29/1.64 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.29/1.64 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.29/1.64 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.29/1.64 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~(
% 1.29/1.64 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.29/1.64 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.29/1.64 ,
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.29/1.64 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~(
% 1.29/1.64 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.29/1.64 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.29/1.64 ,
% 1.29/1.64 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.29/1.64 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), 'tc_nat'
% 1.29/1.64 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.29/1.64 , Y, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.29/1.64 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.29/1.64 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.29/1.64 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.29/1.64 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.29/1.64 ,
% 1.29/1.64 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.29/1.64 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.29/1.64 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.29/1.64 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.29/1.64 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.29/1.64 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.29/1.64 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.29/1.64 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.29/1.64 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.29/1.64 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.29/1.64 ,
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), ~( =(
% 1.29/1.64 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 1.29/1.64 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =( hAPP(
% 1.29/1.64 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 1.29/1.64 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =( hAPP(
% 1.29/1.64 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.29/1.64 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.29/1.64 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X,
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.29/1.64 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( =(
% 1.29/1.64 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( 'c_lessequals'(
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Z,
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.29/1.64 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( =(
% 1.29/1.64 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( 'c_lessequals'(
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Y,
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.29/1.64 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.29/1.64 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.29/1.64 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), ~( =( hAPP(
% 1.29/1.64 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.29/1.64 ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.29/1.64 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.29/1.64 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.29/1.64 X ), 'c_HOL_Oinverse__class_Odivide'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.29/1.64 , X ) ) ), =( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.29/1.64 [ =( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), hAPP( hAPP( Y, hAPP( X, Z ) ),
% 1.29/1.64 hAPP( X, T ) ) ), ~( 'c_Ring__and__Field_Oordered__idom'( U, W, V0, V1,
% 1.29/1.64 V2, V3, X, V4, Y, V5, V6 ) ) ],
% 1.29/1.64 [ =( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), hAPP( hAPP( Y, hAPP( X, Z ) ),
% 1.29/1.64 hAPP( X, T ) ) ), ~( 'c_Ring__and__Field_Oordered__idom'( U, W, V0, V1,
% 1.29/1.64 V2, V3, V4, V5, Y, X, V6 ) ) ],
% 1.29/1.64 [ =( hAPP( hAPP( X, hAPP( Y, Z ) ), hAPP( T, Z ) ), Z ), ~(
% 1.29/1.64 'c_Ring__and__Field_Oordered__idom'( U, W, V0, V1, V2, V3, T, V4, X, Y,
% 1.29/1.64 V5 ) ) ],
% 1.29/1.64 [ =( hAPP( hAPP( X, hAPP( Y, Z ) ), hAPP( Y, Z ) ), hAPP( hAPP( X, Z ),
% 1.29/1.64 Z ) ), ~( 'c_Ring__and__Field_Oordered__idom'( T, U, W, V0, V1, V2, Y, V3
% 1.29/1.64 , X, V4, V5 ) ) ],
% 1.29/1.64 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), hBOOL( hAPP( hAPP( X, Z ), Y ) ),
% 1.29/1.64 =( Z, Y ), ~( 'c_Ring__and__Field_Oordered__idom'( T, U, W, V0, V1, X, V2
% 1.29/1.64 , V3, V4, V5, V6 ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.29/1.64 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X )
% 1.29/1.64 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X )
% 1.29/1.64 ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =(
% 1.29/1.64 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 1.29/1.64 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.29/1.64 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.29/1.64 X ), X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.64 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.29/1.64 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~(
% 1.29/1.64 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.29/1.64 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ),
% 1.29/1.64 Y, X ) ), ~( 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.29/1.64 X ), T ), Z ), X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.64 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.29/1.64 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.29/1.64 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.29/1.64 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T
% 1.29/1.64 ), X ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.29/1.64 ), Y ), T ), Z, X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.64 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.29/1.64 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X )
% 1.29/1.64 , 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X
% 1.29/1.64 ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X
% 1.29/1.64 ) ) ],
% 1.29/1.64 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.29/1.64 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.29/1.64 ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.29/1.64 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.29/1.64 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.29/1.64 ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.29/1.64 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.29/1.64 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.29/1.64 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ) ) ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ) ) ), 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.29/1.64 ],
% 1.29/1.64 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 1.29/1.64 'c_HOL_Ouminus__class_Ouminus'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.29/1.64 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), Z ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), T ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), U ) ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.64 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.29/1.64 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.29/1.64 'c_HOL_Oone__class_Oone'( X ), X ), ~( 'c_lessequals'( Y,
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.29/1.64 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =( Y,
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'(
% 1.29/1.64 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.29/1.64 ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.29/1.64 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.29/1.64 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.29/1.64 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =(
% 1.29/1.64 'c_HOL_Oinverse__class_Odivide'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.29/1.64 , 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.29/1.64 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.29/1.64 'class_Int_Onumber'( X ) ), ~( =( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.29/1.64 Z, X ) ) ), =( 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.64 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.29/1.64 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ),
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.64 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.29/1.64 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ),
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.29/1.64 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.29/1.64 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.29/1.64 X ), Y ), Z ), Z, X ), Y ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.29/1.64 ,
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.29/1.64 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( Y,
% 1.29/1.64 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.29/1.64 X ), Y ), Z ), Z, X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.29/1.64 [ ~( 'class_OrderedGroup_Olordered__ab__group__add__abs'( X ) ),
% 1.29/1.64 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ),
% 1.29/1.64 'c_HOL_Oabs__class_Oabs'( T, X ) ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.29/1.64 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), Z, X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'(
% 1.29/1.64 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), Y, X ), Z ) ]
% 1.29/1.64 ,
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Oinverse__class_Odivide'(
% 1.29/1.64 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), Y, X ) ) ],
% 1.29/1.64 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 1.29/1.64 'c_HOL_Ouminus__class_Ouminus'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Z
% 1.29/1.64 , X ) ) ), =( Y, Z ) ],
% 1.29/1.64 [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), ~( =(
% 1.29/1.64 'c_HOL_Ouminus__class_Ouminus'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Z
% 1.29/1.64 , X ) ) ), =( Y, Z ) ],
% 1.29/1.64 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Z, Y
% 1.29/1.64 , X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.29/1.64 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Z, Y
% 1.29/1.64 , X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.29/1.64 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ), =( Y, X ),
% 1.29/1.64 'c_HOL_Oord__class_Oless'( Y, X, 'tc_Int_Oint' ) ],
% 1.29/1.64 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Y, Z
% 1.29/1.64 , X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ],
% 1.29/1.64 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.29/1.64 'c_HOL_Oabs__class_Oabs'( Y, X ), Y ), ~( 'c_lessequals'(
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.29/1.64 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 1.29/1.64 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.29/1.64 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~(
% 1.29/1.64 'c_lessequals'( Z, T, X ) ) ],
% 1.29/1.64 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 1.29/1.64 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.29/1.64 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~(
% 1.29/1.64 'c_lessequals'( Y, T, X ) ) ],
% 1.29/1.64 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.29/1.64 , 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.29/1.64 'c_HOL_Oplus__class_Oplus'( X ), T ), Y ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ) ) ],
% 1.29/1.64 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.29/1.64 , 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.29/1.64 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~(
% 1.29/1.64 'c_lessequals'( Z, T, X ) ) ],
% 1.29/1.64 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.29/1.64 , 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.29/1.64 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ],
% 1.29/1.64 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.29/1.64 , 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.29/1.64 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~(
% 1.29/1.64 'c_lessequals'( Y, T, X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.29/1.64 'c_HOL_Oabs__class_Oabs'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.29/1.64 Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.29/1.64 'c_HOL_Oabs__class_Oabs'( Y, X ) ), 'c_HOL_Oabs__class_Oabs'( Z, X ) ) )
% 1.29/1.64 ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Opordered__ring__abs'( X ) ), =(
% 1.29/1.64 'c_HOL_Oabs__class_Oabs'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.29/1.64 Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.29/1.64 'c_HOL_Oabs__class_Oabs'( Y, X ) ), 'c_HOL_Oabs__class_Oabs'( Z, X ) ) )
% 1.29/1.64 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.29/1.64 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Opordered__ring__abs'( X ) ), =(
% 1.29/1.64 'c_HOL_Oabs__class_Oabs'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.29/1.64 Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.29/1.64 'c_HOL_Oabs__class_Oabs'( Y, X ) ), 'c_HOL_Oabs__class_Oabs'( Z, X ) ) )
% 1.29/1.64 , ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.29/1.64 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Opordered__ring__abs'( X ) ), =(
% 1.29/1.64 'c_HOL_Oabs__class_Oabs'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.29/1.64 Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.29/1.64 'c_HOL_Oabs__class_Oabs'( Y, X ) ), 'c_HOL_Oabs__class_Oabs'( Z, X ) ) )
% 1.29/1.64 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.29/1.64 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Opordered__ring__abs'( X ) ), =(
% 1.29/1.64 'c_HOL_Oabs__class_Oabs'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.29/1.64 Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.29/1.64 'c_HOL_Oabs__class_Oabs'( Y, X ) ), 'c_HOL_Oabs__class_Oabs'( Z, X ) ) )
% 1.29/1.64 , ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.29/1.64 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.29/1.64 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z
% 1.29/1.64 , X ) ), 'c_HOL_Oinverse__class_Odivide'( T, U, X ) ),
% 1.29/1.64 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.29/1.64 X ), Y ), T ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ), X
% 1.29/1.64 ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 1.29/1.64 'c_HOL_Ouminus__class_Ouminus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.29/1.64 X ), Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.29/1.64 'c_HOL_Ouminus__class_Ouminus'( Y, X ) ), Z ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 1.29/1.64 'c_HOL_Ouminus__class_Ouminus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.29/1.64 X ), Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.29/1.64 'c_HOL_Ouminus__class_Ouminus'( Z, X ) ) ) ],
% 1.29/1.64 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, Y ), T ) ), hAPP( hAPP( Z, Y ),
% 1.29/1.64 'c_Suc'( T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, Z, W, V0,
% 1.29/1.64 V1 ) ) ],
% 1.29/1.64 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), Z ), hAPP( hAPP( Y, Z ),
% 1.29/1.64 'c_Suc'( T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, Y, W, V0,
% 1.29/1.64 V1 ) ) ],
% 1.29/1.64 [ =( hAPP( hAPP( X, Y ), 'c_Suc'( Z ) ), hAPP( hAPP( T, Y ), hAPP( hAPP(
% 1.29/1.64 X, Y ), Z ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, T, X, W, V0, V1
% 1.29/1.64 ) ) ],
% 1.29/1.64 [ =( hAPP( hAPP( X, Y ), 'c_Suc'( Z ) ), hAPP( hAPP( T, Y ), hAPP( hAPP(
% 1.29/1.64 X, Y ), Z ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, T, X, W, V0, V1
% 1.29/1.64 ) ) ],
% 1.29/1.64 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.29/1.64 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.29/1.64 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ) ],
% 1.29/1.64 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.29/1.64 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), ~(
% 1.29/1.64 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.29/1.64 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.29/1.64 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ),
% 1.29/1.64 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X
% 1.29/1.64 , 'c_Int_OPls', 'tc_Int_Oint' ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.29/1.64 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.29/1.64 , Y ), 'c_HOL_Oone__class_Oone'( X ) ), X ) ],
% 1.29/1.64 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =( hAPP(
% 1.29/1.64 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.64 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.29/1.64 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.29/1.64 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.29/1.64 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~( 'c_lessequals'(
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.29/1.64 ), X ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.29/1.64 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ), ~(
% 1.29/1.64 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.29/1.64 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.64 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.29/1.64 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.29/1.64 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.29/1.64 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~( 'c_lessequals'(
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.29/1.64 ), X ) ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.29/1.64 , X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X )
% 1.29/1.64 ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.64 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.29/1.64 'class_Int_Onumber'( X ) ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X
% 1.29/1.64 ), 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.29/1.64 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.29/1.64 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.29/1.64 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X ),
% 1.29/1.64 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.64 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.29/1.64 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.29/1.64 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.29/1.64 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.29/1.64 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.29/1.64 'class_Int_Onumber'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( hAPP(
% 1.29/1.64 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.29/1.64 'c_Int_Onumber__class_Onumber__of'( Z, X ) ),
% 1.29/1.64 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y ), =(
% 1.29/1.64 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.29/1.64 ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.29/1.64 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.29/1.64 'class_Int_Onumber'( X ) ), =( Y, 'c_HOL_Oinverse__class_Odivide'( hAPP(
% 1.29/1.64 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.29/1.64 'c_Int_Onumber__class_Onumber__of'( Z, X ) ),
% 1.29/1.64 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ), =(
% 1.29/1.64 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.29/1.64 ) ) ],
% 1.29/1.64 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.29/1.64 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.29/1.64 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.29/1.64 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.29/1.64 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.29/1.64 [ =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( 'tc_nat' ), X ),
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'(
% 1.29/1.64 'tc_nat' ) ) ],
% 1.29/1.64 [ ~( 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.29/1.64 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.29/1.64 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.29/1.64 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.29/1.64 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.64 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.29/1.64 'class_Int_Onumber'( X ) ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X
% 1.29/1.64 ), Y, X ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'(
% 1.29/1.64 Z, X ), 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.29/1.64 ), X ), ~( 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( T,
% 1.29/1.64 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.64 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.29/1.64 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.29/1.64 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.29/1.64 , X ), X ), T, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T
% 1.29/1.64 , X ) ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.29/1.64 , X ), 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.29/1.64 ), X ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.64 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.29/1.64 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.29/1.64 X ), X ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'(
% 1.29/1.64 Z, X ), 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.29/1.64 ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Oinverse__class_Odivide'( T,
% 1.29/1.64 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.64 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.29/1.64 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.29/1.64 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.29/1.64 , X ), X ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.29/1.64 ) ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.29/1.64 ), 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.29/1.64 ), X ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.29/1.64 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.29/1.64 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.29/1.64 ), =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ),
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ) ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.29/1.64 , =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.29/1.64 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.29/1.64 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y
% 1.29/1.64 ), 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.29/1.64 'tc_nat' ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.29/1.64 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ), ~(
% 1.29/1.64 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X )
% 1.29/1.64 ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.29/1.64 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 1.29/1.64 X ), X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.29/1.64 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.29/1.64 X ), X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.29/1.64 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.29/1.64 Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 1.29/1.64 X ), X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.29/1.64 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 1.29/1.64 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.29/1.64 X ), X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.29/1.64 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.29/1.64 , Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.29/1.64 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.29/1.64 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.29/1.64 ,
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.29/1.64 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.29/1.64 , Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.29/1.64 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.29/1.64 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.29/1.64 ,
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.29/1.64 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.29/1.64 , Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.29/1.64 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.29/1.64 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 1.29/1.64 ,
% 1.29/1.64 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.29/1.64 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ), ~(
% 1.29/1.64 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ) ) ],
% 1.29/1.64 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.29/1.64 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.29/1.64 ), Z ) ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP(
% 1.29/1.64 hAPP( 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.29/1.64 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), Z ) ) ) ],
% 1.29/1.64 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.29/1.64 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X ) )
% 1.29/1.64 , Z ) ), Z ) ],
% 1.29/1.64 [ =( hAPP( X, hAPP( hAPP( 'c_Power_Opower_Opower'( Y, Z, T ), U ), W ) )
% 1.29/1.64 , hAPP( hAPP( 'c_Power_Opower_Opower'( Y, Z, T ), hAPP( X, U ) ), W ) ),
% 1.29/1.64 ~( 'c_Ring__and__Field_Oordered__idom'( V0, V1, V2, V3, V4, V5, X, Y, Z,
% 1.29/1.64 V6, T ) ) ],
% 1.29/1.64 [ =( hAPP( X, hAPP( hAPP( 'c_Power_Opower_Opower'( Y, Z, T ), hAPP( U, W
% 1.29/1.64 ) ), V0 ) ), hAPP( X, hAPP( hAPP( 'c_Power_Opower_Opower'( Y, Z, T ), W
% 1.29/1.64 ), V0 ) ) ), ~( 'c_Ring__and__Field_Oordered__idom'( V1, U, V2, V3, V4,
% 1.29/1.64 V5, X, Y, Z, V6, T ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.29/1.64 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.29/1.64 , Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 1.29/1.64 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 1.29/1.64 ,
% 1.29/1.64 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.29/1.64 'tc_nat' ) ) ) ],
% 1.29/1.64 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.29/1.64 'tc_nat' ) ), Y ) ) ],
% 1.29/1.64 [ ~( 'c_Ring__and__Field_Oordered__idom'( X, Y, Z, T, U, W, V0, V1, V2,
% 1.29/1.64 V3, V4 ) ), hBOOL( hAPP( hAPP( W, Z ), hAPP( hAPP(
% 1.29/1.64 'c_Power_Opower_Opower'( V1, V2, V4 ), hAPP( V0, V5 ) ),
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.29/1.64 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), =( Y
% 1.29/1.64 , 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.29/1.64 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.29/1.64 , X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.29/1.64 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.29/1.64 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oinverse__class_Odivide'( Y, Z,
% 1.29/1.64 X ), X ), 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Omult__mono1'( X ) ), 'c_lessequals'( hAPP(
% 1.29/1.64 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~( 'c_lessequals'(
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Z, T, X ) )
% 1.29/1.64 ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ), 'c_lessequals'( hAPP(
% 1.29/1.64 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~( 'c_lessequals'(
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Z, T, X ) )
% 1.29/1.64 ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ), 'c_lessequals'( hAPP(
% 1.29/1.64 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ), ~( 'c_lessequals'(
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 1.29/1.64 ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.29/1.64 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~( 'c_lessequals'( Y,
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( T, Z, X ) ) ]
% 1.29/1.64 ,
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.29/1.64 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ), ~( 'c_lessequals'( Z,
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( T, Y, X ) ) ]
% 1.29/1.64 ,
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.29/1.64 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.29/1.64 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.29/1.64 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =(
% 1.29/1.64 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.29/1.64 'c_HOL_Oinverse__class_Odivide'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.29/1.64 ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.29/1.64 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.29/1.64 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.29/1.64 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( 'c_HOL_Ozero__class_Ozero'(
% 1.29/1.64 X ), 'c_HOL_Oinverse__class_Odivide'( Z,
% 1.29/1.64 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.29/1.64 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.29/1.64 'c_Power_Opower__class_Opower'( X ), Y ), T ) ), hAPP( hAPP(
% 1.29/1.64 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ) ) ],
% 1.29/1.64 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.29/1.64 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.29/1.64 ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.29/1.64 ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oabs__if'( X ) ), =(
% 1.29/1.64 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.29/1.64 ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.29/1.64 ) ],
% 1.29/1.64 [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 1.29/1.64 'class_OrderedGroup_Olordered__ab__group__add__abs'( X ) ), =(
% 1.29/1.64 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.29/1.64 ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.29/1.64 ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( =( hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ) ), =( Y,
% 1.29/1.64 'c_HOL_Ouminus__class_Ouminus'( Z, X ) ), =( Y, Z ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.29/1.64 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.29/1.64 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.29/1.64 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.29/1.64 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ),
% 1.29/1.64 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.29/1.64 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ),
% 1.29/1.64 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.29/1.64 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'( Y
% 1.29/1.64 , 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'(
% 1.29/1.64 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), Z, X ) ), ~(
% 1.29/1.64 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ]
% 1.29/1.64 ,
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.29/1.64 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Y
% 1.29/1.64 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ), ~(
% 1.29/1.64 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 1.29/1.64 ,
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.64 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.29/1.64 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.29/1.64 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.29/1.64 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ),
% 1.29/1.64 Z, X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.64 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.29/1.64 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), T, X ), ~(
% 1.29/1.64 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.29/1.64 'c_lessequals'( Y, 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ]
% 1.29/1.64 ,
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.64 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.29/1.64 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~(
% 1.29/1.64 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.29/1.64 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z
% 1.29/1.64 ), X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.64 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.29/1.64 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ), ~(
% 1.29/1.64 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.29/1.64 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), Z, X ) ) ]
% 1.29/1.64 ,
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.29/1.64 X ) ), ~( =( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) )
% 1.29/1.64 , =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.29/1.64 [ ~( =( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y )
% 1.29/1.64 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.29/1.64 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), X
% 1.29/1.64 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.29/1.64 [ ~( 'class_Nat_Osemiring__char__0'( X ) ), ~( =(
% 1.29/1.64 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 1.29/1.64 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ) ) ), =( Y, Z ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.64 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.29/1.64 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.29/1.64 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.29/1.64 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.29/1.64 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.29/1.64 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.29/1.64 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ), ~(
% 1.29/1.64 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.29/1.64 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.29/1.64 [ ~( 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'( X )
% 1.29/1.64 , 'c_Power_Opower_Opower'( 'c_HOL_Oone__class_Oone'( X ),
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), X ) ) ],
% 1.29/1.64 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.29/1.64 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X, 'c_Suc'(
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.29/1.64 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.29/1.64 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.64 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.29/1.64 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oone__class_Oone'( X ),
% 1.29/1.64 X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.29/1.64 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.29/1.64 X ), Y ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z )
% 1.29/1.64 ), X ) ],
% 1.29/1.64 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.29/1.64 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.29/1.64 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ), Z ) ),
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X
% 1.29/1.64 , 'c_Int_OPls', 'tc_Int_Oint' ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.64 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.29/1.64 'c_HOL_Oone__class_Oone'( X ), Y, X ), X ), ~( 'c_lessequals'(
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.64 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.29/1.64 'c_HOL_Oone__class_Oone'( X ), Y, X ), X ) ) ],
% 1.29/1.64 [ =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_HOL_Oone__class_Oone'(
% 1.29/1.64 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.64 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.29/1.64 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.29/1.64 ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ),
% 1.29/1.64 ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.64 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.29/1.64 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.29/1.64 ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.29/1.64 ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.29/1.64 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.29/1.64 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 1.29/1.64 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ), ~(
% 1.29/1.64 'c_lessequals'( Y, Z, X ) ), ~( 'c_lessequals'(
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ],
% 1.29/1.64 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.29/1.64 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 1.29/1.64 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ), ~(
% 1.29/1.64 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'(
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.29/1.64 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.29/1.64 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oabs__class_Oabs'(
% 1.29/1.64 Y, X ), X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.29/1.64 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.29/1.64 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ),
% 1.29/1.64 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ),
% 1.29/1.64 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X,
% 1.29/1.64 'c_Int_OPls', 'tc_Int_Oint' ) ) ],
% 1.29/1.64 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( hAPP( hAPP(
% 1.29/1.64 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), 'tc_nat' ) ],
% 1.29/1.64 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( hAPP( hAPP(
% 1.29/1.64 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ) ), 'tc_nat' ) ],
% 1.29/1.64 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( hAPP( hAPP(
% 1.29/1.64 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), 'tc_nat' ) ],
% 1.29/1.64 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( X ) ) ) ],
% 1.29/1.64 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( X ) ) ) ],
% 1.29/1.64 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.29/1.64 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 1.29/1.64 'c_HOL_Ouminus__class_Ouminus'( Z, X ), 'c_HOL_Ouminus__class_Ouminus'( Y
% 1.29/1.64 , X ), X ) ) ],
% 1.29/1.64 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.29/1.64 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.29/1.64 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), ~( 'c_lessequals'( Z, Y, X )
% 1.29/1.64 ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Olordered__ring'( X ) ), 'c_lessequals'(
% 1.29/1.64 'c_HOL_Oabs__class_Oabs'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.29/1.64 Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.29/1.64 'c_HOL_Oabs__class_Oabs'( Y, X ) ), 'c_HOL_Oabs__class_Oabs'( Z, X ) ), X
% 1.29/1.64 ) ],
% 1.29/1.64 [ =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( 'tc_nat' ), X ),
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_Suc'(
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.29/1.64 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.29/1.64 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.29/1.64 'c_Suc'( Y ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.29/1.64 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.29/1.64 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( Y
% 1.29/1.64 , X ), Z, X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.29/1.64 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.29/1.64 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X )
% 1.29/1.64 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.29/1.64 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.29/1.64 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.29/1.64 T, X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.29/1.64 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.29/1.64 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.29/1.64 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Oinverse'( Y
% 1.29/1.64 , X ), 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y
% 1.29/1.64 , X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.64 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.29/1.64 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.29/1.64 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.29/1.64 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.29/1.64 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.29/1.64 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.29/1.64 , 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ),
% 1.29/1.64 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.64 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.29/1.64 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.29/1.64 , X ) ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.29/1.64 'c_HOL_Oinverse__class_Odivide'( T, Z, X ),
% 1.29/1.64 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.29/1.64 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.29/1.64 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.29/1.64 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), 'c_HOL_Oone__class_Oone'(
% 1.29/1.64 'tc_nat' ) ), Y ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.64 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.29/1.64 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.29/1.64 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.29/1.64 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.29/1.64 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.29/1.64 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ), ~(
% 1.29/1.64 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.29/1.64 , Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.64 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.29/1.64 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.29/1.64 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.29/1.64 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.29/1.64 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.29/1.64 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ), ~(
% 1.29/1.64 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.29/1.64 ), T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.64 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.29/1.64 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.29/1.64 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.29/1.64 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.29/1.64 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.29/1.64 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.29/1.64 , 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ), ~(
% 1.29/1.64 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.29/1.64 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.64 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.29/1.64 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.29/1.64 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ), ~(
% 1.29/1.64 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ), ~( 'c_lessequals'( Y
% 1.29/1.64 , 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Z, T, X ) )
% 1.29/1.64 ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.29/1.64 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.29/1.64 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ), ~(
% 1.29/1.64 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ), ~( 'c_lessequals'(
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( T, Z, X ) )
% 1.29/1.64 ],
% 1.29/1.64 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.29/1.64 X ), 'c_HOL_Oone__class_Oone'( X ) ), 'c_HOL_Oone__class_Oone'( X ) ) ),
% 1.29/1.64 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 1.29/1.64 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( Y ), X ) ) ],
% 1.29/1.64 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.29/1.64 Y ) ],
% 1.29/1.64 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 1.29/1.64 Y ) ],
% 1.29/1.64 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =( hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 1.29/1.64 Y ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 1.29/1.64 Y ) ],
% 1.29/1.64 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.29/1.64 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), X ), X ) ],
% 1.29/1.64 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.29/1.64 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), X ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.29/1.64 Y ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 1.29/1.64 Y ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.29/1.64 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.29/1.64 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ), ~(
% 1.29/1.64 'c_HOL_Oord__class_Oless'( U, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ), U, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 1.29/1.64 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) )
% 1.29/1.64 ],
% 1.29/1.64 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Suc'(
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.29/1.64 'tc_nat' ) ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.29/1.64 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.29/1.64 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), hAPP(
% 1.29/1.64 hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), hAPP( hAPP(
% 1.29/1.64 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.29/1.64 'c_HOL_Oone__class_Oone'( X ), Y, X ) ), Z ) ) ],
% 1.29/1.64 [ =( 'c_Suc'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.29/1.64 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), X ) ) ],
% 1.29/1.64 [ =( 'c_Suc'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X
% 1.29/1.64 ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.29/1.64 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.29/1.64 ), X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.29/1.64 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ), =( Z,
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.29/1.64 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oabs__class_Oabs'(
% 1.29/1.64 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.29/1.64 'c_HOL_Ouminus__class_Ouminus'( 'c_Int_Onumber__class_Onumber__of'( Y, X
% 1.29/1.64 ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.29/1.64 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.29/1.64 ), X ) ) ],
% 1.29/1.64 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.29/1.64 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.29/1.64 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.29/1.64 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.29/1.64 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.29/1.64 X ) ), =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.29/1.64 X ), Y ), T ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z )
% 1.29/1.64 ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.29/1.64 X ) ), =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.29/1.64 X ), Y ), T ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z )
% 1.29/1.64 ) ) ],
% 1.29/1.64 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.29/1.64 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.29/1.64 [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 1.29/1.64 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.29/1.64 'tc_nat' ) ), 'tc_nat' ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =(
% 1.29/1.64 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.29/1.64 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.29/1.64 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.29/1.64 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.29/1.64 , 'c_HOL_Oabs__class_Oabs'( Y, X ) ), 'c_HOL_Oabs__class_Oabs'( Z, X ) )
% 1.29/1.64 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X ), ~(
% 1.29/1.64 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Z, X ), U, X ) ),
% 1.29/1.64 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Y, X ), T, X ) )
% 1.29/1.64 ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.64 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.29/1.64 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.29/1.64 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.29/1.64 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.29/1.64 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.29/1.64 ), X ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.29/1.64 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.64 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.29/1.64 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.29/1.64 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.29/1.64 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 'c_HOL_Oord__class_Oless'(
% 1.29/1.64 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.29/1.64 ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.29/1.64 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 1.29/1.64 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.29/1.64 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oinverse__class_Oinverse'( Y, X
% 1.29/1.64 ), X ), Y ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.64 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.29/1.64 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.29/1.64 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.29/1.64 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.29/1.64 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.29/1.64 ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.29/1.64 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ), ~(
% 1.29/1.64 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.29/1.64 , Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.64 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.29/1.64 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.29/1.64 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.29/1.64 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.29/1.64 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.29/1.64 ), X ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.29/1.64 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ), ~(
% 1.29/1.64 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.29/1.64 ), T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.29/1.64 'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( Z ) ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.29/1.64 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.29/1.64 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.29/1.64 'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( Z ) ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.29/1.64 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), Y ) ) ],
% 1.29/1.64 [ ~( 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.29/1.64 'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( Z ) ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.29/1.64 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.29/1.64 'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( Z ) ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.29/1.64 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.29/1.64 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.29/1.64 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.29/1.64 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), 'c_Suc'( Z ) ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.29/1.64 ), Z ) ) ) ],
% 1.29/1.64 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.29/1.64 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.29/1.64 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), 'c_Suc'( Z ) ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.29/1.64 ), Z ) ), Y ) ) ],
% 1.29/1.64 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~(
% 1.29/1.64 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.29/1.64 =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ) ],
% 1.29/1.64 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.29/1.64 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.29/1.64 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =( hAPP(
% 1.29/1.64 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.29/1.64 , 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.29/1.64 ,
% 1.29/1.64 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.29/1.64 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X ) ) ],
% 1.29/1.64 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP(
% 1.29/1.64 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), T ) ) ) ), =( Z, T ), =( Y
% 1.29/1.64 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.29/1.64 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ) ) ), =( T, U ), =( Z,
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =( hAPP(
% 1.29/1.64 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.29/1.64 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =( hAPP(
% 1.29/1.64 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.29/1.64 X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.29/1.64 [ ~( =( X, 'c_Suc'( X ) ) ) ],
% 1.29/1.64 [ ~( =( 'c_Suc'( X ), X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~( =( hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), 'c_HOL_Oone__class_Oone'( X
% 1.29/1.64 ) ) ), =( 'c_HOL_Oinverse__class_Oinverse'( Y, X ), Z ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.29/1.64 'class_Power_Opower'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.29/1.64 , 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( hAPP( hAPP(
% 1.29/1.64 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.29/1.64 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.29/1.64 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.64 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.29/1.64 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.29/1.64 ), Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.29/1.64 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), Z, X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.64 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.29/1.64 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.29/1.64 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z,
% 1.29/1.64 X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.64 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.29/1.64 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.29/1.64 , Y ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.29/1.64 Y, 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.64 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.29/1.64 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.29/1.64 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 1.29/1.64 X ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), Z, X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.29/1.64 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.29/1.64 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ), ~(
% 1.29/1.64 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 1.29/1.64 ,
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.29/1.64 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.29/1.64 , X ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), Z, X ) ), ~(
% 1.29/1.64 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ]
% 1.29/1.64 ,
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.64 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.29/1.64 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.29/1.64 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.29/1.64 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.29/1.64 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.64 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.29/1.64 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.29/1.64 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.29/1.64 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.29/1.64 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.64 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.29/1.64 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.29/1.64 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.29/1.64 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.29/1.64 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.64 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.29/1.64 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.29/1.64 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.29/1.64 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.29/1.64 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.29/1.64 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.29/1.64 ), X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.29/1.64 , X ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.29/1.64 ,
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.29/1.64 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.29/1.64 ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z
% 1.29/1.64 , X ) ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.29/1.64 ,
% 1.29/1.64 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =( hAPP(
% 1.29/1.64 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ), Y ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.29/1.64 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.29/1.64 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X )
% 1.29/1.64 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.29/1.64 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.29/1.64 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.29/1.64 T, X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 1.29/1.64 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( =(
% 1.29/1.64 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.29/1.64 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ) ), =( Y, Z ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~( =(
% 1.29/1.64 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.29/1.64 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ) ), =( Y, Z ), =( Z,
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.29/1.64 ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 1.29/1.64 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.29/1.64 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.29/1.64 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.64 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.29/1.64 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.29/1.64 , X ) ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.29/1.64 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.29/1.64 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.64 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.29/1.64 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.29/1.64 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.29/1.64 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.29/1.64 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.29/1.64 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.29/1.64 , 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.29/1.64 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_Suc'( X
% 1.29/1.64 ) ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_Suc'(
% 1.29/1.64 X ) ), Z ) ) ), =( Y, Z ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.64 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.29/1.64 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.29/1.64 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.29/1.64 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.29/1.64 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.29/1.64 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.29/1.64 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.64 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.29/1.64 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.29/1.64 , X ) ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.29/1.64 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.29/1.64 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.64 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.29/1.64 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.29/1.64 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.29/1.64 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'(
% 1.29/1.64 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.29/1.64 ), X ) ), 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X )
% 1.29/1.64 , X ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.29/1.64 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.64 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.29/1.64 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.29/1.64 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.29/1.64 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'(
% 1.29/1.64 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.29/1.64 ), X ) ), ~( 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.29/1.64 X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ),
% 1.29/1.64 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 1.29/1.64 'c_Nat_Osemiring__1__class_Oof__nat'( hAPP( hAPP(
% 1.29/1.64 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ), X ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Oplus__class_Oplus'( X ), 'c_Nat_Osemiring__1__class_Oof__nat'( Y
% 1.29/1.64 , X ) ), 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ) ) ) ],
% 1.29/1.64 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.29/1.64 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.29/1.64 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.29/1.64 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_Suc'(
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.64 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.29/1.64 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.29/1.64 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), ~( 'c_lessequals'(
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 1.29/1.64 ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.64 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.29/1.64 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.29/1.64 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), ~( 'c_lessequals'( Z,
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( T, Y, X ) ) ]
% 1.29/1.64 ,
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 1.29/1.64 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.29/1.64 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.29/1.64 , X ), 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oinverse__class_Oinverse'(
% 1.29/1.64 Y, X ), X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.29/1.64 X ), Y ), Z ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z
% 1.29/1.64 , X ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.29/1.64 ,
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.29/1.64 X ), Y ), Z ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.29/1.64 , X ) ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.29/1.64 ,
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.29/1.64 X ), Y ), Z ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.29/1.64 , X ) ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.29/1.64 ,
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.29/1.64 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ), X ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.29/1.64 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.29/1.64 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~( 'c_lessequals'( Z,
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.29/1.64 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =(
% 1.29/1.64 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Oone__class_Oone'( X )
% 1.29/1.64 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, Z ) ],
% 1.29/1.64 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Ouminus__class_Ouminus'(
% 1.29/1.64 Y, X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.29/1.64 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oone__class_Oone'( X ), X ) ), Y )
% 1.29/1.64 ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.64 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.29/1.64 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.29/1.64 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.29/1.64 , X ), X ), T, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T
% 1.29/1.64 , X ) ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.29/1.64 , X ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y, hAPP(
% 1.29/1.64 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.29/1.64 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.64 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.29/1.64 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.29/1.64 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.29/1.64 , X ), X ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.29/1.64 ) ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.29/1.64 ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.29/1.64 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.29/1.64 [ ~( 'class_OrderedGroup_Oab__semigroup__mult'( X ) ), =( hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), Z ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), Z ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ],
% 1.29/1.64 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.29/1.64 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.29/1.64 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.29/1.64 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.29/1.64 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.29/1.64 ) ) ],
% 1.29/1.64 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.29/1.64 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.29/1.64 ) ) ],
% 1.29/1.64 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.29/1.64 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.29/1.64 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.29/1.64 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.29/1.64 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.29/1.64 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.29/1.64 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), hAPP(
% 1.29/1.64 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ) ],
% 1.29/1.64 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.29/1.64 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.29/1.64 ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Ocomm__semiring'( X ) ), =( hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.29/1.64 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.29/1.64 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.29/1.64 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.29/1.64 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ), ~( 'c_lessequals'( U, Z
% 1.29/1.64 , X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), U
% 1.29/1.64 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_lessequals'(
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.29/1.64 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.29/1.64 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' )
% 1.29/1.64 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y
% 1.29/1.64 , 'tc_nat' ) ) ],
% 1.29/1.64 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.29/1.64 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' )
% 1.29/1.64 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X
% 1.29/1.64 , 'tc_nat' ) ) ],
% 1.29/1.64 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.29/1.64 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.29/1.64 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ) ) ],
% 1.29/1.64 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.29/1.64 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ), ~(
% 1.29/1.64 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.29/1.64 ,
% 1.29/1.64 [ =( 'c_FFT__Mirabelle_OFFT'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X
% 1.29/1.64 ), X ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.29/1.64 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.29/1.64 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.29/1.64 ), X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.29/1.64 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.29/1.64 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.29/1.64 ), X ), 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ouminus__class_Ouminus'(
% 1.29/1.64 Y, X ), Z, X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.64 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.29/1.64 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.29/1.64 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.29/1.64 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.29/1.64 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.29/1.64 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.29/1.64 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.64 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.29/1.64 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Z
% 1.29/1.64 , X ) ), T ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'(
% 1.29/1.64 'c_HOL_Oinverse__class_Odivide'( Y, T, X ),
% 1.29/1.64 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.64 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.29/1.64 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.29/1.64 X ), ~( 'c_lessequals'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.29/1.64 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.29/1.64 ,
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.29/1.64 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.29/1.64 X ), Y ), Z ), X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.29/1.64 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.29/1.64 X ), Z ), Y ), X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.29/1.64 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.29/1.64 X ), Y ), Z ), X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.29/1.64 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.29/1.64 X ), Z ), Y ), X ) ) ],
% 1.29/1.64 [ =( hAPP( hAPP( X, Y ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Z ),
% 1.29/1.64 ~( 'c_Groebner__Basis_Ogb__semiring'( T, U, X, W, Z, V0 ) ) ],
% 1.29/1.64 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ), ~( =(
% 1.29/1.64 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y ) ), =( Y,
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 1.29/1.64 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.29/1.64 X ), 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.29/1.64 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), X
% 1.29/1.64 ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.29/1.64 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.29/1.64 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.29/1.64 X ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ) ) ), =( hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.29/1.64 , X ) ), T ), Z ), =( T, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.29/1.64 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.29/1.64 'c_HOL_Oone__class_Oone'( X ), Y, X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.29/1.64 X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.29/1.64 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oone__class_Oone'( X ), X ),
% 1.29/1.64 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.29/1.64 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.29/1.64 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.29/1.64 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.29/1.64 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.29/1.64 'c_HOL_Oone__class_Oone'( X ) ), X ) ],
% 1.29/1.64 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.29/1.64 ), Z ), 'c_HOL_Ouminus__class_Ouminus'( hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ) ) ],
% 1.29/1.64 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.29/1.64 ), Z ), 'c_HOL_Ouminus__class_Ouminus'( hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ) ) ],
% 1.29/1.64 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ouminus__class_Ouminus'( Z
% 1.29/1.64 , X ) ), 'c_HOL_Ouminus__class_Ouminus'( hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ) ) ],
% 1.29/1.64 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ouminus__class_Ouminus'( Z
% 1.29/1.64 , X ) ), 'c_HOL_Ouminus__class_Ouminus'( hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), =( hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.29/1.64 ), 'c_HOL_Ouminus__class_Ouminus'( Y, X ) ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.29/1.64 ), 'c_HOL_Ouminus__class_Ouminus'( Z, X ) ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X
% 1.29/1.64 ) ), Y ), 'c_HOL_Oone__class_Oone'( X ) ), =( Y,
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =( hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X
% 1.29/1.64 ) ), Y ), 'c_HOL_Oone__class_Oone'( X ) ), =( Y,
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =( hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Oinverse__class_Oinverse'(
% 1.29/1.64 Y, X ) ), 'c_HOL_Oone__class_Oone'( X ) ), =( Y,
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ), 'c_lessequals'(
% 1.29/1.64 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X ), ~( 'c_lessequals'(
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( Z, U, X ) )
% 1.29/1.64 , ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ), 'c_lessequals'(
% 1.29/1.64 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X ), ~( 'c_lessequals'(
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Z, U, X ) )
% 1.29/1.64 , ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.64 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.29/1.64 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.29/1.64 , X ) ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.29/1.64 'c_HOL_Oinverse__class_Odivide'( T, Z, X ),
% 1.29/1.64 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.64 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.29/1.64 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.29/1.64 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.29/1.64 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.29/1.64 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.29/1.64 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.29/1.64 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ),
% 1.29/1.64 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.29/1.64 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.29/1.64 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.29/1.64 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.29/1.64 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 1.29/1.64 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.29/1.64 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.29/1.64 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.29/1.64 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.29/1.64 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.29/1.64 X ), Y ), Z ) ), T ) ) ],
% 1.29/1.64 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.29/1.64 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 1.29/1.64 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), X ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), Y ), Z ) ) ) ],
% 1.29/1.64 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ) ],
% 1.29/1.64 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), X ), hAPP(
% 1.29/1.64 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), Y ), Z ) ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), Y ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), X ), Z ) ) ) ],
% 1.29/1.64 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ) ],
% 1.29/1.64 [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =( hAPP( hAPP(
% 1.29/1.64 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.29/1.64 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.29/1.64 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.29/1.64 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.29/1.64 X ), Y ), Z ) ), T ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.29/1.64 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.29/1.64 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.29/1.64 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.29/1.64 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.29/1.64 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.29/1.64 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.29/1.64 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 1.29/1.64 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.29/1.64 'tc_nat' ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.29/1.64 'tc_nat' ), Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ],
% 1.29/1.64 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X ) )
% 1.29/1.64 ), =( 'c_HOL_Ozero__class_Ozero'( X ), Y ) ],
% 1.29/1.64 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.29/1.64 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.29/1.64 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.29/1.64 'c_Power_Opower__class_Opower'( X ), Y ), T ) ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.29/1.64 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.29/1.64 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.29/1.64 ), ~( =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.29/1.64 ) ) ],
% 1.29/1.64 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.29/1.64 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( hAPP( hAPP(
% 1.29/1.64 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oabs__class_Oabs'( Y, X ) ),
% 1.29/1.64 'c_HOL_Oabs__class_Oabs'( Z, X ) ), X ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y
% 1.29/1.64 , Y, X ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.29/1.64 'c_HOL_Oinverse__class_Odivide'( Y, Y, X ), 'c_HOL_Oone__class_Oone'( X )
% 1.29/1.64 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.29/1.64 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.29/1.64 'c_HOL_Oinverse__class_Odivide'( Y, Y, X ), 'c_HOL_Oone__class_Oone'( X )
% 1.29/1.64 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.64 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Z, Y, X
% 1.29/1.64 ), X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.64 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.29/1.64 ), X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.64 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Z, Y, X
% 1.29/1.64 ), X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.64 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.29/1.64 ), X ) ) ],
% 1.29/1.64 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.29/1.64 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), =( X, 'c_HOL_Oone__class_Oone'(
% 1.29/1.64 'tc_nat' ) ) ],
% 1.29/1.64 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.29/1.64 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), =( Y, 'c_HOL_Oone__class_Oone'(
% 1.29/1.64 'tc_nat' ) ) ],
% 1.29/1.64 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.29/1.64 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ),
% 1.29/1.64 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.29/1.64 , Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 1.29/1.64 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.29/1.64 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.29/1.64 'c_Power_Opower__class_Opower'( X ), T ), Z ), X ), ~( 'c_lessequals'(
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 1.29/1.64 ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), ~( 'class_Int_Onumber'(
% 1.29/1.64 X ) ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.29/1.64 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.29/1.64 X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), Z ) ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.29/1.64 , X ) ), T ) ) ) ],
% 1.29/1.64 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.29/1.64 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), ~(
% 1.29/1.64 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.29/1.64 'tc_nat' ) ), =( Y, Z ) ],
% 1.29/1.64 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.29/1.64 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ), 'tc_nat' ) ) ],
% 1.29/1.64 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.29/1.64 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), X ), 'tc_nat' ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.64 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.29/1.64 'c_HOL_Oone__class_Oone'( X ), Y, X ), 'c_lessequals'( Y,
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.29/1.64 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oone__class_Oone'( X ),
% 1.29/1.64 X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_lessequals'( Y,
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.29/1.64 'c_Power_Opower__class_Opower'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 1.29/1.64 X ), X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.29/1.64 'c_lessequals'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.29/1.64 'c_lessequals'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.29/1.64 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.29/1.64 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~(
% 1.29/1.64 'c_lessequals'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.29/1.64 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ), ~(
% 1.29/1.64 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ]
% 1.29/1.64 ,
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.29/1.64 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.29/1.64 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~(
% 1.29/1.64 'c_lessequals'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.29/1.64 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ), ~(
% 1.29/1.64 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.29/1.64 ,
% 1.29/1.64 [ =( X, 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X
% 1.29/1.64 , 'c_Suc'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat'
% 1.29/1.64 ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.29/1.64 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.29/1.64 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.29/1.64 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ),
% 1.29/1.64 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ) ) ],
% 1.29/1.64 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 1.29/1.64 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.29/1.64 Z, X ), 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oinverse__class_Odivide'(
% 1.29/1.64 Y, Z, X ), X ) ) ],
% 1.29/1.64 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.29/1.64 'c_Suc'( X ), 'tc_nat' ) ],
% 1.29/1.64 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.29/1.64 'c_Suc'( X ), 'tc_nat' ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.64 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.29/1.64 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.29/1.64 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ),
% 1.29/1.64 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), =( hAPP( hAPP(
% 1.29/1.64 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.29/1.64 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ), U ) ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.29/1.64 X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ), U )
% 1.29/1.64 ) ],
% 1.29/1.64 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ), T ) ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ), Y ) ), T ) ) ],
% 1.29/1.64 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.29/1.64 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X ) )
% 1.29/1.64 , Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.29/1.64 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.29/1.64 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X ) )
% 1.29/1.64 , Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.29/1.64 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.29/1.64 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ouminus__class_Ouminus'( Y,
% 1.29/1.64 X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.29/1.64 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.29/1.64 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X ) )
% 1.29/1.64 , Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.29/1.64 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.29/1.64 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.29/1.64 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y
% 1.29/1.64 ), 'tc_nat' ) ) ],
% 1.29/1.64 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.29/1.64 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.29/1.64 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X
% 1.29/1.64 ), 'tc_nat' ) ) ],
% 1.29/1.64 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.29/1.64 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.29/1.64 ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.29/1.64 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.29/1.64 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.29/1.64 ,
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( Y,
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.29/1.64 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.29/1.64 X ), Z ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y )
% 1.29/1.64 ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( Y,
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.29/1.64 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.29/1.64 X ), Y ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z )
% 1.29/1.64 ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.29/1.64 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.29/1.64 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.29/1.64 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), U ), Z ) ), X ), hAPP( hAPP(
% 1.29/1.64 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.29/1.64 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), T ), hAPP( hAPP(
% 1.29/1.64 'c_Power_Opower__class_Opower'( X ), Y ), U ), X ) ), Z ) ), =( Y,
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.29/1.64 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.29/1.64 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.29/1.64 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.29/1.64 'c_HOL_Oinverse__class_Odivide'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.29/1.64 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.29/1.64 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.29/1.64 'c_HOL_Oinverse__class_Odivide'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.29/1.64 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.29/1.64 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 1.29/1.64 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.29/1.64 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.64 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.29/1.64 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.29/1.64 , X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.29/1.64 ,
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.64 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.29/1.64 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.29/1.64 , X ) ) ],
% 1.29/1.64 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.29/1.64 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.29/1.64 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.29/1.64 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.29/1.64 'c_HOL_Oplus__class_Oplus'( X ), X ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.29/1.64 ), Z ) ), T ) ) ],
% 1.29/1.64 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.29/1.64 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.29/1.64 'tc_nat' ), 'c_Suc'( Z ) ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.29/1.64 'tc_nat' ), 'c_Suc'( Z ) ), Y ), 'tc_nat' ) ) ],
% 1.29/1.64 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.29/1.64 'tc_nat' ), 'c_Suc'( X ) ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.29/1.64 'tc_nat' ), 'c_Suc'( X ) ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.29/1.64 Y, Z, 'tc_nat' ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.29/1.64 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( =(
% 1.29/1.64 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oone__class_Oone'( X ) )
% 1.29/1.64 ), =( Y, 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.64 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.29/1.64 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ),
% 1.29/1.64 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.29/1.64 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.29/1.64 'c_HOL_Oone__class_Oone'( X ), X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.64 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.29/1.64 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.29/1.64 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.29/1.64 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.29/1.64 X ), 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~(
% 1.29/1.64 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.29/1.64 , Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.64 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.29/1.64 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.29/1.64 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.29/1.64 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.29/1.64 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ), ~(
% 1.29/1.64 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( T,
% 1.29/1.64 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.64 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.29/1.64 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.29/1.64 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.29/1.64 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.29/1.64 ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.29/1.64 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.64 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.29/1.64 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.29/1.64 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.29/1.64 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.29/1.64 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~(
% 1.29/1.64 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.29/1.64 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), Z, X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.64 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.29/1.64 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ),
% 1.29/1.64 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oabs__class_Oabs'( Y, X ), X ) )
% 1.29/1.64 ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.64 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.29/1.64 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X )
% 1.29/1.64 , 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.29/1.64 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ) ],
% 1.29/1.64 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.29/1.64 'c_HOL_Oabs__class_Oabs'( Y, X ), Y ), ~( 'c_HOL_Oord__class_Oless'(
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.29/1.64 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.29/1.64 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ), ~(
% 1.29/1.64 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.29/1.64 ,
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.64 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.29/1.64 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.29/1.64 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ), ~(
% 1.29/1.64 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.29/1.64 ,
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.64 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.29/1.64 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.29/1.64 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.29/1.64 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.29/1.64 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.29/1.64 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, 'c_Suc'(
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.29/1.64 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.29/1.64 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.29/1.64 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), T ) ), hBOOL( hAPP(
% 1.29/1.64 hAPP( U, T ), W ) ), ~( hBOOL( hAPP( hAPP( X, Z ), V0 ) ) ), ~(
% 1.29/1.64 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, U, X, V4, V0, Y, V5,
% 1.29/1.64 V6 ) ) ],
% 1.29/1.64 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), T ) ), ~( hBOOL( hAPP(
% 1.29/1.64 hAPP( X, U ), Z ) ) ), hBOOL( hAPP( hAPP( W, V0 ), T ) ), ~(
% 1.29/1.64 'c_Ring__and__Field_Oordered__idom'( V1, V2, V0, V3, W, X, V4, U, Y, V5,
% 1.29/1.64 V6 ) ) ],
% 1.29/1.64 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), Y ) ) ), hBOOL( hAPP(
% 1.29/1.64 hAPP( U, Y ), W ) ), ~( hBOOL( hAPP( hAPP( X, V0 ), T ) ) ), ~(
% 1.29/1.64 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, U, X, V4, V0, Z, V5,
% 1.29/1.64 V6 ) ) ],
% 1.29/1.64 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), Y ) ) ), ~( hBOOL( hAPP(
% 1.29/1.64 hAPP( X, T ), U ) ) ), hBOOL( hAPP( hAPP( W, V0 ), Y ) ), ~(
% 1.29/1.64 'c_Ring__and__Field_Oordered__idom'( V1, V2, V0, V3, W, X, V4, U, Z, V5,
% 1.29/1.64 V6 ) ) ],
% 1.29/1.64 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), Z ) ), hBOOL( hAPP(
% 1.29/1.64 hAPP( U, Z ), W ) ), ~( hBOOL( hAPP( hAPP( X, T ), V0 ) ) ), ~(
% 1.29/1.64 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, U, X, V4, V0, Y, V5,
% 1.29/1.64 V6 ) ) ],
% 1.29/1.64 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), Z ) ), ~( hBOOL( hAPP(
% 1.29/1.64 hAPP( X, U ), T ) ) ), hBOOL( hAPP( hAPP( W, V0 ), Z ) ), ~(
% 1.29/1.64 'c_Ring__and__Field_Oordered__idom'( V1, V2, V0, V3, W, X, V4, U, Y, V5,
% 1.29/1.64 V6 ) ) ],
% 1.29/1.64 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, Y ), T ) ) ), hBOOL( hAPP(
% 1.29/1.64 hAPP( U, Y ), W ) ), ~( hBOOL( hAPP( hAPP( X, V0 ), T ) ) ), ~(
% 1.29/1.64 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, U, X, V4, V0, Z, V5,
% 1.29/1.64 V6 ) ) ],
% 1.29/1.64 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, Y ), T ) ) ), ~( hBOOL( hAPP(
% 1.29/1.64 hAPP( X, T ), U ) ) ), hBOOL( hAPP( hAPP( W, V0 ), Y ) ), ~(
% 1.29/1.64 'c_Ring__and__Field_Oordered__idom'( V1, V2, V0, V3, W, X, V4, U, Z, V5,
% 1.29/1.64 V6 ) ) ],
% 1.29/1.64 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), T ) ), hBOOL( hAPP(
% 1.29/1.64 hAPP( U, T ), W ) ), ~( hBOOL( hAPP( hAPP( X, Z ), V0 ) ) ), ~(
% 1.29/1.64 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, X, U, V4, V0, Y, V5,
% 1.29/1.64 V6 ) ) ],
% 1.29/1.64 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), T ) ), ~( hBOOL( hAPP(
% 1.29/1.64 hAPP( X, U ), Z ) ) ), hBOOL( hAPP( hAPP( W, V0 ), T ) ), ~(
% 1.29/1.64 'c_Ring__and__Field_Oordered__idom'( V1, V2, V0, V3, X, W, V4, U, Y, V5,
% 1.29/1.64 V6 ) ) ],
% 1.29/1.64 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), Y ) ) ), hBOOL( hAPP(
% 1.29/1.64 hAPP( U, Y ), W ) ), ~( hBOOL( hAPP( hAPP( X, V0 ), T ) ) ), ~(
% 1.29/1.64 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, X, U, V4, V0, Z, V5,
% 1.29/1.64 V6 ) ) ],
% 1.29/1.64 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), Y ) ) ), ~( hBOOL( hAPP(
% 1.29/1.64 hAPP( X, T ), U ) ) ), hBOOL( hAPP( hAPP( W, V0 ), Y ) ), ~(
% 1.29/1.64 'c_Ring__and__Field_Oordered__idom'( V1, V2, V0, V3, X, W, V4, U, Z, V5,
% 1.29/1.64 V6 ) ) ],
% 1.29/1.64 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), Z ) ), hBOOL( hAPP(
% 1.29/1.64 hAPP( U, Z ), W ) ), ~( hBOOL( hAPP( hAPP( X, T ), V0 ) ) ), ~(
% 1.29/1.64 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, X, U, V4, V0, Y, V5,
% 1.29/1.64 V6 ) ) ],
% 1.29/1.64 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), Z ) ), ~( hBOOL( hAPP(
% 1.29/1.64 hAPP( X, U ), T ) ) ), hBOOL( hAPP( hAPP( W, V0 ), Z ) ), ~(
% 1.29/1.64 'c_Ring__and__Field_Oordered__idom'( V1, V2, V0, V3, X, W, V4, U, Y, V5,
% 1.29/1.64 V6 ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =( hAPP( hAPP(
% 1.29/1.64 'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( Z ) ), hAPP( hAPP(
% 1.29/1.64 'c_Power_Opower__class_Opower'( X ), T ), 'c_Suc'( Z ) ) ) ), =( Y, T ),
% 1.29/1.64 ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.29/1.64 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.29/1.64 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.29/1.64 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.29/1.64 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =(
% 1.29/1.64 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.29/1.64 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.29/1.64 X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), Z ), Z, X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.64 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.29/1.64 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.29/1.64 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.29/1.64 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.29/1.64 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), Y
% 1.29/1.64 , X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.64 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.29/1.64 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.29/1.64 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 1.29/1.64 X ) ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.29/1.64 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ]
% 1.29/1.64 ,
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.64 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.29/1.64 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.29/1.64 , X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.29/1.64 X ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), Y, X ) ), ~(
% 1.29/1.64 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.29/1.64 ), T ), Z ), X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.64 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.29/1.64 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.29/1.64 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 1.29/1.64 X ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), Y, X ) ), ~(
% 1.29/1.64 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.29/1.64 ), T ), Z ), X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.64 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.29/1.64 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.29/1.64 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.29/1.64 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.29/1.64 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( T, Z, X )
% 1.29/1.64 , X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.64 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.29/1.64 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.29/1.64 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.29/1.64 X ) ), 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.29/1.64 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ]
% 1.29/1.64 ,
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.64 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.29/1.64 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.29/1.64 , X ), ~( 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.29/1.64 X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ), ~(
% 1.29/1.64 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.29/1.64 , Y ), T ), Z, X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.64 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.29/1.64 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.29/1.64 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.29/1.64 X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ), ~(
% 1.29/1.64 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.29/1.64 , Y ), T ), Z, X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.29/1.64 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.29/1.64 , Y ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP(
% 1.29/1.64 hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 1.29/1.64 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.29/1.64 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.29/1.64 ,
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.29/1.64 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.29/1.64 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.29/1.64 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.29/1.64 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.29/1.64 ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.29/1.64 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.29/1.64 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.29/1.64 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.29/1.64 , Z ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X )
% 1.29/1.64 ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.29/1.64 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.29/1.64 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 1.29/1.64 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.29/1.64 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.29/1.64 ,
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.29/1.64 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.29/1.64 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 1.29/1.64 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.29/1.64 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.29/1.64 ,
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.64 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.29/1.64 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.29/1.64 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 1.29/1.64 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.29/1.64 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.29/1.64 ,
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.64 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.29/1.64 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.29/1.64 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 1.29/1.64 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.29/1.64 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.29/1.64 ,
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.64 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.29/1.64 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), ~(
% 1.29/1.64 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.29/1.64 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.29/1.64 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X )
% 1.29/1.64 ), 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.29/1.64 X ), Y ), Z ) ), 'c_HOL_Oinverse__class_Oinverse'( Y, X ) ) ),
% 1.29/1.64 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ) ), =( Z,
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.29/1.64 ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =( hAPP( hAPP(
% 1.29/1.64 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X )
% 1.29/1.64 ), 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X
% 1.29/1.64 ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) ),
% 1.29/1.64 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ) ), =( Z,
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.29/1.64 ) ],
% 1.29/1.64 [ =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( 'tc_nat' ), 'c_Suc'(
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), X ), 'c_Suc'(
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.29/1.64 [ =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( 'tc_nat' ), 'c_Suc'(
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), X ), 'c_Suc'(
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.29/1.64 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.29/1.64 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.29/1.64 'c_HOL_Oone__class_Oone'( X ) ), X ), Z, X ), ~(
% 1.29/1.64 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.29/1.64 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.29/1.64 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.29/1.64 'c_HOL_Oone__class_Oone'( X ) ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.29/1.64 Y, Z, X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.29/1.64 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.29/1.64 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.29/1.64 ) ), T ), 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.29/1.64 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ), Z, X ) ), =( Z,
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.29/1.64 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.29/1.64 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Oinverse__class_Odivide'( Z
% 1.29/1.64 , T, X ) ), 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.29/1.64 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), T, X ) ), =( T,
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.29/1.64 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.29/1.64 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) )
% 1.29/1.64 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), hAPP( hAPP(
% 1.29/1.64 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.29/1.64 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.29/1.64 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ),
% 1.29/1.64 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ) ), =( Z,
% 1.29/1.64 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.29/1.64 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.29/1.64 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), ~(
% 1.29/1.64 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.29/1.64 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.29/1.64 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.29/1.64 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.29/1.65 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( T, Y, X ) ) ],
% 1.29/1.65 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), hAPP( hAPP( Y, U ), T ) )
% 1.29/1.65 , hAPP( hAPP( Y, hAPP( hAPP( X, Z ), U ) ), T ) ), ~(
% 1.29/1.65 'c_Groebner__Basis_Ogb__semiring'( X, Y, W, V0, V1, V2 ) ) ],
% 1.29/1.65 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), T ), hAPP( hAPP( Y, hAPP(
% 1.29/1.65 hAPP( X, Z ), U ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, Y, W
% 1.29/1.65 , V0, U, V1 ) ) ],
% 1.29/1.65 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), Y ) ), hAPP( hAPP( Z, hAPP(
% 1.29/1.65 hAPP( X, T ), U ) ), Y ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, Z, W
% 1.29/1.65 , V0, U, V1 ) ) ],
% 1.29/1.65 [ =( hAPP( hAPP( X, Y ), Y ), hAPP( hAPP( Z, hAPP( hAPP( X, T ), T ) ),
% 1.29/1.65 Y ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, Z, U, W, T, V0 ) ) ],
% 1.29/1.65 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.29/1.65 X, T, U, Y, W, V0 ) ) ],
% 1.29/1.65 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.29/1.65 X, T, U, Z, W, V0 ) ) ],
% 1.29/1.65 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 1.29/1.65 'c_Groebner__Basis_Ogb__semiring'( T, X, U, W, V0, V1 ) ) ],
% 1.29/1.65 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), U ), hAPP( hAPP( Y, hAPP(
% 1.29/1.65 hAPP( X, Z ), U ) ), hAPP( hAPP( X, T ), U ) ) ), ~(
% 1.29/1.65 'c_Groebner__Basis_Ogb__semiring'( Y, X, W, V0, V1, V2 ) ) ],
% 1.29/1.65 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.29/1.65 T, X, U, Y, W, V0 ) ) ],
% 1.29/1.65 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.29/1.65 T, X, U, Z, W, V0 ) ) ],
% 1.29/1.65 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.29/1.65 T, X, U, W, Y, V0 ) ) ],
% 1.29/1.65 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.29/1.65 T, X, U, W, Z, V0 ) ) ],
% 1.29/1.65 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 1.29/1.65 , hAPP( hAPP( X, hAPP( hAPP( X, Y ), T ) ), hAPP( hAPP( X, Z ), U ) ) ),
% 1.29/1.65 ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, V0, V1, V2, V3 ) ) ],
% 1.29/1.65 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 1.29/1.65 , hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), hAPP( hAPP( X, T ), U ) ) ) ),
% 1.29/1.65 ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, V0, V1, V2, V3 ) ) ],
% 1.29/1.65 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 1.29/1.65 , hAPP( hAPP( X, T ), hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), U ) ) ),
% 1.29/1.65 ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, V0, V1, V2, V3 ) ) ],
% 1.29/1.65 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, hAPP(
% 1.29/1.65 hAPP( X, Y ), T ) ), Z ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, W
% 1.29/1.65 , V0, V1, V2 ) ) ],
% 1.29/1.65 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, Y ),
% 1.29/1.65 hAPP( hAPP( X, Z ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X,
% 1.29/1.65 W, V0, V1, V2 ) ) ],
% 1.29/1.65 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 1.29/1.65 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, W
% 1.29/1.65 , V0, V1, V2 ) ) ],
% 1.29/1.65 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, Z ),
% 1.29/1.65 hAPP( hAPP( X, Y ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X,
% 1.29/1.65 W, V0, V1, V2 ) ) ],
% 1.29/1.65 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 1.29/1.65 , hAPP( hAPP( X, hAPP( hAPP( X, Y ), T ) ), hAPP( hAPP( X, Z ), U ) ) ),
% 1.29/1.65 ~( 'c_Groebner__Basis_Ogb__semiring'( X, W, V0, V1, V2, V3 ) ) ],
% 1.29/1.65 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, Y ),
% 1.29/1.65 hAPP( hAPP( X, Z ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U,
% 1.29/1.65 W, V0, V1, V2 ) ) ],
% 1.29/1.65 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, Z ),
% 1.29/1.65 hAPP( hAPP( X, Y ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U,
% 1.29/1.65 W, V0, V1, V2 ) ) ],
% 1.29/1.65 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, hAPP(
% 1.29/1.65 hAPP( X, Y ), T ) ), Z ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U, W
% 1.29/1.65 , V0, V1, V2 ) ) ],
% 1.29/1.65 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 1.29/1.65 'c_Groebner__Basis_Ogb__semiring'( X, T, U, W, V0, V1 ) ) ],
% 1.29/1.65 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 1.29/1.65 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U, W
% 1.29/1.65 , V0, V1, V2 ) ) ],
% 1.29/1.65 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.29/1.65 X, T, U, Y, W, V0 ) ) ],
% 1.29/1.65 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 1.29/1.65 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U, W
% 1.29/1.65 , V0, V1, V2 ) ) ],
% 1.29/1.65 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 1.29/1.65 'c_Groebner__Basis_Ogb__semiring'( X, T, U, W, V0, V1 ) ) ],
% 1.29/1.65 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.29/1.65 T, X, U, Y, W, V0 ) ) ],
% 1.29/1.65 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.29/1.65 T, X, U, W, Y, V0 ) ) ],
% 1.29/1.65 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 1.29/1.65 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, W
% 1.29/1.65 , V0, V1, V2 ) ) ],
% 1.29/1.65 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 1.29/1.65 'c_Groebner__Basis_Ogb__semiring'( T, X, U, W, V0, V1 ) ) ],
% 1.29/1.65 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), U ) ), hAPP( hAPP( Z, hAPP(
% 1.29/1.65 hAPP( X, Y ), T ) ), hAPP( hAPP( X, Y ), U ) ) ), ~(
% 1.29/1.65 'c_Groebner__Basis_Ogb__semiring'( Z, X, W, V0, V1, V2 ) ) ],
% 1.29/1.65 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), U ), hAPP( hAPP( Y, hAPP(
% 1.29/1.65 hAPP( X, Z ), U ) ), hAPP( hAPP( X, T ), U ) ) ), ~(
% 1.29/1.65 'c_Groebner__Basis_Ogb__semiring'( W, Y, X, V0, V1, V2 ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.29/1.65 'c_HOL_Oabs__class_Oabs'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X
% 1.29/1.65 ), 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.29/1.65 ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z
% 1.29/1.65 , X ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.29/1.65 ,
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.29/1.65 ), X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.29/1.65 , X ) ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.29/1.65 ,
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.29/1.65 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), Z, X ), ~(
% 1.29/1.65 'c_lessequals'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.29/1.65 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.29/1.65 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.29/1.65 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), Y, X ), ~(
% 1.29/1.65 'c_lessequals'( Z, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.29/1.65 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.29/1.65 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.29/1.65 'c_HOL_Oinverse__class_Odivide'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y
% 1.29/1.65 ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.29/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.29/1.65 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.29/1.65 ,
% 1.29/1.65 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.29/1.65 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ), ~(
% 1.29/1.65 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ) ), ~(
% 1.29/1.65 'c_lessequals'( Y, Z, X ) ) ],
% 1.29/1.65 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.29/1.65 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ), ~(
% 1.29/1.65 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ) ), ~(
% 1.29/1.65 'c_lessequals'( Y, Z, X ) ) ],
% 1.29/1.65 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.29/1.65 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ),
% 1.29/1.65 'c_HOL_Oabs__class_Oabs'( Y, X ) ) ],
% 1.29/1.65 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.29/1.65 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ) ) ), =( X, Z
% 1.29/1.65 ) ],
% 1.29/1.65 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.29/1.65 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ), =( Y, Z
% 1.29/1.65 ) ],
% 1.29/1.65 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.29/1.65 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ), =( Y, Z
% 1.29/1.65 ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.29/1.65 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP(
% 1.29/1.65 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 1.29/1.65 [ ~( 'class_OrderedGroup_Ocancel__ab__semigroup__add'( X ) ), ~( =( hAPP(
% 1.29/1.65 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.29/1.65 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 1.29/1.65 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =( hAPP(
% 1.29/1.65 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.29/1.65 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 1.29/1.65 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =( hAPP(
% 1.29/1.65 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.29/1.65 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ), =( Y, T ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.29/1.65 , Y ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.29/1.65 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.29/1.65 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.29/1.65 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.29/1.65 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.29/1.65 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.29/1.65 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.29/1.65 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.29/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.29/1.65 'c_HOL_Oinverse__class_Oinverse'( hAPP( hAPP(
% 1.29/1.65 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), hAPP( hAPP(
% 1.29/1.65 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X
% 1.29/1.65 ) ), 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 1.29/1.65 'c_HOL_Oinverse__class_Oinverse'( hAPP( hAPP(
% 1.29/1.65 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), hAPP( hAPP(
% 1.29/1.65 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Oinverse'( Z, X
% 1.29/1.65 ) ), 'c_HOL_Oinverse__class_Oinverse'( Y, X ) ) ), =( Z,
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.29/1.65 ) ],
% 1.29/1.65 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.29/1.65 'c_HOL_Oplus__class_Oplus'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X
% 1.29/1.65 ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T ) ), hAPP( hAPP(
% 1.29/1.65 'c_HOL_Oplus__class_Oplus'( X ), 'c_Int_Onumber__class_Onumber__of'( hAPP(
% 1.29/1.65 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), Y ), Z ), X ) ), T ) )
% 1.29/1.65 ],
% 1.29/1.65 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.29/1.65 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ozero__class_Ozero'( X )
% 1.29/1.65 , X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.29/1.65 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.29/1.65 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.29/1.65 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.29/1.65 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.29/1.65 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 1.29/1.65 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oinverse__class_Oinverse'( Y, X
% 1.29/1.65 ), X ), Y ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.29/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.29/1.65 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.29/1.65 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =(
% 1.29/1.65 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.29/1.65 X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), Z ), Z, X ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 1.29/1.65 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Ozero__class_Ozero'(
% 1.29/1.65 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.29/1.65 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.29/1.65 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Z
% 1.29/1.65 , X ) ), T ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.29/1.65 'c_HOL_Oinverse__class_Odivide'( Y, T, X ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.29/1.65 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.29/1.65 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.29/1.65 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.29/1.65 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, Y ), T ) ) ), hBOOL( hAPP(
% 1.29/1.65 hAPP( U, Y ), W ) ), ~( hBOOL( hAPP( hAPP( X, V0 ), T ) ) ), ~(
% 1.29/1.65 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, X, U, V4, V0, Z, V5,
% 1.29/1.65 V6 ) ) ],
% 1.29/1.65 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, Y ), T ) ) ), ~( hBOOL( hAPP(
% 1.29/1.65 hAPP( X, T ), U ) ) ), hBOOL( hAPP( hAPP( W, V0 ), Y ) ), ~(
% 1.29/1.65 'c_Ring__and__Field_Oordered__idom'( V1, V2, V0, V3, X, W, V4, U, Z, V5,
% 1.29/1.65 V6 ) ) ],
% 1.29/1.65 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( Z, T ) ) ), ~( hBOOL( hAPP( hAPP( X,
% 1.29/1.65 Y ), T ) ) ), ~( 'c_Ring__and__Field_Oordered__idom'( U, W, Y, V0, V1, X
% 1.29/1.65 , V2, V3, V4, Z, V5 ) ) ],
% 1.29/1.65 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( X, Y ), hAPP(
% 1.29/1.65 T, Z ) ) ) ), ~( 'c_Ring__and__Field_Oordered__idom'( U, W, Y, V0, V1, X
% 1.29/1.65 , V2, V3, V4, T, V5 ) ) ],
% 1.29/1.65 [ hBOOL( hAPP( hAPP( X, hAPP( Y, Z ) ), T ) ), ~( hBOOL( hAPP( hAPP( X,
% 1.29/1.65 Z ), T ) ) ), ~( 'c_Ring__and__Field_Oordered__idom'( U, W, T, V0, V1, X
% 1.29/1.65 , V2, V3, V4, Y, V5 ) ) ],
% 1.29/1.65 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( X, hAPP( T, Y
% 1.29/1.65 ) ), Z ) ) ), ~( 'c_Ring__and__Field_Oordered__idom'( U, W, Z, V0, V1, X
% 1.29/1.65 , V2, V3, V4, T, V5 ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.29/1.65 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.29/1.65 X ), Y ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z )
% 1.29/1.65 ), X ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.29/1.65 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.29/1.65 X ), Y ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z )
% 1.29/1.65 ), X ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ),
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ),
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.29/1.65 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( hAPP( hAPP(
% 1.29/1.65 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), Y ), Z ), X ), hAPP( hAPP(
% 1.29/1.65 'c_HOL_Oplus__class_Oplus'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X
% 1.29/1.65 ) ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =( hAPP( hAPP(
% 1.29/1.65 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.29/1.65 'c_Power_Opower__class_Opower'( X ), T ), Z ) ) ), =( Y, T ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.29/1.65 'tc_nat' ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X )
% 1.29/1.65 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.29/1.65 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =( hAPP( hAPP(
% 1.29/1.65 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.29/1.65 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), Z ) ), =( Y,
% 1.29/1.65 'c_HOL_Ouminus__class_Ouminus'( T, X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.29/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.29/1.65 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.29/1.65 X ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X
% 1.29/1.65 ), 'c_HOL_Oinverse__class_Odivide'( Y, T, X ) ), =( Z,
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.29/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.29/1.65 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.29/1.65 X ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X
% 1.29/1.65 ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ) ), =( Y,
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.29/1.65 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.29/1.65 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.29/1.65 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.29/1.65 X ), 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~( 'c_lessequals'(
% 1.29/1.65 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.29/1.65 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.29/1.65 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ), ~( 'c_lessequals'( Y,
% 1.29/1.65 'c_HOL_Oinverse__class_Odivide'( T, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.29/1.65 , X ), X ), X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.29/1.65 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.29/1.65 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.29/1.65 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.29/1.65 ), X ) ), ~( 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.29/1.65 X ), T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.29/1.65 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, hAPP( hAPP(
% 1.29/1.65 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~( 'c_lessequals'(
% 1.29/1.65 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( T
% 1.29/1.65 , X ), X ), Z, X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.29/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.29/1.65 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z
% 1.29/1.65 , X ) ), T ), 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.29/1.65 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), Z, X ) ) ],
% 1.29/1.65 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.29/1.65 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'(
% 1.29/1.65 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.29/1.65 'c_Groebner__Basis_Ogb__semiring'( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.29/1.65 'c_HOL_Otimes__class_Otimes'( X ), 'c_Power_Opower__class_Opower'( X ),
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ), X ) ]
% 1.29/1.65 ,
% 1.29/1.65 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.29/1.65 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.29/1.65 ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__comm__semiring__strict'( X ) ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.29/1.65 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.29/1.65 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) )
% 1.29/1.65 , ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.29/1.65 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X )
% 1.29/1.65 , ~( 'c_HOL_Oord__class_Oless'( T, Y, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.29/1.65 Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.29/1.65 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X )
% 1.29/1.65 , ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.29/1.65 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X )
% 1.29/1.65 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) )
% 1.29/1.65 , ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.29/1.65 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X )
% 1.29/1.65 , ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.29/1.65 , ~( 'c_HOL_Oord__class_Oless'( T, Y, X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.29/1.65 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.29/1.65 , ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.29/1.65 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.29/1.65 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.29/1.65 , ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.29/1.65 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.29/1.65 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) )
% 1.29/1.65 , ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.29/1.65 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.29/1.65 , ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.29/1.65 , ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.29/1.65 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.29/1.65 , ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.29/1.65 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP(
% 1.29/1.65 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ]
% 1.29/1.65 ,
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.29/1.65 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.29/1.65 , ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.29/1.65 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.29/1.65 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), hAPP( hAPP(
% 1.29/1.65 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.29/1.65 ,
% 1.29/1.65 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.29/1.65 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.29/1.65 ), X ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' )
% 1.29/1.65 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.29/1.65 , X, 'tc_nat' ) ) ],
% 1.29/1.65 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.29/1.65 'tc_nat' ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.29/1.65 ), Z ), Y ), 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_nat' ) ) ],
% 1.29/1.65 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.29/1.65 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.29/1.65 ), Z ), Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 1.29/1.65 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.29/1.65 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.29/1.65 ), X ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 1.29/1.65 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.29/1.65 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.29/1.65 ), X ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' )
% 1.29/1.65 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.29/1.65 , X, 'tc_nat' ) ) ],
% 1.29/1.65 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.29/1.65 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.29/1.65 ), Z ), Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' )
% 1.29/1.65 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.29/1.65 , Y, 'tc_nat' ) ) ],
% 1.29/1.65 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( 'c_Power_Opower_Opower'( Z, T,
% 1.29/1.65 U ), hAPP( W, V0 ) ), V1 ) ) ), ~( 'c_Ring__and__Field_Oordered__idom'(
% 1.29/1.65 V2, V3, Y, V4, X, V5, W, Z, T, V6, U ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), 'c_Nat_Osemiring__1__class_Oof__nat'( Y
% 1.29/1.65 , X ), X ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), 'c_Nat_Osemiring__1__class_Oof__nat'( Y
% 1.29/1.65 , X ), X ) ],
% 1.29/1.65 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 1.29/1.65 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.29/1.65 Y ) ],
% 1.29/1.65 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 1.29/1.65 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.29/1.65 Y ) ],
% 1.29/1.65 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.29/1.65 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.29/1.65 Y ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.29/1.65 X ) ), =( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.29/1.65 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.29/1.65 Y ) ],
% 1.29/1.65 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.29/1.65 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.29/1.65 Y ) ],
% 1.29/1.65 [ =( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.29/1.65 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ],
% 1.29/1.65 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), X ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.29/1.65 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.29/1.65 Y ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.29/1.65 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.29/1.65 Y ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.29/1.65 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'( Y,
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Z, hAPP( hAPP(
% 1.29/1.65 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ), ~( 'c_lessequals'(
% 1.29/1.65 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), Z, X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.29/1.65 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'( Y,
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( T,
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'( Z,
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'( Y,
% 1.29/1.65 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.29/1.65 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'(
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.29/1.65 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), Y, X ) ), ~( 'c_lessequals'(
% 1.29/1.65 Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.29/1.65 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'(
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 'c_HOL_Oord__class_Oless'( Z,
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Oord__class_Oless'( Z,
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.29/1.65 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), Y, X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.29/1.65 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.29/1.65 X ), Y ), Z ), T, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.29/1.65 'c_HOL_Oinverse__class_Odivide'( Y, T, X ) ),
% 1.29/1.65 'c_HOL_Oinverse__class_Odivide'( Z, T, X ) ) ) ],
% 1.29/1.65 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 1.29/1.65 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.29/1.65 X ), Y ), Z ), T, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.29/1.65 'c_HOL_Oinverse__class_Odivide'( Y, T, X ) ),
% 1.29/1.65 'c_HOL_Oinverse__class_Odivide'( Z, T, X ) ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP(
% 1.29/1.65 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Z, X ) ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.29/1.65 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.29/1.65 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 1.29/1.65 ), Y ) ],
% 1.29/1.65 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( Y,
% 1.29/1.65 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 1.29/1.65 ) ) ],
% 1.29/1.65 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( Y,
% 1.29/1.65 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 1.29/1.65 ) ) ],
% 1.29/1.65 [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), =(
% 1.29/1.65 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 1.29/1.65 ), Y ) ],
% 1.29/1.65 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.29/1.65 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 1.29/1.65 ), Y ) ],
% 1.29/1.65 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.29/1.65 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 1.29/1.65 'c_lessequals'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ]
% 1.29/1.65 ,
% 1.29/1.65 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.29/1.65 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ]
% 1.29/1.65 ,
% 1.29/1.65 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.29/1.65 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ), ~(
% 1.29/1.65 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Z, X ), Y, X ) ) ],
% 1.29/1.65 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.29/1.65 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ), ~(
% 1.29/1.65 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Z, X ), Y, X ) ) ],
% 1.29/1.65 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.29/1.65 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), ~(
% 1.29/1.65 'c_lessequals'( Z, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ],
% 1.29/1.65 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.29/1.65 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), ~(
% 1.29/1.65 'c_lessequals'( Z, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ],
% 1.29/1.65 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.29/1.65 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.29/1.65 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), 'c_Suc'( hAPP( hAPP(
% 1.29/1.65 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.29/1.65 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ), hAPP( hAPP(
% 1.29/1.65 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ),
% 1.29/1.65 hAPP( hAPP( 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.29/1.65 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), Z ) ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.29/1.65 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ],
% 1.29/1.65 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.29/1.65 ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X
% 1.29/1.65 ) ) ],
% 1.29/1.65 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.29/1.65 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_lessequals'( T, Z, X
% 1.29/1.65 ) ) ],
% 1.29/1.65 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.29/1.65 , X ), ~( 'c_lessequals'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T
% 1.29/1.65 , X ) ) ],
% 1.29/1.65 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.29/1.65 , X ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_lessequals'( Y, T
% 1.29/1.65 , X ) ) ],
% 1.29/1.65 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.29/1.65 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.29/1.65 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.29/1.65 , 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.29/1.65 , Y ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ),
% 1.29/1.65 ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.29/1.65 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.29/1.65 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.29/1.65 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP(
% 1.29/1.65 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ],
% 1.29/1.65 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.29/1.65 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.29/1.65 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.29/1.65 , 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.29/1.65 , Y ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ),
% 1.29/1.65 ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.29/1.65 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.29/1.65 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.29/1.65 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Y ), hAPP( hAPP(
% 1.29/1.65 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ) ) ],
% 1.29/1.65 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.29/1.65 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.29/1.65 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.29/1.65 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.29/1.65 T, X ) ) ],
% 1.29/1.65 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.29/1.65 , X ), 'c_lessequals'( Z, Y, X ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.29/1.65 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.29/1.65 ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.29/1.65 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), hAPP( hAPP(
% 1.29/1.65 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.29/1.65 ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.29/1.65 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), hAPP( hAPP(
% 1.29/1.65 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ) ],
% 1.29/1.65 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.29/1.65 ), =( Z, Y ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.29/1.65 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.29/1.65 ), ~( 'c_lessequals'( Y, Z, X ) ), =( Z, Y ) ],
% 1.29/1.65 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 1.29/1.65 ,
% 1.29/1.65 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( 'c_Power_Opower_Opower'( Z, T,
% 1.29/1.65 U ), hAPP( W, V0 ) ), V1 ) ) ), =( V0, Y ), ~(
% 1.29/1.65 'c_Ring__and__Field_Oordered__idom'( V2, V3, Y, V4, V5, X, W, Z, T, V6, U
% 1.29/1.65 ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.29/1.65 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.29/1.65 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.29/1.65 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.29/1.65 ), X ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.29/1.65 ), T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ), ~(
% 1.29/1.65 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.29/1.65 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.29/1.65 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.29/1.65 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.29/1.65 ), X ) ), ~( 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.29/1.65 X ), Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ), ~(
% 1.29/1.65 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.29/1.65 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'(
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.29/1.65 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), Y, X ) ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.29/1.65 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'(
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 'c_HOL_Oord__class_Oless'( Z,
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y, hAPP( hAPP(
% 1.29/1.65 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.29/1.65 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'( Y,
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Z, hAPP( hAPP(
% 1.29/1.65 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.29/1.65 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'( Y,
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( T,
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.29/1.65 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), Z, X ) ) ],
% 1.29/1.65 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.29/1.65 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.29/1.65 Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X, 'tc_nat' ) ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.29/1.65 ) ), Y, 'tc_nat' ) ) ],
% 1.29/1.65 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Suc'( X ) )
% 1.29/1.65 , Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), 'c_Suc'(
% 1.29/1.65 Y ) ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 1.29/1.65 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_Suc'( Y ), X ), hAPP( hAPP(
% 1.29/1.65 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.29/1.65 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ) ) ) ],
% 1.29/1.65 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.29/1.65 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( Y, 'c_Suc'(
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.29/1.65 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.29/1.65 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( X,
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, 'c_Suc'(
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.29/1.65 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.29/1.65 'c_HOL_Oplus__class_Oplus'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X
% 1.29/1.65 ) ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( hAPP( hAPP(
% 1.29/1.65 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), Y ), Z ), X ) ) ],
% 1.29/1.65 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( hAPP( hAPP(
% 1.29/1.65 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), X ), Y ), 'tc_nat' ) ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( Y, 'c_Int_OPls', 'tc_Int_Oint' ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( X, 'c_Int_OPls', 'tc_Int_Oint' ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =(
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ) ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 1.29/1.65 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Oone__class_Oone'( 'tc_nat'
% 1.29/1.65 ), X ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.29/1.65 [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.29/1.65 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.29/1.65 'tc_nat' ) ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ]
% 1.29/1.65 ,
% 1.29/1.65 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.29/1.65 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.29/1.65 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.29/1.65 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ],
% 1.29/1.65 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.29/1.65 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.29/1.65 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ), ~( 'c_lessequals'( Y,
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.29/1.65 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.29/1.65 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.29/1.65 ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( T
% 1.29/1.65 , 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.29/1.65 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.29/1.65 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.29/1.65 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.29/1.65 ), X ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.29/1.65 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.29/1.65 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.29/1.65 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X ),
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.29/1.65 ), X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Oinverse__class_Odivide'(
% 1.29/1.65 Y, 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.29/1.65 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.29/1.65 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.29/1.65 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.29/1.65 ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP(
% 1.29/1.65 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), =(
% 1.29/1.65 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ),
% 1.29/1.65 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oabs__class_Oabs'( Y, X ), X ) )
% 1.29/1.65 , =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), =(
% 1.29/1.65 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X )
% 1.29/1.65 , 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.29/1.65 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'(
% 1.29/1.65 X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), =( Y
% 1.29/1.65 , 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X )
% 1.29/1.65 , X ) ) ],
% 1.29/1.65 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =( hAPP( hAPP(
% 1.29/1.65 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.29/1.65 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.29/1.65 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) ) ), =( hAPP( hAPP(
% 1.29/1.65 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), U ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.29/1.65 ), Y ), 'c_Suc'( Z ) ), 'c_HOL_Oone__class_Oone'( X ), X ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.29/1.65 ,
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.29/1.65 'c_HOL_Oinverse__class_Oinverse'( Z, X ),
% 1.29/1.65 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.29/1.65 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.29/1.65 'c_HOL_Oinverse__class_Oinverse'( Z, X ),
% 1.29/1.65 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.29/1.65 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.29/1.65 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oabs__class_Oabs'( Y, X ) ),
% 1.29/1.65 Z ), X ) ],
% 1.29/1.65 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.29/1.65 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.29/1.65 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.29/1.65 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.29/1.65 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.29/1.65 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), hAPP( hAPP(
% 1.29/1.65 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.29/1.65 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.29/1.65 ), Z ) ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.29/1.65 ), T ) ) ) ],
% 1.29/1.65 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.29/1.65 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.29/1.65 'c_HOL_Oplus__class_Oplus'( X ), X ), hAPP( hAPP(
% 1.29/1.65 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.29/1.65 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.29/1.65 ), T ) ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Z
% 1.29/1.65 ), T ) ) ) ],
% 1.29/1.65 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 1.29/1.65 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.29/1.65 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 1.29/1.65 'c_lessequals'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X )
% 1.29/1.65 , X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X )
% 1.29/1.65 , X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.29/1.65 ,
% 1.29/1.65 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.29/1.65 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.29/1.65 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.29/1.65 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ) ) ],
% 1.29/1.65 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.29/1.65 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.29/1.65 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ), ~( 'c_lessequals'(
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.29/1.65 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.29/1.65 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( X ) )
% 1.29/1.65 ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'(
% 1.29/1.65 'c_HOL_Oone__class_Oone'( X ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.29/1.65 ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'(
% 1.29/1.65 'c_HOL_Oone__class_Oone'( X ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.29/1.65 ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.29/1.65 ) ],
% 1.29/1.65 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ),
% 1.29/1.65 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'(
% 1.29/1.65 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Int_OPls',
% 1.29/1.65 'tc_Int_Oint' ) ) ],
% 1.29/1.65 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.29/1.65 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.29/1.65 , Z ), T ), X ), ~( 'c_lessequals'( Y, T, X ) ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 1.29/1.65 ,
% 1.29/1.65 [ =( hAPP( X, Y ), hAPP( Z, T ) ), ~( hBOOL( hAPP( hAPP( U, Y ), W ) ) )
% 1.29/1.65 , ~( 'c_Ring__and__Field_Oordered__idom'( V0, Z, W, V1, V2, U, V3, T, V4
% 1.29/1.65 , X, V5 ) ) ],
% 1.29/1.65 [ =( hAPP( X, Y ), Z ), ~( hBOOL( hAPP( hAPP( T, U ), Y ) ) ), ~(
% 1.29/1.65 'c_Ring__and__Field_Oordered__idom'( W, V0, U, V1, V2, T, V3, Z, V4, X,
% 1.29/1.65 V5 ) ) ],
% 1.29/1.65 [ ~( =( hAPP( X, Y ), hAPP( Z, T ) ) ), ~(
% 1.29/1.65 'c_Ring__and__Field_Oordered__idom'( U, Z, W, V0, V1, V2, V3, T, V4, X,
% 1.29/1.65 V5 ) ), hBOOL( hAPP( hAPP( V2, Y ), W ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.29/1.65 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.29/1.65 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.29/1.65 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.29/1.65 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.29/1.65 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ],
% 1.29/1.65 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.29/1.65 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ), ~(
% 1.29/1.65 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.29/1.65 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.29/1.65 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.29/1.65 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X ) ) ],
% 1.29/1.65 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.29/1.65 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X ), ~(
% 1.29/1.65 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.29/1.65 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ),
% 1.29/1.65 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.29/1.65 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ],
% 1.29/1.65 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ),
% 1.29/1.65 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ), ~(
% 1.29/1.65 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.29/1.65 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ),
% 1.29/1.65 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.29/1.65 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X ) ) ],
% 1.29/1.65 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ),
% 1.29/1.65 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X ), ~(
% 1.29/1.65 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.29/1.65 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.29/1.65 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.29/1.65 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ), ~(
% 1.29/1.65 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.29/1.65 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'(
% 1.29/1.65 X ), Y ), Z ), X ), ~( 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), Y,
% 1.29/1.65 X ) ) ],
% 1.29/1.65 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.29/1.65 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oabs__class_Oabs'( Y, X ), X ),
% 1.29/1.65 'c_HOL_Oabs__class_Oabs'( Y, X ) ) ],
% 1.29/1.65 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Suc'( X ) )
% 1.29/1.65 , Y ), 'c_Suc'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.29/1.65 Y ) ) ) ],
% 1.29/1.65 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), 'c_Suc'( Y
% 1.29/1.65 ) ), 'c_Suc'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y
% 1.29/1.65 ) ) ) ],
% 1.29/1.65 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.29/1.65 'c_HOL_Oabs__class_Oabs'( Y, X ), X ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.29/1.65 X ) ) ],
% 1.29/1.65 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, Y ),
% 1.29/1.65 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ) ), ~(
% 1.29/1.65 'c_Groebner__Basis_Ogb__semiring'( U, W, X, V0, V1, V2 ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.29/1.65 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.29/1.65 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.29/1.65 ), X ), ~( 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( T,
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.29/1.65 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.29/1.65 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.29/1.65 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.29/1.65 ), X ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.29/1.65 ), T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.29/1.65 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, hAPP( hAPP(
% 1.29/1.65 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X ),
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.29/1.65 ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.29/1.65 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.29/1.65 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.29/1.65 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.29/1.65 ), X ) ), ~( 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.29/1.65 X ), Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.29/1.65 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.29/1.65 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.29/1.65 , 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.29/1.65 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.29/1.65 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.29/1.65 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.29/1.65 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.29/1.65 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.29/1.65 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.29/1.65 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.29/1.65 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.29/1.65 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.29/1.65 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.29/1.65 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.29/1.65 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.29/1.65 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.29/1.65 , 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.29/1.65 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.29/1.65 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.29/1.65 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 1.29/1.65 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), hAPP(
% 1.29/1.65 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ) ) ],
% 1.29/1.65 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), X ), Y ),
% 1.29/1.65 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), Y ), X ) ) ]
% 1.29/1.65 ,
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.29/1.65 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.29/1.65 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 1.29/1.65 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.29/1.65 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.29/1.65 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.29/1.65 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.29/1.65 ), X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.29/1.65 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.29/1.65 ), X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'( Z,
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.29/1.65 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.29/1.65 ), X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'( Y,
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.29/1.65 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.29/1.65 ), X ) ) ],
% 1.29/1.65 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ), 'c_Suc'( U ) )
% 1.29/1.65 , hAPP( hAPP( Y, T ), hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T )
% 1.29/1.65 , U ) ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oring__1'( X ) ), =( hAPP( hAPP(
% 1.29/1.65 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X
% 1.29/1.65 ) ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.29/1.65 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ouminus__class_Ouminus'(
% 1.29/1.65 'c_HOL_Oone__class_Oone'( X ), X ) ), Z ) ), hAPP( hAPP(
% 1.29/1.65 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'( Y
% 1.29/1.65 , Z, X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.29/1.65 Z, X ) ), ~( 'c_lessequals'( 'c_HOL_Oinverse__class_Oinverse'( Z, X ),
% 1.29/1.65 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.29/1.65 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.29/1.65 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.29/1.65 'c_lessequals'( Z, Y, X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'( Y
% 1.29/1.65 , Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.29/1.65 ), X ) ), ~( 'c_lessequals'( 'c_HOL_Oinverse__class_Oinverse'( Z, X ),
% 1.29/1.65 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.29/1.65 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.29/1.65 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.29/1.65 'c_lessequals'( Z, Y, X ) ) ],
% 1.29/1.65 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), hAPP( hAPP( Y, Z ), U ) )
% 1.29/1.65 , hAPP( hAPP( Y, Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.29/1.65 , T ), U ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, Y, V0, V1, V2
% 1.29/1.65 ) ) ],
% 1.29/1.65 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.29/1.65 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ), =( Y
% 1.29/1.65 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, Z ) ],
% 1.29/1.65 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.29/1.65 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), =( X
% 1.29/1.65 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y, Z ) ],
% 1.29/1.65 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.29/1.65 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), =( Y
% 1.29/1.65 , Z ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.29/1.65 , Y ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.29/1.65 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), Y, X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.29/1.65 , X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.29/1.65 X ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.29/1.65 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), Y, X ) ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.29/1.65 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 1.29/1.65 X ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.29/1.65 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), Y, X ) ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.29/1.65 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 1.29/1.65 X ) ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.29/1.65 , ~( 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.29/1.65 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.29/1.65 ), Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( T,
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'( Z
% 1.29/1.65 , 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.29/1.65 , X ), ~( 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.29/1.65 X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP(
% 1.29/1.65 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.29/1.65 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Y
% 1.29/1.65 , Z, X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ) ],
% 1.29/1.65 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.29/1.65 ), ~( 'c_lessequals'( Y, Z, X ) ), =( Y, Z ) ],
% 1.29/1.65 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.29/1.65 ), =( Y, Z ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.29/1.65 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 1.29/1.65 ,
% 1.29/1.65 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.29/1.65 ), =( Y, Z ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.29/1.65 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.29/1.65 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.29/1.65 Z, Y, X ) ) ],
% 1.29/1.65 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.29/1.65 'c_HOL_Ouminus__class_Ouminus'( Z, X ), 'c_HOL_Ouminus__class_Ouminus'( Y
% 1.29/1.65 , X ), X ) ) ],
% 1.29/1.65 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_lessequals'( Y, Z, X ) )
% 1.29/1.65 , ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.29/1.65 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.29/1.65 , X ), 'c_lessequals'( Z, Y, X ) ],
% 1.29/1.65 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'( Y, Y, X ) )
% 1.29/1.65 , ~( 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ],
% 1.29/1.65 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Y
% 1.29/1.65 , X ), 'c_lessequals'( Y, Y, X ) ],
% 1.29/1.65 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.29/1.65 , Z, X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ],
% 1.29/1.65 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( Z, Y, X ) ],
% 1.29/1.65 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.29/1.65 , X ), 'c_lessequals'( Z, Y, X ) ],
% 1.29/1.65 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'( Y, Z, X ) )
% 1.29/1.65 , ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.29/1.65 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X )
% 1.29/1.65 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Z, X ), Y
% 1.29/1.65 , X ) ) ],
% 1.29/1.65 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X )
% 1.29/1.65 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Z, X ), Y
% 1.29/1.65 , X ) ) ],
% 1.29/1.65 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X )
% 1.29/1.65 , ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.29/1.65 , X ) ) ],
% 1.29/1.65 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X )
% 1.29/1.65 , ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.29/1.65 , X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.29/1.65 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oabs__class_Oabs'(
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), 'c_HOL_Oord__class_Oless'(
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.29/1.65 ), X ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.29/1.65 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.29/1.65 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( T,
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.29/1.65 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.29/1.65 ), X ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.29/1.65 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ),
% 1.29/1.65 ~( 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.29/1.65 , 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.29/1.65 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.29/1.65 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.29/1.65 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X
% 1.29/1.65 ), X ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.29/1.65 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ),
% 1.29/1.65 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X )
% 1.29/1.65 , 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.29/1.65 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.29/1.65 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.29/1.65 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.29/1.65 ), X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.29/1.65 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.29/1.65 ), X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( T,
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.29/1.65 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.29/1.65 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.29/1.65 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 'c_HOL_Oord__class_Oless'(
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.29/1.65 ), X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.29/1.65 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Oord__class_Oless'(
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.29/1.65 ), X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( T,
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP(
% 1.29/1.65 'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( Z ) ), X ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.29/1.65 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.29/1.65 'tc_nat' ) ), X ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.29/1.65 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP(
% 1.29/1.65 hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), X ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP(
% 1.29/1.65 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.29/1.65 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), X ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.29/1.65 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), T ), hAPP( hAPP(
% 1.29/1.65 'c_Power_Opower__class_Opower'( X ), Z ), T ), X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.29/1.65 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y
% 1.29/1.65 ), X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.29/1.65 ), Y ), Z ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), T ), Z ),
% 1.29/1.65 X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.29/1.65 , Z, 'tc_nat' ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y
% 1.29/1.65 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.29/1.65 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( Y ), X ), hAPP( hAPP(
% 1.29/1.65 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.29/1.65 X ), 'c_HOL_Oone__class_Oone'( X ) ), 'c_Int_Onumber__class_Onumber__of'(
% 1.29/1.65 Y, X ) ) ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.29/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.29/1.65 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', X ), X ),
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.29/1.65 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( Y ), X ), hAPP( hAPP(
% 1.29/1.65 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.29/1.65 X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ) ],
% 1.29/1.65 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.29/1.65 'c_HOL_Oplus__class_Oplus'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X
% 1.29/1.65 ) ), 'c_HOL_Oone__class_Oone'( X ) ), 'c_Int_Onumber__class_Onumber__of'(
% 1.29/1.65 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), Y ),
% 1.29/1.65 'c_Int_OBit1'( 'c_Int_OPls' ) ), X ) ) ],
% 1.29/1.65 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.29/1.65 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( hAPP( hAPP(
% 1.29/1.65 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), 'c_Int_OBit1'( 'c_Int_OPls'
% 1.29/1.65 ) ), Y ), X ) ) ],
% 1.29/1.65 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ),
% 1.29/1.65 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ) ) ]
% 1.29/1.65 ,
% 1.29/1.65 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ),
% 1.29/1.65 'tc_Int_Oint' ) ) ],
% 1.29/1.65 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ),
% 1.29/1.65 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ) ) ]
% 1.29/1.65 ,
% 1.29/1.65 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ),
% 1.29/1.65 'tc_Int_Oint' ) ) ],
% 1.29/1.65 [ ~( 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', 'c_Int_OPls',
% 1.29/1.65 'tc_Int_Oint' ) ) ],
% 1.29/1.65 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ),
% 1.29/1.65 'c_Int_OPls' ), X ), X ) ],
% 1.29/1.65 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), X ),
% 1.29/1.65 'c_Int_OPls' ), X ) ],
% 1.29/1.65 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.29/1.65 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.29/1.65 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.29/1.65 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.29/1.65 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), T ) ) ],
% 1.29/1.65 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.29/1.65 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Oone__class_Oone'(
% 1.29/1.65 'tc_nat' ) ), Y ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.29/1.65 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Oone__class_Oone'(
% 1.29/1.65 'tc_nat' ) ), Y ) ],
% 1.29/1.65 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.29/1.65 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.29/1.65 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), Y ), hAPP( hAPP(
% 1.29/1.65 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.29/1.65 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.29/1.65 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.29/1.65 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y )
% 1.29/1.65 , 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 1.29/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.29/1.65 'c_HOL_Oinverse__class_Oinverse'( hAPP( hAPP(
% 1.29/1.65 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), hAPP( hAPP(
% 1.29/1.65 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y
% 1.29/1.65 , X ) ), Z ) ) ],
% 1.29/1.65 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =( hAPP( hAPP(
% 1.29/1.65 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.29/1.65 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.29/1.65 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.29/1.65 'c_Power_Opower__class_Opower'( X ), Y ), T ) ), hAPP( hAPP(
% 1.29/1.65 'c_Power_Opower__class_Opower'( X ), Z ), T ) ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.29/1.65 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.29/1.65 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.29/1.65 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.29/1.65 'c_Power_Opower__class_Opower'( X ), Y ), T ) ), hAPP( hAPP(
% 1.29/1.65 'c_Power_Opower__class_Opower'( X ), Z ), T ) ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oring__1__no__zero__divisors'( X ) ), ~(
% 1.29/1.65 =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ),
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.29/1.65 ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.29/1.65 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.29/1.65 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.29/1.65 ), ~( =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ),
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.29/1.65 ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.29/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.29/1.65 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.29/1.65 Z, X ) ), T ), 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.29/1.65 'c_Power_Opower__class_Opower'( X ), Y ), T ), hAPP( hAPP(
% 1.29/1.65 'c_Power_Opower__class_Opower'( X ), Z ), T ), X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.29/1.65 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.29/1.65 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.29/1.65 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.29/1.65 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.29/1.65 'c_HOL_Oabs__class_Oabs'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X )
% 1.29/1.65 , Y ), Z ), X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ),
% 1.29/1.65 'c_HOL_Oabs__class_Oabs'( Y, X ) ), Z ) ) ],
% 1.29/1.65 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.29/1.65 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.29/1.65 , X ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) )
% 1.29/1.65 ],
% 1.29/1.65 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.29/1.65 'tc_nat' ), Z ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.29/1.65 , Z ), Y ), 'tc_nat' ) ) ],
% 1.29/1.65 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.29/1.65 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.29/1.65 , Z ), Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) )
% 1.29/1.65 ],
% 1.29/1.65 [ ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.29/1.65 'tc_nat' ), X ), Y ), X, 'tc_nat' ) ) ],
% 1.29/1.65 [ ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.29/1.65 'tc_nat' ), X ), Y ), Y, 'tc_nat' ) ) ],
% 1.29/1.65 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 1.29/1.65 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.29/1.65 'tc_nat' ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.29/1.65 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.29/1.65 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.29/1.65 , Z ), T ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, T, 'tc_nat' ) )
% 1.29/1.65 , ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 1.29/1.65 [ =( X, Y ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ],
% 1.29/1.65 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_Suc'( X ), 'tc_nat' ) )
% 1.29/1.65 , 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ],
% 1.29/1.65 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) )
% 1.29/1.65 , 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ],
% 1.29/1.65 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.29/1.65 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ) ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'(
% 1.29/1.65 X, T, 'tc_nat' ) ],
% 1.29/1.65 [ ~( 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.29/1.65 ), 'tc_nat' ) ) ],
% 1.29/1.65 [ ~( 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.29/1.65 ), 'tc_nat' ) ) ],
% 1.29/1.65 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ],
% 1.29/1.65 [ ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( Y, 'c_Suc'( X ), 'tc_nat' ) ) ],
% 1.29/1.65 [ 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 1.29/1.65 X, 'c_Suc'( X ), 'tc_nat' ) ],
% 1.29/1.65 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ) ) ],
% 1.29/1.65 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.29/1.65 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.29/1.65 'tc_nat' ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.29/1.65 ), Z ), Y ), 'tc_nat' ) ) ],
% 1.29/1.65 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.29/1.65 'tc_nat' ), X ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.29/1.65 ), Y ), Z ), 'tc_nat' ) ) ],
% 1.29/1.65 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ],
% 1.29/1.65 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ],
% 1.29/1.65 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 1.29/1.65 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.29/1.65 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 1.29/1.65 'tc_nat' ) ) ],
% 1.29/1.65 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.29/1.65 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z,
% 1.29/1.65 'tc_nat' ) ) ],
% 1.29/1.65 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.29/1.65 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ) ],
% 1.29/1.65 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.29/1.65 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 1.29/1.65 'tc_nat' ) ) ],
% 1.29/1.65 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.29/1.65 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z,
% 1.29/1.65 'tc_nat' ) ) ],
% 1.29/1.65 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ), =( 'c_Suc'( X
% 1.29/1.65 ), Y ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.29/1.65 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.29/1.65 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ) ) ]
% 1.29/1.65 ,
% 1.29/1.65 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.29/1.65 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ),
% 1.29/1.65 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ) ) ]
% 1.29/1.65 ,
% 1.29/1.65 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ),
% 1.29/1.65 'tc_Int_Oint' ) ) ],
% 1.29/1.65 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ),
% 1.29/1.65 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ) ) ]
% 1.29/1.65 ,
% 1.29/1.65 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ),
% 1.29/1.65 'tc_Int_Oint' ) ) ],
% 1.29/1.65 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ),
% 1.29/1.65 'c_Int_OBit0'( X ) ), 'c_Int_OBit0'( Y ) ), 'c_Int_OBit0'( hAPP( hAPP(
% 1.29/1.65 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), X ), Y ) ) ) ],
% 1.29/1.65 [ =( 'c_Int_OBit0'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.29/1.65 'tc_Int_Oint' ), X ), X ) ) ],
% 1.29/1.65 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( X, Y ), hAPP(
% 1.29/1.65 hAPP( 'c_Power_Opower_Opower'( T, U, W ), Z ), 'c_Suc'( hAPP( hAPP(
% 1.29/1.65 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.29/1.65 'c_Int_OPls' ) ), 'tc_nat' ) ), V0 ) ) ) ) ) ), ~(
% 1.29/1.65 'c_Ring__and__Field_Oordered__idom'( V1, V2, Y, V3, X, V4, V5, T, U, V6,
% 1.29/1.65 W ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.29/1.65 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.29/1.65 X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP(
% 1.29/1.65 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.29/1.65 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.29/1.65 X ) ), 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.29/1.65 , ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.29/1.65 X ), Y ), T ), Z, X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.29/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.29/1.65 'class_Int_Onumber'( X ) ), =( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.29/1.65 , 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.29/1.65 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.29/1.65 , X ) ), Z ), Z, X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.29/1.65 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oone__class_Oone'( X ),
% 1.29/1.65 X ), ~( 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.29/1.65 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), hAPP( hAPP(
% 1.29/1.65 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.29/1.65 X ), 'c_HOL_Oone__class_Oone'( X ) ), 'c_HOL_Oone__class_Oone'( X ) ) ),
% 1.29/1.65 Y ) ) ],
% 1.29/1.65 [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ],
% 1.29/1.65 [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ],
% 1.29/1.65 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.29/1.65 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.29/1.65 'c_HOL_Oabs__class_Oabs'( Y, X ), X ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.29/1.65 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.29/1.65 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.29/1.65 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.29/1.65 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.29/1.65 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( T,
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.29/1.65 hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.29/1.65 [ =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'c_Suc'(
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.29/1.65 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.29/1.65 'c_lessequals'( Y, 'c_HOL_Oabs__class_Oabs'( Y, X ), X ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.29/1.65 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.29/1.65 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.29/1.65 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.29/1.65 , 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.29/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.29/1.65 'class_Int_Onumber'( X ) ), =( Y, hAPP( hAPP(
% 1.29/1.65 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ), =(
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.29/1.65 ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.29/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.29/1.65 'class_Int_Onumber'( X ) ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.29/1.65 X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y ), =(
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.29/1.65 ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.29/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( hAPP(
% 1.29/1.65 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.29/1.65 ), Y ), Y, X ) ) ],
% 1.29/1.65 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.29/1.65 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ],
% 1.29/1.65 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.29/1.65 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( X,
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.29/1.65 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.29/1.65 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( Y, 'c_Suc'(
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_Suc'(
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.29/1.65 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =( hAPP( hAPP(
% 1.29/1.65 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X
% 1.29/1.65 ) ) ), =( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z ) ],
% 1.29/1.65 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =( hAPP( hAPP(
% 1.29/1.65 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X
% 1.29/1.65 ) ) ), =( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 1.29/1.65 'c_Nat_Osemiring__1__class_Oof__nat'( hAPP( hAPP(
% 1.29/1.65 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ), X ), hAPP( hAPP(
% 1.29/1.65 'c_HOL_Otimes__class_Otimes'( X ), 'c_Nat_Osemiring__1__class_Oof__nat'(
% 1.29/1.65 Y, X ) ), 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ) ) ) ],
% 1.29/1.65 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.29/1.65 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.29/1.65 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.29/1.65 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.29/1.65 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), T ) ), hAPP( hAPP(
% 1.29/1.65 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ) ), =( Y, T ), =( X
% 1.29/1.65 , Z ) ],
% 1.29/1.65 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.29/1.65 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.29/1.65 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.29/1.65 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.29/1.65 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), T ) ), hAPP( hAPP(
% 1.29/1.65 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ) ), =( Y, T ), =( X
% 1.29/1.65 , Z ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.29/1.65 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.29/1.65 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.29/1.65 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.29/1.65 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.29/1.65 X ), Y ), U ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.29/1.65 ) ) ), =( Z, U ), =( Y, T ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.29/1.65 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.29/1.65 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.29/1.65 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.29/1.65 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.29/1.65 X ), Y ), U ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.29/1.65 ) ) ), =( Z, U ), =( Y, T ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP( hAPP(
% 1.29/1.65 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oabs__class_Oabs'( Y, X ) ),
% 1.29/1.65 'c_HOL_Oabs__class_Oabs'( Y, X ) ), hAPP( hAPP(
% 1.29/1.65 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 1.29/1.65 'c_HOL_Oinverse__class_Oinverse'( hAPP( hAPP(
% 1.29/1.65 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), hAPP( hAPP(
% 1.29/1.65 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y
% 1.29/1.65 , X ) ), Z ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 1.29/1.65 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.29/1.65 , X ), 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oinverse__class_Oinverse'(
% 1.29/1.65 Y, X ), X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.29/1.65 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.29/1.65 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Z
% 1.29/1.65 , X ) ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( T,
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.29/1.65 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.29/1.65 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.29/1.65 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.29/1.65 ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.29/1.65 [ ~( =( X, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y
% 1.29/1.65 ) ) ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 1.29/1.65 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.29/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.29/1.65 'class_Int_Onumber'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( hAPP(
% 1.29/1.65 hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), Z ), Z, X ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), =( Z,
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.29/1.65 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.29/1.65 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.29/1.65 ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.29/1.65 , 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.29/1.65 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.29/1.65 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.29/1.65 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.29/1.65 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, hAPP( hAPP(
% 1.29/1.65 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Z
% 1.29/1.65 , X ) ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( T,
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_lessequals'(
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.29/1.65 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.29/1.65 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.29/1.65 ) ), 'c_HOL_Oinverse__class_Odivide'( T, U, X ) ),
% 1.29/1.65 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.29/1.65 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), U ) ), hAPP(
% 1.29/1.65 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ), hAPP( hAPP(
% 1.29/1.65 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ), X ) ), =( U,
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.29/1.65 ) ],
% 1.29/1.65 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_Suc'(
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_Suc'(
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_Suc'(
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.29/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( Y, hAPP( hAPP(
% 1.29/1.65 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z
% 1.29/1.65 , X ) ), Z ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.29/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.29/1.65 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z
% 1.29/1.65 , X ) ), Z ), Y ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ), X ) ]
% 1.29/1.65 ,
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.29/1.65 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.29/1.65 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.29/1.65 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.29/1.65 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.29/1.65 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.29/1.65 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.29/1.65 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.29/1.65 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.29/1.65 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.29/1.65 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.29/1.65 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.29/1.65 'tc_nat' ) ) ],
% 1.29/1.65 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), 'c_HOL_Ozero__class_Ozero'(
% 1.29/1.65 'tc_nat' ) ) ],
% 1.29/1.65 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.29/1.65 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.29/1.65 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.29/1.65 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.29/1.65 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.29/1.65 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.29/1.65 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.29/1.65 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =( hAPP( hAPP(
% 1.29/1.65 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.29/1.65 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =( hAPP( hAPP(
% 1.29/1.65 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.29/1.65 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =( hAPP(
% 1.29/1.65 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.29/1.65 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =( hAPP(
% 1.29/1.65 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.29/1.65 X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.29/1.65 'c_HOL_Oabs__class_Oabs'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X )
% 1.29/1.65 , 'c_HOL_Ouminus__class_Ouminus'( Y, X ) ), Z ), X ),
% 1.29/1.65 'c_HOL_Oabs__class_Oabs'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X )
% 1.29/1.65 , Y ), Z ), X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.29/1.65 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.29/1.65 X ), Y ), Z ) ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP(
% 1.29/1.65 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Oone__class_Oone'( X )
% 1.29/1.65 ) ), Z ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.29/1.65 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.29/1.65 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ), hAPP( hAPP(
% 1.29/1.65 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.29/1.65 X ), Z ), 'c_HOL_Oone__class_Oone'( X ) ) ), Y ) ) ],
% 1.29/1.65 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.29/1.65 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.29/1.65 'c_HOL_Oplus__class_Oplus'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.29/1.65 Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.29/1.65 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.29/1.65 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.29/1.65 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.29/1.65 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), ~( 'class_Int_Onumber'(
% 1.29/1.65 X ) ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.29/1.65 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( T, X ) ), hAPP( hAPP(
% 1.29/1.65 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.29/1.65 X ), Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ), hAPP( hAPP(
% 1.29/1.65 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =( Y,
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_Int_Oiszero'( Y, X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP( hAPP(
% 1.29/1.65 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oabs__class_Oabs'( Y, X ) ), Z
% 1.29/1.65 ), 'c_HOL_Oabs__class_Oabs'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.29/1.65 ), Y ), Z ), X ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.29/1.65 Z, X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.29/1.65 'c_HOL_Oone__class_Oone'( X ), X ), ~( 'c_lessequals'(
% 1.29/1.65 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.29/1.65 X ) ) ],
% 1.29/1.65 [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.29/1.65 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Suc'(
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.29/1.65 'tc_nat' ) ) ) ],
% 1.29/1.65 [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_Int_Oint' ) ) ],
% 1.29/1.65 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.29/1.65 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.29/1.65 ,
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 1.29/1.65 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'(
% 1.29/1.65 X ), X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.29/1.65 [ =( hAPP( hAPP( X, Y ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), Y ),
% 1.29/1.65 ~( 'c_Groebner__Basis_Ogb__semiring'( Z, T, X, U, W, V0 ) ) ],
% 1.29/1.65 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.29/1.65 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X ) )
% 1.29/1.65 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ), Z ) ],
% 1.29/1.65 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.29/1.65 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X ) )
% 1.29/1.65 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), Z ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.29/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.29/1.65 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oone__class_Oone'( X ), X ),
% 1.29/1.65 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.29/1.65 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.29/1.65 ,
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 1.29/1.65 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oone__class_Oone'( X ), X ),
% 1.29/1.65 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.29/1.65 ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ),
% 1.29/1.65 ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.29/1.65 ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.29/1.65 ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.29/1.65 [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.29/1.65 [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.29/1.65 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.29/1.65 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ), ~( 'c_lessequals'( U, Z
% 1.29/1.65 , X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), U
% 1.29/1.65 , X ) ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'(
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.29/1.65 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( 'c_lessequals'(
% 1.29/1.65 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.29/1.65 , X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.29/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.29/1.65 'class_Int_Onumber'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( hAPP(
% 1.29/1.65 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.29/1.65 ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.29/1.65 'c_HOL_Oone__class_Oone'( X ), X ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.29/1.65 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.29/1.65 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.29/1.65 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.29/1.65 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.29/1.65 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ouminus__class_Ouminus'(
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.29/1.65 Y, Z, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ),
% 1.29/1.65 ~( 'c_lessequals'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.29/1.65 'c_Suc'( T ) ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.29/1.65 'c_Suc'( T ) ), X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.29/1.65 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X )
% 1.29/1.65 , 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.29/1.65 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.29/1.65 'tc_nat' ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 1.29/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( =(
% 1.29/1.65 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.29/1.65 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~( =(
% 1.29/1.65 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.29/1.65 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.29/1.65 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X )
% 1.29/1.65 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ]
% 1.29/1.65 ,
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.29/1.65 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X )
% 1.29/1.65 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) )
% 1.29/1.65 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.29/1.65 'c_lessequals'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ]
% 1.29/1.65 ,
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.29/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.29/1.65 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.29/1.65 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =(
% 1.29/1.65 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( Y
% 1.29/1.65 , X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.29/1.65 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.29/1.65 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.29/1.65 'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( Z ) ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.29/1.65 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.29/1.65 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), Y ), hAPP( hAPP(
% 1.29/1.65 'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( Z ) ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP( hAPP(
% 1.29/1.65 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.29/1.65 ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.29/1.65 'c_HOL_Ouminus__class_Ouminus'( Z, X ) ) ) ],
% 1.29/1.65 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( 'c_Power_Opower_Opower'( Y, Z, T ),
% 1.29/1.65 U ), 'c_Suc'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.29/1.65 'c_Int_OPls' ) ), 'tc_nat' ) ), W ) ) ) ), V0 ) ), ~( hBOOL( hAPP( hAPP(
% 1.29/1.65 X, U ), V0 ) ) ), ~( 'c_Ring__and__Field_Oordered__idom'( V1, V2, V0, V3
% 1.29/1.65 , V4, X, V5, Y, Z, V6, T ) ) ],
% 1.29/1.65 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.29/1.65 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.29/1.65 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), hAPP( hAPP(
% 1.29/1.65 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.29/1.65 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), hAPP( hAPP(
% 1.29/1.65 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.29/1.65 'c_HOL_Oplus__class_Oplus'( X ), X ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.29/1.65 ), Z ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.29/1.65 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ],
% 1.29/1.65 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.29/1.65 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.29/1.65 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.29/1.65 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.29/1.65 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ) ), Y ) ) ],
% 1.29/1.65 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( Y, 'c_Int_OPls', 'tc_Int_Oint' ) ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( X, 'c_Int_OPls', 'tc_Int_Oint' ) ],
% 1.29/1.65 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( X, 'c_Int_OPls', 'tc_Int_Oint' ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.29/1.65 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.29/1.65 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.29/1.65 ), =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ),
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.29/1.65 , 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ), =(
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.29/1.65 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.29/1.65 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ) ), =( 'c_Int_Onumber__class_Onumber__of'(
% 1.29/1.65 Y, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_lessequals'( Y,
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.29/1.65 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ),
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.29/1.65 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.29/1.65 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.29/1.65 ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( =( hAPP( hAPP(
% 1.29/1.65 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =( hAPP( hAPP(
% 1.29/1.65 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ouminus__class_Ouminus'(
% 1.29/1.65 'c_HOL_Oone__class_Oone'( X ), X ) ), 'c_Suc'( hAPP( hAPP(
% 1.29/1.65 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.29/1.65 'c_Int_OPls' ) ), 'tc_nat' ) ), Y ) ) ), 'c_HOL_Ouminus__class_Ouminus'(
% 1.29/1.65 'c_HOL_Oone__class_Oone'( X ), X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.29/1.65 'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( hAPP( hAPP(
% 1.29/1.65 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.29/1.65 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ), X ) ) ],
% 1.29/1.65 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( 'c_Power_Opower_Opower'( Z, T,
% 1.29/1.65 U ), W ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.29/1.65 'c_Int_OPls' ) ), 'tc_nat' ) ), V0 ) ) ) ), ~(
% 1.29/1.65 'c_Ring__and__Field_Oordered__idom'( V1, V2, Y, V3, X, V4, V5, Z, T, V6,
% 1.29/1.65 U ) ) ],
% 1.29/1.65 [ =( hAPP( hAPP( X, Y ), 'c_Suc'( hAPP( hAPP(
% 1.29/1.65 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.29/1.65 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ), hAPP( hAPP( T, Y ), hAPP( hAPP(
% 1.29/1.65 T, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, Y ), Z ) ) ) ), ~(
% 1.29/1.65 'c_Groebner__Basis_Ogb__semiring'( U, T, X, W, V0, V1 ) ) ],
% 1.29/1.65 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.29/1.65 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.29/1.65 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.29/1.65 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.29/1.65 ), Y ), Y ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.29/1.65 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.29/1.65 ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_Int_OPls', 'tc_Int_Oint' ) )
% 1.29/1.65 ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.29/1.65 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.29/1.65 'c_Int_OPls', 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.29/1.65 ), X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.29/1.65 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X
% 1.29/1.65 ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', Y, 'tc_Int_Oint' ) )
% 1.29/1.65 ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.29/1.65 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'( 'c_Int_OPls'
% 1.29/1.65 , Y, 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X
% 1.29/1.65 ), X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.29/1.65 ), Y ), Z ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), T ),
% 1.29/1.65 X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X )
% 1.29/1.65 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.29/1.65 ), ~( 'c_HOL_Oord__class_Oless'( T, Z, 'tc_nat' ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP(
% 1.29/1.65 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.29/1.65 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X )
% 1.29/1.65 , Y, X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.29/1.65 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ), X ) ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =(
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Oord__class_Oless'(
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.29/1.65 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ), X ) ],
% 1.29/1.65 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ),
% 1.29/1.65 'tc_nat' ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.29/1.65 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.29/1.65 'c_Int_OPls' ) ), 'tc_nat' ), 'c_Suc'( 'c_Suc'( 'c_Suc'(
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ) ],
% 1.29/1.65 [ =( 'c_Suc'( 'c_Suc'( 'c_Suc'( X ) ) ), hAPP( hAPP(
% 1.29/1.65 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.29/1.65 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ) ],
% 1.29/1.65 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ), 'tc_nat' ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', X, 'tc_Int_Oint' ) ) ],
% 1.29/1.65 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', X, 'tc_Int_Oint' ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.29/1.65 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.29/1.65 'c_HOL_Oone__class_Oone'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.29/1.65 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), X ), X ), X ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.29/1.65 'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( hAPP( hAPP(
% 1.29/1.65 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.29/1.65 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ), hAPP( hAPP(
% 1.29/1.65 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.29/1.65 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.29/1.65 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.29/1.65 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.29/1.65 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.29/1.65 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.29/1.65 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.29/1.65 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.29/1.65 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.29/1.65 ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.29/1.65 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.29/1.65 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.29/1.65 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.29/1.65 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.29/1.65 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.29/1.65 ],
% 1.29/1.65 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.29/1.65 'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( hAPP( hAPP(
% 1.29/1.65 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.29/1.65 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ), hAPP( hAPP(
% 1.29/1.65 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.29/1.65 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.29/1.65 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.29/1.65 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =( hAPP( hAPP(
% 1.29/1.65 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ouminus__class_Ouminus'(
% 1.29/1.65 'c_HOL_Oone__class_Oone'( X ), X ) ), hAPP( hAPP(
% 1.29/1.65 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.29/1.65 'c_Int_OPls' ) ), 'tc_nat' ) ), Y ) ), 'c_HOL_Oone__class_Oone'( X ) ) ]
% 1.29/1.65 ,
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.29/1.65 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.29/1.65 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.29/1.65 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), X ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.29/1.65 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.29/1.65 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.29/1.65 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.29/1.65 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.29/1.65 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ]
% 1.29/1.65 ,
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.29/1.65 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.29/1.65 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.29/1.65 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.29/1.65 ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.29/1.65 X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.29/1.65 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.29/1.65 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.29/1.65 'c_Int_OPls' ) ), 'tc_nat' ) ) ), X ) ],
% 1.29/1.65 [ =( 'c_FFT__Mirabelle_OIFFT'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X
% 1.29/1.65 ), X ) ],
% 1.29/1.65 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'class_Int_Onumber'( X ) ),
% 1.29/1.65 'c_lessequals'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ],
% 1.29/1.65 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'class_Int_Onumber'( X ) ),
% 1.29/1.65 ~( 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.29/1.65 , 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ), ~( 'c_lessequals'(
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.29/1.65 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z,
% 1.29/1.65 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.29/1.65 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_Int_Oint' ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =( hAPP( hAPP(
% 1.29/1.65 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.29/1.65 'c_Power_Opower__class_Opower'( X ), Y ), T ) ) ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ), =( Z
% 1.29/1.65 , T ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.29/1.65 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.29/1.65 ,
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.29/1.65 ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 1.29/1.65 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.29/1.65 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 1.29/1.65 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.29/1.65 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Oone__class_Oone'( X )
% 1.29/1.65 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_Int_OBit1'( 'c_Int_OPls' ),
% 1.29/1.65 'tc_Int_Oint' ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.29/1.65 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.29/1.65 'c_Int_OBit1'( 'c_Int_OPls' ), 'tc_Int_Oint' ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.29/1.65 'c_HOL_Oone__class_Oone'( X ), X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.29/1.65 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.29/1.65 'c_HOL_Oone__class_Oone'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.29/1.65 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( 'c_Int_OPls' ), Y,
% 1.29/1.65 'tc_Int_Oint' ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.29/1.65 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.29/1.65 'c_Int_OBit1'( 'c_Int_OPls' ), Y, 'tc_Int_Oint' ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.29/1.65 [ ~( 'class_Int_Oring__char__0'( X ) ), ~( 'class_Int_Onumber__ring'( X
% 1.29/1.65 ) ), ~( 'c_Int_Oiszero'( 'c_Int_Onumber__class_Onumber__of'(
% 1.29/1.65 'c_Int_OBit1'( Y ), X ), X ) ) ],
% 1.29/1.65 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Ozero__class_Ozero'( X
% 1.29/1.65 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', X ) ) ],
% 1.29/1.65 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', X ),
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.29/1.65 [ ~( 'class_Int_Onumber__ring'( X ) ), 'c_Int_Oiszero'(
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', X ), X ) ],
% 1.29/1.65 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.29/1.65 'c_HOL_Oplus__class_Oplus'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.29/1.65 'c_Int_OPls', X ) ), Y ), Y ) ],
% 1.29/1.65 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.29/1.65 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_Int_Onumber__class_Onumber__of'(
% 1.29/1.65 'c_Int_OPls', X ) ), Y ) ],
% 1.29/1.65 [ ~( 'class_Int_Oring__char__0'( X ) ), ~( 'class_Int_Onumber__ring'( X
% 1.29/1.65 ) ), 'c_Int_Oiszero'( 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.29/1.65 ~( 'c_Int_Oiszero'( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( Y
% 1.29/1.65 ), X ), X ) ) ],
% 1.29/1.65 [ ~( 'class_Int_Oring__char__0'( X ) ), ~( 'class_Int_Onumber__ring'( X
% 1.29/1.65 ) ), 'c_Int_Oiszero'( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.29/1.65 Y ), X ), X ), ~( 'c_Int_Oiszero'( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.29/1.65 , X ), X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.29/1.65 ), Y ), 'c_Suc'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.29/1.65 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.29/1.65 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.29/1.65 X ) ) ],
% 1.29/1.65 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.29/1.65 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.29/1.65 'c_HOL_Oone__class_Oone'( X ) ), 'c_Int_Onumber__class_Onumber__of'(
% 1.29/1.65 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), X ) ) ],
% 1.29/1.65 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.29/1.65 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.29/1.65 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), X ) ), Y ), hAPP( hAPP(
% 1.29/1.65 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ) ) ],
% 1.29/1.65 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.29/1.65 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.29/1.65 'c_Int_OPls' ) ), X ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y )
% 1.29/1.65 , Y ) ) ],
% 1.29/1.65 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OPls',
% 1.29/1.65 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Int_OPls',
% 1.29/1.65 'tc_Int_Oint' ) ) ],
% 1.29/1.65 [ 'c_HOL_Oord__class_Oless'( X, 'c_Int_OPls', 'tc_Int_Oint' ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OPls',
% 1.29/1.65 'tc_Int_Oint' ) ) ],
% 1.29/1.65 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ),
% 1.29/1.65 'c_Int_OBit1'( X ) ), 'c_Int_OBit0'( Y ) ), 'c_Int_OBit1'( hAPP( hAPP(
% 1.29/1.65 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), X ), Y ) ) ) ],
% 1.29/1.65 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ),
% 1.29/1.65 'c_Int_OBit0'( X ) ), 'c_Int_OBit1'( Y ) ), 'c_Int_OBit1'( hAPP( hAPP(
% 1.29/1.65 'c_HOL_Oplus__class_Oplus'( 'tc_Int_Oint' ), X ), Y ) ) ) ],
% 1.29/1.65 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OBit0'( Y ),
% 1.29/1.65 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ) ) ]
% 1.29/1.65 ,
% 1.29/1.65 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OBit0'( Y ),
% 1.29/1.65 'tc_Int_Oint' ) ) ],
% 1.29/1.65 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OBit0'( Y ),
% 1.29/1.65 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ) ) ]
% 1.29/1.65 ,
% 1.29/1.65 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OBit0'( Y ),
% 1.29/1.65 'tc_Int_Oint' ) ) ],
% 1.29/1.65 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', 'c_Int_OBit0'( X ),
% 1.29/1.65 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', X,
% 1.29/1.65 'tc_Int_Oint' ) ) ],
% 1.29/1.65 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', X, 'tc_Int_Oint' ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', 'c_Int_OBit0'( X ),
% 1.29/1.65 'tc_Int_Oint' ) ) ],
% 1.29/1.65 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OBit0'( X ), 'c_Int_OPls',
% 1.29/1.65 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Int_OPls',
% 1.29/1.65 'tc_Int_Oint' ) ) ],
% 1.29/1.65 [ 'c_HOL_Oord__class_Oless'( X, 'c_Int_OPls', 'tc_Int_Oint' ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_Int_OBit0'( X ), 'c_Int_OPls',
% 1.29/1.65 'tc_Int_Oint' ) ) ],
% 1.29/1.65 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.29/1.65 'c_Int_OPls' ) ), 'tc_nat' ), 'c_Suc'( 'c_Suc'(
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.29/1.65 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.29/1.65 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.29/1.65 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), hAPP( hAPP( T, hAPP(
% 1.29/1.65 hAPP( X, Y ), Z ) ), hAPP( hAPP( X, Y ), Z ) ) ), ~(
% 1.29/1.65 'c_Groebner__Basis_Ogb__semiring'( U, T, X, W, V0, V1 ) ) ],
% 1.29/1.65 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( 'c_Power_Opower_Opower'( Z, T,
% 1.29/1.65 U ), W ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.29/1.65 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), =( W, Y ), ~(
% 1.29/1.65 'c_Ring__and__Field_Oordered__idom'( V0, V1, Y, V2, V3, X, V4, Z, T, V5,
% 1.29/1.65 U ) ) ],
% 1.29/1.65 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, hAPP( hAPP(
% 1.29/1.65 'c_Power_Opower_Opower'( T, U, W ), V0 ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.29/1.65 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( T
% 1.29/1.65 , U, W ), V1 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.29/1.65 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ), =( V1, Y ), ~(
% 1.29/1.65 'c_Ring__and__Field_Oordered__idom'( V2, V3, Y, Z, V4, X, V5, T, U, V6, W
% 1.29/1.65 ) ) ],
% 1.29/1.65 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, hAPP( hAPP(
% 1.29/1.65 'c_Power_Opower_Opower'( T, U, W ), V0 ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.29/1.65 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( T
% 1.29/1.65 , U, W ), V1 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.29/1.65 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ), =( V0, Y ), ~(
% 1.29/1.65 'c_Ring__and__Field_Oordered__idom'( V2, V3, Y, Z, V4, X, V5, T, U, V6, W
% 1.29/1.65 ) ) ],
% 1.29/1.65 [ ~( hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, hAPP( hAPP(
% 1.29/1.65 'c_Power_Opower_Opower'( T, U, W ), Y ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.29/1.65 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( T
% 1.29/1.65 , U, W ), Y ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.29/1.65 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ) ), ~(
% 1.29/1.65 'c_Ring__and__Field_Oordered__idom'( V0, V1, Y, Z, V2, X, V3, T, U, V4, W
% 1.29/1.65 ) ) ],
% 1.29/1.65 [ ~( hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, hAPP( hAPP(
% 1.29/1.65 'c_Power_Opower_Opower'( Z, T, U ), W ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.29/1.65 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( Z
% 1.29/1.65 , T, U ), V0 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.29/1.65 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), V1 ) ) ), ~(
% 1.29/1.65 'c_Ring__and__Field_Oordered__idom'( V2, V3, V1, Y, V4, X, V5, Z, T, V6,
% 1.29/1.65 U ) ) ],
% 1.29/1.65 [ ~( hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( 'c_Power_Opower_Opower'( Z,
% 1.29/1.65 T, U ), Y ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.29/1.65 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ), ~(
% 1.29/1.65 'c_Ring__and__Field_Oordered__idom'( W, V0, Y, V1, V2, X, V3, Z, T, V4, U
% 1.29/1.65 ) ) ],
% 1.29/1.65 [ ~( hBOOL( hAPP( hAPP( X, hAPP( hAPP( 'c_Power_Opower_Opower'( Y, Z, T
% 1.29/1.65 ), U ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.29/1.65 'c_Int_OPls' ) ), 'tc_nat' ) ) ), W ) ) ), ~(
% 1.29/1.65 'c_Ring__and__Field_Oordered__idom'( V0, V1, W, V2, V3, X, V4, Y, Z, V5,
% 1.29/1.65 T ) ) ],
% 1.29/1.65 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.29/1.65 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'(
% 1.29/1.65 'tc_nat' ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.29/1.65 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ],
% 1.29/1.65 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.29/1.65 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), 'c_Suc'( 'c_Suc'( X ) ) ) ],
% 1.29/1.65 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.29/1.65 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_Suc'( 'c_Suc'( X ) ) ) ],
% 1.29/1.65 [ ~( 'c_Ring__and__Field_Oordered__idom'( X, Y, Z, T, U, W, V0, V1, V2,
% 1.29/1.65 V3, V4 ) ), =( hAPP( hAPP( T, hAPP( hAPP( 'c_Power_Opower_Opower'( V1, V2
% 1.29/1.65 , V4 ), Z ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.29/1.65 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.29/1.65 'c_Power_Opower_Opower'( V1, V2, V4 ), Z ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.29/1.65 'c_Int_OPls' ) ), 'tc_nat' ) ) ), Z ) ],
% 1.29/1.65 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), hAPP( T, U ) ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.29/1.65 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y
% 1.29/1.65 , Z ), U ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.29/1.65 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ), ~(
% 1.29/1.65 'c_Ring__and__Field_Oordered__idom'( W, V0, V1, V2, V3, V4, T, X, Y, V5,
% 1.29/1.65 Z ) ) ],
% 1.29/1.65 [ =( hAPP( X, hAPP( hAPP( 'c_Power_Opower_Opower'( Y, Z, T ), U ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.29/1.65 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( Y
% 1.29/1.65 , Z, T ), U ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.29/1.65 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ), ~(
% 1.29/1.65 'c_Ring__and__Field_Oordered__idom'( W, V0, V1, V2, V3, V4, X, Y, Z, V5,
% 1.29/1.65 T ) ) ],
% 1.29/1.65 [ ~( 'c_Ring__and__Field_Oordered__idom'( X, Y, hAPP( hAPP(
% 1.29/1.65 'c_Power_Opower_Opower'( Z, T, U ), W ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.29/1.65 'c_Int_OPls' ) ), 'tc_nat' ) ), V0, V1, V2, V3, Z, T, V4, U ) ), =( W,
% 1.29/1.65 hAPP( hAPP( 'c_Power_Opower_Opower'( Z, T, U ), W ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.29/1.65 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ],
% 1.29/1.65 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( 'c_Power_Opower_Opower'( Z, T,
% 1.29/1.65 U ), W ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.29/1.65 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), ~(
% 1.29/1.65 'c_Ring__and__Field_Oordered__idom'( V0, V1, Y, V2, X, V3, V4, Z, T, V5,
% 1.29/1.65 U ) ) ],
% 1.29/1.65 [ ~( 'c_Ring__and__Field_Oordered__idom'( X, Y, Z, T, U, W, V0, V1, V2,
% 1.29/1.65 V3, V4 ) ), hBOOL( hAPP( hAPP( U, hAPP( hAPP( T, hAPP( hAPP(
% 1.29/1.65 'c_Power_Opower_Opower'( V1, V2, V4 ), Z ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.29/1.65 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( V1
% 1.29/1.65 , V2, V4 ), Z ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.29/1.65 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), Z ) ) ],
% 1.29/1.65 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, hAPP( hAPP(
% 1.29/1.65 'c_Power_Opower_Opower'( T, U, W ), V0 ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.29/1.65 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( T
% 1.29/1.65 , U, W ), V1 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.29/1.65 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ), ~(
% 1.29/1.65 'c_Ring__and__Field_Oordered__idom'( V2, V3, Y, Z, X, V4, V5, T, U, V6, W
% 1.29/1.65 ) ) ],
% 1.29/1.65 [ ~( 'c_Ring__and__Field_Oordered__idom'( X, Y, hAPP( hAPP( Z, hAPP(
% 1.29/1.65 hAPP( 'c_Power_Opower_Opower'( T, U, W ), V0 ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.29/1.65 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( T
% 1.29/1.65 , U, W ), V1 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.29/1.65 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ), Z, V2, V3, V4, T, U, V5
% 1.29/1.65 , W ) ), =( V1, hAPP( hAPP( Z, hAPP( hAPP( 'c_Power_Opower_Opower'( T, U
% 1.29/1.65 , W ), V0 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.29/1.65 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.29/1.65 'c_Power_Opower_Opower'( T, U, W ), V1 ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.29/1.65 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ],
% 1.29/1.65 [ ~( 'c_Ring__and__Field_Oordered__idom'( X, Y, hAPP( hAPP( Z, hAPP(
% 1.29/1.65 hAPP( 'c_Power_Opower_Opower'( T, U, W ), V0 ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.29/1.65 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( T
% 1.29/1.65 , U, W ), V1 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.29/1.65 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ), Z, V2, V3, V4, T, U, V5
% 1.29/1.65 , W ) ), =( V0, hAPP( hAPP( Z, hAPP( hAPP( 'c_Power_Opower_Opower'( T, U
% 1.29/1.65 , W ), V0 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.29/1.65 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.29/1.65 'c_Power_Opower_Opower'( T, U, W ), V1 ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.29/1.65 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ],
% 1.29/1.65 [ =( 'c_Suc'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.29/1.65 'c_Int_OPls' ) ), 'tc_nat' ) ) ],
% 1.29/1.65 [ =( X, Y ), ~( hBOOL( hAPP( hAPP( Z, hAPP( hAPP( T, hAPP( hAPP(
% 1.29/1.65 'c_Power_Opower_Opower'( U, W, V0 ), V1 ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.29/1.65 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( U
% 1.29/1.65 , W, V0 ), X ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.29/1.65 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), Y ) ) ), ~(
% 1.29/1.65 'c_Ring__and__Field_Oordered__idom'( V2, V3, Y, T, Z, V4, V5, U, W, V6,
% 1.29/1.65 V0 ) ) ],
% 1.29/1.65 [ =( X, Y ), ~( hBOOL( hAPP( hAPP( Z, hAPP( hAPP( T, hAPP( hAPP(
% 1.29/1.65 'c_Power_Opower_Opower'( U, W, V0 ), X ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.29/1.65 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( U
% 1.29/1.65 , W, V0 ), V1 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.29/1.65 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), Y ) ) ), ~(
% 1.29/1.65 'c_Ring__and__Field_Oordered__idom'( V2, V3, Y, T, Z, V4, V5, U, W, V6,
% 1.29/1.65 V0 ) ) ],
% 1.29/1.65 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.29/1.65 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.29/1.65 'tc_nat' ), X ), X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.29/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.29/1.65 'class_Int_Onumber'( X ) ), ~( =( 'c_HOL_Oinverse__class_Odivide'( Y, Z,
% 1.29/1.65 X ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ), =( Y, hAPP( hAPP(
% 1.29/1.65 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( T
% 1.29/1.65 , X ) ), Z ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.29/1.65 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.29/1.65 'tc_nat' ), X ), Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.29/1.65 ) ), X, 'tc_nat' ) ) ],
% 1.29/1.65 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.29/1.65 'tc_nat' ), Y ), X ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.29/1.65 ) ), X, 'tc_nat' ) ) ],
% 1.29/1.65 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.29/1.65 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.29/1.65 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ), =(
% 1.29/1.65 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.29/1.65 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), hAPP( hAPP(
% 1.29/1.65 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Oinverse__class_Oinverse'(
% 1.29/1.65 Z, X ) ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.29/1.65 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.29/1.65 Z, X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.29/1.65 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), 'c_Int_Oiszero'(
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.29/1.65 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), X
% 1.29/1.65 ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.29/1.65 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), X
% 1.29/1.65 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.29/1.65 ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( 'class_Int_Onumber'( X )
% 1.29/1.65 ), =( 'c_HOL_Oinverse__class_Oinverse'(
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.29/1.65 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.29/1.65 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.29/1.65 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.29/1.65 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.29/1.65 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.29/1.65 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.29/1.65 [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 1.29/1.65 'class_OrderedGroup_Olordered__ab__group__add__abs'( X ) ), =(
% 1.29/1.65 'c_HOL_Oabs__class_Oabs'( Y, X ), Y ), 'c_HOL_Oord__class_Oless'( Y,
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oabs__if'( X ) ), =(
% 1.29/1.65 'c_HOL_Oabs__class_Oabs'( Y, X ), Y ), 'c_HOL_Oord__class_Oless'( Y,
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.29/1.65 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.29/1.65 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'(
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.29/1.65 ), X ) ), ~( 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.29/1.65 X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ), ~(
% 1.29/1.65 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.29/1.65 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.29/1.65 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'(
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.29/1.65 ), X ) ), 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X )
% 1.29/1.65 , X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X )
% 1.29/1.65 ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.29/1.65 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.29/1.65 ), X ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.29/1.65 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ),
% 1.29/1.65 ~( 'c_lessequals'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.29/1.65 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.29/1.65 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.29/1.65 Z, X ) ), T ), 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.29/1.65 'c_Power_Opower__class_Opower'( X ), Y ), T ), hAPP( hAPP(
% 1.29/1.65 'c_Power_Opower__class_Opower'( X ), Z ), T ), X ) ), =( Z,
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.29/1.65 [ ~( =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( 'tc_nat' ), X ), Y )
% 1.29/1.65 , 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X, 'c_Suc'(
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.29/1.65 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.29/1.65 'c_HOL_Oabs__class_Oabs'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.29/1.65 'c_HOL_Oabs__class_Oabs'( Y, X ) ), 'c_HOL_Oabs__class_Oabs'( Z, X ) ), X
% 1.29/1.65 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oabs__class_Oabs'(
% 1.29/1.65 Y, X ) ), 'c_HOL_Oabs__class_Oabs'( Z, X ) ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.29/1.65 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), T, X ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.29/1.65 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), Y, X ) ) ]
% 1.29/1.65 ,
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.29/1.65 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.29/1.65 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ),
% 1.29/1.65 Y, X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z,
% 1.29/1.65 X ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.29/1.65 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~(
% 1.29/1.65 'c_lessequals'( Z, 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ) ) ]
% 1.29/1.65 ,
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.29/1.65 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.29/1.65 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T
% 1.29/1.65 ), X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T
% 1.29/1.65 , X ) ],
% 1.29/1.65 [ ~( 'c_Ring__and__Field_Oordered__idom'( X, Y, Z, T, U, W, V0, hAPP( V1
% 1.29/1.65 , V2 ), V3, V1, V4 ) ), hBOOL( hAPP( hAPP( W, Z ), V2 ) ) ],
% 1.29/1.65 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.29/1.65 ), ~( hBOOL( hAPP( hAPP( X, W ), hAPP( hAPP( V0, W ), Z ) ) ) ), ~(
% 1.29/1.65 'c_Ring__and__Field_Oordered__idom'( V1, V2, U, V3, X, T, V4, Y, V0, V5,
% 1.29/1.65 V6 ) ) ],
% 1.29/1.65 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.29/1.65 ), ~( hBOOL( hAPP( hAPP( X, U ), hAPP( hAPP( V0, U ), Y ) ) ) ), ~(
% 1.29/1.65 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, X, T, V4, Z, V0, V5,
% 1.29/1.65 V6 ) ) ],
% 1.29/1.65 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, Y ), T ) ) ), hBOOL( hAPP(
% 1.29/1.65 hAPP( U, Y ), W ) ), hBOOL( hAPP( hAPP( U, W ), Y ) ), ~(
% 1.29/1.65 'c_Ring__and__Field_Oordered__idom'( V0, V1, W, V2, X, U, V3, V4, Z, V5,
% 1.29/1.65 V6 ) ) ],
% 1.29/1.65 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, Y ), T ) ) ), ~( hBOOL( hAPP(
% 1.29/1.65 hAPP( X, T ), U ) ) ), ~( hBOOL( hAPP( hAPP( X, U ), T ) ) ), ~(
% 1.29/1.65 'c_Ring__and__Field_Oordered__idom'( W, V0, V1, V2, X, V3, V4, U, Z, V5,
% 1.29/1.65 V6 ) ) ],
% 1.29/1.65 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.29/1.65 ), ~( hBOOL( hAPP( hAPP( X, hAPP( hAPP( V0, W ), Y ) ), W ) ) ), ~(
% 1.29/1.65 'c_Ring__and__Field_Oordered__idom'( V1, V2, U, V3, X, T, V4, Z, V0, V5,
% 1.29/1.65 V6 ) ) ],
% 1.29/1.65 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.29/1.65 ), ~( hBOOL( hAPP( hAPP( X, hAPP( hAPP( V0, U ), Z ) ), U ) ) ), ~(
% 1.29/1.65 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, X, T, V4, Y, V0, V5,
% 1.29/1.65 V6 ) ) ],
% 1.29/1.65 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), Z ) ), hBOOL( hAPP(
% 1.29/1.65 hAPP( U, Z ), W ) ), hBOOL( hAPP( hAPP( U, W ), Z ) ), ~(
% 1.29/1.65 'c_Ring__and__Field_Oordered__idom'( V0, V1, W, V2, X, U, V3, V4, Y, V5,
% 1.29/1.65 V6 ) ) ],
% 1.29/1.65 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), Z ) ), ~( hBOOL( hAPP(
% 1.29/1.65 hAPP( X, U ), T ) ) ), ~( hBOOL( hAPP( hAPP( X, T ), U ) ) ), ~(
% 1.29/1.65 'c_Ring__and__Field_Oordered__idom'( W, V0, V1, V2, X, V3, V4, U, Y, V5,
% 1.29/1.65 V6 ) ) ],
% 1.29/1.65 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.29/1.65 ), ~( hBOOL( hAPP( hAPP( X, W ), hAPP( hAPP( V0, Z ), W ) ) ) ), ~(
% 1.29/1.65 'c_Ring__and__Field_Oordered__idom'( V1, V2, U, V3, X, T, V4, Y, V0, V5,
% 1.29/1.65 V6 ) ) ],
% 1.29/1.65 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.29/1.65 ), ~( hBOOL( hAPP( hAPP( X, U ), hAPP( hAPP( V0, Y ), U ) ) ) ), ~(
% 1.29/1.65 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, X, T, V4, Z, V0, V5,
% 1.29/1.65 V6 ) ) ],
% 1.29/1.65 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), Y ) ) ), hBOOL( hAPP(
% 1.29/1.65 hAPP( U, Y ), W ) ), hBOOL( hAPP( hAPP( U, W ), Y ) ), ~(
% 1.29/1.65 'c_Ring__and__Field_Oordered__idom'( V0, V1, W, V2, X, U, V3, V4, Z, V5,
% 1.29/1.65 V6 ) ) ],
% 1.29/1.65 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), Y ) ) ), ~( hBOOL( hAPP(
% 1.29/1.65 hAPP( X, T ), U ) ) ), ~( hBOOL( hAPP( hAPP( X, U ), T ) ) ), ~(
% 1.29/1.65 'c_Ring__and__Field_Oordered__idom'( W, V0, V1, V2, X, V3, V4, U, Z, V5,
% 1.29/1.65 V6 ) ) ],
% 1.29/1.65 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.29/1.65 ), ~( hBOOL( hAPP( hAPP( X, hAPP( hAPP( V0, Y ), W ) ), W ) ) ), ~(
% 1.29/1.65 'c_Ring__and__Field_Oordered__idom'( V1, V2, U, V3, X, T, V4, Z, V0, V5,
% 1.29/1.65 V6 ) ) ],
% 1.29/1.65 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.29/1.65 ), ~( hBOOL( hAPP( hAPP( X, hAPP( hAPP( V0, Z ), U ) ), U ) ) ), ~(
% 1.29/1.65 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, X, T, V4, Y, V0, V5,
% 1.29/1.65 V6 ) ) ],
% 1.29/1.65 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), T ) ), hBOOL( hAPP(
% 1.29/1.65 hAPP( U, T ), W ) ), hBOOL( hAPP( hAPP( U, W ), T ) ), ~(
% 1.29/1.65 'c_Ring__and__Field_Oordered__idom'( V0, V1, W, V2, X, U, V3, V4, Y, V5,
% 1.29/1.65 V6 ) ) ],
% 1.29/1.65 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), T ) ), ~( hBOOL( hAPP(
% 1.29/1.65 hAPP( X, U ), Z ) ) ), ~( hBOOL( hAPP( hAPP( X, Z ), U ) ) ), ~(
% 1.29/1.65 'c_Ring__and__Field_Oordered__idom'( W, V0, V1, V2, X, V3, V4, U, Y, V5,
% 1.29/1.65 V6 ) ) ],
% 1.29/1.65 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.29/1.65 ), ~( hBOOL( hAPP( hAPP( X, W ), hAPP( hAPP( V0, W ), Z ) ) ) ), ~(
% 1.29/1.65 'c_Ring__and__Field_Oordered__idom'( V1, V2, U, V3, T, X, V4, Y, V0, V5,
% 1.29/1.65 V6 ) ) ],
% 1.29/1.65 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.29/1.65 ), ~( hBOOL( hAPP( hAPP( X, U ), hAPP( hAPP( V0, U ), Y ) ) ) ), ~(
% 1.29/1.65 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, T, X, V4, Z, V0, V5,
% 1.29/1.65 V6 ) ) ],
% 1.29/1.65 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, Y ), T ) ) ), hBOOL( hAPP(
% 1.29/1.65 hAPP( U, Y ), W ) ), hBOOL( hAPP( hAPP( U, W ), Y ) ), ~(
% 1.29/1.65 'c_Ring__and__Field_Oordered__idom'( V0, V1, W, V2, U, X, V3, V4, Z, V5,
% 1.29/1.65 V6 ) ) ],
% 1.29/1.65 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, Y ), T ) ) ), ~( hBOOL( hAPP(
% 1.29/1.65 hAPP( X, T ), U ) ) ), ~( hBOOL( hAPP( hAPP( X, U ), T ) ) ), ~(
% 1.29/1.65 'c_Ring__and__Field_Oordered__idom'( W, V0, V1, V2, V3, X, V4, U, Z, V5,
% 1.29/1.65 V6 ) ) ],
% 1.29/1.65 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.29/1.65 ), ~( hBOOL( hAPP( hAPP( X, hAPP( hAPP( V0, W ), Y ) ), W ) ) ), ~(
% 1.29/1.65 'c_Ring__and__Field_Oordered__idom'( V1, V2, U, V3, T, X, V4, Z, V0, V5,
% 1.29/1.65 V6 ) ) ],
% 1.29/1.65 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.29/1.65 ), ~( hBOOL( hAPP( hAPP( X, hAPP( hAPP( V0, U ), Z ) ), U ) ) ), ~(
% 1.29/1.65 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, T, X, V4, Y, V0, V5,
% 1.29/1.65 V6 ) ) ],
% 1.29/1.65 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), Z ) ), hBOOL( hAPP(
% 1.29/1.65 hAPP( U, Z ), W ) ), hBOOL( hAPP( hAPP( U, W ), Z ) ), ~(
% 1.29/1.65 'c_Ring__and__Field_Oordered__idom'( V0, V1, W, V2, U, X, V3, V4, Y, V5,
% 1.29/1.65 V6 ) ) ],
% 1.29/1.65 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), Z ) ), ~( hBOOL( hAPP(
% 1.29/1.65 hAPP( X, U ), T ) ) ), ~( hBOOL( hAPP( hAPP( X, T ), U ) ) ), ~(
% 1.29/1.65 'c_Ring__and__Field_Oordered__idom'( W, V0, V1, V2, V3, X, V4, U, Y, V5,
% 1.29/1.65 V6 ) ) ],
% 1.29/1.65 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.29/1.65 ), ~( hBOOL( hAPP( hAPP( X, W ), hAPP( hAPP( V0, Z ), W ) ) ) ), ~(
% 1.29/1.65 'c_Ring__and__Field_Oordered__idom'( V1, V2, U, V3, T, X, V4, Y, V0, V5,
% 1.29/1.65 V6 ) ) ],
% 1.29/1.65 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.29/1.65 ), ~( hBOOL( hAPP( hAPP( X, U ), hAPP( hAPP( V0, Y ), U ) ) ) ), ~(
% 1.29/1.65 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, T, X, V4, Z, V0, V5,
% 1.29/1.65 V6 ) ) ],
% 1.29/1.65 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), Y ) ) ), hBOOL( hAPP(
% 1.29/1.65 hAPP( U, Y ), W ) ), hBOOL( hAPP( hAPP( U, W ), Y ) ), ~(
% 1.29/1.65 'c_Ring__and__Field_Oordered__idom'( V0, V1, W, V2, U, X, V3, V4, Z, V5,
% 1.29/1.65 V6 ) ) ],
% 1.29/1.65 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), Y ) ) ), ~( hBOOL( hAPP(
% 1.29/1.65 hAPP( X, T ), U ) ) ), ~( hBOOL( hAPP( hAPP( X, U ), T ) ) ), ~(
% 1.29/1.65 'c_Ring__and__Field_Oordered__idom'( W, V0, V1, V2, V3, X, V4, U, Z, V5,
% 1.29/1.65 V6 ) ) ],
% 1.29/1.65 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.29/1.65 ), ~( hBOOL( hAPP( hAPP( X, hAPP( hAPP( V0, Y ), W ) ), W ) ) ), ~(
% 1.29/1.65 'c_Ring__and__Field_Oordered__idom'( V1, V2, U, V3, T, X, V4, Z, V0, V5,
% 1.29/1.65 V6 ) ) ],
% 1.29/1.65 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.29/1.65 ), ~( hBOOL( hAPP( hAPP( X, hAPP( hAPP( V0, Z ), U ) ), U ) ) ), ~(
% 1.29/1.65 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, T, X, V4, Y, V0, V5,
% 1.29/1.65 V6 ) ) ],
% 1.29/1.65 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), T ) ), hBOOL( hAPP(
% 1.29/1.65 hAPP( U, T ), W ) ), hBOOL( hAPP( hAPP( U, W ), T ) ), ~(
% 1.29/1.65 'c_Ring__and__Field_Oordered__idom'( V0, V1, W, V2, U, X, V3, V4, Y, V5,
% 1.29/1.65 V6 ) ) ],
% 1.29/1.65 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), T ) ), ~( hBOOL( hAPP(
% 1.29/1.65 hAPP( X, U ), Z ) ) ), ~( hBOOL( hAPP( hAPP( X, Z ), U ) ) ), ~(
% 1.29/1.65 'c_Ring__and__Field_Oordered__idom'( W, V0, V1, V2, V3, X, V4, U, Y, V5,
% 1.29/1.65 V6 ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.29/1.65 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.29/1.65 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.29/1.65 , X ), X ), T, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T
% 1.29/1.65 , X ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.29/1.65 , T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.29/1.65 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.29/1.65 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.29/1.65 , X ), X ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.29/1.65 ) ), ~( 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.29/1.65 , Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.29/1.65 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ),
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ],
% 1.29/1.65 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), ~( =(
% 1.29/1.65 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.29/1.65 =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.29/1.65 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), ~(
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.29/1.65 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ozero__class_Ozero'( X ), X ), X ) ) ]
% 1.29/1.65 ,
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.29/1.65 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.29/1.65 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.29/1.65 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.29/1.65 'tc_Int_Oint' ), X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.29/1.65 'tc_Int_Oint' ), Z ), Y ), 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.29/1.65 X, Z, 'tc_Int_Oint' ) ) ],
% 1.29/1.65 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Y, X ) ]
% 1.29/1.65 ,
% 1.29/1.65 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Y, X ) ],
% 1.29/1.65 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.29/1.65 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T )
% 1.29/1.65 , X ), ~( 'c_lessequals'( U, T, X ) ), ~( 'c_lessequals'( Y, hAPP( hAPP(
% 1.29/1.65 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ), X ) ) ],
% 1.29/1.65 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.29/1.65 'c_lessequals'( T, Z, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.29/1.65 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.29/1.65 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.29/1.65 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.29/1.65 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( T, Z, X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.29/1.65 'c_HOL_Oone__class_Oone'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.29/1.65 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.29/1.65 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_Suc'(
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_Suc'(
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.29/1.65 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.29/1.65 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~( 'c_lessequals'(
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.29/1.65 ), X ) ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.29/1.65 , X ), ~( 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.29/1.65 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.29/1.65 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.29/1.65 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~( 'c_lessequals'(
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.29/1.65 ), X ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.29/1.65 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.29/1.65 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.29/1.65 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.29/1.65 , X ), X ), T, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T
% 1.29/1.65 , X ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.29/1.65 , T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ), ~(
% 1.29/1.65 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.65 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.29/1.65 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.29/1.65 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.29/1.65 , X ), X ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.29/1.65 ) ), ~( 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.29/1.65 , Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ), ~(
% 1.29/1.65 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.29/1.65 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( hAPP(
% 1.29/1.65 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.29/1.65 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ) ) ), hAPP( hAPP(
% 1.29/1.65 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.29/1.65 ,
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.29/1.65 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), hAPP( hAPP(
% 1.29/1.65 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.29/1.65 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.29/1.65 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 1.29/1.65 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.29/1.65 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), hAPP( hAPP(
% 1.29/1.65 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.29/1.65 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.29/1.65 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), hAPP( hAPP(
% 1.29/1.65 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), ~( 'c_Int_Oiszero'(
% 1.29/1.65 'c_HOL_Oone__class_Oone'( X ), X ) ) ],
% 1.29/1.65 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.29/1.66 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.29/1.66 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.29/1.66 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.29/1.66 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.29/1.66 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.29/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.29/1.66 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ],
% 1.29/1.66 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.29/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.29/1.66 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.29/1.66 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.29/1.66 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =(
% 1.29/1.66 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.29/1.66 'c_HOL_Oinverse__class_Odivide'( T, U, X ) ) ), =( U,
% 1.29/1.66 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.29/1.66 ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), U ), hAPP(
% 1.29/1.66 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ],
% 1.29/1.66 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =( hAPP( hAPP(
% 1.29/1.66 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.29/1.66 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) ), =( Z,
% 1.29/1.66 'c_HOL_Ozero__class_Ozero'( X ) ), =( U, 'c_HOL_Ozero__class_Ozero'( X )
% 1.29/1.66 ), =( 'c_HOL_Oinverse__class_Odivide'( Y, U, X ),
% 1.29/1.66 'c_HOL_Oinverse__class_Odivide'( T, Z, X ) ) ],
% 1.29/1.66 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.29/1.66 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.29/1.66 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X )
% 1.29/1.66 ) ],
% 1.29/1.66 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.29/1.66 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X )
% 1.29/1.66 , ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.29/1.66 ],
% 1.29/1.66 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.29/1.66 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oabs__class_Oabs'(
% 1.29/1.66 Y, X ), X ) ],
% 1.29/1.66 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.29/1.66 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.29/1.66 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.29/1.66 X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ), Y, X ),
% 1.29/1.66 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.29/1.66 [ ~( =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), hAPP( hAPP(
% 1.29/1.66 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ), =( Y,
% 1.29/1.66 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.29/1.66 [ ~( =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), hAPP( hAPP(
% 1.29/1.66 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ), =( X,
% 1.29/1.66 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.29/1.66 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.29/1.66 'c_HOL_Ouminus__class_Ouminus'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.29/1.66 ), Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.29/1.66 'c_HOL_Ouminus__class_Ouminus'( Z, X ) ), 'c_HOL_Ouminus__class_Ouminus'(
% 1.29/1.66 Y, X ) ) ) ],
% 1.29/1.66 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.29/1.66 'c_HOL_Ouminus__class_Ouminus'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.29/1.66 ), Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.29/1.66 'c_HOL_Ouminus__class_Ouminus'( Y, X ) ), 'c_HOL_Ouminus__class_Ouminus'(
% 1.29/1.66 Z, X ) ) ) ],
% 1.29/1.66 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 1.29/1.66 'c_lessequals'( Z, Y, X ) ],
% 1.29/1.66 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.29/1.66 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.29/1.66 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), hAPP( hAPP(
% 1.29/1.66 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), X ) ) ],
% 1.29/1.66 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ),
% 1.29/1.66 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.29/1.66 'c_Int_OPls' ) ), 'tc_nat' ) ), T ), ~( 'c_Ring__and__Field_Osemiring__1'(
% 1.29/1.66 X, Y, T, U, Z ) ) ],
% 1.29/1.66 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), X ),
% 1.29/1.66 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.29/1.66 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), ~( 'c_Ring__and__Field_Osemiring__1'(
% 1.29/1.66 X, Y, T, U, Z ) ) ],
% 1.29/1.66 [ ~( 'c_Ring__and__Field_Oordered__idom'( X, Y, Z, T, U, W, V0, V1, V2,
% 1.29/1.66 V3, V4 ) ), =( hAPP( hAPP( 'c_Power_Opower_Opower'( V1, V2, V4 ), Z ),
% 1.29/1.66 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.29/1.66 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ],
% 1.29/1.66 [ =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.29/1.66 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', 'tc_nat' ) ) ],
% 1.29/1.66 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', 'tc_nat' ),
% 1.29/1.66 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.29/1.66 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.29/1.66 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.29/1.66 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.29/1.66 ), ~( =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.29/1.66 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ),
% 1.29/1.66 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.29/1.66 ) ) ],
% 1.29/1.66 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ), ~(
% 1.29/1.66 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( X,
% 1.29/1.66 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), 'tc_nat' )
% 1.29/1.66 ) ],
% 1.29/1.66 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 1.29/1.66 'c_Nat_Osemiring__1__class_Oof__nat'( hAPP( hAPP(
% 1.29/1.66 'c_Power_Opower__class_Opower'( 'tc_nat' ), Y ), Z ), X ), hAPP( hAPP(
% 1.29/1.66 'c_Power_Opower__class_Opower'( X ), 'c_Nat_Osemiring__1__class_Oof__nat'(
% 1.29/1.66 Y, X ) ), Z ) ) ],
% 1.29/1.66 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.29/1.66 hAPP( hAPP( 'c_Power_Opower__class_Opower'( 'tc_nat' ), X ), Y ),
% 1.29/1.66 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.29/1.66 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.29/1.66 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.29/1.66 hAPP( hAPP( 'c_Power_Opower__class_Opower'( 'tc_nat' ), X ),
% 1.29/1.66 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ],
% 1.29/1.66 [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 1.29/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.29/1.66 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.29/1.66 'tc_nat' ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( 'tc_nat' ), Y ),
% 1.29/1.66 X ), 'tc_nat' ) ) ],
% 1.29/1.66 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.29/1.66 'tc_nat' ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 1.29/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP(
% 1.29/1.66 hAPP( 'c_Power_Opower__class_Opower'( 'tc_nat' ), X ), Y ), 'tc_nat' ) )
% 1.29/1.66 ],
% 1.29/1.66 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.29/1.66 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'(
% 1.29/1.66 'tc_nat' ), Z ), X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'(
% 1.29/1.66 'tc_nat' ), Z ), Y ), 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.29/1.66 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_nat' ) ) ],
% 1.29/1.66 [ =( 'c_Int_OBit0'( 'v_k' ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.29/1.66 'tc_Int_Oint' ), 'v_k' ), 'v_k' ) ) ],
% 1.29/1.66 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.66 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.29/1.66 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.29/1.66 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.29/1.66 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.29/1.66 'c_Int_OPls' ) ), X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.29/1.66 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.29/1.66 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.29/1.66 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.29/1.66 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.29/1.66 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.29/1.66 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.29/1.66 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.29/1.66 'c_Int_OPls' ) ), X ), X ), X ) ) ],
% 1.29/1.66 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP( hAPP(
% 1.29/1.66 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.29/1.66 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.29/1.66 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.29/1.66 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.29/1.66 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.29/1.66 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.29/1.66 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.29/1.66 ,
% 1.29/1.66 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.29/1.66 Y, Z, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ),
% 1.29/1.66 ~( 'c_lessequals'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.29/1.66 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.29/1.66 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP(
% 1.29/1.66 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.29/1.66 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.29/1.66 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ) ],
% 1.29/1.66 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =( hAPP( hAPP(
% 1.29/1.66 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.29/1.66 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.29/1.66 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.29/1.66 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.29/1.66 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.29/1.66 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.29/1.66 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.29/1.66 =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.29/1.66 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =( hAPP( hAPP(
% 1.29/1.66 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.29/1.66 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.29/1.66 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.29/1.66 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.29/1.66 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.29/1.66 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.29/1.66 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.29/1.66 =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.29/1.66 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =( hAPP( hAPP(
% 1.29/1.66 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X
% 1.29/1.66 ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.29/1.66 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.29/1.66 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), hAPP( hAPP(
% 1.29/1.66 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.29/1.66 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.29/1.66 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.29/1.66 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ) ],
% 1.29/1.66 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.29/1.66 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.29/1.66 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.29/1.66 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.29/1.66 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ],
% 1.29/1.66 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.29/1.66 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.29/1.66 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.29/1.66 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.29/1.66 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), hAPP( hAPP(
% 1.29/1.66 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.29/1.66 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.29/1.66 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.29/1.66 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =( hAPP( hAPP(
% 1.29/1.66 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.29/1.66 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.29/1.66 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP(
% 1.29/1.66 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.29/1.66 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.29/1.66 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), =( Y, Z ), ~( 'c_lessequals'(
% 1.29/1.66 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.29/1.66 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.29/1.66 [ =( X, 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 1.29/1.66 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X
% 1.29/1.66 , 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.29/1.66 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) ) ],
% 1.29/1.66 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.29/1.66 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.29/1.66 ), Y ), Z ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), T ),
% 1.29/1.66 X ), ~( 'c_HOL_Oord__class_Oless'( Z, T, 'tc_nat' ) ), ~(
% 1.29/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.29/1.66 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.29/1.66 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.29/1.66 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), T ), Y ), hAPP( hAPP(
% 1.29/1.66 'c_Power_Opower__class_Opower'( X ), T ), Z ), X ) ), ~(
% 1.29/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), T, X ) ) ],
% 1.29/1.66 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.29/1.66 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.29/1.66 ), Y ), Z ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), T ),
% 1.29/1.66 X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X )
% 1.29/1.66 ), ~( 'c_HOL_Oord__class_Oless'( Z, T, 'tc_nat' ) ) ],
% 1.29/1.66 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.29/1.66 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.29/1.66 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), T ), Y ), hAPP( hAPP(
% 1.29/1.66 'c_Power_Opower__class_Opower'( X ), T ), Z ), X ) ), ~(
% 1.29/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), T, X ) ) ],
% 1.29/1.66 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.29/1.66 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.29/1.66 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.29/1.66 ), Y ), 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ),
% 1.29/1.66 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.29/1.66 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.29/1.66 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Oinverse'(
% 1.29/1.66 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ), X
% 1.29/1.66 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X
% 1.29/1.66 ) ) ],
% 1.29/1.66 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.29/1.66 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.29/1.66 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ), X
% 1.29/1.66 ), Y ) ],
% 1.29/1.66 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.29/1.66 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.29/1.66 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ), X
% 1.29/1.66 ), Y ) ],
% 1.29/1.66 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.29/1.66 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ),
% 1.29/1.66 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.29/1.66 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oone__class_Oone'( X )
% 1.29/1.66 , 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X )
% 1.29/1.66 ) ],
% 1.29/1.66 [ ~( 'class_Int_Onumber__ring'( X ) ), ~( 'c_Int_Oiszero'(
% 1.29/1.66 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ), X
% 1.29/1.66 ) ) ],
% 1.29/1.66 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.29/1.66 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.29/1.66 'c_Int_OBit1'( 'c_Int_OPls' ), X ) ), Y ), Y ) ],
% 1.29/1.66 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.29/1.66 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.29/1.66 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ) )
% 1.29/1.66 , Y ) ],
% 1.29/1.66 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.29/1.66 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.29/1.66 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.29/1.66 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.29/1.66 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.29/1.66 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP(
% 1.29/1.66 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.29/1.66 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.29/1.66 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ) ],
% 1.29/1.66 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.29/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.29/1.66 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.29/1.66 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.29/1.66 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.29/1.66 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.29/1.66 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.29/1.66 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.29/1.66 'c_Int_OPls' ) ), 'tc_nat' ) ) ), X ) ) ],
% 1.29/1.66 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.29/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.29/1.66 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.29/1.66 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.29/1.66 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.29/1.66 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.29/1.66 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.29/1.66 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.29/1.66 'c_Int_OPls' ) ), 'tc_nat' ) ) ), X ), =( Z, 'c_HOL_Ozero__class_Ozero'(
% 1.29/1.66 X ) ) ],
% 1.29/1.66 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.29/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.29/1.66 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.29/1.66 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.29/1.66 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.29/1.66 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.29/1.66 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.29/1.66 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.29/1.66 'c_Int_OPls' ) ), 'tc_nat' ) ) ), X ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.29/1.66 X ) ) ],
% 1.29/1.66 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.29/1.66 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.29/1.66 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.29/1.66 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.29/1.66 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.29/1.66 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.29/1.66 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.29/1.66 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.29/1.66 ],
% 1.29/1.66 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.29/1.66 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.29/1.66 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ),
% 1.29/1.66 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.29/1.66 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.29/1.66 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.29/1.66 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.29/1.66 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.29/1.66 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.29/1.66 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.29/1.66 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.29/1.66 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), hAPP( hAPP(
% 1.29/1.66 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.29/1.66 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.29/1.66 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), X ) ), Y ) ), Z ) ) ) ]
% 1.29/1.66 ,
% 1.29/1.66 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ),
% 1.29/1.66 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.29/1.66 [ =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 1.29/1.66 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ),
% 1.29/1.66 'tc_nat' ) ) ],
% 1.29/1.66 [ 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( X,
% 1.29/1.66 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), 'tc_nat' )
% 1.29/1.66 , ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ) ), ~(
% 1.29/1.66 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', Y, 'tc_Int_Oint' ) ) ],
% 1.29/1.66 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', X, 'tc_Int_Oint' ), ~(
% 1.29/1.66 'c_HOL_Oord__class_Oless'( Y, X, 'tc_Int_Oint' ) ), ~(
% 1.29/1.66 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.29/1.66 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ), 'tc_nat' )
% 1.29/1.66 ) ],
% 1.29/1.66 [ =( 'c_FFT__Mirabelle_ODFT'( hAPP( hAPP( 'c_Power_Opower__class_Opower'(
% 1.29/1.66 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.29/1.66 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), Y, Z ), hAPP(
% 1.29/1.66 'c_FFT__Mirabelle_OFFT'( X, Y ), Z ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.29/1.66 hAPP( hAPP( 'c_Power_Opower__class_Opower'( 'tc_nat' ),
% 1.29/1.66 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.29/1.66 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), 'tc_nat' ) ) ],
% 1.29/1.66 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.29/1.66 hAPP( hAPP( 'c_Power_Opower__class_Opower'( 'tc_nat' ), X ),
% 1.29/1.66 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ), 'tc_nat' ), ~(
% 1.29/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.29/1.66 'tc_nat' ) ) ],
% 1.29/1.66 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.29/1.66 'tc_nat' ), =( 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.29/1.66 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.29/1.66 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( hAPP(
% 1.29/1.66 'c_Power_Opower__class_Opower'( 'tc_nat' ), X ),
% 1.29/1.66 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ), 'tc_nat' ) ) ],
% 1.29/1.66 [ ~( =( 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ),
% 1.29/1.66 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Oord__class_Oless'(
% 1.29/1.66 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( hAPP(
% 1.29/1.66 'c_Power_Opower__class_Opower'( 'tc_nat' ), Y ),
% 1.29/1.66 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ), 'tc_nat' ) ],
% 1.29/1.66 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.29/1.66 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.29/1.66 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.29/1.66 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.29/1.66 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), Y ) ) ]
% 1.29/1.66 ,
% 1.29/1.66 [ =( hAPP( hAPP( X, Y ), Y ), hAPP( hAPP( Z, Y ),
% 1.29/1.66 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.29/1.66 'c_Int_OPls' ) ), 'tc_nat' ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( T
% 1.29/1.66 , X, Z, U, W, V0 ) ) ],
% 1.29/1.66 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.29/1.66 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ), hAPP( hAPP(
% 1.29/1.66 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.29/1.66 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.29/1.66 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ],
% 1.29/1.66 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP( hAPP(
% 1.29/1.66 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.29/1.66 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.29/1.66 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.29/1.66 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =( hAPP( hAPP(
% 1.29/1.66 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.29/1.66 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.29/1.66 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.29/1.66 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =( hAPP( hAPP(
% 1.29/1.66 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.29/1.66 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.29/1.66 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y
% 1.29/1.66 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.29/1.66 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP( hAPP(
% 1.29/1.66 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oabs__class_Oabs'( Y, X ) ),
% 1.29/1.66 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.29/1.66 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP(
% 1.29/1.66 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.29/1.66 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.29/1.66 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ],
% 1.29/1.66 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.29/1.66 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.29/1.66 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.29/1.66 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.29/1.66 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), hAPP( hAPP(
% 1.29/1.66 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.29/1.66 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ),
% 1.29/1.66 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.29/1.66 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ],
% 1.29/1.66 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.29/1.66 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.29/1.66 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.29/1.66 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.29/1.66 X ), Y ), Y ) ) ],
% 1.29/1.66 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =( hAPP( hAPP(
% 1.29/1.66 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.29/1.66 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.29/1.66 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.29/1.66 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =( hAPP( hAPP(
% 1.29/1.66 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X
% 1.29/1.66 ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.29/1.66 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP(
% 1.29/1.66 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.29/1.66 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.29/1.66 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ],
% 1.29/1.66 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.29/1.66 'c_HOL_Oabs__class_Oabs'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X )
% 1.29/1.66 , Y ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.29/1.66 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), hAPP( hAPP(
% 1.29/1.66 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.29/1.66 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.29/1.66 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ],
% 1.29/1.66 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.29/1.66 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.29/1.66 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) ],
% 1.29/1.66 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.29/1.66 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.29/1.66 ), Y ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.29/1.66 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.29/1.66 ,
% 1.29/1.66 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.29/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.29/1.66 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.29/1.66 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.29/1.66 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ) ],
% 1.29/1.66 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.29/1.66 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.29/1.66 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.29/1.66 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.29/1.66 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.29/1.66 ) ) ],
% 1.29/1.66 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), ~( 'class_Int_Onumber'(
% 1.29/1.66 X ) ), =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ),
% 1.29/1.66 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 1.29/1.66 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.29/1.66 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.29/1.66 X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 1.29/1.66 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ) ],
% 1.29/1.66 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Z
% 1.29/1.66 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.29/1.66 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.29/1.66 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.29/1.66 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.29/1.66 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.29/1.66 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.29/1.66 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.29/1.66 [ =( 'c_Int_OBit0'( 'c_Int_OPls' ), 'c_Int_OPls' ) ],
% 1.29/1.66 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.29/1.66 , Y, X ) ) ],
% 1.29/1.66 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.29/1.66 , Y, X ) ) ],
% 1.29/1.66 [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ],
% 1.29/1.66 [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ],
% 1.29/1.66 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Y
% 1.29/1.66 , X ) ) ],
% 1.29/1.66 [ ~( =( 'c_Int_OPls', 'c_Int_OBit1'( X ) ) ) ],
% 1.29/1.66 [ ~( =( 'c_Int_OBit1'( X ), 'c_Int_OPls' ) ) ],
% 1.29/1.66 [ ~( =( 'c_Int_OBit0'( X ), 'c_Int_OPls' ) ), =( X, 'c_Int_OPls' ) ]
% 1.29/1.66 ,
% 1.29/1.66 [ ~( =( 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ) ) ), =( X, Y ) ],
% 1.29/1.66 [ ~( =( 'c_Int_OBit1'( X ), 'c_Int_OBit0'( Y ) ) ) ],
% 1.29/1.66 [ =( 'c_Int_OPls', 'c_Int_OBit0'( 'c_Int_OPls' ) ) ],
% 1.29/1.66 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.29/1.66 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.29/1.66 ), =( Z, Y ) ],
% 1.29/1.66 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 1.29/1.66 'c_HOL_Oord__class_Oless'( Z, Y, X ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.29/1.66 ) ],
% 1.29/1.66 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 1.29/1.66 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.29/1.66 ) ],
% 1.29/1.66 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.29/1.66 , X ), =( Z, Y ), 'c_HOL_Oord__class_Oless'( Z, Y, X ) ],
% 1.29/1.66 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 1.29/1.66 Y, X, 'tc_nat' ), =( Y, X ) ],
% 1.29/1.66 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), 'c_HOL_Oord__class_Oless'( Y, Z,
% 1.29/1.66 'tc_nat' ), =( Z, Y ), 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ],
% 1.29/1.66 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 1.29/1.66 Y, X, 'tc_nat' ), =( Y, X ) ],
% 1.29/1.66 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.29/1.66 , X ), 'c_HOL_Oord__class_Oless'( Z, Y, X ), =( Z, Y ) ],
% 1.29/1.66 [ ~( =( 'c_Int_OPls', 'c_Int_OBit0'( X ) ) ), =( 'c_Int_OPls', X ) ]
% 1.29/1.66 ,
% 1.29/1.66 [ ~( =( 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ) ) ), =( X, Y ) ],
% 1.29/1.66 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.29/1.66 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 1.29/1.66 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 1.29/1.66 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.29/1.66 , X ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~(
% 1.29/1.66 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.29/1.66 [ ~( 'class_Int_Oring__char__0'( X ) ), ~( 'class_Int_Onumber__ring'( X
% 1.29/1.66 ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.29/1.66 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ), =( Y, Z ) ],
% 1.29/1.66 [ ~( =( 'c_Int_OBit0'( X ), 'c_Int_OBit1'( Y ) ) ) ],
% 1.29/1.66 [ 'c_HOL_Oord__class_Oless'( 'v_i', hAPP( hAPP(
% 1.29/1.66 'c_Power_Opower__class_Opower'( 'tc_nat' ),
% 1.29/1.66 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.29/1.66 'c_Int_OPls' ) ), 'tc_nat' ) ), 'v_k' ), 'tc_nat' ) ],
% 1.29/1.66 [ ~( =( 'c_FFT__Mirabelle_OIDFT'( hAPP( hAPP(
% 1.29/1.66 'c_Power_Opower__class_Opower'( 'tc_nat' ),
% 1.29/1.66 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.29/1.66 'c_Int_OPls' ) ), 'tc_nat' ) ), 'v_k' ), 'v_a', 'v_i' ), hAPP(
% 1.29/1.66 'c_FFT__Mirabelle_OIFFT'( 'v_k', 'v_a' ), 'v_i' ) ) ) ],
% 1.29/1.66 [ 'class_Lattices_Oboolean__algebra'( 'tc_fun'( X, Y ) ), ~(
% 1.29/1.66 'class_Lattices_Oboolean__algebra'( Y ) ) ],
% 1.29/1.66 [ 'class_Orderings_Opreorder'( 'tc_fun'( X, Y ) ), ~(
% 1.29/1.66 'class_Orderings_Opreorder'( Y ) ) ],
% 1.29/1.66 [ 'class_Orderings_Oorder'( 'tc_fun'( X, Y ) ), ~(
% 1.29/1.66 'class_Orderings_Oorder'( Y ) ) ],
% 1.29/1.66 [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( 'tc_nat' )
% 1.29/1.66 ],
% 1.29/1.66 [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( 'tc_nat'
% 1.29/1.66 ) ],
% 1.29/1.66 [ 'class_Ring__and__Field_Oordered__comm__semiring__strict'( 'tc_nat' )
% 1.29/1.66 ],
% 1.29/1.66 [ 'class_Ring__and__Field_Opordered__cancel__semiring'( 'tc_nat' ) ]
% 1.29/1.66 ,
% 1.29/1.66 [ 'class_Ring__and__Field_Oordered__semiring__strict'( 'tc_nat' ) ],
% 1.29/1.66 [ 'class_OrderedGroup_Opordered__ab__semigroup__add'( 'tc_nat' ) ],
% 1.29/1.66 [ 'class_OrderedGroup_Opordered__comm__monoid__add'( 'tc_nat' ) ],
% 1.29/1.66 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'( 'tc_nat' ) ],
% 1.29/1.66 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_nat' ) ],
% 1.29/1.66 [ 'class_Ring__and__Field_Opordered__semiring'( 'tc_nat' ) ],
% 1.29/1.66 [ 'class_Ring__and__Field_Oordered__semiring'( 'tc_nat' ) ],
% 1.29/1.66 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_nat' ) ],
% 1.29/1.66 [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_nat' ) ],
% 1.29/1.66 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_nat' ) ],
% 1.29/1.66 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_nat' ) ],
% 1.29/1.66 [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_nat' ) ],
% 1.29/1.66 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_nat' ) ],
% 1.29/1.66 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_nat' ) ],
% 1.29/1.66 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_nat' ) ],
% 1.29/1.66 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_nat' ) ],
% 1.29/1.66 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_nat' ) ],
% 1.29/1.66 [ 'class_Ring__and__Field_Osemiring__0'( 'tc_nat' ) ],
% 1.29/1.66 [ 'class_Ring__and__Field_Omult__mono1'( 'tc_nat' ) ],
% 1.29/1.66 [ 'class_Ring__and__Field_Omult__zero'( 'tc_nat' ) ],
% 1.29/1.66 [ 'class_Ring__and__Field_Omult__mono'( 'tc_nat' ) ],
% 1.29/1.66 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_nat' ) ],
% 1.29/1.66 [ 'class_Ring__and__Field_Osemiring'( 'tc_nat' ) ],
% 1.29/1.66 [ 'class_OrderedGroup_Omonoid__add'( 'tc_nat' ) ],
% 1.29/1.66 [ 'class_Nat_Osemiring__char__0'( 'tc_nat' ) ],
% 1.29/1.66 [ 'class_Orderings_Opreorder'( 'tc_nat' ) ],
% 1.29/1.66 [ 'class_Orderings_Olinorder'( 'tc_nat' ) ],
% 1.29/1.66 [ 'class_Orderings_Oorder'( 'tc_nat' ) ],
% 1.29/1.66 [ 'class_Power_Opower'( 'tc_nat' ) ],
% 1.29/1.66 [ 'class_Int_Onumber'( 'tc_nat' ) ],
% 1.29/1.66 [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'(
% 1.29/1.66 'tc_Int_Oint' ) ],
% 1.29/1.66 [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'(
% 1.29/1.66 'tc_Int_Oint' ) ],
% 1.29/1.66 [ 'class_Ring__and__Field_Oordered__comm__semiring__strict'(
% 1.29/1.66 'tc_Int_Oint' ) ],
% 1.29/1.66 [ 'class_Ring__and__Field_Opordered__cancel__semiring'( 'tc_Int_Oint' )
% 1.29/1.66 ],
% 1.29/1.66 [ 'class_Ring__and__Field_Oring__1__no__zero__divisors'( 'tc_Int_Oint' )
% 1.29/1.66 ],
% 1.29/1.66 [ 'class_Ring__and__Field_Oordered__semiring__strict'( 'tc_Int_Oint' ) ]
% 1.29/1.66 ,
% 1.29/1.66 [ 'class_OrderedGroup_Opordered__ab__semigroup__add'( 'tc_Int_Oint' ) ]
% 1.29/1.66 ,
% 1.29/1.66 [ 'class_OrderedGroup_Opordered__ab__group__add__abs'( 'tc_Int_Oint' ) ]
% 1.29/1.66 ,
% 1.29/1.66 [ 'class_OrderedGroup_Olordered__ab__group__add__abs'( 'tc_Int_Oint' ) ]
% 1.29/1.66 ,
% 1.29/1.66 [ 'class_OrderedGroup_Opordered__comm__monoid__add'( 'tc_Int_Oint' ) ]
% 1.29/1.66 ,
% 1.29/1.66 [ 'class_Ring__and__Field_Oring__no__zero__divisors'( 'tc_Int_Oint' ) ]
% 1.29/1.66 ,
% 1.29/1.66 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'( 'tc_Int_Oint' ) ]
% 1.29/1.66 ,
% 1.29/1.66 [ 'class_Ring__and__Field_Oordered__ring__strict'( 'tc_Int_Oint' ) ]
% 1.29/1.66 ,
% 1.29/1.66 [ 'class_OrderedGroup_Opordered__ab__group__add'( 'tc_Int_Oint' ) ],
% 1.29/1.66 [ 'class_OrderedGroup_Olordered__ab__group__add'( 'tc_Int_Oint' ) ],
% 1.29/1.66 [ 'class_OrderedGroup_Oordered__ab__group__add'( 'tc_Int_Oint' ) ],
% 1.29/1.66 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_Int_Oint' ) ],
% 1.29/1.66 [ 'class_Ring__and__Field_Opordered__semiring'( 'tc_Int_Oint' ) ],
% 1.29/1.66 [ 'class_Ring__and__Field_Opordered__ring__abs'( 'tc_Int_Oint' ) ],
% 1.29/1.66 [ 'class_Ring__and__Field_Oordered__semiring'( 'tc_Int_Oint' ) ],
% 1.29/1.66 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_Int_Oint' ) ],
% 1.29/1.66 [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_Int_Oint' ) ],
% 1.29/1.66 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_Int_Oint' ) ],
% 1.29/1.66 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_Int_Oint' ) ],
% 1.29/1.66 [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_Int_Oint' ) ],
% 1.29/1.66 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_Int_Oint' ) ],
% 1.29/1.66 [ 'class_Ring__and__Field_Opordered__ring'( 'tc_Int_Oint' ) ],
% 1.29/1.66 [ 'class_Ring__and__Field_Olordered__ring'( 'tc_Int_Oint' ) ],
% 1.29/1.66 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_Int_Oint' ) ],
% 1.29/1.66 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_Int_Oint' ) ],
% 1.29/1.66 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_Int_Oint' ) ],
% 1.29/1.66 [ 'class_Ring__and__Field_Oordered__idom'( 'tc_Int_Oint' ) ],
% 1.29/1.66 [ 'class_Ring__and__Field_Ocomm__ring__1'( 'tc_Int_Oint' ) ],
% 1.29/1.66 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_Int_Oint' ) ],
% 1.29/1.66 [ 'class_Ring__and__Field_Osemiring__0'( 'tc_Int_Oint' ) ],
% 1.29/1.66 [ 'class_Ring__and__Field_Omult__mono1'( 'tc_Int_Oint' ) ],
% 1.29/1.66 [ 'class_OrderedGroup_Oab__group__add'( 'tc_Int_Oint' ) ],
% 1.29/1.66 [ 'class_Ring__and__Field_Omult__zero'( 'tc_Int_Oint' ) ],
% 1.29/1.66 [ 'class_Ring__and__Field_Omult__mono'( 'tc_Int_Oint' ) ],
% 1.29/1.66 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_Int_Oint' ) ],
% 1.29/1.66 [ 'class_Ring__and__Field_Osemiring'( 'tc_Int_Oint' ) ],
% 1.29/1.66 [ 'class_OrderedGroup_Omonoid__add'( 'tc_Int_Oint' ) ],
% 1.29/1.66 [ 'class_OrderedGroup_Ogroup__add'( 'tc_Int_Oint' ) ],
% 1.29/1.66 [ 'class_Ring__and__Field_Oring__1'( 'tc_Int_Oint' ) ],
% 1.29/1.66 [ 'class_Ring__and__Field_Oabs__if'( 'tc_Int_Oint' ) ],
% 1.29/1.66 [ 'class_Ring__and__Field_Oring'( 'tc_Int_Oint' ) ],
% 1.29/1.66 [ 'class_Ring__and__Field_Oidom'( 'tc_Int_Oint' ) ],
% 1.29/1.66 [ 'class_Nat_Osemiring__char__0'( 'tc_Int_Oint' ) ],
% 1.29/1.66 [ 'class_Orderings_Opreorder'( 'tc_Int_Oint' ) ],
% 1.29/1.66 [ 'class_Orderings_Olinorder'( 'tc_Int_Oint' ) ],
% 1.29/1.66 [ 'class_Orderings_Oorder'( 'tc_Int_Oint' ) ],
% 1.29/1.66 [ 'class_Int_Oring__char__0'( 'tc_Int_Oint' ) ],
% 1.29/1.66 [ 'class_Int_Onumber__ring'( 'tc_Int_Oint' ) ],
% 1.29/1.66 [ 'class_Power_Opower'( 'tc_Int_Oint' ) ],
% 1.29/1.66 [ 'class_Int_Onumber'( 'tc_Int_Oint' ) ],
% 1.29/1.66 [ 'class_Ring__and__Field_Oring__1__no__zero__divisors'(
% 1.29/1.66 'tc_Complex_Ocomplex' ) ],
% 1.29/1.66 [ 'class_Ring__and__Field_Oring__no__zero__divisors'(
% 1.29/1.66 'tc_Complex_Ocomplex' ) ],
% 1.29/1.66 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'(
% 1.29/1.66 'tc_Complex_Ocomplex' ) ],
% 1.29/1.66 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_Complex_Ocomplex' )
% 1.29/1.66 ],
% 1.29/1.66 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_Complex_Ocomplex' )
% 1.29/1.66 ],
% 1.29/1.66 [ 'class_Ring__and__Field_Odivision__by__zero'( 'tc_Complex_Ocomplex' )
% 1.29/1.66 ],
% 1.29/1.66 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_Complex_Ocomplex' ) ]
% 1.29/1.66 ,
% 1.29/1.66 [ 'class_RealVector_Oreal__normed__algebra'( 'tc_Complex_Ocomplex' ) ]
% 1.29/1.66 ,
% 1.29/1.66 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_Complex_Ocomplex' ) ]
% 1.29/1.66 ,
% 1.29/1.66 [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_Complex_Ocomplex' ) ]
% 1.29/1.66 ,
% 1.29/1.66 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_Complex_Ocomplex' ) ]
% 1.29/1.66 ,
% 1.29/1.66 [ 'class_Ring__and__Field_Odivision__ring'( 'tc_Complex_Ocomplex' ) ]
% 1.29/1.66 ,
% 1.29/1.66 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_Complex_Ocomplex' ) ]
% 1.29/1.66 ,
% 1.29/1.66 [ 'class_RealVector_Oreal__normed__field'( 'tc_Complex_Ocomplex' ) ]
% 1.29/1.66 ,
% 1.29/1.66 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_Complex_Ocomplex' ) ]
% 1.29/1.66 ,
% 1.29/1.66 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_Complex_Ocomplex' ) ]
% 1.29/1.66 ,
% 1.29/1.66 [ 'class_Ring__and__Field_Ocomm__ring__1'( 'tc_Complex_Ocomplex' ) ]
% 1.29/1.66 ,
% 1.29/1.66 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_Complex_Ocomplex' ) ],
% 1.29/1.66 [ 'class_Ring__and__Field_Osemiring__0'( 'tc_Complex_Ocomplex' ) ],
% 1.29/1.66 [ 'class_OrderedGroup_Oab__group__add'( 'tc_Complex_Ocomplex' ) ],
% 1.29/1.66 [ 'class_Ring__and__Field_Omult__zero'( 'tc_Complex_Ocomplex' ) ],
% 1.29/1.66 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_Complex_Ocomplex' ) ],
% 1.29/1.66 [ 'class_Ring__and__Field_Osemiring'( 'tc_Complex_Ocomplex' ) ],
% 1.29/1.66 [ 'class_OrderedGroup_Omonoid__add'( 'tc_Complex_Ocomplex' ) ],
% 1.29/1.66 [ 'class_OrderedGroup_Ogroup__add'( 'tc_Complex_Ocomplex' ) ],
% 1.29/1.66 [ 'class_Ring__and__Field_Oring__1'( 'tc_Complex_Ocomplex' ) ],
% 1.29/1.66 [ 'class_Ring__and__Field_Ofield'( 'tc_Complex_Ocomplex' ) ],
% 1.29/1.66 [ 'class_Ring__and__Field_Oring'( 'tc_Complex_Ocomplex' ) ],
% 1.29/1.66 [ 'class_Ring__and__Field_Oidom'( 'tc_Complex_Ocomplex' ) ],
% 1.29/1.66 [ 'class_Nat_Osemiring__char__0'( 'tc_Complex_Ocomplex' ) ],
% 1.29/1.66 [ 'class_Int_Oring__char__0'( 'tc_Complex_Ocomplex' ) ],
% 1.29/1.66 [ 'class_Int_Onumber__ring'( 'tc_Complex_Ocomplex' ) ],
% 1.29/1.66 [ 'class_Power_Opower'( 'tc_Complex_Ocomplex' ) ],
% 1.29/1.66 [ 'class_Int_Onumber'( 'tc_Complex_Ocomplex' ) ],
% 1.29/1.66 [ 'c_fequal'( X, X, Y ) ],
% 1.29/1.66 [ =( X, Y ), ~( 'c_fequal'( X, Y, Z ) ) ]
% 1.29/1.66 ] .
% 1.29/1.66
% 1.29/1.66
% 1.29/1.66 percentage equality = 0.198549, percentage horn = 0.824473
% 1.29/1.66 This is a problem with some equality
% 1.29/1.66
% 1.29/1.66
% 1.29/1.66
% 1.29/1.66 Options Used:
% 1.29/1.66
% 1.29/1.66 useres = 1
% 1.29/1.66 useparamod = 1
% 1.29/1.66 useeqrefl = 1
% 1.29/1.66 useeqfact = 1
% 1.29/1.66 usefactor = 1
% 1.29/1.66 usesimpsplitting = 0
% 1.29/1.66 usesimpdemod = 5
% 1.29/1.66 usesimpres = 3
% 1.29/1.66
% 1.29/1.66 resimpinuse = 1000
% 1.29/1.66 resimpclauses = 20000
% 1.29/1.66 substype = eqrewr
% 1.29/1.66 backwardsubs = 1
% 1.29/1.66 selectoldest = 5
% 1.29/1.66
% 1.29/1.66 litorderings [0] = split
% 1.29/1.66 litorderings [1] = extend the termordering, first sorting on arguments
% 1.29/1.66
% 1.29/1.66 termordering = kbo
% 1.29/1.66
% 1.29/1.66 litapriori = 0
% 1.29/1.66 termapriori = 1
% 1.29/1.66 litaposteriori = 0
% 1.29/1.66 termaposteriori = 0
% 1.29/1.66 demodaposteriori = 0
% 1.29/1.66 ordereqreflfact = 0
% 1.29/1.66
% 1.29/1.66 litselect = negord
% 1.29/1.66
% 1.29/1.66 maxweight = 15
% 1.29/1.66 maxdepth = 30000
% 1.29/1.66 maxlength = 115
% 1.29/1.66 maxnrvars = 195
% 1.29/1.66 excuselevel = 1
% 1.29/1.66 increasemaxweight = 1
% 1.29/1.66
% 1.29/1.66 maxselected = 10000000
% 1.29/1.66 maxnrclauses = 10000000
% 1.29/1.66
% 1.29/1.66 showgenerated = 0
% 1.29/1.66 showkept = 0
% 1.29/1.66 showselected = 0
% 1.29/1.66 showdeleted = 0
% 1.29/1.66 showresimp = 1
% 1.29/1.66 showstatus = 2000
% 1.29/1.66
% 1.29/1.66 prologoutput = 1
% 1.29/1.66 nrgoals = 5000000
% 1.29/1.66 totalproof = 1
% 1.29/1.66
% 1.29/1.66 Symbols occurring in the translation:
% 1.29/1.66
% 1.29/1.66 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 1.29/1.66 . [1, 2] (w:1, o:151, a:1, s:1, b:0),
% 1.29/1.66 ! [4, 1] (w:0, o:74, a:1, s:1, b:0),
% 1.29/1.66 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.29/1.66 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.29/1.66 hAPP [41, 2] (w:1, o:176, a:1, s:1, b:0),
% 1.29/1.66 'c_Ring__and__Field_Oordered__idom' [52, 11] (w:1, o:195, a:1, s:1
% 1.29/1.66 , b:0),
% 1.29/1.66 'class_Ring__and__Field_Ofield' [55, 1] (w:1, o:79, a:1, s:1, b:0),
% 1.29/1.66 'class_Ring__and__Field_Odivision__by__zero' [56, 1] (w:1, o:83, a:1
% 1.29/1.66 , s:1, b:0),
% 1.29/1.66 'class_Int_Onumber' [57, 1] (w:1, o:84, a:1, s:1, b:0),
% 1.29/1.66 'c_HOL_Ozero__class_Ozero' [58, 1] (w:1, o:85, a:1, s:1, b:0),
% 1.29/1.66 'c_HOL_Otimes__class_Otimes' [59, 1] (w:1, o:86, a:1, s:1, b:0),
% 1.29/1.66 'c_Int_Onumber__class_Onumber__of' [61, 2] (w:1, o:180, a:1, s:1, b:0
% 1.29/1.66 ),
% 1.29/1.66 'c_HOL_Oinverse__class_Odivide' [62, 3] (w:1, o:186, a:1, s:1, b:0),
% 1.80/2.20
% 1.80/2.20 'c_Power_Opower_Opower' [63, 3] (w:1, o:187, a:1, s:1, b:0),
% 1.80/2.20 hBOOL [65, 1] (w:1, o:87, a:1, s:1, b:0),
% 1.80/2.20 'tc_nat' [66, 0] (w:1, o:48, a:1, s:1, b:0),
% 1.80/2.20 'c_Suc' [68, 1] (w:1, o:88, a:1, s:1, b:0),
% 1.80/2.20 'c_HOL_Oplus__class_Oplus' [69, 1] (w:1, o:90, a:1, s:1, b:0),
% 1.80/2.20 'class_Ring__and__Field_Oordered__semiring__strict' [70, 1] (w:1, o:
% 1.80/2.20 97, a:1, s:1, b:0),
% 1.80/2.20 'c_HOL_Oord__class_Oless' [72, 3] (w:1, o:188, a:1, s:1, b:0),
% 1.80/2.20 'class_Ring__and__Field_Oordered__ring__strict' [73, 1] (w:1, o:96
% 1.80/2.20 , a:1, s:1, b:0),
% 1.80/2.20 'class_OrderedGroup_Olordered__ab__group__add' [74, 1] (w:1, o:99, a:
% 1.80/2.20 1, s:1, b:0),
% 1.80/2.20 'class_Ring__and__Field_Oordered__idom' [75, 1] (w:1, o:100, a:1, s:1
% 1.80/2.20 , b:0),
% 1.80/2.20 'class_Ring__and__Field_Oring__no__zero__divisors' [76, 1] (w:1, o:
% 1.80/2.20 101, a:1, s:1, b:0),
% 1.80/2.20 'class_Ring__and__Field_Ono__zero__divisors' [77, 1] (w:1, o:95, a:1
% 1.80/2.20 , s:1, b:0),
% 1.80/2.20 'class_OrderedGroup_Opordered__comm__monoid__add' [78, 1] (w:1, o:103
% 1.80/2.20 , a:1, s:1, b:0),
% 1.80/2.20 'c_lessequals' [80, 3] (w:1, o:189, a:1, s:1, b:0),
% 1.80/2.20 'c_HOL_Ouminus__class_Ouminus' [81, 2] (w:1, o:177, a:1, s:1, b:0),
% 1.80/2.20 'c_HOL_Oabs__class_Oabs' [82, 2] (w:1, o:178, a:1, s:1, b:0),
% 1.80/2.20 'class_Ring__and__Field_Ozero__neq__one' [83, 1] (w:1, o:104, a:1, s:
% 1.80/2.20 1, b:0),
% 1.80/2.20 'c_HOL_Oone__class_Oone' [84, 1] (w:1, o:89, a:1, s:1, b:0),
% 1.80/2.20 'class_Ring__and__Field_Oordered__field' [85, 1] (w:1, o:105, a:1, s:
% 1.80/2.20 1, b:0),
% 1.80/2.20 'class_OrderedGroup_Ogroup__add' [87, 1] (w:1, o:106, a:1, s:1, b:0)
% 1.80/2.20 ,
% 1.80/2.20 'class_Ring__and__Field_Ocomm__semiring__1' [88, 1] (w:1, o:81, a:1
% 1.80/2.20 , s:1, b:0),
% 1.80/2.20 'c_HOL_Oinverse__class_Oinverse' [93, 2] (w:1, o:179, a:1, s:1, b:0)
% 1.80/2.20 ,
% 1.80/2.20 'class_OrderedGroup_Opordered__ab__group__add__abs' [94, 1] (w:1, o:
% 1.80/2.20 107, a:1, s:1, b:0),
% 1.80/2.20 'class_OrderedGroup_Olordered__ab__group__add__abs' [95, 1] (w:1, o:
% 1.80/2.20 108, a:1, s:1, b:0),
% 1.80/2.20 'class_Lattices_Oboolean__algebra' [96, 1] (w:1, o:109, a:1, s:1, b:0
% 1.80/2.20 ),
% 1.80/2.20 'class_Orderings_Oorder' [97, 1] (w:1, o:110, a:1, s:1, b:0),
% 1.80/2.20 'tc_Int_Oint' [98, 0] (w:1, o:54, a:1, s:1, b:0),
% 1.80/2.20 'class_OrderedGroup_Opordered__ab__semigroup__add' [99, 1] (w:1, o:
% 1.80/2.20 111, a:1, s:1, b:0),
% 1.80/2.20 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le' [100, 1]
% 1.80/2.20 (w:1, o:112, a:1, s:1, b:0),
% 1.80/2.20 'class_Ring__and__Field_Opordered__ring__abs' [101, 1] (w:1, o:116
% 1.80/2.20 , a:1, s:1, b:0),
% 1.80/2.20 'class_Ring__and__Field_Oring' [103, 1] (w:1, o:117, a:1, s:1, b:0),
% 1.80/2.20
% 1.80/2.20 'c_Groebner__Basis_Ogb__semiring' [110, 6] (w:1, o:194, a:1, s:1, b:0
% 1.80/2.20 ),
% 1.80/2.20 'c_Int_OPls' [113, 0] (w:1, o:57, a:1, s:1, b:0),
% 1.80/2.20 'class_Ring__and__Field_Oordered__semidom' [114, 1] (w:1, o:113, a:1
% 1.80/2.20 , s:1, b:0),
% 1.80/2.20 'class_OrderedGroup_Oab__semigroup__idem__mult' [115, 1] (w:1, o:118
% 1.80/2.20 , a:1, s:1, b:0),
% 1.80/2.20 'class_OrderedGroup_Opordered__ab__group__add' [116, 1] (w:1, o:119
% 1.80/2.20 , a:1, s:1, b:0),
% 1.80/2.20 'c_Power_Opower__class_Opower' [117, 1] (w:1, o:120, a:1, s:1, b:0),
% 1.80/2.20
% 1.80/2.20 'class_Power_Opower' [119, 1] (w:1, o:133, a:1, s:1, b:0),
% 1.80/2.20 'class_Ring__and__Field_Omult__zero' [120, 1] (w:1, o:92, a:1, s:1
% 1.80/2.20 , b:0),
% 1.80/2.20 'class_Ring__and__Field_Osemiring__0' [121, 1] (w:1, o:136, a:1, s:1
% 1.80/2.20 , b:0),
% 1.80/2.20 'class_OrderedGroup_Ocomm__monoid__add' [122, 1] (w:1, o:121, a:1, s:
% 1.80/2.20 1, b:0),
% 1.80/2.20 'class_Ring__and__Field_Omult__mono1' [123, 1] (w:1, o:93, a:1, s:1
% 1.80/2.20 , b:0),
% 1.80/2.20 'class_Ring__and__Field_Omult__mono' [124, 1] (w:1, o:94, a:1, s:1
% 1.80/2.20 , b:0),
% 1.80/2.20 'class_Ring__and__Field_Opordered__ring' [125, 1] (w:1, o:137, a:1
% 1.80/2.20 , s:1, b:0),
% 1.80/2.20 'class_Ring__and__Field_Oabs__if' [126, 1] (w:1, o:138, a:1, s:1, b:0
% 1.80/2.20 ),
% 1.80/2.20 'class_Orderings_Olinorder' [127, 1] (w:1, o:122, a:1, s:1, b:0),
% 1.80/2.20 'class_Ring__and__Field_Oidom' [128, 1] (w:1, o:139, a:1, s:1, b:0),
% 1.80/2.20
% 1.80/2.20 'class_Ring__and__Field_Oordered__semiring' [129, 1] (w:1, o:114, a:1
% 1.80/2.20 , s:1, b:0),
% 1.80/2.20 'class_Int_Onumber__ring' [130, 1] (w:1, o:140, a:1, s:1, b:0),
% 1.80/2.20 'class_Nat_Osemiring__char__0' [131, 1] (w:1, o:98, a:1, s:1, b:0),
% 1.80/2.20 'c_Nat_Osemiring__1__class_Oof__nat' [132, 2] (w:1, o:181, a:1, s:1
% 12.66/13.04 , b:0),
% 12.66/13.04 'class_Ring__and__Field_Olordered__ring' [135, 1] (w:1, o:91, a:1, s:
% 12.66/13.04 1, b:0),
% 12.66/13.04 'c_Int_OBit0' [137, 1] (w:1, o:141, a:1, s:1, b:0),
% 12.66/13.04 'class_OrderedGroup_Omonoid__mult' [138, 1] (w:1, o:123, a:1, s:1, b:
% 12.66/13.04 0),
% 12.66/13.04 'class_OrderedGroup_Ocomm__monoid__mult' [139, 1] (w:1, o:124, a:1
% 12.66/13.04 , s:1, b:0),
% 12.66/13.04 'class_Ring__and__Field_Odivision__ring' [140, 1] (w:1, o:142, a:1
% 12.66/13.04 , s:1, b:0),
% 12.66/13.04 'class_Ring__and__Field_Osemiring__1' [142, 1] (w:1, o:143, a:1, s:1
% 12.66/13.04 , b:0),
% 12.66/13.04 'class_Ring__and__Field_Opordered__cancel__semiring' [143, 1] (w:1
% 12.66/13.04 , o:144, a:1, s:1, b:0),
% 12.66/13.04 'class_OrderedGroup_Oab__semigroup__mult' [144, 1] (w:1, o:125, a:1
% 12.66/13.04 , s:1, b:0),
% 12.66/13.04 'class_RealVector_Oreal__normed__algebra' [145, 1] (w:1, o:145, a:1
% 12.66/13.04 , s:1, b:0),
% 12.66/13.04 'class_Ring__and__Field_Ocomm__semiring' [150, 1] (w:1, o:82, a:1, s:
% 12.66/13.04 1, b:0),
% 12.66/13.04 'c_FFT__Mirabelle_OFFT' [151, 2] (w:1, o:182, a:1, s:1, b:0),
% 12.66/13.04 'class_OrderedGroup_Oordered__ab__group__add' [152, 1] (w:1, o:102
% 12.66/13.04 , a:1, s:1, b:0),
% 12.66/13.04 'class_Ring__and__Field_Opordered__semiring' [153, 1] (w:1, o:146, a:
% 12.66/13.04 1, s:1, b:0),
% 12.66/13.04 'class_OrderedGroup_Oab__group__add' [154, 1] (w:1, o:126, a:1, s:1
% 12.66/13.04 , b:0),
% 12.66/13.04 'class_OrderedGroup_Oab__semigroup__add' [158, 1] (w:1, o:127, a:1
% 12.66/13.04 , s:1, b:0),
% 12.66/13.04 'class_Ring__and__Field_Osemiring' [159, 1] (w:1, o:147, a:1, s:1, b:
% 12.66/13.04 0),
% 12.66/13.04 'class_RealVector_Oreal__normed__field' [160, 1] (w:1, o:148, a:1, s:
% 12.66/13.04 1, b:0),
% 12.66/13.04 'class_OrderedGroup_Ocancel__ab__semigroup__add' [164, 1] (w:1, o:128
% 12.66/13.04 , a:1, s:1, b:0),
% 12.66/13.04 'class_OrderedGroup_Ocancel__semigroup__add' [165, 1] (w:1, o:129, a:
% 12.66/13.04 1, s:1, b:0),
% 12.66/13.04 'class_Ring__and__Field_Oordered__comm__semiring__strict' [166, 1]
% 12.66/13.04 (w:1, o:115, a:1, s:1, b:0),
% 12.66/13.04 'class_OrderedGroup_Omonoid__add' [167, 1] (w:1, o:130, a:1, s:1, b:0
% 12.66/13.04 ),
% 12.66/13.04 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add' [168, 1]
% 12.66/13.04 (w:1, o:131, a:1, s:1, b:0),
% 12.66/13.04 'c_Int_OBit1' [169, 1] (w:1, o:149, a:1, s:1, b:0),
% 12.66/13.04 'class_Orderings_Opreorder' [170, 1] (w:1, o:132, a:1, s:1, b:0),
% 12.66/13.04 'class_Ring__and__Field_Oring__1' [171, 1] (w:1, o:134, a:1, s:1, b:0
% 12.66/13.04 ),
% 12.66/13.04 'class_Ring__and__Field_Oring__1__no__zero__divisors' [175, 1] (w:1
% 12.66/13.04 , o:135, a:1, s:1, b:0),
% 12.66/13.04 'c_Int_Oiszero' [177, 2] (w:1, o:183, a:1, s:1, b:0),
% 12.66/13.04 'class_Ring__and__Field_Ocomm__ring__1' [178, 1] (w:1, o:80, a:1, s:1
% 12.66/13.04 , b:0),
% 12.66/13.04 'c_FFT__Mirabelle_OIFFT' [180, 2] (w:1, o:184, a:1, s:1, b:0),
% 12.66/13.04 'class_Int_Oring__char__0' [181, 1] (w:1, o:150, a:1, s:1, b:0),
% 12.66/13.04 'c_Ring__and__Field_Osemiring__1' [182, 5] (w:1, o:193, a:1, s:1, b:0
% 12.66/13.04 ),
% 12.66/13.04 'v_k' [183, 0] (w:1, o:65, a:1, s:1, b:0),
% 12.66/13.04 'c_FFT__Mirabelle_ODFT' [184, 3] (w:1, o:190, a:1, s:1, b:0),
% 12.66/13.04 'v_i' [186, 0] (w:1, o:67, a:1, s:1, b:0),
% 12.66/13.04 'v_a' [187, 0] (w:1, o:68, a:1, s:1, b:0),
% 12.66/13.04 'c_FFT__Mirabelle_OIDFT' [188, 3] (w:1, o:191, a:1, s:1, b:0),
% 12.66/13.04 'tc_fun' [191, 2] (w:1, o:185, a:1, s:1, b:0),
% 12.66/13.04 'tc_Complex_Ocomplex' [192, 0] (w:1, o:71, a:1, s:1, b:0),
% 12.66/13.04 'c_fequal' [193, 3] (w:1, o:192, a:1, s:1, b:0).
% 12.66/13.04
% 12.66/13.04
% 12.66/13.04 Starting Search:
% 12.66/13.04
% 12.66/13.04 Resimplifying inuse:
% 12.66/13.04 Done
% 12.66/13.04
% 12.66/13.04
% 12.66/13.04 Intermediate Status:
% 12.66/13.04 Generated: 5420
% 12.66/13.04 Kept: 2327
% 12.66/13.04 Inuse: 95
% 12.66/13.04 Deleted: 1
% 12.66/13.04 Deletedinuse: 0
% 12.66/13.04
% 12.66/13.04 Resimplifying inuse:
% 12.66/13.04 Done
% 12.66/13.04
% 12.66/13.04 Resimplifying inuse:
% 12.66/13.04 Done
% 12.66/13.04
% 12.66/13.04
% 12.66/13.04 Intermediate Status:
% 12.66/13.04 Generated: 12589
% 12.66/13.04 Kept: 4328
% 12.66/13.04 Inuse: 134
% 12.66/13.04 Deleted: 2
% 12.66/13.04 Deletedinuse: 0
% 12.66/13.04
% 12.66/13.04 Resimplifying inuse:
% 12.66/13.04 Done
% 12.66/13.04
% 12.66/13.04 Resimplifying inuse:
% 12.66/13.04 Done
% 12.66/13.04
% 12.66/13.04
% 12.66/13.04 Intermediate Status:
% 12.66/13.04 Generated: 19012
% 12.66/13.04 Kept: 6534
% 12.66/13.04 Inuse: 202
% 12.66/13.04 Deleted: 4
% 12.66/13.04 Deletedinuse: 0
% 12.66/13.04
% 12.66/13.04 Resimplifying inuse:
% 12.66/13.04 Done
% 12.66/13.04
% 12.66/13.04 Resimplifying inuse:
% 12.66/13.04 Done
% 12.66/13.04
% 12.66/13.04
% 12.66/13.04 Intermediate Status:
% 12.66/13.04 Generated: 26991
% 12.66/13.04 Kept: 8794
% 12.66/13.04 Inuse: 262
% 12.66/13.04 Deleted: 9
% 12.66/13.04 Deletedinuse: 0
% 12.66/13.04
% 12.66/13.04 Resimplifying inuse:
% 12.66/13.04 Done
% 12.66/13.04
% 12.66/13.04 Resimplifying inuse:
% 12.66/13.04 Done
% 12.66/13.04
% 12.66/13.04
% 12.66/13.04 Intermediate Status:
% 12.66/13.04 Generated: 34051
% 12.66/13.04 Kept: 10794
% 12.66/13.04 Inuse: 307
% 12.66/13.04 Deleted: 9
% 12.66/13.04 Deletedinuse: 0
% 12.66/13.04
% 12.66/13.04 Resimplifying inuse:
% 12.66/13.04 Done
% 12.66/13.04
% 12.66/13.04 Resimplifying inuse:
% 12.66/13.04 Done
% 12.66/13.04
% 12.66/13.04
% 12.66/13.04 Intermediate Status:
% 12.66/13.04 Generated: 41321
% 12.66/13.04 Kept: 12854
% 12.66/13.04 Inuse: 360
% 40.08/40.48 Deleted: 11
% 40.08/40.48 Deletedinuse: 0
% 40.08/40.48
% 40.08/40.48 Resimplifying inuse:
% 40.08/40.48 Done
% 40.08/40.48
% 40.08/40.48
% 40.08/40.48 Intermediate Status:
% 40.08/40.48 Generated: 45882
% 40.08/40.48 Kept: 14856
% 40.08/40.48 Inuse: 387
% 40.08/40.48 Deleted: 12
% 40.08/40.48 Deletedinuse: 0
% 40.08/40.48
% 40.08/40.48 Resimplifying inuse:
% 40.08/40.48 Done
% 40.08/40.48
% 40.08/40.48 Resimplifying inuse:
% 40.08/40.48 Done
% 40.08/40.48
% 40.08/40.48
% 40.08/40.48 Intermediate Status:
% 40.08/40.48 Generated: 54092
% 40.08/40.48 Kept: 17151
% 40.08/40.48 Inuse: 448
% 40.08/40.48 Deleted: 19
% 40.08/40.48 Deletedinuse: 1
% 40.08/40.48
% 40.08/40.48 Resimplifying inuse:
% 40.08/40.48 Done
% 40.08/40.48
% 40.08/40.48 Resimplifying inuse:
% 40.08/40.48 Done
% 40.08/40.48
% 40.08/40.48
% 40.08/40.48 Intermediate Status:
% 40.08/40.48 Generated: 60875
% 40.08/40.48 Kept: 19421
% 40.08/40.48 Inuse: 507
% 40.08/40.48 Deleted: 20
% 40.08/40.48 Deletedinuse: 1
% 40.08/40.48
% 40.08/40.48 Resimplifying inuse:
% 40.08/40.48 Done
% 40.08/40.48
% 40.08/40.48 Resimplifying clauses:
% 40.08/40.48 Done
% 40.08/40.48
% 40.08/40.48
% 40.08/40.48 Intermediate Status:
% 40.08/40.48 Generated: 67816
% 40.08/40.48 Kept: 21504
% 40.08/40.48 Inuse: 554
% 40.08/40.48 Deleted: 368
% 40.08/40.48 Deletedinuse: 1
% 40.08/40.48
% 40.08/40.48 Resimplifying inuse:
% 40.08/40.48 Done
% 40.08/40.48
% 40.08/40.48
% 40.08/40.48 Intermediate Status:
% 40.08/40.48 Generated: 81198
% 40.08/40.48 Kept: 24238
% 40.08/40.48 Inuse: 589
% 40.08/40.48 Deleted: 368
% 40.08/40.48 Deletedinuse: 1
% 40.08/40.48
% 40.08/40.48 Resimplifying inuse:
% 40.08/40.48 Done
% 40.08/40.48
% 40.08/40.48 Resimplifying inuse:
% 40.08/40.48 Done
% 40.08/40.48
% 40.08/40.48
% 40.08/40.48 Intermediate Status:
% 40.08/40.48 Generated: 85834
% 40.08/40.48 Kept: 26243
% 40.08/40.48 Inuse: 628
% 40.08/40.48 Deleted: 368
% 40.08/40.48 Deletedinuse: 1
% 40.08/40.48
% 40.08/40.48 Resimplifying inuse:
% 40.08/40.48 Done
% 40.08/40.48
% 40.08/40.48
% 40.08/40.48 Intermediate Status:
% 40.08/40.48 Generated: 91349
% 40.08/40.48 Kept: 28557
% 40.08/40.48 Inuse: 639
% 40.08/40.48 Deleted: 368
% 40.08/40.48 Deletedinuse: 1
% 40.08/40.48
% 40.08/40.48 Resimplifying inuse:
% 40.08/40.48 Done
% 40.08/40.48
% 40.08/40.48 Resimplifying inuse:
% 40.08/40.48 Done
% 40.08/40.48
% 40.08/40.48
% 40.08/40.48 Intermediate Status:
% 40.08/40.48 Generated: 97814
% 40.08/40.48 Kept: 30558
% 40.08/40.48 Inuse: 665
% 40.08/40.48 Deleted: 368
% 40.08/40.48 Deletedinuse: 1
% 40.08/40.48
% 40.08/40.48 Resimplifying inuse:
% 40.08/40.48 Done
% 40.08/40.48
% 40.08/40.48 Resimplifying inuse:
% 40.08/40.48 Done
% 40.08/40.48
% 40.08/40.48
% 40.08/40.48 Intermediate Status:
% 40.08/40.48 Generated: 106817
% 40.08/40.48 Kept: 32674
% 40.08/40.48 Inuse: 708
% 40.08/40.48 Deleted: 370
% 40.08/40.48 Deletedinuse: 2
% 40.08/40.48
% 40.08/40.48 Resimplifying inuse:
% 40.08/40.48 Done
% 40.08/40.48
% 40.08/40.48 Resimplifying inuse:
% 40.08/40.48 Done
% 40.08/40.48
% 40.08/40.48
% 40.08/40.48 Intermediate Status:
% 40.08/40.48 Generated: 115857
% 40.08/40.48 Kept: 35490
% 40.08/40.48 Inuse: 743
% 40.08/40.48 Deleted: 373
% 40.08/40.48 Deletedinuse: 2
% 40.08/40.48
% 40.08/40.48 Resimplifying inuse:
% 40.08/40.48 Done
% 40.08/40.48
% 40.08/40.48 Resimplifying inuse:
% 40.08/40.48 Done
% 40.08/40.48
% 40.08/40.48
% 40.08/40.48 Intermediate Status:
% 40.08/40.48 Generated: 122563
% 40.08/40.48 Kept: 37615
% 40.08/40.48 Inuse: 770
% 40.08/40.48 Deleted: 373
% 40.08/40.48 Deletedinuse: 2
% 40.08/40.48
% 40.08/40.48 Resimplifying inuse:
% 40.08/40.48 Done
% 40.08/40.48
% 40.08/40.48 Resimplifying inuse:
% 40.08/40.48 Done
% 40.08/40.48
% 40.08/40.48
% 40.08/40.48 Intermediate Status:
% 40.08/40.48 Generated: 130457
% 40.08/40.48 Kept: 39725
% 40.08/40.48 Inuse: 805
% 40.08/40.48 Deleted: 373
% 40.08/40.48 Deletedinuse: 2
% 40.08/40.48
% 40.08/40.48 Resimplifying inuse:
% 40.08/40.48 Done
% 40.08/40.48
% 40.08/40.48 Resimplifying inuse:
% 40.08/40.48 Done
% 40.08/40.48
% 40.08/40.48 Resimplifying clauses:
% 40.08/40.48 Done
% 40.08/40.48
% 40.08/40.48
% 40.08/40.48 Intermediate Status:
% 40.08/40.48 Generated: 138466
% 40.08/40.48 Kept: 41916
% 40.08/40.48 Inuse: 830
% 40.08/40.48 Deleted: 563
% 40.08/40.48 Deletedinuse: 2
% 40.08/40.48
% 40.08/40.48 Resimplifying inuse:
% 40.08/40.48 Done
% 40.08/40.48
% 40.08/40.48 Resimplifying inuse:
% 40.08/40.48 Done
% 40.08/40.48
% 40.08/40.48
% 40.08/40.48 Intermediate Status:
% 40.08/40.48 Generated: 145695
% 40.08/40.48 Kept: 44175
% 40.08/40.48 Inuse: 855
% 40.08/40.48 Deleted: 563
% 40.08/40.48 Deletedinuse: 2
% 40.08/40.48
% 40.08/40.48 Resimplifying inuse:
% 40.08/40.48 Done
% 40.08/40.48
% 40.08/40.48 Resimplifying inuse:
% 40.08/40.48 Done
% 40.08/40.48
% 40.08/40.48
% 40.08/40.48 Intermediate Status:
% 40.08/40.48 Generated: 152900
% 40.08/40.48 Kept: 46190
% 40.08/40.48 Inuse: 885
% 40.08/40.48 Deleted: 563
% 40.08/40.48 Deletedinuse: 2
% 40.08/40.48
% 40.08/40.48 Resimplifying inuse:
% 40.08/40.48 Done
% 40.08/40.48
% 40.08/40.48
% 40.08/40.48 Intermediate Status:
% 40.08/40.48 Generated: 173254
% 40.08/40.48 Kept: 48621
% 40.08/40.48 Inuse: 895
% 40.08/40.48 Deleted: 563
% 40.08/40.48 Deletedinuse: 2
% 40.08/40.48
% 40.08/40.48 Resimplifying inuse:
% 40.08/40.48 Done
% 40.08/40.48
% 40.08/40.48
% 40.08/40.48 Intermediate Status:
% 40.08/40.48 Generated: 193250
% 40.08/40.48 Kept: 50731
% 40.08/40.48 Inuse: 900
% 40.08/40.48 Deleted: 563
% 40.08/40.48 Deletedinuse: 2
% 40.08/40.48
% 40.08/40.48 Resimplifying inuse:
% 40.08/40.48 Done
% 40.08/40.48
% 40.08/40.48 Resimplifying inuse:
% 40.08/40.48 Done
% 40.08/40.48
% 40.08/40.48
% 40.08/40.48 Intermediate Status:
% 40.08/40.48 Generated: 204151
% 40.08/40.48 Kept: 53646
% 40.08/40.48 Inuse: 910
% 40.08/40.48 Deleted: 563
% 40.08/40.48 Deletedinuse: 2
% 40.08/40.48
% 40.08/40.48 Resimplifying inuse:
% 40.08/40.48 Done
% 40.08/40.48
% 40.08/40.48 Resimplifying inuse:
% 40.08/40.48 Done
% 40.08/40.48
% 40.08/40.48
% 40.08/40.48 Intermediate Status:
% 40.08/40.48 Generated: 211098
% 40.08/40.48 Kept: 55665
% 40.08/40.48 Inuse: 925
% 40.08/40.48 Deleted: 563
% 40.08/40.48 Deletedinuse: 2
% 40.08/40.48
% 40.08/40.48 Resimplifying inuse:
% 40.08/40.48 Done
% 40.08/40.48
% 40.08/40.48 Resimplifying inuse:
% 40.08/40.48 Done
% 40.08/40.48
% 40.08/40.48
% 40.08/40.48 Intermediate Status:
% 40.08/40.48 Generated: 221425
% 40.08/40.48 Kept: 57762
% 40.08/40.48 Inuse: 960
% 40.08/40.48 Deleted: 563
% 40.08/40.48 Deletedinuse: 2
% 40.08/40.48
% 40.08/40.48 Resimplifying inuse:
% 40.08/40.48 Done
% 40.08/40.48
% 40.08/40.48
% 40.08/40.48 Intermediate Status:
% 40.08/40.48 Generated: 234327
% 40.08/40.48 Kept: 59776
% 40.08/40.48 Inuse: 980
% 40.08/40.48 Deleted: 563
% 40.08/40.48 Deletedinuse: 2
% 40.08/40.48
% 40.08/40.48 Resimplifying inuse:
% 40.08/40.48 Done
% 40.08/40.48
% 40.08/40.48 Resimplifying inuse:
% 40.08/40.48 Done
% 40.08/40.48
% 40.08/40.48 Resimplifying clauses:
% 40.08/40.48 Done
% 40.08/40.48
% 40.08/40.48
% 40.08/40.48 Intermediate Status:
% 40.08/40.48 Generated: 273248
% 40.08/40.48 Kept: 61778
% 40.08/40.48 Inuse: 988
% 40.08/40.48 Deleted: 677
% 40.08/40.48 Deletedinuse: 2
% 40.08/40.48
% 40.08/40.48 Resimplifying inuse:
% 40.08/40.48 Done
% 40.08/40.48
% 40.08/40.48
% 40.08/40.48 Intermediate Status:
% 40.08/40.48 Generated: 288147
% 40.08/40.48 Kept: 63969
% 40.08/40.48 Inuse: 1010
% 40.08/40.48 Deleted: 677
% 40.08/40.48 Deletedinuse: 2
% 40.08/40.48
% 40.08/40.48 Resimplifying inuse:
% 40.08/40.48 Done
% 40.08/40.48
% 40.08/40.48 Resimplifying inuse:
% 40.08/40.48 Done
% 40.08/40.48
% 40.08/40.48
% 40.08/40.48 Intermediate Status:
% 40.08/40.48 Generated: 299574
% 40.08/40.48 Kept: 66000
% 40.08/40.48 Inuse: 1040
% 40.08/40.48 Deleted: 677
% 40.08/40.48 Deletedinuse: 2
% 40.08/40.48
% 40.08/40.48 Resimplifying inuse:
% 40.08/40.48 Done
% 40.08/40.48
% 40.08/40.48
% 40.08/40.48 Intermediate Status:
% 40.08/40.48 Generated: 320515
% 40.08/40.48 Kept: 69333
% 40.08/40.48 Inuse: 1050
% 97.69/98.02 Deleted: 677
% 97.69/98.02 Deletedinuse: 2
% 97.69/98.02
% 97.69/98.02 Resimplifying inuse:
% 97.69/98.02 Done
% 97.69/98.02
% 97.69/98.02 Resimplifying inuse:
% 97.69/98.02 Done
% 97.69/98.02
% 97.69/98.02
% 97.69/98.02 Intermediate Status:
% 97.69/98.02 Generated: 333739
% 97.69/98.02 Kept: 71376
% 97.69/98.02 Inuse: 1080
% 97.69/98.02 Deleted: 677
% 97.69/98.02 Deletedinuse: 2
% 97.69/98.02
% 97.69/98.02 Resimplifying inuse:
% 97.69/98.02 Done
% 97.69/98.02
% 97.69/98.02 Resimplifying inuse:
% 97.69/98.02 Done
% 97.69/98.02
% 97.69/98.02
% 97.69/98.02 Intermediate Status:
% 97.69/98.02 Generated: 343532
% 97.69/98.02 Kept: 73420
% 97.69/98.02 Inuse: 1100
% 97.69/98.02 Deleted: 677
% 97.69/98.02 Deletedinuse: 2
% 97.69/98.02
% 97.69/98.02 Resimplifying inuse:
% 97.69/98.02 Done
% 97.69/98.02
% 97.69/98.02 Resimplifying inuse:
% 97.69/98.02 Done
% 97.69/98.02
% 97.69/98.02
% 97.69/98.02 Intermediate Status:
% 97.69/98.02 Generated: 355228
% 97.69/98.02 Kept: 75690
% 97.69/98.02 Inuse: 1125
% 97.69/98.02 Deleted: 677
% 97.69/98.02 Deletedinuse: 2
% 97.69/98.02
% 97.69/98.02 Resimplifying inuse:
% 97.69/98.02 Done
% 97.69/98.02
% 97.69/98.02 Resimplifying inuse:
% 97.69/98.02 Done
% 97.69/98.02
% 97.69/98.02
% 97.69/98.02 Intermediate Status:
% 97.69/98.02 Generated: 367628
% 97.69/98.02 Kept: 77783
% 97.69/98.02 Inuse: 1160
% 97.69/98.02 Deleted: 680
% 97.69/98.02 Deletedinuse: 5
% 97.69/98.02
% 97.69/98.02 Resimplifying inuse:
% 97.69/98.02 Done
% 97.69/98.02
% 97.69/98.02
% 97.69/98.02 Intermediate Status:
% 97.69/98.02 Generated: 381157
% 97.69/98.02 Kept: 81738
% 97.69/98.02 Inuse: 1174
% 97.69/98.02 Deleted: 681
% 97.69/98.02 Deletedinuse: 5
% 97.69/98.02
% 97.69/98.02 Resimplifying inuse:
% 97.69/98.02 Done
% 97.69/98.02
% 97.69/98.02 Resimplifying clauses:
% 97.69/98.02 Done
% 97.69/98.02
% 97.69/98.02
% 97.69/98.02 Intermediate Status:
% 97.69/98.02 Generated: 399761
% 97.69/98.02 Kept: 84359
% 97.69/98.02 Inuse: 1179
% 97.69/98.02 Deleted: 1241
% 97.69/98.02 Deletedinuse: 5
% 97.69/98.02
% 97.69/98.02 Resimplifying inuse:
% 97.69/98.02 Done
% 97.69/98.02
% 97.69/98.02 Resimplifying inuse:
% 97.69/98.02 Done
% 97.69/98.02
% 97.69/98.02
% 97.69/98.02 Intermediate Status:
% 97.69/98.02 Generated: 415937
% 97.69/98.02 Kept: 87088
% 97.69/98.02 Inuse: 1209
% 97.69/98.02 Deleted: 1241
% 97.69/98.02 Deletedinuse: 5
% 97.69/98.02
% 97.69/98.02 Resimplifying inuse:
% 97.69/98.02 Done
% 97.69/98.02
% 97.69/98.02 Resimplifying inuse:
% 97.69/98.02 Done
% 97.69/98.02
% 97.69/98.02
% 97.69/98.02 Intermediate Status:
% 97.69/98.02 Generated: 431518
% 97.69/98.02 Kept: 90149
% 97.69/98.02 Inuse: 1219
% 97.69/98.02 Deleted: 1241
% 97.69/98.02 Deletedinuse: 5
% 97.69/98.02
% 97.69/98.02 Resimplifying inuse:
% 97.69/98.02 Done
% 97.69/98.02
% 97.69/98.02 Resimplifying inuse:
% 97.69/98.02 Done
% 97.69/98.02
% 97.69/98.02
% 97.69/98.02 Intermediate Status:
% 97.69/98.02 Generated: 447606
% 97.69/98.02 Kept: 92154
% 97.69/98.02 Inuse: 1240
% 97.69/98.02 Deleted: 1241
% 97.69/98.02 Deletedinuse: 5
% 97.69/98.02
% 97.69/98.02 Resimplifying inuse:
% 97.69/98.02 Done
% 97.69/98.02
% 97.69/98.02 Resimplifying inuse:
% 97.69/98.02 Done
% 97.69/98.02
% 97.69/98.02
% 97.69/98.02 Intermediate Status:
% 97.69/98.02 Generated: 464186
% 97.69/98.02 Kept: 94405
% 97.69/98.02 Inuse: 1274
% 97.69/98.02 Deleted: 1241
% 97.69/98.02 Deletedinuse: 5
% 97.69/98.02
% 97.69/98.02 Resimplifying inuse:
% 97.69/98.02 Done
% 97.69/98.02
% 97.69/98.02 Resimplifying inuse:
% 97.69/98.02 Done
% 97.69/98.02
% 97.69/98.02
% 97.69/98.02 Intermediate Status:
% 97.69/98.02 Generated: 477427
% 97.69/98.02 Kept: 96700
% 97.69/98.02 Inuse: 1299
% 97.69/98.02 Deleted: 1241
% 97.69/98.02 Deletedinuse: 5
% 97.69/98.02
% 97.69/98.02 Resimplifying inuse:
% 97.69/98.02 Done
% 97.69/98.02
% 97.69/98.02
% 97.69/98.02 Intermediate Status:
% 97.69/98.02 Generated: 487283
% 97.69/98.02 Kept: 98715
% 97.69/98.02 Inuse: 1310
% 97.69/98.02 Deleted: 1241
% 97.69/98.02 Deletedinuse: 5
% 97.69/98.02
% 97.69/98.02 Resimplifying inuse:
% 97.69/98.02 Done
% 97.69/98.02
% 97.69/98.02
% 97.69/98.02 Intermediate Status:
% 97.69/98.02 Generated: 500935
% 97.69/98.02 Kept: 101606
% 97.69/98.02 Inuse: 1329
% 97.69/98.02 Deleted: 1241
% 97.69/98.02 Deletedinuse: 5
% 97.69/98.02
% 97.69/98.02 Resimplifying inuse:
% 97.69/98.02 Done
% 97.69/98.02
% 97.69/98.02 Resimplifying inuse:
% 97.69/98.02 Done
% 97.69/98.02
% 97.69/98.02 Resimplifying clauses:
% 97.69/98.02 Done
% 97.69/98.02
% 97.69/98.02
% 97.69/98.02 Intermediate Status:
% 97.69/98.02 Generated: 510933
% 97.69/98.02 Kept: 103819
% 97.69/98.02 Inuse: 1339
% 97.69/98.02 Deleted: 1414
% 97.69/98.02 Deletedinuse: 5
% 97.69/98.02
% 97.69/98.02 Resimplifying inuse:
% 97.69/98.02 Done
% 97.69/98.02
% 97.69/98.02
% 97.69/98.02 Intermediate Status:
% 97.69/98.02 Generated: 530885
% 97.69/98.02 Kept: 106683
% 97.69/98.02 Inuse: 1354
% 97.69/98.02 Deleted: 1414
% 97.69/98.02 Deletedinuse: 5
% 97.69/98.02
% 97.69/98.02 Resimplifying inuse:
% 97.69/98.02 Done
% 97.69/98.02
% 97.69/98.02 Resimplifying inuse:
% 97.69/98.02 Done
% 97.69/98.02
% 97.69/98.02
% 97.69/98.02 Intermediate Status:
% 97.69/98.02 Generated: 546806
% 97.69/98.02 Kept: 110025
% 97.69/98.02 Inuse: 1374
% 97.69/98.02 Deleted: 1414
% 97.69/98.02 Deletedinuse: 5
% 97.69/98.02
% 97.69/98.02 Resimplifying inuse:
% 97.69/98.02 Done
% 97.69/98.02
% 97.69/98.02 Resimplifying inuse:
% 97.69/98.02 Done
% 97.69/98.02
% 97.69/98.02
% 97.69/98.02 Intermediate Status:
% 97.69/98.02 Generated: 554276
% 97.69/98.02 Kept: 112130
% 97.69/98.02 Inuse: 1389
% 97.69/98.02 Deleted: 1414
% 97.69/98.02 Deletedinuse: 5
% 97.69/98.02
% 97.69/98.02 Resimplifying inuse:
% 97.69/98.02 Done
% 97.69/98.02
% 97.69/98.02 Resimplifying inuse:
% 97.69/98.02 Done
% 97.69/98.02
% 97.69/98.02
% 97.69/98.02 Intermediate Status:
% 97.69/98.02 Generated: 562037
% 97.69/98.02 Kept: 114133
% 97.69/98.02 Inuse: 1405
% 97.69/98.02 Deleted: 1414
% 97.69/98.02 Deletedinuse: 5
% 97.69/98.02
% 97.69/98.02 Resimplifying inuse:
% 97.69/98.02 Done
% 97.69/98.02
% 97.69/98.02
% 97.69/98.02 Intermediate Status:
% 97.69/98.02 Generated: 582659
% 97.69/98.02 Kept: 116315
% 97.69/98.02 Inuse: 1434
% 97.69/98.02 Deleted: 1414
% 97.69/98.02 Deletedinuse: 5
% 97.69/98.02
% 97.69/98.02 Resimplifying inuse:
% 97.69/98.02 Done
% 97.69/98.02
% 97.69/98.02 Resimplifying inuse:
% 97.69/98.02 Done
% 97.69/98.02
% 97.69/98.02
% 97.69/98.02 Intermediate Status:
% 97.69/98.02 Generated: 604130
% 97.69/98.02 Kept: 120332
% 97.69/98.02 Inuse: 1453
% 97.69/98.02 Deleted: 1426
% 97.69/98.02 Deletedinuse: 6
% 97.69/98.02
% 97.69/98.02 Resimplifying inuse:
% 97.69/98.02 Done
% 97.69/98.02
% 97.69/98.02
% 97.69/98.02 Intermediate Status:
% 97.69/98.02 Generated: 613985
% 97.69/98.02 Kept: 122384
% 97.69/98.02 Inuse: 1458
% 97.69/98.02 Deleted: 1426
% 97.69/98.02 Deletedinuse: 6
% 97.69/98.02
% 97.69/98.02 Resimplifying inuse:
% 97.69/98.02 Done
% 97.69/98.02
% 97.69/98.02
% 97.69/98.02 Intermediate Status:
% 97.69/98.02 Generated: 629977
% 97.69/98.02 Kept: 125090
% 97.69/98.02 Inuse: 1463
% 97.69/98.02 Deleted: 1426
% 97.69/98.02 Deletedinuse: 6
% 97.69/98.02
% 97.69/98.02 Resimplifying inuse:
% 97.69/98.02 Done
% 97.69/98.02
% 97.69/98.02 Resimplifying clauses:
% 97.69/98.02 Done
% 97.69/98.02
% 97.69/98.02 Resimplifying inuse:
% 97.69/98.02 Done
% 97.69/98.02
% 97.69/98.02
% 97.69/98.02 Intermediate Status:
% 97.69/98.02 Generated: 641700
% 97.69/98.02 Kept: 127430
% 97.69/98.02 Inuse: 1498
% 97.69/98.02 Deleted: 1797
% 97.69/98.02 Deletedinuse: 7
% 97.69/98.02
% 97.69/98.02 Resimplifying inuse:
% 97.69/98.02 Done
% 97.69/98.02
% 97.69/98.02 Resimplifying inuse:
% 97.69/98.02 Done
% 97.69/98.02
% 97.69/98.02
% 97.69/98.02 Intermediate Status:
% 97.69/98.02 Generated: 650535
% 97.69/98.02 Kept: 129451
% 97.69/98.02 Inuse: 1509
% 97.69/98.02 Deleted: 1797
% 97.69/98.02 Deletedinuse: 7
% 97.69/98.02
% 97.69/98.02 Resimplifying inuse:
% 97.69/98.02 Done
% 97.69/98.02
% 97.69/98.02
% 97.69/98.02 Intermediate Status:
% 97.69/98.02 Generated: 659840
% 185.49/185.93 Kept: 131968
% 185.49/185.93 Inuse: 1538
% 185.49/185.93 Deleted: 1797
% 185.49/185.93 Deletedinuse: 7
% 185.49/185.93
% 185.49/185.93 Resimplifying inuse:
% 185.49/185.93 Done
% 185.49/185.93
% 185.49/185.93 Resimplifying inuse:
% 185.49/185.93 Done
% 185.49/185.93
% 185.49/185.93
% 185.49/185.93 Intermediate Status:
% 185.49/185.93 Generated: 666652
% 185.49/185.93 Kept: 134362
% 185.49/185.93 Inuse: 1548
% 185.49/185.93 Deleted: 1797
% 185.49/185.93 Deletedinuse: 7
% 185.49/185.93
% 185.49/185.93 Resimplifying inuse:
% 185.49/185.93 Done
% 185.49/185.93
% 185.49/185.93 Resimplifying inuse:
% 185.49/185.93 Done
% 185.49/185.93
% 185.49/185.93
% 185.49/185.93 Intermediate Status:
% 185.49/185.93 Generated: 672525
% 185.49/185.93 Kept: 136745
% 185.49/185.93 Inuse: 1558
% 185.49/185.93 Deleted: 1797
% 185.49/185.93 Deletedinuse: 7
% 185.49/185.93
% 185.49/185.93 Resimplifying inuse:
% 185.49/185.93 Done
% 185.49/185.93
% 185.49/185.93 Resimplifying inuse:
% 185.49/185.93 Done
% 185.49/185.93
% 185.49/185.93
% 185.49/185.93 Intermediate Status:
% 185.49/185.93 Generated: 679439
% 185.49/185.93 Kept: 139118
% 185.49/185.93 Inuse: 1568
% 185.49/185.93 Deleted: 1797
% 185.49/185.93 Deletedinuse: 7
% 185.49/185.93
% 185.49/185.93 Resimplifying inuse:
% 185.49/185.93 Done
% 185.49/185.93
% 185.49/185.93 Resimplifying inuse:
% 185.49/185.93 Done
% 185.49/185.93
% 185.49/185.93
% 185.49/185.93 Intermediate Status:
% 185.49/185.93 Generated: 685422
% 185.49/185.93 Kept: 141531
% 185.49/185.93 Inuse: 1578
% 185.49/185.93 Deleted: 1797
% 185.49/185.93 Deletedinuse: 7
% 185.49/185.93
% 185.49/185.93 Resimplifying inuse:
% 185.49/185.93 Done
% 185.49/185.93
% 185.49/185.93 Resimplifying inuse:
% 185.49/185.93 Done
% 185.49/185.93
% 185.49/185.93
% 185.49/185.93 Intermediate Status:
% 185.49/185.93 Generated: 692502
% 185.49/185.93 Kept: 143988
% 185.49/185.93 Inuse: 1588
% 185.49/185.93 Deleted: 1797
% 185.49/185.93 Deletedinuse: 7
% 185.49/185.93
% 185.49/185.93 Resimplifying inuse:
% 185.49/185.93 Done
% 185.49/185.93
% 185.49/185.93 Resimplifying inuse:
% 185.49/185.93 Done
% 185.49/185.93
% 185.49/185.93 Resimplifying clauses:
% 185.49/185.93 Done
% 185.49/185.93
% 185.49/185.93
% 185.49/185.93 Intermediate Status:
% 185.49/185.93 Generated: 698697
% 185.49/185.93 Kept: 146448
% 185.49/185.93 Inuse: 1598
% 185.49/185.93 Deleted: 1931
% 185.49/185.93 Deletedinuse: 7
% 185.49/185.93
% 185.49/185.93 Resimplifying inuse:
% 185.49/185.93 Done
% 185.49/185.93
% 185.49/185.93 Resimplifying inuse:
% 185.49/185.93 Done
% 185.49/185.93
% 185.49/185.93
% 185.49/185.93 Intermediate Status:
% 185.49/185.93 Generated: 720805
% 185.49/185.93 Kept: 149539
% 185.49/185.93 Inuse: 1608
% 185.49/185.93 Deleted: 1931
% 185.49/185.93 Deletedinuse: 7
% 185.49/185.93
% 185.49/185.93 Resimplifying inuse:
% 185.49/185.93 Done
% 185.49/185.93
% 185.49/185.93 Resimplifying inuse:
% 185.49/185.93 Done
% 185.49/185.93
% 185.49/185.93
% 185.49/185.93 Intermediate Status:
% 185.49/185.93 Generated: 731843
% 185.49/185.93 Kept: 151574
% 185.49/185.93 Inuse: 1628
% 185.49/185.93 Deleted: 1931
% 185.49/185.93 Deletedinuse: 7
% 185.49/185.93
% 185.49/185.93 Resimplifying inuse:
% 185.49/185.93 Done
% 185.49/185.93
% 185.49/185.93 Resimplifying inuse:
% 185.49/185.93 Done
% 185.49/185.93
% 185.49/185.93
% 185.49/185.93 Intermediate Status:
% 185.49/185.93 Generated: 744258
% 185.49/185.93 Kept: 154096
% 185.49/185.93 Inuse: 1653
% 185.49/185.93 Deleted: 1931
% 185.49/185.93 Deletedinuse: 7
% 185.49/185.93
% 185.49/185.93 Resimplifying inuse:
% 185.49/185.93 Done
% 185.49/185.93
% 185.49/185.93
% 185.49/185.93 Intermediate Status:
% 185.49/185.93 Generated: 757564
% 185.49/185.93 Kept: 157259
% 185.49/185.93 Inuse: 1667
% 185.49/185.93 Deleted: 1931
% 185.49/185.93 Deletedinuse: 7
% 185.49/185.93
% 185.49/185.93 Resimplifying inuse:
% 185.49/185.93 Done
% 185.49/185.93
% 185.49/185.93
% 185.49/185.93 Intermediate Status:
% 185.49/185.93 Generated: 765713
% 185.49/185.93 Kept: 159431
% 185.49/185.93 Inuse: 1669
% 185.49/185.93 Deleted: 1931
% 185.49/185.93 Deletedinuse: 7
% 185.49/185.93
% 185.49/185.93 Resimplifying inuse:
% 185.49/185.93 Done
% 185.49/185.93
% 185.49/185.93
% 185.49/185.93 Intermediate Status:
% 185.49/185.93 Generated: 808214
% 185.49/185.93 Kept: 164278
% 185.49/185.93 Inuse: 1683
% 185.49/185.93 Deleted: 1931
% 185.49/185.93 Deletedinuse: 7
% 185.49/185.93
% 185.49/185.93 Resimplifying inuse:
% 185.49/185.93 Done
% 185.49/185.93
% 185.49/185.93 Resimplifying inuse:
% 185.49/185.93 Done
% 185.49/185.93
% 185.49/185.93 Resimplifying clauses:
% 185.49/185.93 Done
% 185.49/185.93
% 185.49/185.93
% 185.49/185.93 Intermediate Status:
% 185.49/185.93 Generated: 826982
% 185.49/185.93 Kept: 168089
% 185.49/185.93 Inuse: 1703
% 185.49/185.93 Deleted: 2037
% 185.49/185.93 Deletedinuse: 7
% 185.49/185.93
% 185.49/185.93 Resimplifying inuse:
% 185.49/185.93 Done
% 185.49/185.93
% 185.49/185.93
% 185.49/185.93 Intermediate Status:
% 185.49/185.93 Generated: 858885
% 185.49/185.93 Kept: 173313
% 185.49/185.93 Inuse: 1716
% 185.49/185.93 Deleted: 2037
% 185.49/185.93 Deletedinuse: 7
% 185.49/185.93
% 185.49/185.93 Resimplifying inuse:
% 185.49/185.93 Done
% 185.49/185.93
% 185.49/185.93 Resimplifying inuse:
% 185.49/185.93 Done
% 185.49/185.93
% 185.49/185.93
% 185.49/185.93 Intermediate Status:
% 185.49/185.93 Generated: 873919
% 185.49/185.93 Kept: 175742
% 185.49/185.93 Inuse: 1733
% 185.49/185.93 Deleted: 2038
% 185.49/185.93 Deletedinuse: 8
% 185.49/185.93
% 185.49/185.93 Resimplifying inuse:
% 185.49/185.93 Done
% 185.49/185.93
% 185.49/185.93 Resimplifying inuse:
% 185.49/185.93 Done
% 185.49/185.93
% 185.49/185.93
% 185.49/185.93 Intermediate Status:
% 185.49/185.93 Generated: 884791
% 185.49/185.93 Kept: 179487
% 185.49/185.93 Inuse: 1743
% 185.49/185.93 Deleted: 2038
% 185.49/185.93 Deletedinuse: 8
% 185.49/185.93
% 185.49/185.93 Resimplifying inuse:
% 185.49/185.93 Done
% 185.49/185.93
% 185.49/185.93 Resimplifying inuse:
% 185.49/185.93 Done
% 185.49/185.93
% 185.49/185.93
% 185.49/185.93 Intermediate Status:
% 185.49/185.93 Generated: 892561
% 185.49/185.93 Kept: 181860
% 185.49/185.93 Inuse: 1753
% 185.49/185.93 Deleted: 2038
% 185.49/185.93 Deletedinuse: 8
% 185.49/185.93
% 185.49/185.93 Resimplifying inuse:
% 185.49/185.93 Done
% 185.49/185.93
% 185.49/185.93
% 185.49/185.93 Intermediate Status:
% 185.49/185.93 Generated: 902405
% 185.49/185.93 Kept: 183936
% 185.49/185.93 Inuse: 1768
% 185.49/185.93 Deleted: 2038
% 185.49/185.93 Deletedinuse: 8
% 185.49/185.93
% 185.49/185.93 Resimplifying inuse:
% 185.49/185.93 Done
% 185.49/185.93
% 185.49/185.93 Resimplifying inuse:
% 185.49/185.93 Done
% 185.49/185.93
% 185.49/185.93
% 185.49/185.93 Intermediate Status:
% 185.49/185.93 Generated: 911074
% 185.49/185.93 Kept: 186061
% 185.49/185.93 Inuse: 1783
% 185.49/185.93 Deleted: 2038
% 185.49/185.93 Deletedinuse: 8
% 185.49/185.93
% 185.49/185.93 Resimplifying clauses:
% 185.49/185.93 Done
% 185.49/185.93
% 185.49/185.93 Resimplifying inuse:
% 185.49/185.93 Done
% 185.49/185.93
% 185.49/185.93
% 185.49/185.93 Intermediate Status:
% 185.49/185.93 Generated: 921546
% 185.49/185.93 Kept: 188260
% 185.49/185.93 Inuse: 1793
% 185.49/185.93 Deleted: 2280
% 185.49/185.93 Deletedinuse: 8
% 185.49/185.93
% 185.49/185.93 Resimplifying inuse:
% 185.49/185.93 Done
% 185.49/185.93
% 185.49/185.93 Resimplifying inuse:
% 185.49/185.93 Done
% 185.49/185.93
% 185.49/185.93
% 185.49/185.93 Intermediate Status:
% 185.49/185.93 Generated: 935526
% 185.49/185.93 Kept: 191359
% 185.49/185.93 Inuse: 1808
% 185.49/185.93 Deleted: 2280
% 185.49/185.93 Deletedinuse: 8
% 185.49/185.93
% 185.49/185.93 Resimplifying inuse:
% 185.49/185.93 Done
% 185.49/185.93
% 185.49/185.93 Resimplifying inuse:
% 185.49/185.93 Done
% 185.49/185.93
% 185.49/185.93
% 185.49/185.93 Intermediate Status:
% 185.49/185.93 Generated: 948677
% 185.49/185.93 Kept: 194126
% 185.49/185.93 Inuse: 1823
% 185.49/185.93 Deleted: 2280
% 185.49/185.93 Deletedinuse: 8
% 185.49/185.93
% 185.49/185.93 Resimplifying inuse:
% 185.49/185.93 Done
% 185.49/185.93
% 185.49/185.93 Resimplifying inuse:
% 185.49/185.93 Done
% 185.49/185.93
% 185.49/185.93
% 185.49/185.93 Intermediate Status:
% 185.49/185.93 Generated: 961220
% 185.49/185.93 Kept: 197424
% 185.49/185.93 Inuse: 1838
% 185.49/185.93 Deleted: 2280
% 185.49/185.93 Deletedinuse: 8
% 185.49/185.93
% 185.49/185.93 Resimplifying inuse:
% 185.49/185.93 Done
% 185.49/185.93
% 185.49/185.93 Resimplifying inuse:
% 185.49/185.93 Done
% 185.49/185.93
% 185.49/185.93
% 185.49/185.93 Intermediate Status:
% 185.49/185.93 Generated: 975095
% 185.49/185.93 KeCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------